- ORNL-2396 - . Chemistry-General * " TID-4500 (14th ed.) GUIDE TO THE PHASE DIAGRAMS OF THE FLUORIDE SYSTEMS. Ty, E.Ricei | - OAK RlDGE NATIONAI. I.ABQRATORY operdted by UNION CARBIDE CORPORATION T for the . U S ATOMIC ENERGY COMMISSIO“ ORNL-2396 Chemistry-General TID-4500 (14th ed.) Contract No. W=-7405-eng-26 REACTOR PROJECTS DIVISION GUIDE TO THE PHASE DIAGRAMS OF THE FLUORIDE SYSTEMS J. E. Ricei Consultant to Qak Ridge National Laboratory from New York University, Department of Chemistry DATE ISSUED Ny OAK RIDGE NATIONAL LABORATORY Oak Ridge, Tennessee operated by UNION CARBIDE CORPORATION for the U.S. ATOMIC ENERGY COMMISSION PREFACE A comprehensive study of fused-salt phase equilibria has been in progress at the Oak Ridge National Laboratory for several years in connection with reactor technology. In the course of that study, several complex fused-salt ternary systems have become well enough understood that nearly complete phase diagrams of the systems could be constructed.! Detailed discussion of the phase equilibria occurring in those systems is included herein. Except for the LiF-BeF ,~UF, and NaF-BeF ,—UF, systems, each of the diagrams of ternary systems included in this discussion was derived at ORNL in the Fused Salt Chemistry Section, under the direction of W. R. Grimes. Because it was felt that this collection of fluoride phase diagrams might prove more valuable if accompanied with a discussion of some of the types of phase relations illustrated in them, the following treatment was prepared. The purpose is to present some general principles and explanations which should aid in the reading, interpretation, and use of the actual diagrams in the collection and of other similar diagrams which may still be determined. While the relations are usually explicitly shown, at least as far as they are known, in the temperature-composition diagrams of the binary systems, the corresponding relations are not always equally apparent in the usual *‘phase diagram”’ of a ternary system of any complexity. In either case, moreover, the diagram does not show the actual data and observations upon which the diagram itself, essentially an inference, is based, nor does it give any idea of the amount of work, in experimentation and in thought, underlying the construction of the diagram. This aspect of the diagrams, however, is something best presented and treated by the investigators themselves. All the diagrams in the collection represent ‘‘condensed systems’’: i.e., they show the temperature-composition relations between solid and liquid phases under one atmos- phere of open pressure. For chemical reasons the atmosphere was actually helium or argon. No two-liquid equilibria were encountered. Limited miscibility of solids is involved in some of the diagrams, but there are no critical solution (or consolute) points for solid solution. The discussion will deal only with types of phase equilibria actually represented in the systems. We shall treat first the essentials involved in the binary diagrams of the collection, and then, more extensively, the essential relations for the several ternary diagrams. The last sections will consider specifically the ternary systems and their constituent binary systems. ]R. E. Thoma (ed), Phase Diagrams of Nuclear Reactor Materials, ORNL-2548 (to be published). CONTENTS P REFACE et ettt ettt e e ea et et ettt ettt et et s eeanaee e i LIST OF FIGURES L. ettt et et ee et e ee e e en e een e vii PART I. GENERAL PRINCIPLES Lo BINARY DIAGRAMS e e et ettt ettt e 3 1.1. Pure Components as Solid Phases ..........ccccoooveviiviieini, ettt 3 1.2, Pure Compounds ..ottt bt bt e, 3 Relation Between Congruence and Incongruence of Melting for a Binary Compound ................ 4 130 S0lid SOIUtION oo et et 4 Continuous Solid SolUtion ..o 4 Miscibility Gap in Solid SolUtion ... i e e, 5 Solid Solution and Polymorphism ..ottt 5 2. TERNARY EQUILIBRIUM OF LIQUID AND ONE SOLID (SURFACES) .o, 7 2.1, Fixed Solid oo e e 8 2.2, Variable Solid (Solid Solution) .o e e 8 Fractionation Path ... e bt b e oo e eseeeat e e et e et ete et e et e e e te et e eeeeae s 9 Equilibrium Path o e et st st 9 3. TERNARY EQUILIBRIUM OF LIQUID AND TWO SOLIDS (CURVES) ..o, 11 3.l REACHON T Y POS oo b ettt e, 11 3.2. Maximum and Minimum Temperature Points ..o e, 12 3.3. Equilibrium Crystallization Process for Liquid on a Two-Solid Curve ..., 12 4. TERNARY CONDENSED INVARIANT POINTS (FOUR PHASES) ..o, 14 4.1. Binary Decompositions in Presence of Ternary Liquid ... 14 PUPE T SOlidS oo ettt 14 Effect of the Third Component Entering into Solid Solution ..o, 14 4.2. Types of Ternary InVariants ... e s 15 Type A Invariant: Triangular or Terminal Type of Invariant ... 15 Type B Invariant: Quadrangular, Diagonal, or Metathetical Type of Invariant .................... 15 4.3. Relations of the Three Liquid Curves at Their Invariant Intersection...........cccevvvveivinieinicennne, 15 4.4. Congruent and Incongruent Crystallization End Points ..o 17 4.5. Melting Points of Ternary Compounds ... et st 19 4.6. Invariants Involving Solids Only . 19 5. CRYSTALLIZATION PROCESS WITH PURE SOLIDS e 20 6. CYRSTALLIZATION PROCESS WITH CONTINUOUS BINARY SOLID SOLUTION ..o, 25 6.1, Fractionation ProCess ..ottt oot e e st ean s ee st a e naeaees 26 6.2. Equilibrium Process ... e ettt e ar e 26 7. CRYSTALLIZATION PROCESS WITH SOLID SOLUTIONS AND SEVERAL INVARIANTS .............. 29 7.1, The Phase Diagram ... ettt e et e st eee st e n e enee 29 7.2. Equilibrium Crystallization Process ... 30 7.3. Process of Crystallization with Perfect Fractionation............ccoooiiiiiiiiiiiiiii e 32 7.4. Ternary Solid Selution in Compound D[ i 33 10. 1. 12. 13. 4. 15. Vi PART II. THE ACTUAL DIAGRAMS SYSTEM X—U—V: LiF=UF ;=BeF , i s 37 SYSTEM Y--U~V: NaF=UF ,=BeF , . s 40 SYSTEM Y—U—R: NaF—UF j=RbF .. 44 SYSTEM Y—Z—R: NaF=ZrF [=RBF s 47 11.1. The System According to Figure 11.3 and Neglecting Solid Solution........cccccoieiiiiinicriiennnn, 47 11.2. Consideration of Solid Solution Formation .........cooieiiii e 49 11.3. The Region for Compounds G and H of System R—Z ... 49 The Region As Shown in Figures 11.6 and 11.7 e, 49 The Region As Shown in Figures 11.8 and 11.9 . 51 11.4. The Region Involving Compounds B and D of System Y—Z ..., 52 SYSTEM Y—Z—X: NaF—ZrF ;= LiF 55 12,7, Subsystem Yo AmGoX e o e e et e 56 12.2. SUBSYSEEM EmZmH oottt e et et et e e s 58 12.3. SUbsystem A—E—H—G ...ttt e s 59 12.4. Subsolidus Decompositions of Compounds G and 7 ......coooviiiiiiii i 60 Decomposition of Compound ... ..ottt ettt sa e a e 60 Decomposition of Compound G ... ettt 61 SYSTEM Y—U—X: NaF—UF [—LiF s 64 13.1. The Invariants P ,, P, P, AN P g 64 The Invariant Py oo s 64 The Invariant P o o 65 The Invariant P o s e 66 The Invariant P oo e 66 13.2. The Region DUH ..ot e e et st et e ene e aaa e, 68 13.3. The Region YD HX i ettt e s ae e 71 13.4. Fractionation Process on the Solid Solution Fields ... 73 SYSTEM Y—U=Z: NaF—UF [=ZrF | s 75 TA. 1. General CRaracteriStics .ooiiiiiiiiriiiiieeiee oottt et et e e st em e e 2eae et e eseeseen s s emteamse e aesan e e s eensees 75 14.2. Subsystem Y—A-G ....... ettt N ehteereeht s e e et et et ereehea e et et £ttt £ehe et e eh et nen e e e ene e 75 14.3. Subsystem A-—D—K—G ... s s e e 79 The Region Involving A, B, C, and D oo e e s 80 The Region Involving G, H, I, and K . ...ocoiiiiiiiii et e 87 Fractionation Processes in the Subsystem A—D—K—G .. ..o 89 Subsolidus Reactions Involving Compounds A, H, and ] ..ot e e 90 T4.4, Subsystem D—U—Z—K ...t e b e 21 Equilibrium Crystallization Along Curves ..o e 91 Fractionation Processes in the Subsystem DU—Z—K .......ccoooiiiiiriiiieiiie et 94 Equilibrium Crystallization inthe U_Field ... 95 Subsolidus Compounds F and F ...ttt et e %6 SYSTEM Y—W—Z: NaF—ThF —ZrF 97 1.1, 1.2. 1.3. 1.4. 1.5. 1.6. 1.7. 1.8. 1.9. 1.10. 1.11. 1.12. 1.13. 1.14. 2.1 2.2. 2.3. 2.4. 3.1. 3.2. 3.3. 3.4. 3.5. 3.6. 4.1. 4.2. 4.3. 4.4. 4.5. 4.6. 4.7. 4.8. 4.9. 4.10. 4.11. 4.12. 4.13. LIST OF FIGURES Pure components as solids.......ccccoooivioii i Retrograde solubility curve ..oooievviiiiiiii Binary compounds .........coocoiiiiiii e, “Inverse’’ fusion of binary compound ... ........................................................................ Singular point between congruence and incongruence of melting ..o Continuous solid solution without MAXimMUM OF MIMIMUT oottt reereeeree e veesereaesasnnneeeees Continuous solid solution with minimum .................... Discontinuous solid solution, eutectic case .............. Discontinuous solid solution, peritectic case............ Elevation of transition temperature, involving liquid Elevation of transition temperature, subsolidus ........ ........................................................................ ........................................................................ ........................................................................ ........................................................................ ........................................................................ Depression of transition temperature, involving liquid ..o Depression of transition temperature, subsolidus...... ........................................................................ Depression of transition temperature, lower fOrm pure ..........ccovioiiiiiiiieieet e s Liquidus surface for pure solid A ..., ........................................................................ Fractionation path on surface for liquid in equilibrium with A—B solid solution .....ccoccovvninnn Relation between equilibrium path and fractionation Relation between equilibrium path and fractionation paths: for ternary solid solution.............. paths: for binary solid solution ............... Change from even to odd reaction: two solid solutions ... Change from odd to even reaction: two solid solutions ... Change from odd to even reaction: two pure solids .. Temperature maximum in reaction L — calories —> §, + S, e, Temperature minimum in reaction L + §, ~ calories —> S, i Three-phase triangle on curve for L. — calories —> S, + S, Type A invariant ... Type B invariant ... Arrangement of curves at a eutectic ... Arrangement of curves for case (a) and case () ........ Arrangement of curves for case (c) and case (d) ........ Impossible angles of intersection ..., Eutectic triangle contains only the eutectic “‘point”’ ........................................................................ ........................................................................ ........................................................................ ........................................................................ ........................................................................ ........................................................................ E .................................................................. Eutectic triangle also contains several peritectic “points” ..., Invariant, €ase (@) oo Invariant, €ase (@) ..o Invariant, case (€) oot Invariant, case (b)) oo e Semicongruent melting point of ternary compound M, ........................................................................ ........................................................................ ........................................................................ ........................................................................ ........................................................................ oo o O OO OO0 LWLWW — — O O 0 — ot ek et od AR MR AN ed el = — il e ] e et el et weed med v e e OO0 N0 N N N N O O8O OO vii 5.1 5.2. 5.3. 5.4. 5.5. 5.6. 5.7. 5.8. 5.9. 5.10. 5.11. 5.12. 6.1. 6.2. 6.3. 6.4. 6.5. 7.1, 7.2 7.3. 7.4. 7.5. 7.6. 7.7. 7.8. 7.9. 7.10. 7.1, 7.12. 7.13. 7.14. 8.1. 8.2. 8.3. 8.4. 8.5. 8.6. 8.7. 8.8. viii Two three-solid arrangements for two binary compounds ... 20 Necessary arrangement of curves and invariants for the two cases in Fig. 5.1 ..o 20 Hypothetical ternary system with three binary compounds ... 21 The section A—D, of Fig. 5.3 .o 21 Isotherm between py aNd 7 ..o 2] [sotherm between 7 QN 72 ..o e bbb bbbt e 23 Isotherm above P, and still above Eq and E, i 24 [SOEREIM Gt Py o e s s s s s s e et 24 The SeCtion D =Dy it b s s 24 The SECHon D gD 5 (oo e 24 The SeCtion C—D 5 .o e e 24 The SECHON D 1=B oot 24 Ternary system with continuous A—B solid solution and pure C ........occiviviinnniicicnce, 25 The binary system A—B of Fig. 6.1 .o e 25 Arbitrary section, from C to the AB side ... 25 Fractionation paths for the solid solution sUFFACE .. .o 26 Equilibrium paths and inflection point of fractionation path. ..., 28 Ternary system with discontinuous A—B solid solution and two binary compounds .................... 29 Binary system A—B of Fig. 7.1 .o 29 The invariant reaction planes of Fig. 7.1 e e 30 The SECHON D y=8 o 30 IS Otherm GBOVE [ . oot e e 31 [sotherm just Below P e e 31 Isotherm below m but above P and above F4 s 31 The SECHION D =D o oot 32 The SECHON D =B oot e - 32 The SEction A—D 5 .o 32 Portion of Fig. 7.3, with some ternary solid solution ot Dy ..., 33 Isotherm for Fig. 7.11, between p and P .o e 33 |sotherm [UST GDOVE P 1 oo s 33 Part of the section D =D, for Fig. 7. 1T e, 33 System X—U: LiF=UF ;o 37 System U=V UF =BeF , oo 37 System X—V: LiF=BeF , i i, 37 System X—U—=V: LiF=UF =BeF 38 Isotherm involving the fnvariant P, .. s 39 Isotherm above P, and Py o 39 The section C=V: LiF4UF ,=BeF . 39 The section B—V: 7LiF.OUF ,—BeF ., 39 8.9. 8.10. 9.1. 9.2. 9.3. 9.4. 9.5. 9.6. 9.7. 9.8. 9.9. 10.7. 10.2. 10.3. 10.4. 10.5. 10.6. 10.7. 10.8. 10.9. 10.10. 11.1. 11.2. 11.3. 11.4. 11.5. 11.6. 11.7. 11.8. 11.9. 11.10. 12.1. 12.2. 12.3. 12.4. 12.5. 12.6. 12.7. The section B—-D: 7Li|:-6UF.4—2LiF-BeF2 The section A=D: 4LiF-UF4—2LiF-BeF2 ........................................................................................ .......................................................................................... System Y—U: NaF —UF | System Y—-V: NaF—=BeF , .. i System Y—U—V: NaF=UF =BeF , .o, Isotherms involving compounds E and F (NaF.2UF, and NaF-4UF ) The section F—V: NaF.4UF ,~BeF, The section E—V: NaF.2UF ,-BeF, The section D—=V: 7NaF.6UF ,=BeF , e, The section B—H: 2NaF.UF =2NaF.BeF , ..., The section D—H: 7NaF.6UF ,~2NaF.BeF, ............................................ ................................................................................................ .................................................................................................. ...................................................................................... System R—U: RbF-UF, System Y—R: NaF=RbF . System Y—U—R: NaF=UF ,=RbF . The section D—N: 7NaF.6UF ,—RbF.6UF, The section D—M: 7NaF.6UF (=RbF.3UF | o The section D—K: 7NaF.6UF ,=2RbF.3UF, The section D—I: 7NaF.6UF ,-7RbF.6UF The section B—H: 2NaF.UF ,~2RbF.UF The section Y—0Q: NaF—NaF-RbF-UF ;. The section O-G: NoF-RbF-UF4—3RbF-UF4 ........................................................................................................................ ........................................................................................ ...................................................................................... ........................................................................................ .......................................................................................... .................................................................................... System Y—Z: NaF-ZrF System R—Z: RBF=ZrF | System Y—Z—R: NaF—ZrF ,~RbF s The partial section M,—Z: NoF-RbF-ZrF4-ZrF4 ............................................................................ Divisions of Fig. 1.3 i et e s Detail of binary system Z—R: ZrF ,=RbF ..o Region involving compounds H and G: 5NaF.2ZrF, and 3NaF-ZrF , Detail of system Z—R, for f1 (5NaF.2ZrF ;) assumed pure ..., Region involving H and G, for H pure: 5NaF.2ZrF , (pure} and 3NaF-ZrF .o Region involving solid solutions in Y—7 (NaF=ZrF ;) system ... ...................................................................................................................... System X—Z: LiF-ZrF, System Y=X: NaF =LiF e System Y—Z—X: NaF—ZrF wLiF Region below section A—G (3NcF-ZrF4-—3LiF-ZrF4) The section A—G (BNGF-ZrF4—3LiF-ZrF4) ........................................................................................ Region above section E~H (7NaF-62rF4—2LiF-ZrF4) The section F—I (3NcF-4ZrF4—3LiF-4ZrF4) ........................................................................................................................ ...................................................................... .................................................................... .................................................................................... 50 12.8. 12.9. 12.10. 12.11. 12.12. 13.1. 13.2. 13.3. i3.4. 13.5. 13.6. 13.7. 13.8. 13.9. 13.10. 13.11. 14.1. 14.2. 14.3. 14.4. 14.5. 14.6. 14.7. 14.8. 14.9. 14.10. 14.11. 14.12. 14.13. 14.14. 14.15. 14.16. 14.17. 14.18. 14.19. Middle region of system Y—Z~X: NaF=ZrF =LiF ..o, e et Decomposition of compound 1 {SLiF4ZrF ) i, The section F—I (3NaF-4ZrF4—-3LiF-4ZrF4) .................................................................................... Decomposition of compound G (BLIF-ZrF,) .o The section A-G (3NoF-ZrF4-3LiF-ZrF4) ........................................................................................ System X—Us LiF=UF ;o System Y—U—X: NaF—UF —LiF s The section D—H (7N0F-6UF4-7LiF-6UF4) ...................................................................................... Decomposition of compound C (SNaF-3UF ) .. Decomposition of compound G (4LiF-UF4) ........................................................................................ Formation of compound E (NaF-2UF |} .., Region above section D—H (7NaF.6UF ,=7LiF.6UF ) oo, The section E—H (NcF-ZUF4—7LiF-6UF4) ........................................................................................ Region below section D—H (7N0F-6UF4—7LiF-6UF4) ...................................................................... The section B—G (QNGF-UF4—4LiF-UF4) .......................................................................................... Detail of Fig. 13.2, near compound C (5NaF 3UF ) ..o System Y—7Z: NaF=ZrF ;s System U—Z: UF [=ZrF ;o System Y—U—Z: NaF=UF =ZrF /., et ettt e et naees The section A—G (B_NGF-UF4—3NGF-ZI‘F4) ........................................................................................ The section D—K (7N0F-6UF4—7N0F-6ZrF4) .................................................................................... The section between Y {(NaF) and the point on UZ that represents the composition TUF = 1ZrF | i, Subsystem Y~A—G: NaF=3NaF.UF ,—=3NaF.ZrF , .o Subsystem Y—A—G (NaF-3NaF.UF ,~3NaF.Z¢F ,): fractionation paths ..., Subsystem A—D—K—G: system NaF-UF ,~ZrF , region between 3:1 and 7:6 SOLIA SO UTIONS .o ettt et et b e e et Scheme | for compound C (5NoF-3UF4) .............................................................................................. Sequence of isotherms for Scheme | ... The section between C (5N0F-3UF4) and the point on YZ that represents the composition SNaF-3ZrF ,, in Scheme | ... Scheme Il for compound C (5NoF-3UF4) .............................................................................................. Sequence of isotherms for Scheme 1l ... The section between C (SNGF-SUFA) and the point on YZ that represents the composition SNaF=3ZrF ,, in Scheme Il ... Lower part of subsystem A—D—K~G: the NaF-ZrF, side of Fig. 14.9 .. Solids left after complete solidification, in region YDK (Na F—7N0F-6UF4—7NGF-6ZrF4) ...................................................................................................... Decomposition of compound A (3NoF-UF4) ........................................................................................ Transition in compound {/ (SNQF-ZZer) ............................................................................................ 14.20. 14.21. 14.22. 14.23. 14.24. 15.1. 15.2. 15.3. 15.4. 15.5. 15.6. 15.7. 15.8. Appearance of compound ] (BNOF-QZer) .......................................................................................... 93 Subsystem D—U~Z—K: system NaF-UF ,-ZrF, between the 7:6 solid solution and the UF ,~ZrF, solid solution...........ccccoiiiiiiiiiis e, 93 Subsystem D—U—7—K: temperature CONTOUIS .. ..ooiociiiiieiieeieieesieeieiteee oo 93 Subsystem D—U—Z—K: fractionation paths ... 94 Appearance of compounds £ and F (NaF.2UF, and NaF-4UF ) 96 System Y=W: NaF—ThF e e 97 System W2t ThF = ZrF ;oo 97 System Y—W—Z: NaF—ThF —ZrF ;.. 98 System Y—W—Z7: NcF—ThF4—ZrF4 (revised) ..o, e e e, 99 Middle region of system Y—W—7Z (NaF=ThF ,=ZrF ;) ..o, 100 Subsolidus transition in compound B (5NoF-2ZrF4) .......................................................................... 101 W—Z7 region of system Y—W--Z (ThF ,~ZrF, region of system NaF~ThF ~Z¢F,) ... .. 102 Fractionation paths for the solid solution surface of system Y—W—-Z (NGF=ThE j=ZrF ) oo s e 103 xi PART | GENERAL PRINCIPLES 1. BINARY DIAGRAMS 1.1 PURE COMPONENTS AS SOLID PHASES With the pure components as the only solid phases in a binary system (Fig. 1.1), the melting points (T, and T}) are lowered and the system is always eutectic in type. In Fig. 1.1 the eutectic e involves the high-temperature form of A (A,) and the low-temperature form of B (Bfi); at the temperature of e the phase reaction is: L(e) —calories === A_+ Bg If T:1 is the transition temperature for the forms of A, then the two-solid mixture consists, at equilibrium, of A and B Afi and B, below T7. 1f T is the transition temperature for the polymorphic forms of B, there will be a break in the freezing-point curve (or solubility curve) of the B solid at the temperature T, unaffected by the A if both forms of the B solid are pure. Above TJ, the liquid is in equilibrium with B , below Tj with B If the transition B,~» B above T{; and of fails to occur on cooling, a metastable eutectic e(m) is possible, for liquid in (metastable) equilibrium with A_and B . (It is possible for a solubility curve to show a ‘“‘:etrograde’’ temperature effect, even down to the eutectic, in which case we would have Fig. 1.2. Retrograde changes of solubility with temperature were not encountered in the present systems, whether binary or ternary, but reference will be made to this question later.) Liquids A and e, such as point @ (Fig. 1.1), give A as primary crystallization product when cooled to the curve with composition between T,e. At the temperature T the equilibrium mixture consists of solid A and liquid 7 in the ratio (by weight or by moles, depending on the units of the diagram) x//xs. When the temperature of e (eutectic) is reached, the remaining liquid freezes invariantly to a secondary crystallization product of a mixture of A_and B, crystals in the proportion ev/eu. For liquids between b and B in composition the primary solid will be B , changing to By at Tp, and followed by the eutectic mixture at e. In a two-phase region such as T ,ue, the coexisting equilibrium phases are joined by horizontal tie lines (also called conjugation lines, conodes, joins) running in this case between the liquidus curve T,e ond the solidus curve T,u. A With pure solid A, the solidus is here a vertical fine, the edge of the diagram. The horizontal line uev is also sometimes considered part of the solidus of the diagram. 1.2. PURE COMPOUNDS Figure 1.3 shows three (C; D, E) in the system A-B: 1. Compound C melts congruently at C_; it has a congruent melting point. binary compounds It is stable as a solid phase until it melts to a liquid of its own chemical (analytical) composition. Points e, and e, are eutectics for solids A and C_and for C_ and D, respectively. At TZ, the higher-temperature form C_ undergoes transition . to Cpe At To, Cg decomposes on cooling into the solids A and D. 2. Compound D melts at the temperature D.. |t decomposes as a solid phase incongruently UNCLASSIFIED ORNL~LR-DWG 24748 T — AD+E . E+E /H—CB C£+D 76'\ - ] A+ D | A C D £ B Fig.1.3. (into liquid p and solid B) before reaching its own melting point [the metastable or submerged congruent melting point D _{m)]. In contrast to a eutectic point (e,, e,), the point p is called a peritectic point (also meritectic, sometimes) and the reaction: D + calories = L(¢) + B is a peritectic reaction. 3. Compound E decomposes as a solid phase, into D and B, at the temperature T, before it reaches any equilibrium with liquid. Such a solid phase is sometimes called '*subsoclidus.” Figure 1.3 shows a metastable eutectic, e(m), between solids A and D, possible if compound C fails to form on e’ (m) metastable eutectic for solids C_and B. It is also possible for ¢ compound to undergo cooling; is a similar incongruent melting on cooling (inverse peritectic, or inverse fusion), as shown in Fig. 1.4. No example is found in the actual binary systems studied, but the relation will be referred to under the ternary systems. In Fig. 1.4, T] ts the usual incongruent melting point of C; T, is its inverse fusion point: C —calories=—=L({(p )+ B . Relation Between Congruence and Incongruence of Melting for a Binary Compound The flatness of the freezing-point curve of a compound at the maximum, whether exposed and stable as at C_ in Fig. 1.3 or submerged and metastable as at D_(m), depends on the degree of dissociation of the compound in the liquid state. If the compound C is not dissociated at all, the maximum is a pointed intersection of two unrelated curves: on one side the freezing-point curve of the compound in the binary system A—-C, on the other side the freezing-point curve of the compound in the unrelated binary system C—B. OCnly when the maximum is such a sharp intersection may the whole diagram be said, strictly, to consist of two adjacent binary systems. If there is any dis- sociation of C into A and B in the liquid state, the curve is rounded, and its maximum is lowered, because the liquid, even at the maximum itself, is not pure C (in the molecular sense) but C plus A and B. The greater the degree of dissociation, the flatter and lower is the maximum. Hence, whether the melting point of the compound will be exposed or submerged relative to the freezing- point curves of adjacent solid phases depends on the ‘‘true’’ melting point of the compound without decomposition and on its degree of dis- sociation in the melt. In a comparison of corresponding compounds of given formula, such as A.B in a series of homologous binary systems with A fixed and B varied, the congruence or incongruence of the melting point of the compound will be a function of three variables: the melting point of the second component (B, B’ B", ...), the *‘true’’ melting point of the compound (A:B, AB’, etc.), and the degree of dissociation of the compound in the melt. For a given specific binary system, moreover, the relation may vary with the pressure, because of several effects. Pressure causes some change in the relative melting points of all three solids of the system (A, C, B); it causes corresponding changes in the compositions of the intervening isothermally invariant liquid solutions (e, p, etc.); and it causes changes in the dissociation of the compound. The melting point of the compound may therefore be exposed (congruent) at one pressure and submerged (incongruent) at a different pressure. At some particular or singular value of the pressure, therefore, the diagram would pass through the configuration in Fig. 1.5, When a system at arbitrary pressure seems to give such a diagram, however, it is reasonable to suppose that the maximum is actually either just exposed or just submerged. 1.3. SOLID SOLUTION Continuous Solid Solution In a binary system with continuous solid solution, the usual relation is either an ascending one as in Fig. 1.6, without minimum or maximum, or, as in Fig. 1.7, one with a minimum. Continuous solid solution with a maximum is very rare. The space L + S between the liquidus and solidus curves represents, at equilibrium, two-phase mixtures, the L and § compositions being joined by a horizontal tie line at any temperature. In Fig. 1.6 L and S have the same composition only In Fig. 1.7 the L and § curves touch at the minimum; they touch tan- gentially, however, and the two parts of the diagram are not strictly like two binary systems side by side. Except for the pure components or for the composition m, a given composition has a definite for the pure components. temperature range of freezing or melting, for UNCLASSIFIED ORNL-LR-DWG 24749 é 5 L '.— < o [T} a = Lil }_ 4 A B c Fig.1.5. L /_+5\ s m S A B A B Fig.4.6. Fig. 1.7 equilibrium conditions. Liquid x (Fig. 1.6) begins to freeze at f,, and the solid starts with compo- sition s,. As the temperature falls, the L and § compositions adjust themselves, always on the ends of a tie line, and the sclid reaches the composition x at temperature t,, the last trace of liquid that solidifies having the composition /,. Such a crystallization process assumes complete equilibrium all along, with the time for diffusion in the solid that is formed being sufficient for the solid to remain of uniform composition and in equilibrium with the liquid. As the opposite limiting extreme we may speak of crystallization with perfect fractionation, in which no diffusion at all is assumed to be permitted to occur in the solid. The first trace of solid formed is assumed to be effectively removed from the reaction (as in removal of vapor in distillation), and becomes merely the core of a growing particle with a layered structure, one with infinitesimal layers with infinitesimally changing composition, each layer being taken out of the equilibrium as it is deposited. In such a process the liquid x (Fig. 1.6) begins to freeze at t,, forming solid s, but now, with removal of B-rich solid, the remaining liquid continues to fall in freezing point and approaches the melting point of A as limit. The solid formed has a core with composition near s, and an outermost layer approaching A in composition. As in azeotropic distillation, such fractionation in the case of Fig. 1.7 is limited by the minimum . Miscibility Gap in Solid Selution Figure 1.8 shows limited solid solubility in a system with minimum melting point. The eutectic of this system: I(¢) ~calories=—a+ 6 is similar to that in Fig. 1.1 except that the solids (a, b) are not pure. They represent the limits of solid miscibility at the temperature e. The change of this solid solubility with temperature is then shown by the curves aa’ and bb’, joined by tie lines indicating the compositions of conjugate solid solutions. In Fig. 1.9 the miscibility gap impinges on a system without minimum melting point. The relation: a + calories == L(p) + b6 , is called peritectic, being analogous to the incongruent melting point of a compound (D in Fig. 1.3). Solid Solution and Polymorphism We consider only a few simple relations for the effect of B (in solid solution) on a polymorphic transition point of A. Unlike Fig. 1.1, if B dissolves in solid A, then the transition temper- ature for: Afi + calories == A is either raised or lowered: 1. It is raised if B is more soluble in the lower form than in the upper form of A (Figs. 1.10, 1.11). The region «x represents equilibrium between o phase and B phase, and with the B content in 3 greater than the B content in «, the transition temperature is raised, from T , to T}. In Fig. 1.10 the phase reaction ot T is: A+ calories —A_ +L{p) . In Fig. 1.11: M — Afi +calories=—4A_+B_ , the B_ phase being o solid solution. UNCLASSIFIED ORNL-LR-DWG 24750 Aq + L Fig. 1.10, Fig. 4.41. 2. It is lowered if B is more soluble in the upper form; it is, therefore, always lowered if the lower form is pure Afl (Figs. 1.12, 1.13, and 1.14). Polymorphic transitions of this sort apply to solid solutions of binary compounds, as well as to solid solutions of the components themselves. These are only a few of the relations possible in UNCLASSIFIED ORNL-LR-DWG 24751 A+A 51 ey = Fig.1.42. Ay+1— (Aglgs | At 4,) A YSS| Mgt By 4 g Fig.143. Fig.144. transitions of solid solutions, but they suffice for the systems under consideration. In particular, these systems involve no case of a congruently melting binary compound dissclving adjacent solids on both sides; such a relation always involves the possibility of nonstoichiometric maxima and Berthollide compounds. 2. TERNARY EQUILIBRIUM OF LIQUID AND ONE SOLID (SURFACES) The ternary diagrams under consideration deal with temperature-composition (T vs c¢) relations in additive ternary systems, each with three fluorides as components. The special problems of representation met with for reciprocal ternary systems, those containing two cations and two anions, are not involved. The relations could presumably be completely and explicitly shown in a transparent, ‘‘explodable®’ and sectionable three-dimensional triangular prism model, in which the various phase spaces and the two-, three-, and four-phase equilibria are distinguished. The two-phase spaces contain (isothermal) tie lines compositions of coexisting phases solid, or two solids). horizontal joining the (liguid and The three-phase equilibria occupy spaces triangular in isothermal section — spaces generated by isothermal three-phase triangles, the corners of which move along con- tinuous curves with changing temperature. The four-phase equilibria (isobarically invariant) constitute isothermal planes defined by the four phases of the equilibrium. The relations in the three-dimensional T vs ¢ prism are usvally represented and discussed by means of plane diagrams which are either pro- jections or sections of the prism. The only type of projection used in the present discussion is the polythermal projection of the liquidus surfaces. This is a projection parallel to the temperature axis, upon the ftriangular composition plane, showing, therefore, the various parts of the liquidus surface or surfaces as viewed from the direction of high temperature. The resulting ‘“‘phase diagram'’ thus consists of fields (projected surfoces) for liquid saturated with a single solid, of the boundary curves between surfaces, for liquid saturated with two solids, and of points for the intersection of these curves, three at a time, for liquid in equilibrium with three solids. The direction of temperature change can be shown by arrows on the curves, and some actual temperatures can be shown by means of isothermal contours. Such a polythermal projection shows directly which surface will be reached by a liquid of known composition upon cooling, and hence what the nature, if not the composition, of the primary crystallization product will be. The diagrams under consideration give this information (where it is known) unambiguously in every case because they involve no solid phase with a retrograde effect of temperature on its solubility (Fig. 1.2), so that there is no overlapping, in polythermal projection, of primary phase fields. This re- striction is wunderstood in all the subsequent The absence of retrograde effect means, moreover, that the amount of liquid always diminishes on cooling, while the total amount of solid (or solids) always increases, The T vs ¢ prism is further studied and analyzed by means of plane sections, which may be vertical T vs ¢ sections through two particular binary compositions, or may be horizontal iso- thermal sections which then amount to isothermal solubility diagrams of the ternary system. discussion. We shall now consider the crystallization equilibrium of liquid and one solid (the surfaces of the liquidus); in the immediately following sections we shall consider the equilibrium of liquid with two solids (the boundary curves) and the equilibrium of liquid with three solids (the ‘'condensed invariants’’ of the system). The ‘‘surface’’ (the field, in projection) is variously referred to as crystallization surface, freezing-point surface, solubility surface, primary phase region, or primary phase field. When a liquid is cooled to one of these surfaces it deposits one solid on cooling, as long as the liquid is still on the surface (‘‘on the surface’’ means anywhere short of a boundary curve). Every point on the surface represents equilibrium between that particular liquid (point) and a particular solid composition, and the liquid and solid compositions or points are joined by a tie line (isothermal). If the surface is cut in isothermal section, the isothermal solubility curve is then joined by a series of nonintersecting tie lines to the composition of the saturating solid. If the solid is one of fixed, constant composition, all the tie lines, at any and all temperatures of the surface, meet at the fixed composition of the solid phase. Otherwise the tie lines, at any temperature, simply join the liquidus and solidus curves; the solidus ‘‘curve’ may be a straight line. The direction of falling temperature at any point of the surface is away from the composition of the separating solid in equilibrium with the liquid at that point. |f the solid is one of fixed composition, therefore, straight lines radiating from its composition are lines of falling temper- ature, in every direction, and they cut contours of lower temperature, progressively. 2.1. FIXED SOLID In Fig. 2.1, the region Ae, Ee, is the (projected) surface for saturation with pure solid A. The arrows on the boundaries indicate the direction of falling temperature, and the curves T, ..., T are isothermal contours (T, > ... > T,). If the liquid x, with composition falling on this surface, is cooled, it begins to precipitate solid A ot T, The crystallization path of the liquid, the path followed by the liquid on the A surface while it is being cooled and while it is precipitating 4, is then a straight line extended from A through x. Removal of A from the liquid makes its compo- sition proceed in a straight line from the corner A, The crystallization paths for a field of a solid of fixed composition are therefore simply straight lines radiating from the composition of the solid. The composition of the liquid starting at x, while precipitating A, will therefore be Ly 13 [ 4 etcy, at the successive temperatures shown, and the ratio of solid to liquid is given by xlz/xA, etc., at each temperature. The quantity of liquid is always diminishing, but the liquid is never completely consumed while it is still on the A surface. Some liquid must reach one of the boundary curves of the fieid. These relations hold, moreover, whether the solid A is kept in contact with the liquid while it is being cooled, or whether the solid is continually removed as produced. UNCLASSIFIED ORNL -LR-DWG 24752 Fig. 21 2.2. VARIABLE SOLID (SOLID SOLUTION) If the solid is a ternary solid solution, there is a solidus surface, representing solid solutions which are in equilibrium (point for point) with liquids on the liquidus surface. The solidus surface lies everywhere beneath the liquidus surface in temperature, and it will not be repre- sented at all in the usual ‘‘phase diagram.’”’ Any point on the liquidus is connected by an iso- thermal tie line with one individual point on the solidus, representing the solid composition with which it is in equilibrium. anywhere intersect. These tie lines never The space between the two surfaces is the two-phase space in which mixtures consist, at equilibrium, of liquid and the solid solution, These surfaces are in contact at the composition of a pure component (if the solid phase includes the composition of the pure component), and otherwise only at absolute maxima or absolute minima of temperature, which may be at the binary sides or in the ternary system: only at points, in other words, and not along a whole ridge or trough (valley). [The “‘absolute’ maximum or minimum of ““on'’ the surface — and this means, it must be recalled, not on any a liquidus surface is a point one of its boundaries with another surface. The absolute maximum or minimum may be at a unary point (composition of a component), at a binary point (side of the triangle), or at a ternary point, as at the dome of a continuous ternary liquidus, The surface, moreover, may have more than one absolute maximum (or minimum).] The equilibrium process of the freezing of a liquid now involves a definite temperature range, the vertical distance along the temperature axis, in the T vs c prism, between the liquidus and solidus surfaces. A liquid of composition x, let us say, begins to freeze at T (the liquidus temper- ature at x) and is completely solidified at T, (the solidus temperature for the same composition x). The composition s, of the solid, as it just begins fo form at T,, is different from x. As the crystallization proceeds, however, with falling temperature, and if the liquid and solid phases maintain complete equilibrium with each other, both phases change in composition, so that at T the final solid has the original composition x an the last trace of liquid to solidify has still a Between T, and T, followed o separate, three- different composition [, each phase has dimensional curve with respect to temperature and composition, one along the liquidus surface and one along the solidus surface, but such that the two compositions joined by an equilibrium tie line, at each temperature, passing through the total composition x. The path followed by the liquid, on the liquidus, in such a process, is called its ‘‘equilibrium path’’: the path followed by the composition of the liquid during cooling, if the whole of the solid phase equilibrium with the liquid. Such a process can be attained only as a limit, perhaps, with extremely slow cooling, since the interior of the growing solid can be kept uniform with the surface layer only through diffusion in the solid. At the opposite extreme of behavier we may specify that no diffusion whatever takes place in the growing solid. were always is at every moment in complete The first infinitesimal amount of solid now acts simply as an unchanging core for a growing layered structure, each layer differing infinitesimally in composition from the preceding one, and each layer, because of the absence of diffusion, being effectively equilibrium as it is formed. In such a process there is no longer a definite freezing range for the liquid. As the solid produced is being ef- fectively removed, the remaining liquid tends toward some temperature minimum of the surface before being consumed. The path followed by the removed from the liqguid in such a limiting process of perfect fractionation we shall call a **fractionation path.”’ (When the separating solid is of fixed compo- sition, as in Fig. 2.1, there is no distinction between *‘‘equilibrium path'' and ‘‘fractionation path’’; hence the one term, ‘‘crystallization path.’) Fractionation Path The surface may be considered to be covered by a family of curves (fractionation paths), following the course of falling temperature and hence cutting contours in the order of falling temperature, and all originating at some absolute maximum of the surface. If there is an absolute minimum on the surface, then these paths, after fanning out, converge again at that minimum. All the cases in the systems under consideration concern solid solution surfaces having one or two absolute maxima (in some cases the maximum is metastable); with an there are no solid absolute minimum. submerged or solution surfaces Hence the fractionation paths in these systems do not converge with falling temperature, but end, each at a separate point, at the various boundaries (for liquid in equilibrium with two solids) of the surface. there are two families of crystallization paths, one With two absolute maxima on a surface, originating at each maximum. At any point on the surface, such a path starts with a direction given by the L—S tie line at that point of the surface, but the direction immediately changes because, as the temperature changes, the The direction of motion for the liquid composition is away from the composition of the separating solid. The fraction- ation path is therefore such that its tangent at any point is the L-—S5 tie line at that point (Fig. 2.2). Here the curve Bf is a fractionation path on a surface for precipitation of an A-B solid solution; and the lines /, s, ! separating solid also changes. 25 v gy are L—=S tie lines on this surface at temperatures T >T,>T,>T,. UNCLASSIFIED ORNL-LR-DWG 32546 Fig 22. Equilibrium Path The composition x in Fig. 2.3 is liquid above temperature ¢, and solid below tee When cooled to t,, it just begins to produce solid of compo- sition s.; s, is a point on the solidus surface in equilibrium with the point [, (or x) on the liquidus surface. The line s,y is therefore the S—L tie line for 7, at ¢,. With precipitation of s,, the liquid liquidus in the direction of this tie line (i.e., it tends, with tends to move on the removal of the solid phase, to follow the fraction- ation path Pqr to which the tie line s/, is tangent at /), but its motion is restricted by the condition that the line joining solid and liquid compositions must always pass through the fixed point x, at each temperature, and that this line must always be an equilibrium tie line. These successive tie lines are s,1,, s,l,, etc. The solid follows the curve s. s, ... s, (s, being the same as x), and the liquid follows the curve (its equilibrium path) l]l2 .o 15 (Z, being the same as x). At e the sample is completely solidified, I, being the composition of the last trace of liquid. Since the lines Soly 5414, etc,, are tie lines, they are tangent, at the liquid points, to the fractionation paths (¢, . « . p) through these points. [t is thus seen that the equilibrium path of the liquid x (its path on the liquidus surface) is one which crosses, with falling temperature, successive fractionation paths at points where the tangent to the path passes through the point x. The UNCLASSIFIED ORNL—LR-DWG 24753 Fig. 2.3 10 equilibrium path crosses the fractionation paths from the convex to the concave side. |f a fraction- ation path should be a straight line, it is not crossed by an equilibrium path; it is itself an equilibrium path, as in the case of precipitation of pure solid. In the general case of Fig. 2.3, the solid is a ternary solid solution, and the liquid may com- pletely solidify, as assumed in Fig. 2.3, before it reaches a boundary curve of the surface. If, as in Fig. 2.2, the solid solution is binary, it is impossible for a ternary liquid precipitating the solid solution to solidify completely before it reaches a boundary curve of the surfoce, where a solid involving the third component may also But although, with binary solid the curve s,s. ... s precipitate. becomes a straight line, the relations between equilibrium path and fractionation paths developed in Fig., 2.3 still hold (Fig. 2.4). At t, the mixture is not all solid; it still consists of liquid and solid in the ratio s, x/xI, . Returning to Fig. 2.3, ony total composition, like x itself, on the particular tie line syl will consist, at t,, of the phases s, and /;. Hence the 3 3 equilibrium path of any total composition between solution, s, and [, will pass through one common point, namely, 13. Consequently, while there is but one fractionation path passing through any single point of the surface, there will be an infinite number of equilibrium paths passing through the same point. A surface may therefore be described by the family or families of fractionation paths on it, but not by equilibrium paths. UNCLASSIFIED ORNL ~LR-DWG 24754 3. TERNARY EQUILIBRIUM OF L1QUID AND TWO SOLIDS (CURVES) We now consider the crystallization process for a liquid in equilibrium with two solids, §, and S,: liquid on a curve of twofold saturation (boundary curve, fieid boundary), 3.1. REACTION TYPES The curve constituting the boundary between the surface for S, and the surface for S, represents liquid in equilibrium with both solids, but not necessarily precipitating both solids upon cooling. If the liquid does precipitate both solids on cooling, and the reaction is: [. - calories —— § the crystallization is said to be positive for both solids, §,(+), §,{+), and the curve is said to be one of even reaction. [With retrograde temper- ature effects it is possible to have both solids dissolving on cooling, with negative crystal- lization for both, so that the reaction may still be even: §.(~), S,(=).] The curve is one of odd reaction (a transition curve) if one solid (Sys let us say) is dissolving in or reacting with the liquid and the other, S,, is precipitating during cooling. The crystallization is now S,(=), $,(), and the reaction is: L +S] -~ calories —— Sz The sign of the reaction at a particular point on the two-solid curve involves the direction of the tangent to the curve at that point in relation to the compositions of the two solid phases in equilibrium with the liquid at that point., The liquid is at any point simply one corner L of a three-phase triangle. In the general case, in which all three phases are variable in composition, each equilibrium phase follows its own compo- sition curve in the phase diagram, but the usual polythermal phase diagram shows only the curve for the liquid composition. [f the solids A and §, are of fixed composition, then the S -5, leg of the triangle is o fixed line and only the L-S, and LS, legs move, with L on the liquid curve; if one of the solids is a binary solid solution, then the curve for that solid is a straight line; etc. In any case the liquid curve on the ordinary phase diagram represents simply one corner of the three-phase triangle of the equilibrium, and the whole triangle may in general be moving, with its corners changing in composition, as the temper- ature changes. Figures 3.1, 3.2, and 3.3 show three cases: Figs. 3.1 and 3.2, cases with curves for both A\ and 5., both of which are therefore ternary solid solutions; Fig. 3.3, a case with fixed solids for §, and S,. The arrows on the curves indicate the direction of falling temperature., The surface on the left of the L curve is that for liquid de- positing S, on cooling; that on the right is for liquid depositing S, on cooling. UNCLASSIFIED ORNL-LR-DWG 24755 crystallization Positive (precipitation) of a solid from o liquid corresponds to a direction vector for the motion of the liquid away from the composition of the separating solid; for negative solid in a liquid, the direction vector for the motion of the liquid is toward the solid. The resultant of the direction vectors must make the liquid move in the direction of falling temperature on the L curve. crystallization or dissolving of a Examination of the direction vectors, in Figs. 3.1, 3.2, and 3.3, required to give the indicated motion 11 on the L curve, shows that the reaction is even, in every case, between 7 and s [S,(4), 52(+)], and odd between s and ¢ [S,(-), S,(+)]. Equivalent to this procedure is the test of the tangent to the curve at any point. If the tangent extends between the compositions of the equilibrium solids, i.e., if the tangent cuts the S, -5, leg of fhe three-phase triangle, the curve is even [25 +)]; otherwise it is odd. The sign of ‘rhe reactlon changes at point s, where the tangent to the curve passes through the composition of one of the solids (S, for the cases illustrated); i.e., where one of the -S legs of the triangle is tangent to the L curve, A curve originating at a binary eutectic (pre- sumably as in Fig. 3.1), whether entering the ternary system with falling or with rising temper- ature, always starts as an even curve, while one originating at a binary peritectic (Figs. 3.2 and 3.3) starts as odd. But in all cases the sign may change as the curve proceeds on its course, both because of changing direction of the L curve and because of variation in solid compositions. Hence if "‘eutectic curve” or ‘‘peritectic curve'' refers simply to the origin of the curve, the expression does not necessarily describe the type of reaction later on along the curve. Since the type of re- action at any point on a curve is an important property of the curve, it is better to speak of ““even’’ and ‘‘odd’’ curves in order to distinguish curves for the precipitation of two solids from transition curves, The sign of the reaction on a liquid-solid curve is, then, quite clear, on the ordinary phase dia- gram, if the solids are of fixed composition; but, when the solids are variable, the type of reaction (precipitation of two solids or transition) is often unknown, for it is necessary at any point to know the compositions of the saturating solids in order to test the tangent at that point,. Since the direction of falling temperature on a surface is always away from the composition of the separating solid, it turns out that a two-solid curve of even reaction can be reached from either side, but if the reaction is odd [SI(-')' 52(+)] it can be reached only from the S, side. Both the fractionation paths and the equilibrium paths lead to the odd curve from the S, surface, and away from it on the S, surface. This is at once clear in Fig. 3.3, where all the crystallization paths on the S, surface radiate as straight lines from the point S,, and those on the §, surface are straight lines radiating from the point 5. 12 3.2, MAXIMUM AND MINIMUM TEMPERATURE POINTS A twofold saturation curve may pass through a maximum or a minimum of temperature. This is possible only if at least one of the solids is variable in composition. At the maximum or minimum the three-phase triangle becomes a line: the three phases (L, Sy and 52) have collinear compositions, all lying on one straight line of the diagram. Figure 3.4 shows the case of a maximum on a curve of even reaction, and Fig. 3.5 a minimum on a curve of odd reaction. The leading corner of the three-phase triangle (in the direction of falling temperature) may be said to be the liquid. The collinearity corresponds to the relations at a binary origin of such an equilibrium, which is always a maximum or a minimum for the equilibrium, and where of necessity the three phases are on one straight line, which then opens up into ¢ triangle on entering the ternary diagram. 3.3. EQUILIBRIUM CRYSTALLIZATION PROCESS FOR LIQUID ON A TWO-SOLID CURVE When the liquid is on a two-solid curve, the fixed total composition x of the sample being cooled must lie inside the three-phase triangle (Fig. 3.6). The mixture consists of three phases, UNCLASSIFIED ORNL- LR -DWG 24755 F Wi M MAXIMUM s o 5, 2 gL 36 such that the ratio of the total solids to liquid is xL/xy, and the ratio of S, to Sy is ySz/yS1. As the temperature falls and L travels down the curve, the whole three-phase triangle moves with it, $; and §, in general following their own com- position curves. Since the point x is fixed, it is therefore possible (but not necessary) that one of the three sides of the triangle may come to sweep through x. When this happens, the mixture be- comes a two-phase mixture, the third phase having been consumed in the crystallization process. In the sketch in Fig. 3.6, if the general configuration remains the same while the triangle moves to the right, the amount of solid increases and the liquid diminishes (as always), and when the side .5, sweeps through x, the liquid vanishes, leaving §, and §,. The solidification process would then be completed while L is still on the curve, or before L reaches the end of the curve, J. But if the triangle twists aond changes shape as L moves down the curve, the point x may come to be swept by the S.L leg (S, vanishing) or by the S,L leg (S, vanishing). It S, vanishes and the liquid is left saturated with only §,, the liquid leaves the curve to travel on the §. field; if §, is consumed, the liquid, saturated with § curve onto the S, field. , alone, moves off the Some of the possible variations of behavior are the following: 1. Curve of even reaction: (a) |f the solids are not variable, no phase is consumed while L is on the curve. The liquid diminishes, but some reaches the end of the curve; [. does not leave the curve. (6) If S, is variable and S, constant, either liquid or S, may be consumed, but not §,. Solidification may be complete on the curve, or L may leave the curve for the §. field, or it may reach the end of the curve, (c) If both solids are variable, any one of the three phases may be consumed. Solidifi- cation may be complete on the curve, or L. may leave the curve on either side, or L may reach the end of the curve. 2. Curve of odd reaction [Sl(_)' 52(+)]: Now §, may always be consumed, whatever the nature of the solids. (a) With fixed solids, only S, can be con- sumed. The liquid may leave the curve for the S, field, or it may reach the end. Solidification cannot be completed with L on the curve. (6) If S, is variable (s, fixed or variable), then any one of the three phases may be consumed. Solidification may be com- pleted on the curve, L may leave the curve for either side, or it may reach the end of the curve, A transition curve (odd reaction) is traveled (L. moves along the curve} only if complete equi- librium is maintained between the liquid and the If this solid (S,) is effectively cut of the equilibrium (i.e., if it is removed as formed, if its surface is covered by dissolving, or reacting, solid. deposition of S,, or if the process is too rapid), then a liquid which reaches such a curve by depo- sition of S, merely crosses the curve. It begins to precipitate S, without consuming any SI; it undergoes a change in direction and enters at surface. The new solid §, is merely deposited upon the first (S,) in a non- equilibrium mixture, once upon the § 13 4, TERNARY CONDENSED INVARIANT POINTS (FOUR PHASES) Ternary condensed invariant points are generally the points of intersection of three curves, each for a liquid in equilibrium with two solids, re- sulting in the equilibrium of a liquid with three solids. In addition we shall have to consider reactions involving four solids, below temper. atures of equilibrium with liquid. The four phases of the (isobarically) invariant equilibrium are arranged either as a triangle, with cne phase inside (type A), or as a quadrangle (type B). The special case which may appear to be the limit between triangle and quadrangle, with the fourth phase on a side of the triangle (i.e., with three of the four phases on a straight line), is strictly a binary three-phase invariant, and the fourth phase, while present, is not in- volved in the phase reaction. We shall discuss this case before considering the true ternary in- variant reactions. 4,1. BINARY DECOMPOSITIONS IN PRESENCE OF TERNARY LIQUID Given the four coexisting phases arranged as follows: Ph]\— Pl-|27Ph3 Ph, with Ph,, Ph,, and Ph, collinear, then the equi- librium: Ph, <=2 Ph, + Ph; t calories does not invelve Ph,. Such a situation arises for the interaction of three solids (collinear) in the presence of a liquid phase: B-\— |LC7D the liquid being saturated with all three. In the usual examples found, the three solids are on a binary side of the ternary diagram, but sometimes they are on a line inside the ternary system, 14 “Pure’ Solids If B, C, and D are three successive solids in the binary system A~E, and if they are ‘‘pure’’ in the sense that, although they may involve binary solid solution among themselves, they nevertheless do not take into (ternary) solid solution the third component F, then the temperature (always at constant pressure) of the equilibrium: C == B + D + calories is unchanged by the presence of a liquid, con- taining F, in which these solids are dissolved to safuration. The liquid may even contain more than one such foreign component. Provided that the three solids themselves remain pure in re- spect to any of the foreign components {(F, G, . . .) in the liquid phase, the temperature of the phase reaction is the same as that in the binary system A-FE itself. Not only is the temperature independent of the composition of the liquid phase, but, since the liquid is not invoived in the phase reaction, the very amount of the liquid phase is constant (com- plete equilibrium being assumed) during the phase reaction. Such strictly binary invariant points will be distinguished with a subscript identifying the decomposing solid phase, such as P, or P, in the above examples. A similar invariant would be that of the transition of a binary solid solution in presence of a ternary liquid (points T in Figs. 1.10 to 1.14}. Effect of the Third Component Entering into Solid Solution |f a foreign component enters any of the three solids, forming a solid solution, the temperature of the phase reaction is changed, and it now varies with the composition of the solid solution {or solid solutions)., If C alone forms such a solid solution with the foreign component, then the de- composition temperature is raised if the reaction is: C +calories S<==B +D , and lowered if C —~ calories =— B +D . If C remains *‘pure’’ while either or both of the other solids form a solid solution with the added component, then the decomposition temperature is lowered if the reaction is: C +calories —=— B +D , and raised if C - calories &=—=B +D . If both C and one (or both) of its products form such a solid solution, then the temperature of de- composition may be either raised or lowered, and it may even pass through a maximum or a minimum. Finally, however, when such ternary solid so- lution is involved in one or more of the three solids, their compositions are no longer collinear, The invariant reaction now involves all four phases, it is no longer binary but ternary, and it will pertain to one or other of the ternary types now to be discussed. 4,2, TYPES OF TERNARY INVARIANTS Type A Invariant: Triangular or Terminal Type of Invariant fn the case of a type A invariant (Fig. 4.1), the phase reaction is terminal with respect to the interior phase. The phase reaction is: 4 tcalories — 1 +2+3 . On one side of the invariant temperature we have the three equilibria involving 1, 2, ond 4; 29 3% and 4% and 17, 3%, and 4”; and on the other side only the equilibrium of 17, 2"*, and 3" The interior phase, 4, exists only on one side, and its stable existence is terminated at the type A invariant, If the interior phase is a liquid and the others are solids, the invariant is a eutectic. All four phases may be solids, and then the invariant is the decomposition of solid 4 into three solids. The liquid may be an exterior phase, and then the in- variant is an incongruent melting point of the interior ternary solid 4; two cases arise. Case (@): 4 + calories —1+2 + L is a ternary analog of the incongruent melting point of a binary solid into liquid and another solid, Case (b): 4 — calories — 1 +2 + L is an inverse peritectic or inverse fusion point, like one found in rare cases in binary systems (Fig. 1.4), and (possibly) in one case in the present ternary systems (solid phase C in system Y-U=Z, Fig. 14,10). Type B Invariant: Quadrangular, Diagonal, or Metathetical Type of Invariant In the case of a type B invariant (Fig. 4.2}, the phase reacfion is: 1 +3 tcalories == 2 +4 , not terminal for any phase. On one side of the invariant temperature we have the equilibria in- volving 1, 2, and 3 and 1% 37, and 4’ and on the other side the equilibria involving 17, 2%, and 4° and 277, 377, and 4°”. This invariant is re- lated to double decomposition reactions, even when occurring in additive ternary systems. The combination 1 and 3 is stable only on one side of the invariant temperature, and the combination 2 and 4 only on the other side. The stable di- agonal of the quadrangle changes from 1-3 to 2-4; hence the term ‘‘diagonal reaction.” 4,3, RELATIONS OF THE THREE LIQUID CURVES AT THEIR INVARIANT INTERSECTION On the liquidus diagram the only invariants we see are those involving a liquid phase and three solids, and they occur as intersections of three curves of liquid in equilibrium with two solids. Hence, unless the locations of the three solids are known, relative to the position of the invariant liquid (commonly this position is called '‘the in- variant point,”’ but the invariant is not a point but a plane, either triangular or quadrangular), we cannot always know the type of invariant involved. If, as in Fig. 4.3, all three liquid curves fall in temperature to their intersection, the invariant is a eutectic (type A). The phase reaction is termi- nal for the liquid, which is inside the three-solid triangle: [. - calories fis] +S2 +53 . Conversely, if the liquid of the intersection is known to be inside the three-solid triangle, then the temperature must fall to the intersection on all three curves, and the intersection is a eutectic, the temperature minimum for the liquidus in the area of the three-solid triangle. 15 5 2 ‘.._._-- 2 ——f———————— 4 4/ 3.' 3!! 1 4,’1’ * Fig. 4.1. 3 3/ 3 . —g———— 2 2 41 1 1/ 4 Fig. 4.2. UNCLASSIFIED ORNL-LR-DWG 24757 "t 2 —_— _-_,___.__ i 3 I 1 T 3 4/// 4 H " 1 Fig. 4.3. Fig. 4.4. 16 Fig. 4.5, But any other arrangement of temperature fall of the three curves may mean either a type A or a type B invariant. Thus, the arrangement in Fig. 4.4 may mean either of the following reactions: (@) Type A: S, +calories == S, +S5, +L. (6) Type B: S, +L +calories == §, +5,. That in Fig. 4.5 may be either of the following: —_— (c) Type A: S, = calories == S, +8, +L. (d) Type B: S, +L = calories &= 5, +S,. These four invariants involving liquid (a, 4, ¢, d) are usually called simply ‘‘ternary peritectics®’ as distinct from the eutectic reaction. Moreover, the curves meeting at a eutectic are usually all three of even reaction, but they need not be; one may be odd in reaction. For in- variants (a) and (b) (Fig. 4.4) one of the curves proceeding from the invariant to lower temperature must be odd. For invariants (¢) and (d) (Fig. 4.5) no restrictions of reaction sign hold. For all invariant intersections of three liquid curves, no angle of the intersection can be greater than 180°. This requirement holds both for the truly ternary invariants (types A and B) and for those explained as binary invariants with the three soiids on one straight line. This restriction means that the metastable extension of each curve must extend into the field of the third solid. The metastable extension of the curve for liquid in equilibrium with S and S, for example, must penetrate to temperatures below the surface for liquid in equilibrium with S_, and this require- ment cannot be satisfied, for all three curves simultaneously, if any angle of the intersection is greater than 180°. Thus, in Fig. 4.6, the extension ia’ of the curve for liquid in equilibrium with § and S., which is a boundary of the surface for liquid in equilibrium with S 3+ would have to pene- trate beneath the S, surface itself, an impossi- bility in the absence of retrograde temperature effects, here excluded. The same contradiction would hold for the extension b’ of the curve for liquid in equilibrium with §, and S,, which is also a boundary of the § Only the metastable extension ic” of the curve for liquid in equilibrium with S, and S, would behave correctly. surface. 4,4, CONGRUENT AND INCONGRUENT CRYSTALLIZATION END POINTS In Figs. 4.7 and 4.8, E represents a eutectic liquid in equilibrium with the three solids Sir Sy and ¥ (Sl)' (52), and (53) represent the fields for liquid in equilibrium with each of the three solid phases, With complete equilibrium always main- tained during cooling, the point E must be reached, along one or another of the three curves meeting at E, by liquid from any total composition in the triangle §,5,5,, no matter how many other in- variant points may be traversed on the way; and, with complete equilibrium, only liquids from original compositions in the triangle $,5,5, will reach E. Liquids with original composition x in the triangle §,5,5, cannot dry up, or they cannot be completely solidified, until some liquid finally reaches E. Since liquid E is inside the triangle of its three solids, so that the composition of the liquid E is accountable in terms of its three solids, it is said to dry up congruently; i.e., E is the congruent crystallization end point for compositions in the triangle §,5,5.. Also, when the liquid UNCLASSIFIED ORNL-LR-DWG 24758 Fig. 4.8 17 reaches FE, it is always entirely consumed; it never leaves E. This is so whether the solids involved in the reaction are removed as formed or not. (Exceptions, of course, would occur if there is supercooling with respect to some solid phase; in such a case the liquid, approaching an in- variant point along a two-solid curve, simply con- tinues on the metastable extension of that curve until the metastability is relieved.) Invariant points other than eutectics [peritectic points (a) and (d), Sec 4.3] may be crystallization end points for some compositions, but they are then, in contrast, incongruent crystallization end points. The liquid in these cases is not inside the triangle of its three solids, and its composition is not accountable in terms of these solids. The following consideration of these invariants assumes complete equilibrium in all processes. Case {a): Reaction of type A (Fig. 4.9): L+5,+S, = calories — §, . Here point P is reached by liquids traveling down in temperature along the curve LS,S4, provided the original total composition x is in the triangle PS,S,. Then S, appears in the invariant reaction, and if x is in the triangle $,5,5, the liquid is consumed, leaving the three solids. Point P is therefore the incongruent crystallization end point for the composition triangle S.5.5.. As for the rest of the quadrangle: with x in the friangle PS.S,, the solid 5, is consumed, leaving liquid, Sy, and S,, and the liquid enters upon the curve LS.S,; for x in the triangle PS.S,, S, is con- sume?), and L leaves along the curve LS.S,. This invariant is seen to be the incongruent melting point of the interior phase §,, which may be either a fixed ternary compound or a ternary solid solution. Upon heating, it decomposes or melts incongruently, at the temperature of the invariant, to produce liquid of composition P, S.,, and § 2f ‘ Case (a%: Reaction of type B {Fig. 4.10): 5‘] + [ — calories — 52 +S3 . Liquid P is reached on cooling for x in the quad- rangle §,5,PS,, along the curve LS.S, if x is in the triangle S.5,P and along curve LSS, for x in the ftriangle §,5.P. If x is in the triangle §,PSq S, is consumed and L proceeds along curve L5, S.. But if x is in the triangle §,5,5, 18 the liquid is consumed, leaving the solids ., S, and §S,. Point P is thus the incongruent crystal- lization end point for the composition triangle 515253. The invariants (b} and {c), on the other hand, are never crystallization end points in a cooling process. Case (c): Reaction of type A (Fig. 4.11): S, - calories — S,+8;+L . This is the inverse incongruent melting point of the solid S. (a fixed ternary compound or a ternary solid solution), decomposing or melting incon- gruently, on cooling, into liquid of composition P, S,,and §,; it is somewhat like that in Fig. 1.4 for a binary system. Liquids saturated with S, and Sa along curve LS,S,, reach P on cooling if x is in triangle S,S.P; and liquids on curve LS.S,, saturated with S, and §,, reach P if x is in triangle § S, P. Then at P, solid §, decom- poses, and when all of it is consumed, the liquid proceeds on the curve LS, S.. This case is en- countered later in Fig. 14,10, in system Y-U-Z, For x in triangle §,5,5,, the system is com- pletely solid before the temperature falls to P; but at P the liquid phase reappears in the invariant reaction, as a result of the decomposition of S],, and L then proceeds along curve LSS .. Case {(b): Reaction of type B (Fig. 4.12): S, +8, - calories — S, +L . At this invariant temperature the combination of solids S, and S. reacts, on cooling, to produce liquid of composition P and §,. Liquid saturated with S, and §,, along curve LSS, reaches P on cooling if x is in triangle PS_S,. Then if x is above the diagonal PS., S, is consumed in the invariant reaction, leaving liquid, §,, and §,, and L then moves away on the curve LS S,; for x below the diagenal, S, is consumed, and L leaves upon the curve LS.S.. In this invariant, the cool- ing of two solids, S, and S,, leads to the for- mation of liquid and the solid S, a situation en- countered later in Fig. 13.6, in system Y-U-X. For «x in ftriangle § 5,5, the system is com- pletely solid before the temperature falls to P; but at P the liquid phase reappears in the in- variant reaction, either S, or S, is consumed 2 3 completely, and L then proceeds along one of the curves falling away from P. UNCLASSIFIED ORNL -1 R-DWG 24759 With complete equilibrium, therefore, a liquid reaching point P may be completely solidified at that point in case (a) or case (d), but never in case (b) or case (c). In the absence of complete equilibrium, however, or if the liquid is not given time to react as re- quired with the solid phases at the invariant temperature, the liquid reaching P does not stop there at all, but travels on down in temperature; along one of the issuing two-solid curves if there is an even curve to lower temperature, or onto a surface, of liquid in equilibrium with one solid, if there is noeven curve leaving P for [ower temper- ature. Such crystallization processes will be completed in various ways: on a solid solution liquidus surface (the last crystallization product being a single solid), on a curve of even reaction (the last product being a mixture of two solids), or at a eutectic (the last crystallization product being a mixture of three solids). 4,5. MELTING POINTS OF TERNARY COMPOUNDS There are three types of melting points of ternary compounds, 1. Congruent melting point; The solid ternary compound here melts to a ternary liquid of the same composition. This will occur at an absolute maximum of the surface for liquid in equilibrium with the compound, not at a boundary of that surface. The compound is here said to possess an '‘open’’ or “‘exposed’’ maximum, 2. Semicongruent melting point: In this case the ternary compound M, decomposes to a liquid Ly and another solid M,, with all three compo- sitions, M,, M,, and L, lying on a straight line in the ternary diagram. This temperature will be a maximum (y, in Fig. 4.13) on the boundary curve between the surface (L + M1) and the sur- face (L + M,), and hence on curve LM M,. The temperature on curve LM M, falls away from y in both directions, but, while the temperature on the surface (L + M,) falls toward y, the temperature on the surface (L + M,) falls away from y. 3. Incongruent melting point: In this case the ternary compound S.r decomposes to a liquid P and two other solids, in an invariant reaction in which the ternary compound is the interior phase of a triangle; case (a) above (Fig. 4.9). 4,6, INVARIANTS INVOLVING SOLIDS ONLY Invariant reactions both of type A and of type B may involve simply four solid phases, below temperatures of liquid equilibrium. The usual case would be some double decomposition of type B. The type A reaction would apply for the decom- position, on heating or cooling, of one solid into three others, as already mentioned. Both types will be encountered later. UNCLASSIFIED ORNL-LR—~DWG 24760 Fig. 4.43. 19 5. CRYSTALLIZATION PROCESS WITH PURE SOLIDS In this and in the next two sections we shall consider some of the relations met with in typical ternary systems, first in systems involving only pure solid phases and then in systems involving solid solutions. The ternary system of Fig. 5.1 contains two compounds, D, and Dy, stable at the temperature and not decomposing on binary liquidus cooling. Any ternary liquid, upon complete solidi- fication, must, if complete equilibrium is main- tained throughout, consist finally of a mixture of three of the five solids of the system - A, B, C, D], and D2. But there are two arrangements of the five solids possible: scheme (a) and scheme (b), We know in advance that one of the three- solid combinations will be 4, D,, and D,, but to determine whether the coexistence of solids in the system is {a) or (b), experiment is required, In (@) the pair of solids D combination, and it would react to produce D, and C (plus excess of either D, or B), while in (&) the pair D, and C is unstable and would react to produce D, and B. For this reason the three- solid coexistence triangles shown in either scheme and B is an unstable are sometimes called ‘‘compatibility triangles.” Theoretically, a single experiment, upon a liquid composition at the intersection of the lines D B and D,C, would suffice to establish the coex- istence relations, provided that the final solids obtained upon complete crystallization represented true equilibrium. In scheme (&) the experiment would yield the pair D, and C as sole solids, and in scheme (b) the opposite pair. ment is an Such an experi- application of what is known as Guertier's Kldrkreuzverfahren, In either case, the phase diagram will have five fields equilibrium with three solids, each functioning as and three invariant points of liquid in a crystallization end point, congruent or incon- gruent, for one of the three-solid triangles. The curves of liquid in equilibrium with two solids will be joined by three intersections, as in Figs. 5.2 (a) and (b), Figs. 5.1 (2) and (6). The invariants are numbered to correspond to the three-solid triangles in Fig. 5.1, in either case, at least one of these invariants corresponding respectively to must be a eutectic, with the invariant liquid in- side the three-solid triangle of corresponding number, while the other two points may be either 20 eutectics or peritectics, together or separately. Scheme {a) thus comes to have nine possible arrangements of the three invariant points: Triangle | Triangle H Triongle HI E, E, Es B, P, — E, E, —_ P, E, E, Eqye Py -= -= 10 Eg Eq E|s Py P, — — 10 Py 3 ~= - Pre g Py - - -- Pro Por By The entry "E], P, P, —=""in line 7 means, for example, that the first two intersections are in triangle | and the third in triangle |, so that the first is a eutectic and the other two are peritectics. Although each of the curves for liquid in equi- librium with two solids enters the ternary diagram with falling temperature, the temperature direction on the two interior curves depends on the nature UNCLASSIFIED ORNL-LR-DWG 24761 C C {g) {5) ) 1 /1 11 e B 4 B 02 DZ Fig. 51 Fig. 5.2. of the invariant points involved, for only a eutectic is a temperature minimum, Moreover, each of the nine possibilities enu- merated for scheme (a) will have several variations depending on the congruence or incongruence of the melting points of the binary compounds in their binary systems, with further subvariations (for incongruence) depending on whether the peritectic and eutectic solutions for the incon- gruent compound are on the side of one or of the other component in its binary system. With a congruent melting point, the composition of the compound will be on the binary side of its ternary field, at the maximum temperature of the surface, and the crystallization paths radiate from its composition. The compesition point of an incon- gruently melting compound will be outside its field, but the composition point still represents the (metastable) maximum of its surface, and the crystallization paths radiate, by extension, from its composition. in Fig. 5.3, with three binary compounds, D, melts congruently, and e, and e, are both binary eutectics: L(es) - B+ D2 ’ {(Note: reactions are written for the cooling process.) The compounds D, and D, both melt in- congruently, and b, and p, are the peritectic liquids of the respective binary systems: L{p,) +C»D, , L(p3) +A->D, . There are six fields, projections of surfaces for liquid saturated with a single solid: A, D, C, D,, B, and D, in clockwise order. The system has four ternary invariant points, corresponding to the four three-solid ftriangles. Three of the invariants are eutectics (temperature minima); however, one, P., is not, since its liquid, saturated with the solids of triangle Ill, falis in triangle V. The temperature along the curve E E,, for liquid saturated with D, and D,, has a maximum value at m, the intersection of the boundary curve with the line joining the two solids. This is a **collinear equilibrium,’’ and the three- phase triangle for liquid in equilibrium with D, and D,, starting as the straight line D,mD,, expands, with falling temperature, to end as the triangle D,E,D, at E, and as the triangle D, E, D, at E,. The line D, mD,, joining the compositions of the solids and intersecting the boundary curve between their adjacent fields, is known as an Alkemade line. With the temperature falling toward m on both adjacent surfaces (for liquid in equilibrium with D, and for liquid in equilibrium with D), while the temperature falls away from m on the E,E, curve, the point m is a saddle point on the curve, The line Am ‘D, is another Alkemade line, and m” another saddle point, @ minimum in temper- ature on the surfaces between A and D, but a maximum of temperature on the curve E,P_.. The triangle for liquid in equilibrium with A and D expands, with falling temperature, from the line Am’D, tothe triangle AE,D, and, also with falling temperature, to the triangle AP D .. The section of the diagram through the line Am 'D2, moreover, is a quasi-binary section. The vertical section of the T vs ¢ prism through this line is altogether like the T vs ¢ diagram of a simple binary system (Fig. 5.4). Such a section UNCLASSIFIED ORNL-LR-DWG 24762 E oy Fig.5.5. 2] divides the actual ternary system A-B-C into two separate subsystems, A~C-D_ and A-D,-B. The section through the line D mD,, on the other hand, although also containing a saddle point very similar to m’ is not quasi-binary; one of the solid phases involved in the equilibria traversed on this section is C (between D, that the phase equilibria along line D mD, are and point 7}, so not describable on the basis of o binary system with D, and D, as components. From this pomf on, phase reactions involving one or two or three solids will be written always as occurring in the direction of falling temperature, or in the direction of removal of heat, unless otherwise specified. The equation: L%, +5,, therefore, means: L — calories -85, 4S5, . The reactions along the boundary curves of Fig. 5.3 are as follows: e F. . L - D, + A; 272 paPy L +A-D, (reaction odd); e Byt L-D,+B; 65E4: L -8B +D2,' eéET: L-D,+(C; p E |+ reaction odd from p, to s: L + C - D,;re- action even from s to E,: L - C + D, (the line D, s is tangent to the curve); E]mEz: LD, +D2; E]mP 1 LA +D,; 2 . I 3E4 L D3 +D2. The invariant reactions are: E]: L »D] +C +D2,' E,: LA +D] +D,; Pyt L+A Dy +Dy; E4: L->Dg+ D + B. Liquids wn'rh orlgmal composition x in triangle | must reach E, for complete solldlhcohon, those in triangle I mus'r reach £,; those in triangle Il must reach P; and those in triangle |V must reach Ed' The peritectic P is reached by all liquids with x in the quadrangle AD,P.D.. m D P solld, reaches curve m P3, and then proceeds to For x in the For x in the region , the liquid precipitates D, as the first P, carrying A and D, as solids. re3gion Am°P,, the liquid reaches curve m’P, after precipitating A, and also reaches P carrying AandD,. Liquids th x in the region AP D, and hence on the A surface, precipitate A cnd reach 22 the curve P3P 5 which is then followed while some A reacts with liquid to form D,. At P L+A~>D3+D2 Now for x in triangle Ill, the liquid is consumed, leaving A, D, and D, (complete solidification), But for x in the triangle D,D,P,, A s consumed ! and the liquid proceeds on cur\fe ?3 E,. The eutectic F, is reached by all liquids with x in triangle |V. Those from the triangle DD, P, reach P Those in the quadrangle P.D,e L, precipitate D, as the first solid, reach one of the boundary curves, and as already explained. then proceed to E,, either along curve P.E, precipitating D, and D g OF along curve e E, pre- c:nd B. Those from the B fleld be- have similarly, reaching E cipitating D2 either along curve e, E, with D and B as solids or along curve e E, with D, and B as solids. D, field, p3P3E4e and reach £ Those falling upon the " as first solid, along either curve P,E, or curve ek, . Original compositions in the region D P,p., such as point z, give A as first solid and reac precipitate D, the transition curve p.P. on a straight line from 33 9 A, as at point v. They then travel on the curve, toward P, but solid A is consumed before P is reached, os at point w, on a straight line through D, and u. At this point the liquid is saturated only with D, and travels across the D boundaries, .?3E4 or €4E4, The transition curve p P and it therefore leaves the curve field to one of its finally to reach E,. is therefore left be- hind, after some travel along the curve, by liquids coming from original, total compositions x in the region D P p,, when the tie line D,L of the three- phase triangle for L. on curve p_P. comes to sweep through x, for at that point the solid A will have been consumed to leave D, as the sole solid phase, (We shall speak of the transition curve as thus “‘crossed'’ by the liquid in an equilibrium for x in a specified region. The word ““crossing’’ will be used, for brevity, to mean that being process, the liquid reaches the curve from cone field, travels along the curve for a limited range, ond then, when the original solid is consumed, leaves it before reaching an invariant point, to move across the adjacent field.) While the liquid is on any one field, precipitating a single solid, it travels in a straight line ex- tending from the separating solid, until it reaches one of the boundary curves of the field. Except for the region between point C and the curve between p, and s, the relations in the sub- system A~C-=D, are simple, Precipitation of a first solid leads to a boundary curve, and along the curve to one of the eutectics. Thus compo- sitions in the region rsE,m give D, as first solid, reach either curve sE, or curve mE,, and finally point E, to end as D, C, and D,. But p.s is a transition curve, and it is crossed, as explained for curve p,P ., by liquids criginating in the region p,D,s. The curve p,s is reached by liquids precipitating C, from the region between the curve and the corner C. Those coming from above the tangent line D, s do not leave the curve, but stay on the curve up to the eutectic £,. Along the section p,s the quantity of C is decreasing at the expense of D,, and between s and E, both solids are being precipitated. For solutions from the region p,D,s, solid C is consumed when the tie line D, L of the three-phase triangle passes through the fixed total composition, and the liquid then leaves the curve. For x in the region D, p. 1, the liquid then reaches either curve e, B, or curve mE, fo end at point E,; from the region D.ry (y being on the line D E.), the liquid reaches curve mk and hence point E,. For x in region D, ys, the liquid, having followed the odd curve ys for part of its length, leaves the curve, travels across the D, field, and then reaches the even part of the same curve, sE.. These compositions then give the following sequence of events. The liquid precipitates C as the primary solid and moves on the C field on a straight line from the corner C, to reach the curve between p, and s. Along the curve, as L moves toward s, L+C—>D1 , and C will have been completely redissolved or consumed when L reaches a point on the curve between y and s, on the straight line D, x. The liquid now traverses the D, field, precipitating Dy, and reaches the same curve again between s and E,, where it precipitates both D, and C. Finally, at point E], L—>D1 +C+D2 . The primary solid phase C therefore disappears, but C reappears later as a secondary crystal- lization product together with D . Finally, some of the relations in Fig. 5.3 will be shown on isothermal diagrams and vertical T vs c sections. Attending first to the isothermal solubility curve of D., we note that between p, and r its isothermal solubility curve (simply an isothermal temperature contour on the D, field in Fig. 5.3) is not cut by the line D.D,, while be- tween 7 and m it is, The solid D, is then said to be incongruently soluble in D, in the temperature range between p, and r, but congruently soluble in D, between r and m. A solubility isotherm for this region between p, andrwould be schematically as in Fig. 5.5. Between r and m, we have Fig. 5.6: just above m’, below e,, below e, but above es, above p., and below the freezing point of B. The isotherm shown in Fig. 5.7 is still above E, and E,, below p, but still above P, and e,. Figure 5.8 is at P ond below E,, E,, and e, but still above e,. At the invariant P, the field of A in equilibrium with liquid shrinks to a line (AP3) and vanishes, in the reaction: L(P3)+A—>D3+D2 . The vertical T vs ¢ sections through D, D, and D,D, are relatively simple, as shown in Figs. 5.9 and 5.10 (schematic, not in scale with Fig. 5.3). Figure 5,11 shows the vertical section through CD,, and Fig. 5.12 the section through DB (both schematic). UNCLASSIFIED ORNL-LR-DWG 24763 23 UNCLASSIFIED ORNL~LR-DWG 32574 UNCLASSIFIED ORNL-LR~-DWG 24765 Fig. 5.14. UNCLASSIFIED ORNL-LR-DWG 24764 & j* £ | | | L 0+, | | D3tly | B+03+0p | | ,,f | | e e ) 8 0, D, Dy 0, Fig 5.9 Fig 510 Fig. 5.12 24 6. CRYSTALLIZATION PROCESS WITH CONTINUOUS BINARY SOLID SOLUTION The system of Fig. 6.1 involves two solid phases, pure C and the continuous binary solid solution A=B. The binary system has a minimum freezing point at m, Fig. 6.2. All ternary compo- sitions must solidify to two solids, pure C and a binary A~B solid solution. Curve e, e, represents liquid precipitating these two solids; M is a temperature minimum on this curve, and it is also the temperature minimum of the whole system. (Curve e e, may have either a minimum or a maximum or neither.) Liquids in the C field reach this curve on straight lines from the corner C; those in the solid solution field reach it along curves on the solid solution surface. [n either case the liquid then travels toward M, but for complete equilibrium solidification is complete, leaving the two solids, before L reaches M, unless the total composition x lies on the straight line CMs. The three-phase ftriangles for L on the boundary curve start as the straight lines Ce, A and Ce,B and proceed, with falling temperature, toward M according to the configurations shown UNCLASSIFIED ORNL-LR-DWG 2476€ 5 F 52 54 8 372 T e e -y FoTT 5 Fig. 6.2. in Fig. 6.1, collapsing again, from either side, to the line CMs. A vertical T vs ¢ section from C to the side AB appears as in Fig. 6.3. Here the composition of the solid solution (ss) is not on the plane of the section. Even at point v the liquid of the section is not in equilibrium with solid solution of the same composition as the liquid (but point u of course is simply the melting point of pure C). Only for the section through Cm would v represent liquid and solid of the same composition, but the section through Cm would not pass through the ternary minimum M. The region C + L + ss of Fig. 6.3 collapses to a horizontal (isothermal) line only for the section through M, CMs (and of course also at the binary sides Ce, A and Ce,B). In an equilibrium process, any liquid of original composition x is completely solidified, while traveling on the curve, when the C—ss leg of the three-phase triangle passes through the point x, to leave C and a solid solution of composition on the extension of the line Cx. Solution y, moving on a straight line from C, reaches the curve at / and there begins to precipitate s,. As L travels on the curve toward M, more C and more solid solution will precipitate, but the solid solution changes in composition, leaving the solids C and s when the last trace of liquid vanishes at lqe Liquid z, moving on a curved equilibrium path, reaches the curve e,e, at I,, at which point the solid solution has the composition s,. At /,, C also begins to precipitate, and solidification is completed with liquid at /,, leaving C and s,. The course of the liquid on the solid solution surface, however, is not shown by the ‘‘phase diagram'’ of Fig. 6.1. With a minimum m in the A=B binary equilibrium, this surface has two families of nonintersecting fractionation paths, as sketched in Fig. 6.4. All fractionation paths end, without intersection, at the boundary curve €€, The two families are separated by a limiting fractionation path originating at m. This path reaches the curve e,e, at a point N which may be either on the left or on the right of M. Moreover, the path mN may be either convex toward B, as drawn, or convex toward A, and it may even have a point of inflection. With the arrangement assumed in Fig. 6.4, the fractionation paths on the A side are always convex toward B; those on the 25 ik i e UNCLASSIFIED ORNL~-LR-DWG 24787 Fig.6.4 B side all start as convex toward A, but some of them have an inflection point and become convex toward B before they reach the boundary curve. These inflection points are joined by the locus curve mR. 6.1. FRACTIONATION PROCESS As liquid foliows one of the fractionation paths in a fractionation process, the composition of the layer of solid solution being deposited at any point is given by the tangent to the fractionation path through that point. Then, once the liquid reaches the curve e e,, whether from the C field or from the solid selution field, it moves on the curve toward M as limit. the direction e, » M, the outermost layers of solid solution being deposited have compositions in- creasing in B content, approaching s as the limit, from the A side, Those moving along the curve in the direction e, For liquids traveling in -+ M deposit layers increasing in A content, and also with s as limit. The total process therefore varies according to the various regions of the surface. (In this dis- cussion it must be remembered that the fractionation path is everywhere tangent to an equilibrium tie fine. Hence the layer of solid being precipitated at the point where the fractionation path reaches the curve e e, is given by the tangent at that point, eex're-ndeci2 to the line AB. At M itself this tangent is the line CMs; at N the tangent goes to z, at R to y. Also, the word *'solid’" will here mean ‘‘the layer of solid being deposited.’’) 26 1. Region Ae,M (i.e., between e, and the fractionation path AM): While L is still on the surface, the ''solid’’ increases in B content, to a limit given by the tangent to the particular frac- tionation path involved at its intersection with the curve e, M; and as L then travels on the curve (to M as limit), the *‘solid’ increases still further in B (to s as limit). 2. Region between paths AM and mN: With L on the surface, the ‘‘solid’’ always increases in B, with z as the possible limit for fractionation paths reaching the boundary curve near N. The boundary is reached in the section MN, and then, as L moves toward M, the “*solid’’ increases in A content, toward the limit s. 3. Region BRe,: With L on the surface, the ‘solid’’ increases in A, with y as limit for the path BR itself; then, as L travels on the curve (to M as limit), the **solid’’ increases still further in A (to s as limit). 4. Region between paths BR and mN: The ‘“solid”” increases in A until the inflection point of the fractionation path is reached (intersection of fractionation path with curve mR), and the composition of the '‘solid’” at that point is given by the tangent to the fractionation path at the inflection point. Now the ‘‘solid’’ begins to de- crease in A content, to a limit given by the tan- gent at the end of the fractionation path at the boundary curve, reached in the portion NR. Then as L moves on the curve toward M as limit, the outermost layer of solid again moves to increasing A content, toward s as limit, 5. Path mN: For a solution on the path mN itself, the ‘‘solid’’ increases in B content (be- tween limits m - z), and then moves toward s as L, after reaching point N, moves on the curve toward M. 6.2. EQUILIBRIUM PROCESS process with complete equilibrium between the total solid phase and the liquid, the liquid, such as point @ in Fig. 6.4, follows an equilibrium path {dotted curve a ... b) in its course on the surface to the boundary curve ere,. The relation of this equilibrium path to the fractionation paths which it crosses has been ex- plained in connection with Fig. 2.4. The point b is fixed by a three-phase triangle with the ss—L leg passing through point . Then as L moves on the curve toward M, solidification is complete In o crystailization when the ss=C leg of such a ftriangle passes through a. The changes in the composition of the solid solution as the liquid follows its equilibrium path will depend on the region of the surface involved. Now the word ‘‘solid’”” will mean the total solid, assumed to be uniform in composition and in fuli equilibrium with the liquid. We note first that all equilibrium paths for solutions in the region AsMe, reach the boundary curve between e, and M; those for solutions in BsMe, reach the curve between , and M. Point M is reached only for total com- positions on the line CMs. e 1. Region AMe,: The equilibrium path does not cross the line sM on its way to the boundary curve. The solid increases in B both before and after L reaches the curve. 2. Region AMs: The equilibrium path crosses the line sM on its way to e, M. The solid again in- creases in B both before and after L reaches the curve, 3. Region smNM: The equilibrium path does not cross the path mN; it ends on MN. The solid in- creases in B while L is on the surface, but the reverse change sets in when L begins to travel on the curve. 4. Region BRe,: The equilibrium path does not cross the line Ry; it ends on e R; the solid in- creases in A both before and after L reaches the curve, 5. Region ByR: The equilibrium path crosses Ry; it ends on e,R; the solid increases in A both before and after L reaches the curve. 6. Region yzNR: The equilibrium path does not cross the path mN; it ends on NR. () Region yzdR: The solid increases in A until the equilibrium path crosses curve mR; then the solid increases in B until L reaches curve NR; then the solid increases again in A while L travels on the curve, () Region dNR: The solid increases in B until L reaches curve NR; then it increases in A, 7. Region mzN: The equilibrium path crosses the path mN, to reach the boundary curve on the left of N (between ¢ and N, curve cm being the L-ss leg of a three-phase triangle for L at point c). The behavior for the regions above and below curve mR differs as described for region yzNR, (The preceding discussion of Fig. 6.4 is based on the analysis by Osborn and Schairer.!) The composition of the equilibrium solid for original liquids in the region Rmy, as just stated, reverses its direction of change (increasing first in A, then in B) while the liquid is still on the surface. The equilibrium path for such a liquid first crosses fractionation paths which are convex with respect to A, in the order 1, 2, 3, 4, etc., and in this region the solid is becoming richer in A. But the rate of this composition change of the solid decreases as the equilibrium path meets fractionation paths of smaller and smaller con- vexity. When the equilibrium path finally reaches the locus curve mR, it has reached a fractionation path exactly at its inflection point, with no con- vexity at all at that point. This fractionation path will not be crossed by the equilibrium path, which here turns away and begins to recross the fractionation paths, which are now convex with respect to B; i.e., it now crosses the fractionation paths in the order 1% 2% 3% ..., 7%, while the solid increases in B content. It has been argued by Bowen? that when the equilibrium path just touches a fractionation path at the point of inflection of the latter (on curve mR), the equilibrium path undergoes an abrupt change in direction {a ‘‘corner’’). This seems to be incorrect. The equilibrium path crosses frac- tionation paths only from their convex to their concave side. The sharper the curvature of a fractionation path, the greater is the angle of in- tersection where the equilibrium path crosses it. As the fractionation paths lose their curvature, approaching their inflection points, this angle of intersection diminishes; a zero angle of contact is approached (no longer an intersection) when the equilibrium path reaches a fractionation curve exactly at the latter’s inflection point. |f an equilibrium path has to cross the fractionation paths 1, 2, 3 before reaching path 4 at the in- flection point of path 4, the intersection angle de- creases as it crosses paths nearer and nearer to path 4, because the intersection is occurring nearer and nearer to an inflection point of a path. VE. F. Osborn and J. F. Schairer, Am. J. Sci. 239, 715 (1941). 2N, L. Bowen, Proc. Natl, Acad. Sci. U.S. 27, 301 (1941). 27 The contact at such a point must therefore be tangential, and the equilibrium curve changes its course smoothly, without a cusp (Fig. 6.5). If : is the inflection point on the fractionation path Bf, and is is the tangent at 7, then equilibrium paths for all total compositions (@, b, c) on the line is reach point i, changing their directions (with respect to the family of fractionation paths) as shown. The change in direction is more marked the farther the total composition is from the point i, but the equilibrium path is nevertheless tangent to Bf at i, 28 UNCLASSIFIED QRNL—-LR-DWG 24768 Fig. 6.5. 7. CRYSTALLIZATION PROCESS WITH SOLID SOLUTIONS AND SEVERAL INVARIANTS 7.1. THE PHASE DIAGRAM In Fig. 7.1 the binary system A=B forms dis- continuous solid solution with a eutectic at o liquid saturated with solids whose compositions are S§_ and §7. These points are to be compared with the binary diagram shown separateily as Fig. 7.2. system,C,D,, D,, are pure; D, is an incongruently The other solid phases of the ternary melting binary compound, D, melts congruently. There are five fields —~ for C, Dy Dy A (the A-rich binary solid solution of A and B), and B (the Berich binary solid solution of A and B) - and there are three invariant points, each per- taining to a three-solid triangle. From the di- rections of temperature fall, one is a peritectic, P, and two are eutectics, £, and E . The curve E,E. must have a saddle point m on it, and the A_ solid solution which (together with solid D,} saturates the liquid at point m must lie on the extension of the straight line D m to the side AB, at §_. The solid solutions saturating liquid £, are somewhere close to the points §_ and Se’, than e,, the compositions of the limiting solids of the A-B miscibility gap at £, will depend on the effect of temperature on the solid-solid solubility. The three-solid triangles for any of the three in- variant points, therefore, cannot be drawn in with- out the experimental determination of tie lines Since the temperature of E_ is lower along the curves near the invariants, and ultimately of the solid solution compositions at the in- variants. The invariant P_, a peritectic, involves the solids C, D, and §, (a solid solution of composition somewhere near A) in the reaction: L(P.!)+D] +C+S] , and P is outside triangle | (CD,S,). The eutectic E, must be inside triangle |l (CDZSQ, where S, is another unknown solid solution composition); E must be inside triangle Il (D,S,57). In the last case, S, and S are known points if the solid so- lution iimits in the binary system A-=B are known for the temperature of E, (as in Fig. 7.2). In Fig. 7.3, we assume that these key solid so- lution compositions have been determined and that the three-solid triangles may therefore be drawn. The solid miscibility gap in system A-B has been assumed to widen with falling temperature (Fig. 7.2) so that S_ and S lie between the points 53 and S:;. Since §,, S,, and S, are different compositions, the three-solid 'rriangfes are not adjacent. They do not have common sides, and they do not cover the whole of the diagram. Only original compo- sitions x falling inside one of these three-solid triangles will, on cooling with complete equilibrium, UNCLASSIFIED ORNL-LR-DWG 24769 Fig. 7. 2. 29 UNCLASSIFIED ORNL -LR-NDWG 24770 solidify to mixtures of three solids: those in triangle | solidify incongruently at P,, those in triangle 1l and triangle Ill solidify congruently at E, and E,, respectively. The areas not included in these ftriangles solidify to two-solid mixtures, and hence these areas are shown with tie lines: D, and a solid solution whose composition is be- tween A and S, for the area D, AS,; C and a solid solution between S, and § Eor the area CS,S,; D, and a solid solution between § and S, for the area D,S,S,; and D, and a solid solution between §3 and B for the area D,S3B. The three-solid triangles do not overlap unless solid-phase interactions (here excluded) should occur at temperatures between the invariants, But when peritectic invariants are involved, the in- variant planes (which include the liquid phase 30 besides the three solids) may overlap, as is the case here for the invariant quadrangle CD,S,P,, overlapping, on the polythermal projection, the invariant triangle CS,D, (with E, as interior phase). These planes are at different temper- atures; the P, plane is above the E, plane, which is above the E, piane. Also, the solid solution compositions S, and S, it must be kept in mind, are not on the solidus curve aS_ of Fig. 7.2. They are simply compo- sitions in the area of soiid solution below this binary solidus curve. Liquids on the curve e,E ., including the points e, and £, are in equilibrium with conjugate solid solutions ~ solid solutions defined by the miscibility gap of Fig. 7.2. But the solid solutions involved along all other curves (oP,,P|E,, E,E,, and e E,, with the exception of just the point E,) are simply compositions in the solid solution areas of Fig. 7.2. 7.2, EQUILIBRIUM CRYSTALLIZATION PROCESS The reactions on curves e, P, and ¢, E, of Fig. 7.3 are simple precipitations of two pure solids; on e]P1: L~»C+D] . and on ezEz: L>C+D, . On curve e, E,, the liquid precipitates two solid solutions, starting as §_ and S at e, and changing in composition to §, and §7 at E,. On curve ek, the liquid precipitates D, and a solid solution starting as pure B at e sition to SJ at K. is precipitating D2 3 and changing in compo- For curve E E,, the liquid It s is the composition of the solid solution for L at and o solid solution. m {maximum of the curve), then along curve mE, the solid solution varies from S to § and along ’ curve mE, it varies from S to S.. %'he vertical T vs c section on the line D mS Fig. 7.4. It looks like a quasi-binary section but it is not. The liquid on the curve am of Fig. 7.4 is in equilibrium, not with S, but with a solid {not on the is shown in solution of changing composition plane of the diagram) which is S only for L at point m itself, Along curve P.E,, the liquid precipitates C and a solid solution changing from §, (at P,) to S, (at E2)' Curve pP, is a transition curve, along which the liquid reacts with solid solution and precipitates D.. The three-phase triangle starts as the line pD,A and ends as P,D,5,, so that the solid solution in equilibrium with liquid on the curve varies from A at p to §, at P,. Since the solid solutions in the system are only binary, solidification cannot be complete while liquid is traveling on one of the surfaces; the liquid must reach either a curve involving a solid The course of the liquid on a surface precipitating a pure solid (C, D,, or D2) is clear: a straight line from the composition of the separating solid (Fig. 7.1). On the two surfaces for solid solution, the paths, whether for fractionation or for equilibrium crystal- are curved, Fractionation paths are sclution or one of the invariants. tization, shown in Fig. 7.1; equilibrium paths cross these curves as explained under Fig. 2.4. In the region D,S B, only liquids from an original composition x in triangle [l (D,5,57) reach E,, to solidify to three solids. Those for x in triangle E,S,S7 reach E, along curve e E,, carrying two solid solutions, and these liquids c?o not solidify completely until they reach E,, to produce D, as third phase. For x in the region D,E,SiB, the liquid reaches the curve e, E, but if x is in triangle D, S:B, the liquid is consumed (in complete equilibrium) before reaching the eutectic, to leave D, and a solid solution between B and $.. Liquids in the region D,S S.E. reach curve mE,, and again those in triangle D, S S, solidify completely on the curve, before reaching E,, to leave D, and a solid solution between S and § 5 (Similar behavior is shown in the region D,S,S,E,.) The curve pP, is reached by liquids originating in the region pAS P, after first precipitating a solid solution between A and §.. For x in triangle D, AS,, the liquid is consumed on the curve pP’,, leaving D, and solid solution. pD,P, the solid solution is consumed on the curve, leaving liquid and D ; L then leaves the curve, crosses the D, field to curve ¢ P,, and travels to P,. For x in triangle D,5 P., no phase is completely consumed along curve pP,, and the liquid reaches P. The peritectic P, D, field and for x in the region Ce P, - along curve e P.; P. is thus reached only for x in the quadrangle CD, S, P,. At P,, For x in triangle is also reached for x in the L+D]~3C+S] . Hence solidification is completed here for x in CD,S, (triangle 1), in an incongruent crystal- lization end point, Otherwise (for x in triangle CSTP]) D, is consumed and L begins to move along curve P E.. This curve is also reached directly from the C field, for x in the region CP|E,, and from the A_ field for x in the region P.S,S,E,. As L travels on this curve, pre- cipitating C and solid solution, it completes its solidification if the total original composition x is in triangle CS,S,; otherwise it reaches Ey, the crystallization end point for triangle |l. Some isothermal relations are shown in Figs. 7.5, 7.6, and 7.7. Figure 7.5 is still above the temperature of p, Fig. 7.6 just below p. Points s, I, s’ and [’ in these diagrams are related to the solidus and liquidus curves of the binary system A-B shown in Fig. 7.2, The points s” s*in Fig. 7.7 are between §_ and S, and between S and 5], respectively, of Fig. 7.2, The temper- ature of Fig. 7.7 is between m and the eutectics E,, E,, below all the binary eutectics, but still above P,. At P, the tie-line region for D, in UNCLASSIFIED ORNL~LR-DWG 24774 31 equilibrium with liquid shrinks to a line and vanishes. Some vertical sections are shown in Figs. 7.8, 7.9, 7.10. The m in Fig. 7.9 is at the temperature of point m but does not represent its composition. UNCLASSIFIED ORNL-LR-DWG 24772 02 EE 01 02 Fig. 7.8. UNCLASSIFIED ORNL~LR-DWG 24773 L P (Tf & ATEMPERATURE A S OF m) €3 E, =-— , L+ 02+A5 e w by oo | S + + © Q o, 5 Fig. 7.9. 32 UNCLASSIFIED ORNL-LR-DWG 24774 S,+C+D, Fig. 7.40. 7.3. PROCESS OF CRYSTALLIZATION WITH PERFECT FRACTIONATION The fractionation paths in the two solid so- lution fields (Fig. 7.1) are families of curves radiating from points A and B, respectively. Those in the A_ field are convex with respect to B, meaning that as L travels along such a path on cooling, in a fractionation process, it deposits successive solid solution layers always richer in B content; those in the B field are convex with respect to A, and the outermost solid solution layer here continually increases in A content while L is traveling on the surface. In fractionation, a liquid in the region between e, and the path BE, reaches the curve ¢,F ,, and on this curve the solid solution continues to in- crease in A content. Liquid between e, and the path BE, reaches curve ¢ E, but now two solid solutions precipitate, and their outermost layers vary from S, and S’ to §, and S; in composition (Fig. 7.3). In an equilibrium process, the curve e B,y s reached by all liquids below the line E,S;, which is tangent, of course, to the frac- tionation path BE, at E,, and e,Eqis reached only by liquids between e, and line E, S5 In a fractionation process on the A _ field, the curve P,E, is reached by liquids between the froctionation paths AP, and AE,, and the solid solution continues to increase in B content along this curve. Curve E_,m is reached by liquids between the paths AE, and Am, but in this case the outermost solid solution layer being deposited begins to increase in A content as L travels on this curve in the direction m » E,. The frac- tionation process for the region between the paths AP, and Am ends at E,. The curve mE 5 is reached for liquids between paths Am and AE,, with the solid solution increasing in B content both before and after L reaches the curve; and curve e, L, is reached for liquids between e, and the path AE . In these regions the fractionation ends at E3. Liquid between p and the path AP, reaches the curve pP. and immediately crosses this curve to deposit D, on the solid solution already deposited before the curve was reached. The liquid then reaches curve e, P, deposits a mixture of D, and C while traveling on this curve, reaches P, and without stopping at P1 continues on curve P.E,, depositing C and a solid solution. The process ends at E,. In this process the precipitation of the solid solution is interrupted while L is cross- ing the D, field and then returning to P, on the curve e, P.. There will consequently be a gap in the composition of the solid solution finally obtained. In the fractionation process all liquids in the region bounded by the lines mD,, D,B, BA, and the fractionation path Am end at E_, to leave three solids, A, B, and D,. Liquids in the rest of the system end at E; of these, moreover, those in the region bounded by lines P.C, CA, and the path AP, end as a mixture of four solids, A, D,, C, and D,, while the rest end as three solids, Ay, C,and D, 7.4. TERNARY SOLID SOLUTION IN COMPOUND D, Finally, we shall assume that the solid D, forms solid solution with both A and C in its binary system and with the third component B, to give at any temperature a small isothermal area of solid solution of ternary composition. This will affect all the equilibria involving solid D,. The pertinent region of Fig. 7.3 becomes that shown in Fig. 7.11. Figures 7.6 and 7.7 change as shown in Figs. 7.12 and 7.13. A section like Fig. 7.8 now shows the region of homogeneous ternary solid at the D, side, labeled D (s} in Fig. 7.14. UNCLASSIFIED ORNL-_R-DWG 24775 Fig. 7.1, Fig. 7.42. Fig. 7.43. UNCLASSIFIED ORNL-LR-DWG 247786 01(5)~II—- C+D,(5)+S5, - . PART Il THE ACTUAL DIAGRAMS The following sections will consider, one at a time, the ternary diagrams which have been con- structed. For ease of drawing and for the sake of clarity, the diagrams used in these sections are not according to actual scale, but schematic in their quantitative relations. The formulas and the actual numerical values, including the tempera- may be obtained from the experimental diagrams. tures, For brevity and simplicity, moreover, single letters rather than chemical formulas have been used to represent the solid phases. The following is the key for the letters regularly used for the components of all the systems: Symbol Component R RbF U UF4 Symbol Component Vv BeF2 W ThF, X LiF NaF z Zrl:4 The letters A, B, ..., N wiil be used, as needed, for the various binary compounds in the binary systems. They donot represent the same compounds from one section (ternary system) to another, whereas the components are always referred to by the same letters. The letter x will be used throughout to mean “‘the total original composition of a sample being cooled and solidified.”” 8. SYSTEM X~U-V: LiF-UF,-BeF, The schematic phase diagrams for the binary systems of the first ternary system to be dis- cussed, system X—U-V, are shown in Figs. 8.1, 8.2, and 8.3. No solid solution is involved, either in the binary systems or in the ternary system. Compound A in system X—U decomposes on cooling, at T ,, into the solids X and B; and compound E in system X~V forms on cooling, at T, from the solids D and V. Every solid reaching equilibrium with liquid in its binary system must have its own primary phase field, bordering on the side of the triangle, in the ternary system. The field for compound A of the system X—U, however, will have T , (designated P, in the ternary system) as its lower temperature {imit of stability, inasmuch as A decomposes on cooling to this temperature. At P, the X and B surfaces of the ternary liquidus, separated above that temperature by the A field, will come into contact. The compound E of system X—V may or may not have a field (for liquid in equilibrium with solid E) in the ternary system. It will have a field oniy if the ternary liquid saturated with the two solids D and V exists down to the temperature Ty of Fig. 8.3, the temperature for the formation of E from D and V upon cooling. The phase diagram of the ternary system is given in Fig. 8.4 (schematic). There are seven fields, identified by letters in parentheses, (U), (C), etc. The A field vanishes with falling temper- ature at P ,, ot the temperature of decomposition of solid A in its binary system, T ,, but now in presence of ternary liquid. The temperature of UNCLASSIFIED ORNL-LR-DWG 25579 Fig. 8.3. 37 UNCLASSIFIED ORNL-_R-0DWG 25580 Fig 8.4. decomposition is unchanged, because the com- ponent V does not form solid solution with any of the three solids involved in the reaction. Since solid A decomposes before its field touches any field involving the component V, it is not part of one of the three-solid triangles of the system, of which there are only four, I, I, I, 1V, with the corresponding invariant liquids Py Py Eg Ey The reactions on the curves are as follows (all written as the reactions occurring upon cooling): P Pl: L+U-C. P, P2: L +C-B. paP gt L+Xo A, 6‘3 PA: L A+B, : L +X > D. But this may change to: pgE 4 L->X+D o it does change if the tangent to the curve comes to fall between X and D. as the curve approaches F 6653: L>D+V, €7P.|: L->U=+YV. P]P2: L->-C+V, P2E3: L--B+V. EfEst L>B+D. Accordingly, m is a saddle point, with temperature falling away both toward E, and toward £,. But the line BD is not a quasi-binary section, for it includes the C field and the X field. The invariant reactions are as follows: Py L+ U>C+V. Point P either of the two curves falling to it, for x in is reached along 38 the quadrangle P, CUV. It is the incongruent crystallization end point for triangle | (CUV). If x is in triangle P, CV, the liquid continues, completing its solidification at P, for x in triangle 1lI, or continuing still further and completing its solidification at E, for x in triangle 1. Py L +C> B+ V. Point P, is reached along either of the curves p, P, or PyP,, for x in the quadrangle P, BCV. It is the incongruent solidification end point for x in triangle |l. E,o L > D+ B+ V. Point Ey is the congruent solidification end point for triangle Ifl. The final equilibrium solids for this triangle, left at the lowest liquid reaction (E,) of the region (triangle Ill), are therefore B, D, and V. How- ever, at a still lower temperature (T of Fig. 8.3) the solids D and V react to form Below T ., therefore, the triangle |I| becomes two three-solid triangles, one for B, D, and E and one for B, E, and V. E,o L - X+ B+ D, Point E, is the congruent solidification end point for triangle 1V. P, A> X+ B, inthe presence of liquid P ,. The point P, is reached by liquid for x in the triangle XBP ,, liquid in equilibrium with X and A) or curve e, P 4, (as liquid in equilibrium with A and B), At P, the solid A decomposes to produce more X and B, and the liquid moves on along curve P E . Four of the boundary curves are of odd reaction (transition curves). They are crossed by equi- librium crystallization paths as follows. (The the compound E. along either curve p, P, (as expression ‘‘crossing of ftransition curves’' is used with the meaning explained in Sec 5 in con- nection with curve p, P, of Fig. 5.3. For restricted values of x, the liquid reaching a transition curve travels along the curve only for part of its length and then leaves it for another field.) 1. p,P,: Liquids reaching this curve for x in p,CP, (i.e., in the region between C and the curve p, P,) travel along the curve only until all solid U is consumed, when the CL leg of the three-phase triangle passes through x; L then leaves the curve and crosses the C field. 2. p,P,: Similarly crossed by liquids reaching it from x in the region p,BP,, L proceeding onto the B field. 3. Py PA: region p ,AP ,, L. proceeding to travel upon the A field. Similarly crossed by L for x in the UNCLASSIFIED ORNL-LR-DWG 25581 Fig. 8.5, 4. pE,: Crossed for x in the region p Ds (s is the point of tangency of the LD leg of the three- phase triangle with curve p E ). Then, for the re- gion between the line Ds and the line DE ,, the primary X solid, which has been entirely consumed while L travels on the curve p.s, appears again as a secondary crystallization product, mixed with D, when L, traversing the D field, reaches the curve sE , (cf. curve p,E, of Fig. 5.3). The isothermal relations for the A solid are shown in Fig. 8.5, {a) between py and ey, (b) be- tween e, and P ,, (c) at P ,, and (d) below P ,. Figure 8.6 is a schematic isotherm between e and p,, above P, and F,, above p,, and below e The L + U region will vanish as a line when the temperature falls to P and the L + C region vanishes similarly at P, Some vertical T vs ¢ sections are shown in Figs. 8.7, 8.8, 8.9, and 8.10. UNCLASSIFIED ORNL-LR-DWG 25582 Fig 8.9 Fig. 8 40 39 9. SYSTEM Y=-U-V: For the ternary system Y—U-V, we have the binary systems Y—U in Fig. 9.1 and Y-V in Fig. 9.2; the system U=V is as in Fig. 8.2, except that point e, is now designated e,. The ternary diagram is given in Fig. 9.3. The horizontal dotted lines in Figs. 9.1 and 9.2 represent polymorphic changes in pure phases: one in solid A, two in H, and one in G. Even when these transitions occur at liquidus tempera- tures, as in the transition T~ for compound G, there is hardly any effect in the ternary diagram. Strictly, the freezing-point curve of G in the binary system Y—V has a slight break at ¢ This break becomes an isothermal crease on the G surface in the ternary system. The crease starts at ¢t and enters the ternary diagram to look simply like an isothermal contour on the surface. |t represents liquid in equilibrium with both forms of G. Above this temperature the surface is for liquid in equi- librium with G, and below this temperature it is the surface for liquid in equilibrium with G .. This crease has been sketched in Fig. 9.3 as ’rfie curve t 't ”” across the G field. UNCLASSIFIED ORNL-LR-DWG 25583 ~ ) hq o ~ NoF-UF ~BeF, In the system Y—U, Fig. 9.1, we note two binary compounds, A and C, decompesing upon cooling and two, E and F, forming from other solids upon cooling. The first two decompose before reaching an invariant involving a solid containing component V,; hence, as in the case of compound A in system X—U=V, these solids have primary phase fields but do not take part in the three-solid triangles of the ternary system. The compounds E and F of the present system, unlike the similar compound E of system X-U-V (Fig. 8.4), do have ternary fields in the system, because the curve for liquid in equilibrium with D and U extends down to the temperature T . for the formation of E from D and U, and the resulting curve for liquid in equilibrium with £ and U further extends down to the tempera- ture T . for the formation of I from E and U. The ternary diagram thus has eleven fields and seven three-solid triangles (with corresponding in- variant liquids). It also has four invariant points for liquids accompanying binary solid-phase re- actions: P, and P for the decompositions of sclids A and C on cooling, and Pp and P for the formation of solids E and F on cooling. The limited A field is divided into two regions by an isothermal crease, wv on Fig. 9.3. This crease is at the temperature T’ of Fig. 9.1, the transition temperature for: A_ - calories = Ag . The higher-temperature region of the field repre- sents liquid in equilibrium with A _, the lower region liquid in equilibrium with Afi; the form decomposing at P , is A 5. The similar transitions in the solid H are assumed to occur below the temperature of equilibrium with any ternary liquid, and hence are assumed to have no effect on the phase diagram. Five curves are of odd reaction. (The even curves simply precipitate the solids of both ad- jacent fields.) The transition curves are as follows: pgPci L+Do C; crossed by L for x in region CpyP pyPct L +CoB; crossed by L for x in region Bp3 PC. P P L+U>E; crossed forx!n EP P PPyt L+U>F,; crossed for x in FP o P,. PpoPy L+F-E,; crossed for x in EP P . UNCLASSIFIED ORNL-LR-DWG 25584 \ \ \\ '\ F \ AN \ \ N\ I " \\ \\ £ AN \ N N \ \\\ \\ . n \ : Ay €5 \\ \\ \ S () N N\ N, . \ S \\ \\ . ~, . N\ \ . \ \\\\ N : \\\ N . SN\ ®c - N - o \\ . L Fr N . (F) S . f” \\\. \\\ {£) p b T \ Es i‘m(G)\ EaNG \2 - - — *‘3 9 Lo e (V) N V eTf’ G €q Fig. 9.3. Invariant reactions are: P,: L +U->F +V;incongruent crystallization end point for triangle . L +F s E +V; same, for triangle Il L +E D +V; same, for triangle Il L +B »D 4+ H; same, for triangle VI. E, Eg, E,i eutectics for triangles IV, V, VII. There are two saddle points: m on curve E E and m” on curve P E. But only the line DG isa quasi-binary section, dividing the whole diagram (Note: P,: P P, into essentially independent subsystems. The composition diagram of a ternary system does not have to be a triangle. As long as it is a plane, with only two independent composition variables, it may have any shape.) Some relations in the subsystem D—U—~V—G may be illustrated by consideration of the equilibrium crystallization process for solution a4, Fig. 9.3. This point is located on the left of line UP o, in the region FP P, in the region EP P, in the quadrangle P, DEV, and in triangle IV. The first solid on cooling is U, and the liquid travels on the 41 straight line Ua to the curve P P . With L on the curve, L+U-E , but not all the U solid is consumed, and L reaches P . At this point all the E solid so fa. produced is consumed in reaction with U, to form F, and then the liquid, saturated with U and F, begins to travel on the curve P _P .. On this curve, the rest of the U solid is consumed, and L leaves the curve to traverse the F field on the straight line Fa. When L reaches the curve P P, L+F->FL , and now when all the F is consumed the liquid leaves this curve to traverse the E field, on the straight line Ea, until it reaches the curve P, P,. Now precipitating E and V, the liquid reaches P,, where L +E->D4+V Here F is consumed, and L. moves on down the curve P, E,, precipitating D and V. |t reaches E, and there solidifies completely to G, D, and V. The original sclution a thus gives only three solids upon solidification with complete equi- If the phases are not given sufficient time for reaction during the cooling process, the licuid from the composition @ would still reach E, before complete solidification, but the final mixture would contain all the csolids of the sub- system: U, E, F, V, D, and G. The point P is reached, in equilibrium crystal- lization, for x in the region DP _ U, by L on curve e P . carrying solids D and U; at P these solids librium, react to form E, leaving one of them in excess. Hence, if x is in the region DEP , U is consumed and L takes the curve P P,; for x in the region EUP., D is consumed and L travels on curve PP The point P is similarly reached, for x in the region EP U, by L on curve P P carrying solids E and U. Then for x in the region EFP ., 42 U is consumed and L leaves on curve PP, while for x in FUP, E is consumed and L takes the curve P P,. Isotherms near P above P are shown in Fig. 9.4 (a) just £ and (b) just below Pp. At P the equi- librium area for liquid in equilibrium with F appeats as the line FP . Vertical T vs ¢ diagrams for three sections of this subsystem are shown in Figs. 9.5, 9.6, and 9.7, and two T vs c sections for the subsystem Y—D—G are shown in Figs. 9.8 and 9.9. UNCLASSIFIED ORNL-LR-DWG 25585 () ‘< A\ £ \ . 0 .\ ; L ‘ L ey . / G G Fig. 9.4. UNCLASSIFIED ORNL-LR-DWG 25586 Fig. .5, UNCLASSIFIED ORNL-LR-DWG 25587 ol o L+ E+V Fs D+v D Vv Fig. 9.7. UNCLASSIFIED ORNL-LR-DWG 25588 Fig. 9.8. Fig. 9.9. 43 10. SYSTEM Y-U-R: NaF-UF ~RbF For the ternary system Y—U—R, Fig. 10.1 shows the binary system R—U, and Fig. 10.2 the system Y—R. The binary system Y—U is that of Fig. 9.1, with the same lettering. Figure 10.3 is the ternary diagram. We note first the restricted fieids for the binary compounds A and C of the system Y-U, ending at points P, and P, respectively, at the tempera- tures of decomposition of these solids on cooling (Fig. 9.1). The isothermal curve uv on the A field has been explained in connection with Fig. 9.3. The low-temperature compounds E and F of Fig. 9.1 do not appear at liquidus temperatures in Fig. 10.3, since the curve of liquid in equilibrium with D and U (esE] ) ends at a temperature higher than T . of Fig. 9.1. The new item in the present ternary system is the ternary compound (, with P,P3E,P, as its primary phase field. This compound is stable When heated it decomposes in a into the If the ternary compound Q is not only below the temperature of P .. to the temperature of P strictly binary solids B and H. pure, but is mixed either with a little Y or with a little R, it still decomposes as a solid phase into solid-phase reaction, UNCLASSIFIED ORNL-LR~DWG 25589 Fig. 10.2 the same solids, B and H, at the same tempera- ture, namely that of point P, but now in the presence of the liquid Py The invariant point P is therefore entirely analogous to P in Fig. 9.3, where solid E decomposes, when heated, into D and U in the presence of the liquid P . Figure 10.3 shows fifteen primary phase fields and eleven three-solid triangles with corresponding invariant liquids. There are five saddle points: m, on curve E]Ez, m, On curve ESPQ' M, On curve P E, m, on curve E,Eg, and m, on curve PloEqr Two of these saddle points, m, and m,, are on quasi-binary sections,Ym, G and Dm, J; Fig. 10.3 therefore consists of three subsystems. The subsystem D—U~] is relatively simple, with two eutectics, Fy and F,,, and two peritectics, Py and Plo Three of the curves are transition curves: py3E 1 L + U~ N;crossed by liquids originating in region Np,,E,,. This curve may become even in reaction close to point Eyy P1oP 0t L + N~ M;crossed by liquids originating in region Mp,, P .. p11Pet L+ M- K;crossed by liquids originating in region Kp,,P,. Compositions in triangle X| solidity to D, U, and N, but at T of Fig. 9.1, D and U react to form £, and the triangle DUN is divided into two triangles of three coexisting solids, DEN and EUN. At a still lower temperature (T of Fig. 9.1), the triangle EUN divides into EFN and FUN. In the middle subsystem, Y—D—]J—G, there are the following transition curves: pyP ot L+C o B crossed for x in Bp, P . Py P L +D - C; crossed for x in Cp, P . py P, L+ G- Hjcrossed forx in Hp, P ,. pgEqsr L +] > 1 crossed for x in Ipg E . PoPy L+ H -0 crossed for x in OP P, PP L+D B, upto point s {line Bs tangent to the curve). The relations along this curve are like those explained for curve p‘sE,l in Fig. 5.3. Point P, is reached by liquid from original compositions x in the triangle BP _H. The liquid reaches the curve m, P either from the left side, carrying solid B, or from the right side carrying solid H. It then travels on the curve, precipitating both B and H, and reaches P .. At this point, B and H react to form solid O, ang one of the original UNCLASSIFIED ORNL-LR-DWG 25590 Fig. 10.3. solids will be completely consumed. For x in the triangle P,BQ, H is consumed and the liquid travels down the curve PQP3,‘ for x in the triangle PQQH, B is consumed and . moves onto curve PP 4 Consider a total composition x in the region QP ,P,. On cooling, the first solid is H, and L moves on a straight line from H to reach either curve P P, directly, or first curve m,P ,, then 2 ! point P, and then the curve PoP,. Vfi-nile L travels along this curve, H reacts with liquid to form O, and eventually L leaves the curve, when all H is consumed, to enter the Q field. Traversing this field on a straight line from O, it can reach any one of the three other boundaries of the @ field. These are all even curves, and liquid cannot leave them. If x is in triangle Hl, L will reach P along curve P P, and complete its crystallization at P, to leave solids Y, B, and Q; for x in triangle I, L ends at E,, leaving Y, O, and G. 45 For a liquid with composition O itself, the first solid is H, and L travels to the saddle point m,, where the liquid solidifies completely into B and H, which solids will be present at the end in the exact proportions corresponding to Q. Then at the temperature of Po these solids combine to produce Q. Compositions in triangle V complete their crystal- lization at Eg, into a mixture of B, H, and I. But UNCLASSIFIED ORNL-LR-DWG 255914 L+ U LN+~ 46 on cooling further, B and H combine to produce Q, leaving, below the temperature of P o either B, O, and I or Q, H, and 1. Some T vs c vertical sections are shown in Figs. 10.4-10.10. UNCLASSIFIED ORNL-LR-DWG 25592 L+G~ ‘ (+G+H - P 1. SYSTEM Y-Z-R: NaF-ZrF ,~RbF For the ternary system Y-Z-~R, the binary system Y~Z is shown (schematically) in Fig. 11.1 and R-Z in Fig. 11.2. The system Y-R is as in Fig. 10.2, but now with e 3 In each of the first two compounds, A and B, of in place of e, ,. the system Y~Z, there is some solid solution on the Z side of the stoichiometric composition. In the case of B, solid solution is limited to the upper form, B, The transition temperature is accordingly lowered, from T’ to T”. solid solution extending in the direction of the Y side. The subsolidus compound D, which forms from the solids € and E (a solid solution) at T', forms solid solution on the Z side. The compounds D and E, in other words, may be said te form a [imited series of solid solutions with each other. The compound E forms similar The 1:1 compound will not be considered in con- nection with the ternary system. It is observed to be formed at relatively low temperature, but its relation to the established phase equilibria of the binary system has not been even tentatively clarified. The phase diagram for the system R-Z shows some solid solution, on the Z side, for the two At T’ the compound H is polymorphic transition: compounds G and H. shown as undergoing a H, ~ calories ——= H[3 , and the transition temperature is shown as being lowered to T " as the result of the solid solution formation. The relations for compound H, however, It seems possible that it may in fact be a pure solid phase, without any solid solution, and moreover, without any are experimentally not clear. polymorphic transition, The ternary diagram for the system is given in Fig. 11.3. With regard to this diagram, which is shown as it has so far been worked out, we note the absence of any primary phase field for the incongruently melting compound B of the system Y=Z and for the subsolidus compound D of the same system. Both of these solids should have primary phase fields in the ternary system. The regions involved were investigated before the relations for these compounds were definitely established in the binary system, and they have not yet been rein- vestigated. while the lower form, B g, is pure. We shall first discuss briefly the relations for the ternary system as reported in the diagram of Fig. 11.3, assuming, moreover, that the solids form no solid solution. This will serve as a basis, then, for a more detailed discussion of special regions of the system involving the missing solids, together with the solid solutions formed. 11,1. THE SYSTEM ACCORDING TO FIGURE 11.3 AND NEGLECTING SOLID SOLUTION There are primary phase fields for three ternary compounds, My, M, and M,, all with the same (1:1) ratio of the components Y and R, and varying only in Z content. They lie on a line with the corner Z, Both M, and M, have congruent melting points, with a temperature maximum in each field at the composition of the compound itself, Crystal- lization paths in each of these two fields radiate in all directions as straight lines from the maxi- Liquid can be in equilibrium with solid M, and any of seven other solids (the M, field has seven boundaries). The M, field has five bound- aries (but the field for the here missing compound B will probably add a sixth boundary). The ternary compound M, has a semicongruent melting point, at the temperature of point y on the boundary curve between the M, and M, fields (cf. Fig. 4.13). Instead of reaching a congruent melting point, the compound M,, when heated to the temperature of y, decomposes, or melts incon- mum. gruently, into compound M, and liquid y, collinear with M. toward y, the M, surface falls away from y, and the temperature on the boundary curve PP, falls away from y in both directions. With saddle points (m’ and m "} on each of the other two boundary curves crossed by the line M M,M,Z, this line is a quasi-binary section (from M, to Z) of the ternary system (Fig. 11.4); y is seen to be simply the incongruent melting The M, surface falls in temperature point for the compound M. in this binary system. Figure 11.3 shows fifteen primary phase fields and sixteen three-solid triangles with corresponding invariant liquids, There are ten saddle points (m-points), only one of which, with all solids assumed pure, is not on a quasi-binary section; this is on the curve E, E, .. The nine quasi- divide the diagram into eight quite simple ternary subsystems, shown as the eight areas of Fig. 11,5, binary sections 47 UNCLASSIFIED ORNL-LR-DWG 25643 Pg F (1:1) £ Fig 111, 11.2. Fig. 48 “NCLASSIFIED CRNL-.®-DW5 25 502 Only five of the boundary curves in Fig. 11.3 seem to be of odd reaction (pPB, PP ror P19F 110 PgP gt and P5P16); all the others seem to be even. The curve P P, ., for L+M »M,, is crossed by L for x between the curve and the lines P .M, and P My The binary peritectic peint p has been left un- numbered in Fig. 11.3, because it may represent either p, or p, of Fig. 11.1; and the invariant PS’ has been primed, because there must be two invariants here (P, and P,) in place of just the one., Also, a primary field for compound D of Fig. 11.1 should make its appearance somewhere along the curve e P/, the prime on P. being used because there should be two invariants here also, P, and P.. 11,2, CONSIDERATION OF SOLID SOLUTION FORMATION If the actual solid solutions in this system are considered, the phase diagram is no longer divided into as many independent subsystems as assumed in Fig. 11.5. Five of the areas of Fig, 11.5 re- main simple, involving only pure solids: EZM, with just P, and Eg as invariants; M Z] with Py, and E,,; M ]I with E YGR with E YAG with El' However, although the solids A and G are present as pure solids in their equilibria below the line and 137 187 AG, they both form solid solutions, containing excess Z, in their binary systems. |n cther words, the liquid on curve m, - E, precipitates pure A and pure G, but the liquid on the part my > E, (of the same curve) precipitates two solid so- lutions, starting as pure A and pure G at m, and ending as A, (on the side YZ} and G, (on the side RZ), for E,. The A solid solution extends be- yond A,, toward Z, for the equilibrium with liquid on curve P.E,, and the saddle point m, is no longer on a quasi-binary section. At My, the liguid is in equilibrium with M, and a solid so- lution of composition Ama, between A, and Ags the composition corresponding to L at P,. Simi- larly, the saddle point mg is no longer on a quasi- binary section, since here the liquid is in equi- librium with M. and a solid solution of composition G, , between G, and G the composition for L 17¢ at Ig”. On the other hand, Moy ON the curve E,E,, is exactly on the line AG, o quasi-binary section. The fractionation paths in the A field, then, originating from point A, are straight lines for the line Am, and below, but they are curves convex with respect to the Z corner above the line Am,, with the limiting paths Ap and Am, both straight (sketched on Fig. 11.3). The paths for the G field are similar: straight lines from G below the line Gm,, and curves, convex with respect to Z, above this line. The region AEM,IG, then, although it contains the quasi-binary line M,M,, is not subdivided into separate subsystems; the line MM, does not cut the region into two parts, For convenience, however, the right and left portions will be dis- cussed separately, 1.3, THE REGION FOR COMPOUNDS G AND H OF SYSTEM R-Z The Region As Shown in Figures 11.6 and 11.7 The relations for compounds G and H, as assumed in Fig. 11,2, are shown in schematic detail in Fig. 11.6. On the basis of these relations the region M M,IG of the ternary system would be schematically as sketched in Fig. 11.7. For the H solid solution field the fractionation paths are curves, convex with respect to Z, originating by extension from the point . On the curve my » P, the liquid precipitates M, and solid solution on the binary side starting 1 at Gm8 for L. at mg and ending ot G, for P, 49 e < @ L o0 W w == w0 @ o =1 29 .ML =z @ o G 7 - ~ \\\jgw/ > 7 S 7 foi \ 7 H\,\ \.\ _,, \ 7_ ,.\ .;.\_ ,,,_, N Lh\ \_\ \ ; - _,_, Z ///./“‘\‘\\‘ = - A.,,,M .,,.,, e = ,,, \ , \ : \ N ) Y § s I Y =l S "~ } / | Wt \ . | b ~ Fig. 11.5. 4. 11 Fig. T — SN Q\qu mi:4|1x L\J.v.l\.fi\ F+L— TH 6. 14 Fig. UNCLASSIFIED ORNL-LR-0OWG 25595 These solid solutions are not on the ‘‘solidus’’ curve of Fig. 11.6, but G, itself is. On the curve bg > Pz L + G (solid solution) » H, (pure) . The three-phase triangle starts as the line pBHaGp (see Fig. 11.6), and ends as the triangle P HG, S This curve is crossed for x in the region Hpgt |4 The invariant reaction at P17 is L+G M +H, . This is an incongruent crystallization end point for x in triangle XVII (MlHG”); for x in M, P, .H, the liquid moves onto curve P, P M, and an H, and ending as H, . 14¢ Precipitating solid solution starting as pure H (As shown on Fig. 11.6, H, is not on a solidus curve of the binary system. Cn curve y » P, L +M1 -—>M2 ; this curve is crossed for x in the region M,yP, .. The point P, is reached for x in the quadrangle M1M2P]6H]6; its reaction is L+M] ~>M2+H‘6 . and it is the incongruent crystallization end point for triangle XVIi (M]MzH]é). "\'12P16H1Qa L. then travels on curve 1_316 - E_15' precipitating M, and an H solid solution starting For x in the region at H, . and ending at H, .. Along curve e, > E, , the liquid precipitates I and an H, sclid solution starting at H_ and ending at H, . (see Fig. 11.6). 9 Along curve E,,»E L - M2 +1 . The point E, . is reached for x in triangle XV (M IH, ). For x in the regions M, G,.G, MH, H, and MoH, (Hy liquid is consumed, to leave two solids, while traveling on curves E,P.., P P, ., and P ¢E s respectively, The H solid solution produced in these processes, with compositions ranging from H to H, ., is the a form of H. As the temperature is lowered, however, the solid so- lution undergoes transition to the 3 form, starting at T’ for pure H and ending at 7", as shown in Fig. 11.6; and these temperatures are unaffected by the coexistence with solid M since the H, and Hyg solid solutions are purely binary. We have here assumed the order of decreasing temperature to be: T’ = Pig >eg > E s >T7% But if T > E,, then there is an isothermal crease, at temperature T, running across the H surface between curves e £, and P, E .. The surface between this crease and E, . represents solid solution; the rest of the H field represents liquid in equilibrium or solid M, liquid in equilibrium with H with H, solid solution. For the relations assumed in Fig. 11.7, liquid of composition @ gives M, as first solid, and L moves on a straight line from M, (i.e., on the extension of the straight line M,a) to the curve yP Here 16° L+M »M, M, is consumed; . leaves the curve, traverses the M, field on a straight line from M, and reaches curve m,E, .. Here L—»M2+I . and at E, ., H The Region As Shown in Figures 11.8 and 11.9 The other possibility for the region M, M,IG seems to be, as already stated, that H forms no solid solution, and has but one form. Then Fig. 11.6 becomes Fig. 11.8, and Fig. 11.7 becomes Fig. 11.9. In Fig. 11.9, the first solid for liquid also precipitates. 51 UNCLASSIFIED ORNL-LR-DWG 2559¢ Fig. 1.9 a is the G solid solution, between G and G,,. The liquid reaches the curve m P,., traveling on a curved equilibrium path over the G surface. On the curve, the liquid precipitates M, and more solid solution, ending at G, AtP,_, L+G”»M] +H ; G is consumed; the liquid travels on curve 17 P17P16' precipitating M] and H, and reaches Plé' where the liquid is consumed in the reaction L+M] ->M2+H . 1.4, THE REGION INVOLVING COMPOUNDS B AND D OF SYSTEM Y -Z Figure 11,10 shows a probable arrangement for the missing primary phase fields for compounds B and D of system Y~Z, Also, since four of the solids of system Y-Z form binary solid solutions, there must be various two-solid areas reached upon complete solidification in this region, whenever one of these solids crystallizes together with a solid involving the third component R; i.e., for every case of a boundary curve invelving one of 52 these solids and a solid containing component K. These areas are shown with tie lines, the relations being essentially as already explained schemati- cally for Fig. 7.3. The field for compound B is introduced as p,p 5P P4, and that for compound D as PP P.. There are now two more three-solid triangles, for The compo- is simply the ternary the two added ternary invariants. sition represented by P, solution present when the compound D forms on cooling from solids C and E (a solid sclution); it is similar to P and P, in Fig. 9.3, where, how- ever, only pure solids are involved. As explained for the solid phase H under Fig. 11.7, the solid form of B involved on the B field and along its boundaries is the solid solution in the upper polymorphic form B, ranging in compo- sition from pure B to the solid solution limit indi- cated in Fig. 11.10. As the temperature is lowered, however, the B, phase undergoes transition to the pure 3 form, starting at T’ for pure B, and ending at T” for the solid solution (Fig. 11.2). As in the case of compound H these temperatures are un- affected by the coexistence with solid M. Wherever the compound C is invelved as a solid phase, its form is €, above the temperature of (Fig. 11.1), C, between 3 and t,, C.,, between t, and tas and Cj5 below t,. The C surface, (C), is, strictly, divided into four parts, by the special isothermal contours at ¢,, t,, and t;. These con- tours constitute slight creases in the surface, defining the regions for liquid in equilibrium with Co Ca Cy,cnd Cs, respectively. Since A, B, D, and E are binary solid solutions, the fractionation paths on the fields for these solids are curved. Those for the E field are are similar to those on the A field: above the they are straight lines from F, and below this line they are curves convex with respect to For the B and D fields the paths originate by extension from the points B and D line Em4 the corner Y, respectively, and they are convex toward Z in both cases, Along the binary curve Ee, (from the congruent melting point of E to e,), the liquid precipitates a solid solution starting as pure E at the melting point of E and ending at E_ for L at ¢,. Along the ternary curve e, P, the liquid precipitates C and a solid solution of E, strictly varying in composition between the temperatures of e, and P, but practically constant because the solidus UNCLASSIFIED ORNL-LR-DWG 25597 Fig. 11.10. (Fig. 11.1) is practically vertical, At P, there- fore, C+E_ - calories » D , For x in the region CDP ,, E_ L. travels on curve P P, is consumed, and precipitating D in the reaction L+C->D . For x in the region DE P, Cis consumed, and L. travels on curve N DI precipitating two solid solutions, conjugate solid solutions of the com- pounds D and E. The D solid starts as pure D at P and ranges to D_ when P is reached, and the E solid, already at E_, changes slightly but is still practically constant at E_, The point P is then the invariant liquid for the solids D, E and M,, in the reaction st L+DS—>ES+M2 . For x in the region £ _P_M,, L. moves along curve P7E8, precipitating M, and D_ is consumed, and 53 E_ (still practically constant, we are assuming). The saddle points m,, m,, m,, and m” involve liquid saturated with two pure solids, as does also the special point y; m, and mgy, as already discussed, involve M, and a solid solution (A and G, reSpecfiveiy]). For liquid of composition @ ir Fig. 11.10 the first solid on cooling is a solid solution of A, and A,. between A The liquid reaches curve p,P 4 where 3 L +A(ss)->B . The A solid solution is consumed; L {eaves the curve, traverses the B field precipitating solid solution B, and reaches the curve p.P,. Here L ""IB(SS)—)C‘~ . The B solid solution is consumed; [ leaves the curve, traverses the C field on a straight line from C, and reaches curve P P.. Here L—yC+M] . L +MT - +M2 ; M, is consumed, and L moves to P, where D also precipitates to leave C, D, and M,., The path of the liquid on the solid solution fields (A and B) is curved, convex with respect to the corner Z. Liquid & gives M, as first solid, reaches curve PP, precipitates C and M, and reaches P, where M] is consumed in the reaction L +M] > C +z\"12 . Now [. moves on P5P6 sumed in the reaction to P, where C is con- L+C—~>D+M2 . The liquid now starts out on curve P P, pre- ‘ 7 cipitating M, and solid solution, but the liquid vanishes on the curve to leave a two-solid mixture of M, and a solid solution between D and D, on a straight line through # and M, 12, SYSTEM Y=Z~X: NaF-ZrF -LiF For the ternary system Y=Z-X, the diagram of the binary system Y=Z, already considered under Fig. 11,1, is used here with the same lettering. The binary systems X-Z and Y=X are shown, schematically, in Figs. 12.1 and 12,2. Two of the compounds cooling, one of them, G, also showing a polymorphic transition, at T°, The ternary diagram, as far as it has been worked out, is shown in Fig. 12,3. Like Fig. 11,3, the diagram does not show the primary phase fields for compounds B and D of the Y=Z system, which should appear. of the system X-Z decompose on This system involves several series of solid solutions. It has not only the binary solid so- lutions of the system Y~Z (Fig. 11.1), but also solid solutions, with compositions on straight lines (crosshatched on Fig. 12.3) across the diagram, formed between corresponding binary compounds of the systems Y-Z and X-Z. The compound A of system Y-Z (3Y.1Z) forms solid solution with G (also 3:1 in composition) of system X—=Z. The solid solution is not continuous, Since both compounds melting points and since the but has a miscibility gap. have congruent UNCLASSIFIED ORNL-LR-DWG 25598 section Am,G of Fig. 12,3 is quasi-binary, it is clear that the ternary system may immediately be divided at this point into separate subsystems, With m, a femperature minimum between A and G, the binary system A=G is eutectic in nature, Solid A, however, also forms solid solution (with excess Z in its composition) in the binary Y-Z system. The solid solution originating at point A of Fig, 12,3 is therefore actually ternary in composition, occupying an area of the diagram, and one edge of this area is the straight line from point A to point G. The corresponding compounds F and I, both 3:4 in composition, also form solid solution with a miscibility gap. Both have incongruent melting points, however, and the section FI of Fig. 12.3 is of course not quasi-binary, even though the solutions formed are strictly on the, line FI. The section EH, however, through the on the curve E E, divides the upper part of Fig. 12.3 into two independent sub- systems. This is so since E forms solid solution with D (Fig. 11.1) but not with F, and H is pure. We shall therefore discuss this system part by part, for it consists of three practically inde- pendent subsystems: Y=A=G=X, A=E=H=G, and E~Z~H. (Note: This independence holds at least to just below liquidus temperatures, but not all the way, since compounds G and | of system X—7 decompose at low temperature.) We shall first describe the fractionation paths for the solid solution surfaces, The field for the A-rich solid solution of A and G, i.e., the surface for liquid in equilibrium with A _, is e, ApP [P E E,. The maximum of this surface is point A itself, since this quasi-binary saddle point m compound melts congruently. The fractionation paths therefore radiate as curves from point A, and they may be said to consist of two families of paths, divided by the straight-line fractionation path running from A to m,. All the paths, diverging from this line, are convex with respect to point G, A similar arrangement holds for the G_ field (field for liquid in equilibrium with Gerich solid solution), e,Ge P E,, with a and all other paths diverging from this line and convex with respect to the point A, For the surface estyP1oPors for liquid in equilibrium with F_ (F-rich solid solution of F and I}, the temperature maximum for the origin of the fractionation paths straight-line path running from G to m, is the metastable congruent melting point of F. 55 Hence the fractionation paths do not show & common origin on the field itself, but radiate, as curves convex toward I, from point F. The fractionation paths for the I_ surface, ep, (P, PoEg, similarly radiate, as curves convex toward F, from the sub- merged maximum at point I, The fractionation paths for the fields for solid solutions of the compounds B, D, and E of system Y—-Z, to be considered later, will be as described for the same fields in the preceding system (Sec 11.4). UNCLASSIFIED ORNL-LR-DWG 25599 (Z) A 12,1, SUBSYSTEM Y-A-G-X The region YAGX is shown in Fig. 12.4, ond the vertical T vs ¢ section AG is given, sche- matically, in Fig. 12.5, Liquid on the curve solid starting as s moE, precipitates two mutually saturating solutions, with con- jugate compositions and s’ » and S5 These limiting solid so- lutions may be identified on the miscibility gap in at the temperature of m, and ending as s, at the temperature of F . UNCLASSIFIED ORNL-LR-DWG 25600 Fig. Fig. 12.5, which shows the solid-solid solubility as diminishing with decreasing temperature. On curve e £, liquid precipitates Y and solid so- ; ot E}; similarly, liquid on curve e,E, precipitates X and solid solution G _ ranging from G to 55. Liquid lution A_ ranging from pure A at e, to s on curve E.E, precipitates X and A_ solid so- lution starting at s for sclution m, and ranging ] to s, for liquid following curve m E, and ranging to s, for liquid following curve m,E,. The solid are not related solution compositions s, and s _ 1 1 to the miscibility gap of Fig. 12.5; they are merely 12.0. points inthe A _ solid solution area of that diagram, Also, as explained under Fig. 7.3, the line s_ m, X is not a quasi-binary section. 1 Liquids with original composition x in the region s,GX reach the curve e, L, and solidify com- pletely before reaching E,, to leave X and G_. Similarly, liquids from x in the s s, X solidify on the curve m E, to leave A_ c1nd X. Only liquids for x in the triangle s,s7X reach E, to give the three solids s,, sJ, and X. Similarly, only liquids for x in the triangle Ys, X reach E, to form the three solids of triangle I. 57 Summarizing the equilibrium crystallization process for the curves: curve e E, is reached for x in region YAs I, but the liquid vanishes on the curve for x in Yas,; curve e E_ is reached for x in XGsJE,, but the liquid is consumed for x in XGsz',' curve E.E, s reached for x in s 5,E XE, but the liquid is consumed for x in s,X; curve e, E, is reached for x in YE X, for x in 5252'52, but on these curves the liquid does not vanish, Sy and curve m_E 12.2. SUBSYSTEM E~Z~H The region EZH is shown in Fig. 12.6, and the vertical T vs ¢ section FI is shown in Fig. 12.7. The miscibility gap in the F=I solid solution is shown as The three invariant planes in Fig. 12.6 are seen The quadrangle P, s, Zs{, is the widening with falling temperature. to overlap. UNCLASSIFIED ORNL-LR-DWG 258601 Fig. 12 7. 58 highest in temperature. Below it is the quadrangie g° is the triangle for Eg, Es H. (This diagram has certain similarities to the hypothetical case of Fig. 7.3.) Polsys The lowest in temperature In the relations as assumed in these figures, liquids in the field DgZp 4Py, give pure Z as primary solid, and travel on a straight line from Z to one of the transition curves p P, and p, P, .. On the curve p P, , L+Z~»F_, the F-rich solid solution. The three-phase triangle for this equilibrium starts as the line p,FZ and ends as the triangle P $y0Z. For xin the region FZsyq the liquid vanishes on the curve, leaving Z and F_ (between [ and Sm). region Petsy 0P For x in the , Z is consumed while L is on the curve, and the liquid then leaves the curve to travel, on o curved path, across the F_ field. Similar relations hold on the | side, with respect to curve p, P, ., with the reaction L+Z—>IS For x in the region IZS]’O, the liquid vanishes on the curve, leaving Z and [_ (between | and SI’O)' and for x in pwls' P L. leaves the curve when 107 10 all Z is consumed, to travel, on a curved path, across the I_ field. Only liquids for x in the quadrangle s, Zs/ P reach P,., where the ) ) 10 reaction 1s L +Z~»s]0 +S1g - For x in s, Zs]’ , therefore, the liquid is consumed at P, to leave the three solids of triangle X, Sy o 51’0, and Z; and otherwise, with Z consumed, L moves down along curve P. P 107 9/ two conjugate solid solutions with compositions precipitating changing from s, ¢ and 59', according to the miscibility gap in Fig. 12.7. The curve P, P may also be reached directly from either the F_ field or the I_ field, for x in and 5'0 to s the regions 89.510P]OP9 and 51059_P9%)10’ re- spectively. Foint P is reached by liquids for x in the quadrangle Es_ s/P., and with the reaction 979" 9! L + Sg > E +59' , this is the incongruent crystallization end point for triangle 1X, Esgsg. If sg reaction, the liquid moves down on curve Polg, is consumed in the P9 precipitating E and I_ solid solution ranging from 59' to sg. (With reference to Fig. 12.7, s_ is in the I_ area but not on the solidus edge of the misci- bility gap.) Also, liquids reaching curve egE travel on it precipitating H and I_ (between I ang sy)» For x in Hsgl, the liquid vanishes on the curve to leave f/ and 1. The point E_, then, is reached for x in triangle VIl EsgH, for which it is the eutectic. Finally, liquid traveling on curve e Py, but with x in the region EFs,, vanishes on the curve to leave E and F_; liquid traveling on the curve PyEg and with x in ES;SB vanishes to leave E and I _ between s and s,. As an example of some of the relations we con- sider point @ in Fig. 12.6. For liquid of this composition, the first solid on cooling is Z, and L. reaches curve p P, on a straight line from Z, On the curve, 0 L+Z-F_, starting between F and s, and moving toward But before the composition of the solid S . of solution reaches s Z is consumed; L leaves 10/ the curve and travels on a curved path, convex with respect to I, across the F_ field. While L is on the F_ surface, the solid solution continues to become richer in I. When [ reaches curve PP, the I-rich solid solution begins to pre- cipitate together with F_, the compositions of the solid solutions being given at each temperature by the miscibility gap of Fig. 12.7. When L reaches P, L+sg>F+sg, and sg vanishes. The liquid then travels on the curve PoE ., while s changes toward Sge Crystal- lization is completed at Eg to leave the solids E, Sgs and H, 12,3. SUBSYSTEM A-E~-H-G The phase diagram as constructed in Fig. 12.3 omits fields for the binary compounds B and D of the system Y=Z (Fig. 11.1). We shall, however, discuss the region AEHG, not as shown in Fig. 12.3, but as it might probably appear with the necessary fields for B and D (Fig. 12,8), as was done for the system Y=Z~R in Fig. 11,10. o and s” of Fig. 12.8 are The points s, m 2 the same as those so labelled in Fig. 12.4. The UNCLASSIFIED ORNL-LR—-DWG 25602 59 and s, (like s 12.4) are also conjugate solid solutions of the solid solutions s and s, in Fig. A~G solid solution miscibility gap, identifiable in Fig. 12.5, As liquid travels on the curve m, » P, cipitates solid solutions beginning as s and 2 s, and ending as s, and sJ. The solids of triangle |11, S 31 53’, and /{, are in equilibrium with it pre- , the invariant liquid P,, where the reaction is » L+53~953+H If 53: is consumed in this reaction, the liquid moves down the curve P.P,, precipitating A_ solid so- lution and H., The A_ solid solution, however, is here shown as ternary in composition, and it has the composition s, when L reaches Py Point a is the limiting composition in the binary system Y=Z at the temperature of . Compositions x in the area Aas s, would solidify (in full equilibrium} to a single ternary solid solution phase while the liquid is traveling on the A_ field, before the liquid reaches any boundary curve (cf, Fig. 2.3). For x in the region aBs,, L reaches the transition curve o 4 aleng which L +AS~+B ’ and the liquid vanishes while on that curve, to leave A_(on the curve as,) and B. The rest of the relations in this diagram are altogether similar to those in Fig. 11.10, with H, so to speak, in place of the various ternary com- pounds of that diagram, 12,4, SUBSOLIDUS DECOMPOSITIONS OF COMPOUNDS G AND | As shown in Fig. 12,1, for the binary system X-Z, the compounds G and I undergo solid-phase and T, respectively. In the ternary system Y-Z-X, both of these compounds form solid solution with the third component, Y, while their products of de- composition do not. The decomposition temper- ature is therefore lowered, in both cases, and we decompositions at the temperatures TG shall say to T/ and T/, respectively. The com- pound [ is considered first, Decomposition of Compound [ The changes in the two- and three-solid equilibria accompanying the low-temperature decomposition of compound I are shown in the successive iso- therms of Fig. 12.9. Isotherm (a) is just below [, of Fig. 12.6, and it represents the various two- and three-solid mixtures which will be obtained UNCLASSIFIED ORNL-LR-DWG 25603 Fig. 12.9. 60 upon complete solidification of any composition in this subsystem. Only the number of phases is shown inthe figure; the phases may be identified, if necessary, from Fig. 12,6. Figure 12,9 () is just below T, of Fig. 12,1, where the three-solid area for Z, H, and I_ appeared on cooling. Figure 12.9 (c) is at the temperature of a four-solid in- variant, for the reaction F+l - F +H S 5 on cooling, and Fig. 12.9 (d) is just below this invariant, Figure 12.9 (e) is at the temperature T,, the lowest temperature for the existence of the I_ solid phase (point s). Figure 12.9 (/) is below this temperature. The T vs ¢ section FI (Fig. 12.10) shows little of all these changes. Decomposition of Compound G According to Fig. 12.1, the compound G under- goes a fransition on cooling, at 77, from G, to Gy before the 3 form decomposes at 7 .. In the successive solid-phase isotherms of Fig. 12.11 it is assumed that, as in the case of the aecompeo- sition temperature itself, the transition temper- ature is also lowered, from T to T, as the result of the presence of the third component in solid solution. The temperature-composition relations assumed, then, for the section AG are shown in Fig. 12.12. The first isotherm, (a), of Fig. 12.11 represents the two- and three-solid combinations for equi- librium just below the temperature of point P, of Fig. 12.8, for the region YBHX (the ternary solid solution area for A_ is omitted). At T’ there appears a length of G, solid solution, with four new equilibria for H and (G ) ; X and (G ) ; H, (G.), and (G ) ; and X, (G ), and (GS)B. Figure a 12.]?(b)showslfhese new combinations, at a temper- ature between 7 7and I'”, Figure 12.11(c) isat T”, the lowest temperature for existence of the ternary G, solid solution, Figure 12.11(d) is between 77 and T, where the 3 form begins to decompose (into H and X) in the binary system. Figure 12.11(e) is between T . and T(';. Figure 12.11(/) is at 7., the lowest temperature of existence of the G, solid solution in the ternary system. Figure 12.11(g) is below 7. UNCLASSIFIED ORNL-LR-DWG 25604 61 UNCLASSIFIED ORNL-LR-DWG 25605 Fig. 12 1. 62 L+ A Ac+(6)q = b 7 UNCLASSIFIED ORNL-LR-DWG 32522 7! ///’(63)3 1 /“‘\* s B+ X+H D Fig. 12 12. 63 13. SYSTEM Y-U-X: NaF-UF,-LiF For the ternary system Y—U—X, the binary system Y—U is used with the lettering shown on Fig. 9.1. The binary system Y—X is that of Fig. 12.2, with e, Mow in place of e,,. The binary system X-U, already given in Fig. 8.1, is repeated here in Fig. 13.1 to show the new lettering tequired in the present section. We note the binary compounds A and C of system Y—U and G of system X-U, de- composing on cooling. The system Y-U also has two compounds, E and F, which form below the liquidus temperature. UNCLASSIFIED ORNL-LR-DWG 25606 Fig. 13 1. The ternary diagram is given in Fig. 13.2. There are no binary solid solutions involved in this system, but there are two large primary phase fields for solid solutions formed across the diagram by corresponding 7:6 compounds D and H. These compounds form discontinuous solid solution with a considerable miscibility gap. The primary phase fields for D (the D-rich solid solution) and for H, {the H-rich solid solution) are in contact along the boundary curve £, E,, and the point m,; on this curve is a saddle point, being on the line DH. However, compound D has a congruent melting point, while compound H melts incongruently, so that the line Dmy H is not a quasi-binary section. The system has three saddle points but no quasi- binary section at all. The fine Dm, X looks like one but is not, because of the solid solution in the D solid phase. The extent of solid-solid solubility at the liquidus temperatures, across the section DH, is suggested by the crosshatching on this line in Fig. 13.2. 64 The fractionation paths on the D _ surface origi- nate at point D and radiate, on either side of the straight-line path Dm,, as curves convex with respect to point H. The paths on the H field must be imagined as radiating by extension from point H (the submerged, metastable maximum of the field); they curve similarly on either side of the straight- line path Hm, (of which only the portion r » m, is on the stable surface for liquid in equilibrium with H_) and are convex with respect to point D. The vertical T vs c relations for the section DH of the ternary system are shown in Fig. 13.3. The point 7 is on curve pg P, of Fig. 13.2, and s s the composition of the solid solution in equilibrium with liquid 7. The solids s and s/ are the conjugate solid solutions in equilibrium w3i’rh liquid m., the minimum of the section. The compositions below this temperature on Fig. 13.3 correspond to liquids at the ternary eutectics £, and E,, and will be referred to later. The system (Fig. 13.2) has ten primary phase fields and ten invariant points. Four of these invariants, however, involve simply the decompo- There are consequently only six three-solid triangles for sition or formation of binary compounds. ultimate combinations of solids on complete solidi- fication, related to two ternary peritectics and four ternary eutectics. We shall consider first the four invariant points for appearance or dis- appearance of binary compounds and then the trelations involved in the principal invariants. special 13.1. THE INVARIANTS P, P Pe. AND P_ Cl The Invariant PA The decomposition of compound A involves pure solids: A—bY+B r and the temperature of the invariant P, is there- fore the same as T , in Fig. 9.1. (The changes in isothermal relations near P to those shown in Fig. 8.5.) The curves ¢, P, and esz are both curves of even reaction, L—)A+Y are entirely similar and [.A+B I respectively; the first is reached by liquid for total composition x in the region YAP ,, the second for x in ABP ,. At P ,, solid A decomposes, and the UNCLASSIFIED CRNL-LR-DWG 25607 Fig 13.2. liquid travels on curve P ,E, precipitating B and Y. The isothermal curve wv represents liquid in equilibrium with A_and A ; and divides the A field into regions for liquid in equilibrium with A_ and for liquid in equilibrium with AB' lts temperature is T’ in Fig. 9.1. The Invariant P _ The temperature of the invariant P~ for the decomposition of compound C in the presence of ternary liquid, is higher than T . of Fig. 9.1, be- cause C is here decomposing not into pure solids but into B and a solid solution of D and H. The isothermal relations involving P . are shown in Fig. 13.4: {(a) between Py and P () at P (c) between P and T ., and {d) below T The Cl reaction on curve p, P i cis L+D »C , s the three-phase triangle starting as line p,CD and ending as P-Cy (isotherm &). This curve is reached for x in the region p,DyP . For x in CDy, the liquid is consumed on the curve to leave 65 UNCLASSIFIED ORNL-LR-DWG 25608 Fig. 13 3. C and D _ (between D and y). For x inp,CP ., D_ is consumed on the curve, and L then traverses the C field on a straight line from C, to reach curve p, P . Forcurve p, P, L+C->»B The curve is reached for x in p, CP ; then for x in p4BP -, C vanishes on the curve and L leaves the curve to travel on the B field. The point P, with the invariant reaction L+C-sB+y , is reached only for x in the quadrangle BCyP . For x in the triangle BCy, the liquid is consumed to leave the three solids, while for x in ByP ., C is consumed and the liquid moves away on curve P-E,, precipitating B and D _, the solid solution ranging from point y at P to s, {Fig. 13.9) at E,. At P _ the equilibrium between C and liquid, shown in isotherm (a), is replaced by the equi- librium between B and D _, shown in isotherm (c), with the D_ composition ranging between limits y’ and y”. The limit y” reaches pure D aof T . and the limit y " reaches s, ot E,. As the temperature begins to fall below P, compositions in the region BDy have already been completely solidified, either as C and D _ (from D to y) or as B, C, and y. of Fig. 13.4 (c) moves to the left, the C vanishes from the three-solid mixtures to leave B and D, and the two-solid (C and D) mixtures first change A 66 Now as the tie line By~ to B, C, and y“ and then lose the C phase to leave B and D_. The lowest temperature for coexistence of C with liquid is P, but C finally vanishes from coexistence with solids B and D_at T, to leave Fig. 13.4 (d). The Invariant PG The relations at P . are similar, except that one of the boundaries of the G field is a curve of even reaction. At P, the decomposition of G involves pure X and H_ solid solution, and the temperature is higher than T _ of Fig. 13.1. The isothermal relations are shown in Fig. 13.5: (4) between e, and P, (b) at P, {c) between P and T, and (d) below T . The reaction on curve p, P is L+X-G ; the curve is reached for x in Xp, P, and crossed for x in Gp, P.. Oncurvee, P, L—>G+H S ’ the solid solution starting as pure H and ending at z [Fig. 13.5 (b)]. The curve is reached for x in P zHG. For x in zHG, the liquid vanishes on the curve to leave G and H_. The point P, for the reaction L+Gasz+X I is reached for x in the quadrangle P . zGX. For x in the triangle zGX, the liquid vanishes to leave the three solids; for x in P =zX, G is consumed, and the liquid travels on curve P _F, precipitating X and H_ solid solution ranging from z to s (Fig. 13.9) ot E;. In the two- and three-solid mixtures containing G, left in region zHX as the temperature falls below P, solid G vanishes to leave simply X and H_, as the tie line z”X of Fig. 13.5 (¢} moves to the side of the diagram, which it reaches at T ., to leave the isotherm of Fig. 13.5 (d). The Invariant PE The invariant P . represents the formation of the binary compound E in the presence of ternary liquid, not from pure solids but from U and D _ solid solution; the temperature of P is therefore g in Fig. 9.1. The pertinent isothermal relations are shown in Fig. 13.6: {(a) between e and T, (b) between T and P, (c) at P, and {d) below P Curve es P with the reaction lower than T 1 L->U+D s is reached for x in the region e, UP . by liquid UNCLASSIFIED ORNL-LR-DWG 25609 Fig. 13.4. precipitating U or for x in De P _d by liquid precipitating D _ solid solution which starts as pure D at e, and ends as 4 at P [Fig. 13.6 (c)]. For x in the region DUd, the liquid vanishes while on the curve between e and P, when the tie line 4’U, moving from DU at e. to dU at P, comes to pass through x, to leave D_and U. At T, however (between es and P in temperature), the tie lines d”'E and d U also begin to enter the diagram [Fig. 13.6 (b)]. When x comes to be swept by the line d”'U, solid E appears in the mixture, and the two-solid mixture of D and U becomes a mixture of D _, E, and U. Moreover, if x is in the region DEd [Fig. 13.6 (c)}, it comes next to be swept by the line d”’E, when solid U vanishes from the mixture, to leave D_and E. Mixtures in the region DUd are therefore com- pletely solidified before L reaches P, and at that temperature, when d°" and 4’ meet to give point d of the invariant quadrangle in Fig. 13.6 (c), and when the region for D_ and U has shrunk to the line dU, the solids present are either D_and E in DEd, or D_ (of composition 4), F, and U in dEU. Liquids traveling on the curve e, P reach P only if x is in the triangle JUP . The reaction at the temperature of P ., however, is D (d)+U-E+L(P,) ; it requires simply the solids d and U, and proceeds whether or not the liquid phase is present. Hence 67 UNCLASSIFIED ORNL~-LR-DWG 25610 Fig. 13 5. those mixtures which had already solidified to E, d, and U now produce liquid of the compesition P . again, in the invariant reaction. The invariant P, is an example of the type of invariant dis- cussed as case (b) under Fig. 4.12. Now for x in the region EUP ., the solid solution d is consumed and L travels away on curve P _ P E 6 along which L+U-»E ; and for x in JEP _, U is consumed and L moves onto curve P o E , for r L-E+D s the solid solution starting at 4 and ending at s 4 (Fig. 13.7). 68 13.2. THE REGION DUH Figure 13.7 gives the schematic arrangement for the reactions involving the invariant points in the upper half of the ternary system, the region DUH. The invariant quadrangle pertaining to P is shown by dashed lines. seen to overlap in various ways. temperature is PE > P6 > P5 > E4. are dEUP , EUIP ,, Elsg P, The invariant planes are The order of The planes and 54554 {for E4). The transition curve P _P for the reaction E" & L+U—>E ' is reached, directly or indirectly, by liquids for x in the region P EUP; but for x in PpEP,, L then leaves the curve when U is consumed, to UNCLASSIFIED ORNL—-LR—-DWG 2561414 ”/ / / /// /) 7 y Z 69 UNCLASSIFIED ORNL-LR-DWG 25642 ~ VI Fig 13 7. travel across the E field. pg P4 for the reaction L +U->1 The transition curve r is reached from the region pgo UP , ond it is left by liquid for x in poIP,. The point P, is reached only for x in P EUI its reaction is L+U-E+1 i and it is the incongruent solidification end point for triangle VI (EUI). At a still lower temperature, solid F of system Y-U forms from the solids F and U, and then we have either E, F, and [ or F, U, and [, The reaction on curve P Pg is odd, L+E-T, if, as assumed in Fig. 13.7, to the right of 1. In this case the curve is reached either from P, (for x in the region PéEI) or directly from the E field for x in P.EP,. But for x in P 1P, the curve is left by the liquid when E is consumed, when the liquid, saturated only with I, moves onto the [ field. Next, the transition curve pgP, is reached, directly or indirectly, for x in the region /P p.. The reaction on this curve is L+I"HS its tangent extends The three-phase triangle for liquid in equilibrium with H_and [ starts as the straight line p4 HI and 70 extends into the diagram to end as P s I. Conse- quently either the liquid or the solid I may be completely consumed while L is on the curve. For x in s.IH, the liquid is consumed when the H _~I leg of the three-phase triangle sweeps through the point x, to leave [ and H_ (between H and ss). For x in the region p, P s, H, solid I is consumed when the L—H_ leg passes through x; this leg starts as the line p °H and sweeps around to become rs, for L at 7, and finally Pgs.. When I has vanlshed L leaves the curve to travel upon the H < field, on a curved path (a straight path only between 7 and m,, but otherwise curving always away from this line). The invariant P_ is reached only for x in the quadrangle P, Els,. Its reaction is I L+I»E+55 and it is the incongruent crystallization end point for triangle V (Els). For x in the region P, Es, down the curve P E precipifo'ring E and solid solution H_, beginning at s. and ending at s The curve P E, is also reached directly, from the E field for x in £, EP, and from the H _ field for x ins.PgE s, Forx m Es’s., the liquid vanishes on f?'ue curve to leave F and a solid solution {be- tween s/ and s_.). The curve P.E, is reached from the E field for x in PLEE,, from P itself for x in dEP (d shown in Fig. 13.6); and from the D_ field for x in dP L E s . Liquid on the curve P o E, precipitates F and D, starting at 4 and ending at s,. Compositions in dEs, solidify com- pletely on the curve to leave E and D _. (It will be recalled that compositions in DEd solidify completely on the curve e P..) The invariant E is also reached along curve m, E,, with the liquid precipitating two mutually saturated solid soiufions ranging from s and sm at m, to s, and s, (cf. "3 Fig. 13.3). From the D side, m E for x in saEgmyi from fhe H_ the liquid moves on is reqched side, directly or The invariant EA' a is therefore reached for x in triangle IV indirectly, for x in my E s,. eutectic, (54 Es‘;). The vertical T vs c section through EH is shown schematically in Fig. 13.8. Solution of composition a, in Fig. 13.7, gives U as first solid, and L reaches curve P,P, ona straight line from U. On the curve, L +U>E The solid U is consumed; L leaves the curve, UNCLASSIFIED ORNL-LR-DWG 25613 Fig. 13.8. travels on a straight line from E, and reaches curve P, P,. On this curve L +E->I The liquid reaches P, where L+I¢E+s5 The compound I is consumed, and the liquid follows curve P » E , precipitating E and a solid solution ranging from s to s ;. At E sy also precipitates, and the liquid vanishes to leave sg E and s /. Liquid b gives U as first solid and reaches curve pg P4 On the curve, L +U->1 The solid U is consumed; L leaves the curve, crosses the I field, and reaches curve pgP.. On this curve L+I—»H$ , the solid solution starting with composition just to the right of s and reaching s; when L is at Pq. Now L+1~>E+55 The compound [ is consumed, and L starts out on curve P, E,, but the liquid is consumed before reaching E,, to leave E and a solid solution be- tween s and sy Liquid c gives U as first solid and reaches curve On the curve L-U+D_, s eSPE' and the liquid vanishes, on the curve, to leave U and a solid solution between D and d, fixed by the straight line Uc. As the temperature continues to fall, solid E forms to give E, U, and D _, the compo- sition of the solid solution moving toward point 4. The D_ solid reaches point d at the temperature of P . Here U+d»E+L(PE) The solid U is consumed, and liquid reappears, therefore, with composition P .. Now the liquid travels along curve P E,, precipitating E and D, with D _ starting at d; but the liquid vanishes while on this curve to leave E and a solid solution between d and s, fixed by the line Ec. Finally, consider a liquid of composition x on the line DH. The first solid is I, and liquid reaches curve pg P, for the reaction L +I1I-H s If x is between r and s, then when L reaches point r, I will just have been consumed, and the solid solution has the composition s_. Now the liquid leaves the curve and travels to m,, where it vanishes to leave the conjugate solid solutions s_ and s But for x between s_ and H, the liquid and I vanish simultaneously, leaving H_ as sole solid phase, before L reaches point r on the curve, when the H _ corner of the L—H —I three- phase triangle passes through point x. 13.3. THE REGION YDHX The lower part of the ternary system is repre- sented in Fig. 13.9. The relations involving the fields of the decomposing solids A, C, and G have already been discussed. The Y, B, and X fields involve pure solids, with straight-line crystal- lization paths radiating from the points Y, B, and X, respectively. The transition curve pg P, was discussed under Fig. 13.7. Liquids reach this curve on straight-line paths from the point I (Fig. 13.7), but for x in the portion of the I field in- cluded in Fig. 13.9, I is completely consumed while L is still on the curve. On leaving the curve, L then travels across the H_ field, on a curved path, to reach one of its boundaries m F, PGE 31 OF e7PG. 71 UNCLASSIFIED ORNL-LR-DWG 256414 Fig. 13.9) The eutectic E, is reached for x in triangle (YBX). The reaction on the curve E\m E, is L—»B-}-X r in both directions. The reaction for curve E,m, E, is L-X+D_, the solid solution ranging from s for L at m,, to s, at E, and to s, at E,. For x in the region 5,54 X, the liquid is consumed on the curve, before reaching a eutectic, to leave X and D {between s, and s3). The point m, is a saddle point, but the section s, m, X is not quasi-binary; the liquid with composition s_ is in equilibrium 2 with a solid solution not of composition s but between D and s . 2 The reaction on curve P _E, is probably of even sign, L-B+D_ , £ along its whole length. The solid D _ for this curve 72 starts as point y (see Fig. 13.4) for L at P _ and ranges to s, for L at E£,. For x in the region CDy, solidification is complete on curve p, P . to leave C and D_; compositions in BCy solidify at P . to leave B, C, and y. As the temperature falls further, C then begins to vanish from these solid mixtures, disappearing completely on the binary side of the system at T .. For x in Bys,, solidification is complete on the curve P.E, to leave B and D . The point E, is reached onfy for x in triangle Il (BS2X). Similarly, compositions in the region zHG solidify completely on curve e, P to leave G and H_, and those in zGX solidify at P . Then as the temperature falls further, G begins to decompose in these solid mixtures, vanishing last on the binary side ai T . liquid vanishes on the curve P E, to leave X and H_. On curve my E,, the liquid precipitates conju- gate solid solutions ending at s, and s;. The point E; is reached for x in triangle Ill (535?: X). The vertical T vs ¢ section BG is shown in Fig. 13.10. to leave G, X, and =z. For x in s/ zX, the j L+B+ X X+0, —¥ UNCLASSIFIED ORNL—LR-DWG 25615 1 : o —-—— TEMPERATURE OF m, e £y ) Fig. 43 .10. Liquid a in Fig. 13.9 gives X as first solid, reaches curve p, P, reaches P . carrying G and X, and there solidifies to G, X, and z. With falling temperature, the composition of the solid solution moves to the right from z, and G vanishes to leave X and a solid solution fixed by the line Xa. Liquid & gives G as first solid, reaches curve e P and solidifies on this curve to leave G and a solid solution z” [Fig. 13.5 (c)] between z and H. Then as the temperature falls further and z~ moves to the right, X appears as third solid when the line Gz’ passes through &, and finally G vanishes when the line Xz’ passes through &. Liquid ¢ gives C as first solid, reaches curve py P, leaves this curve when C is consumed, reaches curve e, P, on the left of v, and begins to precipitate A _together with B. At v, A changes to A, At P, Afi decomposes, and the liquid travefia on curve P, » E, to solidify at E, to Y, B, and X. 13.4. FRACTIONATION PROCESS ON THE SOLID SOLUTION FIELDS In a fractionation process, L follows one of the fractionation paths to a boundary of the field; the solid increases in H on the D _ field and increases in D on the H_ field. The fractionation end point is E, above the line DH. Liquids starting in the region between e, and the path DP . end as four solids, D, U, E, and H_, but all others starting in the solid solution fields above line DH end as DS, E, and H _. Below the line DH the fractionation process for the H_ field ends at E, leaving H_, X, and D 73 the same holds for the D _ field above the path Dm,. The rest of the D_ field is divided by the fractionation path Dg of Fig. 13.11; ¢ is the intersection of p, P with line Ct, and ¢ is the intersection of curve p, P . with line Bm,. Liquid in the region between p, and the path Dg reaches curve p, 4. Without stopping on the curve, L crosses it and traverses the C field in a straight line from C to reach curve p,i. Without stopping on this curve, L crosses it and traverses the B field to one of its boundaries, e, P ,, P, E,, and m,E,. The process ends at E, to leave D, B, Y, and X, since solids C and A will have de- composed. The fractionation end point for the D _ field between the paths Dg and Dm, is E,, the final solids being D_, B, and X. For the region between the paths Dg and DP ., the precipitation of the solid solution is interrupted while I. crosses the C field and then the B field between curve tP . and curve m E,, finally reaching E,, where D_ begins to precipitate again with the composition s,. Consequently, there is then a gap in the composition of the D_ solid solution finally ob- tained. UNCLASSIFIED ORNL-LR-DWG 25616 Fig. 13 .11, 74 14. SYSTEM Y-U-Z: NoF_-UF,_Z(F, For the ternary system Y-U-Z, the binary system Y-—U appears in Fig. 9.1, and it is here used with the same lettering. The Y—Z binary diagram was given in Fig. 11.1, but it is redrawn here (Fig. 14.1) to show the different lettering necessary in the preseni section. The system U-—Z is given in Fig. 14.2. 14.1. GENERAL CHARACTERISTICS The phase diagram of the ternary system is given schematically in Fig. 14.3. The principal feature in this system is the existence of three continuous series of solid solutions: that between the components U and Z, with @ minimum at m’, that between the congruently melting corresponding 7:6 compounds D and K, aond that between the congruently melting corre- sponding 3:] compounds A and G. For brevity these solid solutions will be called U_, D_, and A, respectively. The primary phase fields for these solid solutions are the three largest fields of the diagram. Moreover, each of the sections AG and DK constitutes a quasi-binary section of the system (Figs. 14.4 and 14.5). At least as far as the equilibria involving the liquidus are concerned, therefore, the system as a whole may be divided into three independent subsystems, Y-A-G, A=-De-K-G, and D-lU..Z-.K, whick will thus be considered separately. In the subsystem Y—~A—G, with only two fields (pure Y and A ), there is only one boundary curve (66 » e,), and the temperature on this curve falls in the same direction as for the quasi-binary section G » A itself, In the subsystem D-U~-Z-K the liquidus pertains almost entirely to the primary fields for two continuous (effectively binary) solid solutions. The boundary curve is slightly compli- cated by the field for compound M, but it has no minimum of temperature. The temperature of the boundary curve falls continvously from the YU to the YZ side, as in the section DK itself, despite the minimum m” in the U~Z system. The middle subsystem, however, is unusual in having opposite directions of falling temperature in its bounding quasi-binary solid solution systems, D » K and A « G. No ““normal’’ behavior can be predicted for the boundary curve between the solid solution fields. This boundary curve is complicated by the minor fields of the four other solids of this sub- system, but essentially it falls in temperature from the AD to the GK side, with a slight maximum m near point e.. The A—G and DK solid solutions, moreover (as shown in exaggerated form in Fig. 14.6), are actually ternary in composition on the YZ side. They occupy small areas of ternary composition near points G and K, respectively, not lying simply on the straight lines AG and DK. This is so because the compounds G and K form solid solutions in the Y—Z system itself, besides forming the continuous solid solutions with the analogous compounds of the Y—U system, The only invariant points (for liquid in equilibrium with three solids) in the entire system are five peritectic points. There is no eutectic, nor is there a minimum on any curve of liquid in equi- librium with two solids. The vertical T vs ¢ section of the system from the corner Y to a point midway between U and 7 is merely a section passing successively through the three adjacent but independent subsystems (Fig. 14.6). Details of this diagram will be mentioned later. 14.2. SUBSYSTEM Y_A_G The relations in the subsystem Y-~A—G (Figs. 14.7 and 14.8) are similar to those discussed under Figs. 6.1 to 6.4, but simpler, since there is here no minimum either in the binary edge AG or in the boundary curve e, ey All mixtures in the system solidify to two solids, Y oend A_. The reaction on the curve (2]66 IS LY+ A s t and the three-phase triangle, starting as the line Ye G, moves, with the configuration shown in Fig. 14.7, across the diagram to end as the line Ye A. All liquids reach the boundary curve, and they are completely solidified on that curve when the total composition x is swept by the leg YA of the three-phase triangle. Liquid « (Fig. 14.7) gives Y as first solid and reaches the curve on a straight line from Y. On the curve, the liquid precipitates Y and a solid solution starting with composition s;. The liquid vanishes on the curve, while moving toward e, when the solid solution reaches a composition on the extension of the straight line Ya. Liquid & precipitates a solid solution beginning between G and s,. The liquid reaches the curve on a curved equilibrium path 75 UNCLASSIFIED ORNL-LR-DWG 25617 214 (1.4} M K 14 1. Fig. 14.2. Fig. 76 UNCLASSIFIED ORNL-LR-DWG 25618 ™N 77 UNCLASSIFIED ORNL-LR-DWG 25619 , G A.S‘ G Fig. 14 .4. Fig.14.5. L ,’ L+ U, v/ | Os+L | ' | L+ A J \ \ : Y+ L+A, \ll ' L+ D : De+ L+ Ug | | ;|A5+L | ) | PN A | N ¥+ A | | N | A5+ D f | I ,; Fig. 14 .6. Fig.14.7. (as discussed in Sec 6) convex with respect to point A, When it reaches the curve, the liquid is at I, and the solid at s;. Now Y begins to pre- cipitate with the solid solution; the liquid moves toward e, and vanishes when the solid solution reaches a composifion on the extension of line Y&, The vertical T vs ¢ section (first third of Fig. 14.6) is similar to Fig. 6.3; but in the present case the area for liquid in equilibrium with Y and A_ collapses to a line only at e, and at ¢,, since there is no minimum in the boundary curve. Crystallization paths in the Y field are straight lines from Y. Fractionation paths in the A_ field are a family of curves originating at G, diverging from the line G » A, convex with respect to A, and each ending at the boundary curve (Fig. 14.8). 4.3, SUBSYSTEM A_D_K-G The two large fields in the subsystem A-D—K—-G (Fig. 14.9) pertain to solid solutions A_and D_. Part of the A_ field is in the subsystem Y-A-G already discussed, and part of the D_ tield is in the subsystem D—-U—-Z—K, The line G » A is simply the line of maximum temperature running from G to A, and it is the limiting fractionation path of the field dividing the curved paths of the two subsystems. The line D » K is a similar UNCLASSIFIED ORNL-LR-DWG 25620 Fig.14.8. UNCLASSIFIED ORNL-LR-DWG 25621 79 limiting straight-line fractionation path running from the melting point of D to the melting point of K, and dividing the curved families of fractionation paths of the two fractionation paths in the A_ field (on either side of the line AG - i.e., both in Fig. 14.8 and in Fig. 14.9) are convex with respect to point A, and those in the D_ field are convex with respect to point K. The tangents for the two fractionation curves meeting from two sides at the curve PP, must be such that the three-phase triangle for this curve points toward P, (direction of falling temperature), as shown for point 2 in Fig. 14.9. The vertical T vs ¢ section across the curve P,P, is shown as the middle part of Fig. 14.6. There is theoretically a single-phase ternary solid solution band reaching very slightly into the section both from the AG line and from the DK line; the dimensions are exaggerated in order to show the schematic relations. The region “A_ + adjacent subsystems. The L + D" is a cut through the space generated by the moving three-phase triangles of curve PP .. The coexisting phases are not on the plane of the diagram. The order of temperature for the three corners of this cut (L. > A_ > D) results from the fact that the section involved, from Y to the 1:1 ratio on the UZ side, is reached, with falling temperature, first by’the L corner of the three-phase triangle, next by the A_ corner, and last by the D_ corner, according to the configuration of the triangle drawn on Fig. 14.9. The solid H_ of system Y~Z forms some binary solid solution on the side of compound /, and hence the fractionation paths in the H_field are curved and are convex with respect to K. The common origin of these paths, extended back, is the metastable congruent melting point of H_ in the Y—Z binary system. The fransition from H_solid solution to pure H,, all occurring below liquidus temperature, will be discussed later. The compound ¢, as will be explained shortly, also forms solid solution with composition extending into the diagram toward the GK side; hence the paths on the C field are also curved, are convex with respect to K, and originate by extension from the point C. Only the solids B and ! are pure, in Fig. 14.9. The 1 field is divided into three portions, by isothermal creases at the temperatures f, and ¢ of Fig. 14.1; the portions represent, with falling temperature, liquid in equilibrium with [, liquid in equilibrium with 1., and liquid in equilibrium with I_ . The t, transition, to I, occurs at a [ow temperature and does not affect the liquidus surfaces. 80 The crosshatched lines in Fig. 14.9 indicate where the solid solution compositions are found. The Region Involving A, B, C, and D With regard to the evidence for solid solution formation by compound C, we note that this incongruently melting 5:3 compound decomposes on cooling, at T -(630°), into the pure solids B and D in the binary system Y—-U, But its primary phase field in the ternary system Y-U~—Z extends down to the temperature of P_ (610°). Since D is known to form solid solution with K in the ternary system, the decomposition temperature of C is expected to be raised in the ternary system unless the solid phase C itself forms a solid solution third This solid solution, which the compound C must therefore form, may be imagined as involving the hypothetical corresponding 5:3 compound in the Y—Z system, so that the composition of the solid phase to be called C_ (solid solution of 5:3 compounds originating at point C) probably extends on a line into the diagram paralle! to the edges AG and DK, Morecever, the point P, may either represent the lowest temperature of existence of this solid phase containing the component, in the ternary system; or it may represent simply the lowest temperature for its equilibrium with ternary liquid, while the lowest temperature for its may be still (in subsolidus In absence of the information required existence lower relations). for deciding between these alternatives, we shall consider both relations for this region of the system, referring to the first as Scheme | and to the second as Scheme |l. Scheme |. ~ The point P, is here assumed to be the lowest temperature of existence of the C_ solid solution, with the third compenent, in other lowering the decomposition temperature of C. The schematic relations for the invariant four-phase planes would be as shown in Fig. 14.10. There are three such planes. The highest-temperature plane is the quadrangle for P], involving B, C,, Ay, and L(P,); the next, in dashed lines, which will be referred to as the invariant Q_, is a quadrangle involving B, A,, D, and C,; the lowest is the triangle for P,, for the phases A,, D,, L(P,), and C, as the interior words, continually phase. The order of decreasing temperature for the fixed points involved is assumed to be: py>bg>m>e, > P >T>0,>P, . A series of isotherms relating these points is in Fig. 14.11: (a) between P4 and pg; given UNCLASSIFIED ORNL-LR-DWG 25622 Fig. 14 .10, (b) between P, and m; (c) between m and e,; (d) at P.i (e) between P, and T; (f) between T - and O, (g) at Q. () between Q_ and P,; (i) at P,; (j) below P,. The reactions on the curves (of liquid in equi- librium with two solids) and at the invariants are as follows: 1. Dy L +D_» C_. The three-phase triangle, triangle 1 in Fig. 14.11(a), starts as the line ?,CD and ends as P,C,D,. This curve is reached by liquids from the region p,DD,P,, precipitating D_. But for original, total compo- sition x in the region CDD,C,, the liquid vanishes while traveling on the curve, before reaching P, to leave C_ and D_ when the C _—D_ leg of the three-phase triangle comes to pass through =x. (The appearance and disappearance of phases to be considered in this section will most easily be visualized through the sequence of isotherms in Fig. 14.11. The disappearance of the liquid phase is not necessarily the end of the phase changes.) For x in the region p,CC,P,, the D - P2: phase vanishes while L is still on the curve, when the L—C_ leg of the triangle passes through x. Then the liquid, saturated only with C_, traverses the C_ field to reach one of its other boundaries, p,P, or P,P,. 2 py » Pyt L+ Cg » B. The three-phase triangle, [triangle 2 in Fig. 14.11(b}], starts as line p,BC and ends as P BC,. The curve is reached for x in p,CC,P,, by liquid precipitating C,e For x in BCC,, the liquid vanishes on the curve to leave B and C_ when the leg B—C| passes through x; for x in p,BP,, C_ vanishes on the curve when the L—B leg passes through x, and then L traverses the B field. 3. m>e,: LB+ A,. Point mis the temper- ature maximum on the curve e,P,. For this o the three-phase triangle starts as the line A _mB and ends as Ae,B [triangle 3° in Fig. 14.11(c)]. The curve is reached from the B field for x in me,B or from the A_ field for x in AezmAm. reaching e,, to leave B and A, (between A and A ) on a line passing through x. 4. m>F.: L+ B+ A, The three-phase triangle [triangle 3 in Fig. 14.11(c) ] starts again as the line A_mB ond ends as A BP,. The curve is reached from the B field, by liquid precipitating B, for x in mBP ; and it is reached from the Ag field by liquid precipitating A_, for x in A mP,A,. Now if x is in AjA B, the liquid vanishes on the curve to leave B and A_ (between A, and A,) on a line passing through x, Invariant P : The triangles 2 and 3 are seen, in Fig. 14.11{c), to be separated by a region in which B is in equilibrium with liquid. This equilibrium shrinks to a line at P], in the invariant reaction section, m -» ¢ The liquid always vanishes before LPY+B=»A, +C, , and it is replaced by the equilibrium between A and C, which now separates two new three- phase triangles [4 and 5 in Fig. 14.11(e)] for B, C., and A_ and for liquid, A, and C_. Point P, represents a type B diagonal invariant reaction, the triangles 2 and 3 being replaced by 4 and 5. The point P, is reached for x in the quadrangle AyBC,P,. For x in A{BCy, the liquid is consumed in the reaction to leave A,, B, and C, (triangle 4); for x in A,C,P,, the solid B is consumed, and L travels on the curve P, » P, representing the traveling of triangle 5 (L--A_~C ). 5, P, » Pyr L » A, + C,o The three-phase triangle (friangle 5) starts, as just explained, as 81 UNCLASSIFIED ORNL-LR-OWG 25623 5.:\_\4 5 ’ ° 2 W } Fig 1414 (part 1) A C P, and ends as A,C,P,. This curve is Fig. 14.11(f), to separate triangles 4 and 6] reached from the C_ field for x in P,C,C,P,, and from the A_ field for x in AP\ P,A,. For xin A[C,C,4A,, the liquid vanishes on the curve to leave A_ ond C_ when the A —C_ leg of the triangle passes through x. Between the temperatures of P, and P,, however, at T (the decomposition temperature of C in the binary system) the equilibrium between B, C_, and D_ appears as a three-phase triangle [triangle 6 in Fig. 14.11(f)]1. It starts as the line BCD at T and ends as the triangle BC,D, at the invariant temperature O . The invariant O involves four solid phases (three of them variable) in another quadrangular or diagonal invariant reaction of type B. As the Q temperature is approached, equilibrium between B and C_ [which is seen, in z the region for the 82 shrinks to a line, the two triangles come into contact, and we have the reaction B+Cz"Az+Dz . The equilibrium between B and C_ is replaced by one between A_ and D_, now separating the two new triangles originating at Q_ : triangles 7 and 8 of Fig. 14.11(), for B, A,, and D, and for A_, D, and C_. In all the three-phase triangles of Fig. 14.11, the corners representing variable phases (C_, A, D_, L) move continually to the right with falling temperature. Triangle 7, however, will be assumed to remain constant with further decrease of temper- ature; at any rate it will not be involved in any more of the phase changes now under discussion. UNCLASSIFIED ORNL-LR-DWG 25624 Fig. 14 11 (part 2) The invariant reaction Q_ will occur for x in the quadrangle BD,C,A,, leaving B, D,, and A, for x in triangle BD_A_, and otherwise A_, D, and C_, as triangle 8, which continues to move to the right. Finally, the three remaining moving triangles, 1, 5, and 8, come together at P,. The range of existence of the C_ solid phase, in other words, here shrinks to a point, C,e The invariant P,, then, is of type A, triangular, with C, as interior phase; it is terminal for the phase C_. It is an example of the case c¢ invariant discussed under Fig. 4.11. It may be said to be the decomposition point, on cooling, for the C_ solid solution in the ternary system. The reaction is Cy,» D,y + Ay + L(P,) whereupon the liquid then travels down the curve P, » P, with its three-phase triangle 9 [Fig. 14.11(j)f. Some of the relations may be shown, in different fashion, in the T vs c vertical section of Fig. 14.12, between C in system Y-U and the 5:3 ratio in system Y—Z. This section cuts triangles 1, 6, 7, 8, and 9 of the foregoing discussion. The sequence of phase changes upon cooling, for complete equilibrium, starting with a liquid of specified composition in Fig. 14.10 may be followed 83 UNCLASSIFIED ORNL-LR-DWG 25625 with the aid of Fig. 14.11. The fixed composition point x will fall successively in the various two- phase regions (tie line areas) and three-phase triangles (numbered and explained above) as these move through the point with falling temperature. A few particular compositions will be considered, for illustration. Point a (Fig. 14.10): The first solid on cooling is A_, starting between A, and A,. The liquid reaches curve P]P2 and precipitates A and C_ (C, starting between C, and C,). The liquid vanishes before reaching P,, leaving A and C_ on a line through point @. Point 4, in other words, finds itself in the two-solid region between triangles 8 and 5 of Fig. 14.11(h). With further 84 =53 IN Y/ Fig. 14 12 cooling, this region moves to the right, and point a enters triangle 8, with three solids, A, C_, and D_. The solid C_ thus decomposes into 4 and D_ on cooling, and the residual C approaches C, in composition. When the temperature reaches le liquid reappears, in the invariant reaction: C, ~calories » L(P,) + 4, + D, [ This reaction is case (c) of Sec 4, Fig. 4.11, but now with solids of variable composition.] When all C, is consumed, the liquid starts out on curve P,P,, vanishing to leave A and D on a line through point a. Point 6: The first solid is D_, between D and D,. The liquid reaches curve p,P,. Here ’ L+DS—>CS Cs starting between C and C,. The liquid is consumed on the curve, leaving C_ and D, on a line through 5. Point b now comes to be in the region for C_ and D_, between triangles 6 and 1. When triangle 6 reaches b, B appears as a solid phase. Thenat O, B+C,»A_+D, , B is consumed, and b ends as A_ and D, in the region between triangles 7 and 8 [Fig. 14.11(%)1. Point ¢c: As in the case of point b, the liquid reaches curve p,FP, and vanishes to leave C_ and D_. But below T, C begins to decompose; point ¢ comes to be in triangle 6, and finally into the area for B in equilibrium with D_ as triangle 6 moves on. Point d: The first solid is C_, between C and C,. The liquid reaches curve p3P], where L+CS—;B . At P,, A, appears, and L+B->A, +C, . The liquid is consumed, and point 4 finds itself in triangle 4. Next, A_ vanishes, leaving B and C. Then D_ appears, and point d enters triangle 6. At o =~ o B+C_ A _+D, , leaving B, A_, and D, d being in triangle 7. Point e: The first solid is B, and L reaches curve mP,, where L—>B+AS ! the solid solution being between A~ and A,. At P, L+B-A,+Cy, the liquid is consumed, and point e is now in triangle 4. As this triangle moves on, however, the C_ phase vanishes, to leave B and A, on a line through point e. Point f: The first solid is C_, L reaches curve p4P 1, Cs is consumed on the curve, and L traverses the B field to reach curve mP,. At P, L+B~ A, +C, , B is consumed, and the liquid travels on curve PP, precipitating A_ and C_ (triangle 5). The liquid vanishes, however, to leave A_ and C, between triangles 4 and 5, and point f next comes to be in triangle 4, as B, A_, and C_.. Then at Q_, st B+Cz—>Az+Dz / leaving the solids of triangle 7. Scheme ll. — The point P, is here assumed not to be the lowest temperature of existence of the Cs solid solution (with composition C,). The C, phase is assumed to vanish, on cooling, at some intermediate composition (C_, between C and Co) at a still lower temperature, that of a four-solid invariant to be called O_, The relations would be those shown schematically in Fig. 14.13. The highest-temperature invariant plane is again the P, quadrangle, assumed to be identical with that in Scheme | (Fig. 14.10). Next is the P, plane, now a quadrangle, an example of the case (d) invariant discussed under Fig. 4.10. Below these is the triangular plane of the O invariant reaction, terminal for Cy, the interior phase. We now have the temperature order: Py>Te>Py>0, The first six isotherms of Fig. 14.11 apply to Scheme It as they are. The subsequent isotherms are given in Fig. 14.14, and to preserve continuity these will be lettered as follows: (g) at P,, (h) be- tween P, and Q , (i) at Q,, (7) below Oy Excepf for ’rge pOSIfIOjl:IS of the composmons Ay, C, and Dy, involved at P, the crystallization processes on the liquidus surfaces and on the curves of twofold saturation are the same in both schemes. The schemes differ only in the reactions of the solid phases left after complete solidi- fication. Triangles 1-6 originate as in Scheme |, and they again move to the right with falling temperature. The relations in the isotherm (f) (which is between and P, in Scheme Il and between T . and O, in Scheme 1) are topologically the same for both schemes. This is now followed by isotherm (g), at P,. The triangles 1 and 5, separated in (f) by the equilibrium between C_ and liquid, here come into contact, in the reaction L(1‘)2)4-C2~>142+D2 , giving rise to the equilibrium between A_and D, separating the two new triangles 8" and 9% These involve the same phases as the triangles of the same number in Scheme |, but the compositions are different. Also, while triangle 97, like triangle 9 85 UNCLASSIFIED ORNL-LR-DWG 25626 D Fig. 14 .13. in Scheme |, now continues to move to the right as the liquid travels on the curve P,P, precipitating Ao and D, the triangle 8 begins to move to the feft with falling temperature. Eventually it makes contact with triangles 6 and 4, in the O reaction, in the arrangement shown in Fig. 14.14(:). The ternary C solid solution, the interior phase of the triangular, type A invariant reaction, simply decomposes into the solids B, A and D, leaving triangle 77 which corresponds to ftriangle 7 of Scheme . invariant The vertical T vs ¢ section through C and the 5:3 ratio inthe system Y—Z is shown in Fig. 14.15, which is to be compared with Fig. 14.13. In both cases there are two solid-state decomposition reactions for C.: CS_’B+DS 86 and CS-+A5+DS . In Scheme |, the decomposition into B and D_ extends from the binary temperature T . to the invariant Q_, and the decomposition into A_ and D, falls in temperature from Q, to the invariant P,. In Scheme li, the decomposition into B and D falls in temperature from T to Qe and the decomposition into A and D, rises in temperature from Qy to P,. Point a (Fig. 14.13): The first solid is D_. The liquid reaches curve p 4P, where L+DS—>C5 (triangle 1), and the liquid vanishes on the curve to leave C_ and D_. Below T, the point a is reached by triangle 6 (for B, C_, and D), and finally remains as B and D_ when it is left behind by triangle 6. Point b: The first solid is C_. reaches curve p4P,, where The liquid L +C$ > B (triangle 2). At P, L +B-> A] + Cy The compound B is consumed, and the liquid moves on curve P P, precipitating A, and C_ (triangle 5). The liquid vanishes on the curve to leave A_ and C_, and point & is next reached by triangle 4 (for B, C_, and D). At Qy, the C. phase decomposes to leave B, Ay, and D, (triangle 7). The liguid Point ¢: The first solid is D_. reaches curve D 4F o, where [+ DS > CS (friangle 1). At P, The liquid is consumed, and point ¢ is left in triangle 8" (for A_, C_, and D ). But this triangle moves to the left with falling temperature, and before the temperature of O is reached, C_ will have vanished to leave A and D_. Point d: The first solid is C,+ The liquid reaches curve P, P, where L » A_ + C_ (triangle 5). The liquid vanishes on the curve to leave A_ and (g) (A} ‘ frbyra—~—L+¢+ N \‘ ‘ \6,2: T LN C.. But point d is next reached by triangle 87 from the right, to give A, C_, and D_. At Q, the C_ phase decomposes to leave the three solids of triangle 77 (B, Ay, and Dy). The Region Involving G, H, I, and K The lower part of the subsystem A-D-K-G is shown in Fig. 14,16, Liquids on curve P, P, precipitate the solid solutions A_ and D, solidi- fying completely, while on the curve, for x above the line A;D, (joining the solid solution compo- sitions for liquid at P;). (We continue here to call the A~G solid solution A_ and the D—K solid solution D_, even down to the limits G and K.) As the composition of G is approached, the A_ solid solution is shown as occupying an area in composition, since G also forms solid solution in the binary system Y—Z, varying from G to the composition G, at the temperature of p,. The same situation holds at K, which forms solid UNCLASSIFIED ORNL-LR-DWG 25627 Fig. 44 44, solution in the binary system Y—Z, extending from K to the limit Ko at the temperature of €ge For the curve p 3+ Which is reached for x in the region p.G the reaction is 733’ L+ASH’HG. The solid solution starts at G, for L at p, and ends at A, for L at P;. The three-phase triangle starts as The line G Hp7 and ends as A HP,. Hence liquid on the curve is completely solidified, leaving H, and A, (between G, and A,), for x in HG,A;. For x in the area of the ternary solid solution, ss, solidification is complete with L still on the A_ surface, before any curve is reached. The curve p,P 4, moreover, is crossed for x in HP3p7, when, after the A_ phase has been consumed, the liquid leaves ’rhe curve to travel across the H field, but now precipitating not pure H, but the H_solid solution ranging from H to H,. <0 ~ UNCLASSIFIED ORNL-LR-DWG 25628 As+Cot D¢ L+A+D, The point P, is reached for x in the region HA,D,P,, by way of either curve P,P, or curve p4P,. Liquids with x in the triangle A;D,H then solidify completely in the reaction L(P3)+A3~»HG+D3 , while the others travel down the curve P, » P, precipitating two solid solutions, one of H (H to H,) and one of D, (D to D,). Complete solidification is therefore effected on this curve for x in HD,D ,H,. The curve is reached from the H, field for x in HP,P ,H, and from the D_ field for - 3474 xin 3D3D41'34. On the transition curve p P, L+HCI_-’IG . 88 —w53INYZ Fig. 14.15. The H, solid solution in equilibrium along this curve is, strictly, variable in composition, starting just to the right of H, at p. and ending at H,. (Since P, is below pg in temperature, the compo- sition of H, must be just to the left of that for the binary peritectic po of Fig. 14.1.) Since the variation is probably very slight, we have here assumed this solid to be constant at H, for the whole curve. This curve is reached for x in HyP,pg and it is crossed for x in IPpg. The point P, is thus reached, either from curve PP, or from curve p P, for x in the quadrangle H,D P I. The reaction is L(P)+H,»1,+D, , so that liquidus for x in the triangle H,D,I here UNCLASSIFIED ORNL-LR-DWG 25629 Fig. 14.16. solidify completely. The rest move on down the curve P e,, precipitating [ and D_ (between D, and Kg); the form of the compound I deposited will be I down to temperature t,, then I 5 to temperature ty and I, to the temperature e,. All liquids reaching curve F e solidify completely betfore reaching €,. The curve is reached from the I field for x in IP ey and from the D_ field for x in P,D4Kgege Liguids with x in the ss area near K solidify completely while L is still on the D_ surface. For composition a in Fig. 14.16 the first solid to form on cooling is D_. The liquid reaches curve P, where L+AS+DS . L+A3->H+D3 I A3 is consumed, and L starts out on curve PP, on this curve the liquid vanishes, to leave H and D solid solutions on a line through point a. Point &: The first solid is D_. The liquid reaches curve P.P , where it precipitates a solid solution between H and H, and a solid solution between Dy and D,. At Py L+H, 14D, , leaving the three solids H,, 1, and D,. The first solid is H, to the left of H ). The liquid reaches curve p P, Point c: (strictly slightly where L+H4~>]a. The solid H, is consumed, and L crosses the [ field to curve P Here 469. L41+DS ! and the liquid vanishes to leave Iand D_on a line through point c; the polymorphic form of I depends simply on the temperature. Point d: The first solid is A, between G, and A, . The liquid reaches curve p,P,, where L+AS—»Ha . The solid A_ is consumed; L leaves the curve, crosses the H field, and reaches curve PP, Here L->H +D_ . At P,, L+H4H;.'Q+D4 ; H, is consumed; the liquid starts out on curve P eq, and vanishes to leave I and D_ on a line through point 4. Fractionation Processes in the Subsystem A-D-K_G The phase changes so far discussed have been those for crystallization with complete equilibrium. We shall now consider crystallization with perfect fractionation, as explained in Sec 6, simply for the two principal solid solution fields of Fig. 14.9. In a fractionation process, the liquid on a surface follows a single fractionation path (as sketched in Fig. 14.9). These paths are here curves in every case except for the B and I fields, where they are straight lines radiating, by extension, from points B and I, respectively. When the liquid, following such a fractionation path, whether curved or straight, reaches a boundary curve of even reaction (one on which the liquid precipitates two solids on cooling), the liquid travels along this curve. But if it reaches a curve of odd reaction (transition curve), it immediately crosses the curve and begins to travel along a fractionation path — curved or straight — on the next fieid. (See Sec 4-D for the behavior at invariant points.) In the fractionation process, the outermost layer of solid solution being deposited by liquid on the 89 D_ field continually increases in K content. It continues to change in the same direction, moreover, whichever of the four boundary curves is reached, while L travels on the boundary curve. But the boundary curve p,F, is a transition curve; L does not travel on it but immediately crosses it, Hence the ultimate mixture of solids (non- equilibrium mixture) produced by liquid in a fractionation process varies according to the various regions into which the D_ surface may be divided. There is first a very narrow region, close to the p 4D side, from which L will cross the curve p,P,, traverse the C_ field, cross the curve P3P traverse the B field, and reach curve m -» e.. The final mixture of solids obtained therefore contains D, C_, B, and A (although C_ may have decomposed on cooling). Next to this region there is one from which L will traverse the same curves and fields but end on the boundary m » P of the B field. The liquid then follows boundary curves all the way to e, to leave a mixture of all six solids of the subsystem: D,, C,, B, A;, H_ solid solution, and 1. The next region will send L to curve P P,, missing the B field, and now solid B will be missing in the final five-solid mixture, except as formed by decomposition of C_ For these two regions the composition of the D_ solid solution finally obtained will have a discontinuity (a gap), since precipitation of D_ is interrupted between the point when L reaches and crosses the curve p P, and the point when it reaches P, along curve PP, (as explained also in Sec 7.3). The next region, between the fractionation paths DP, and DP,, will miss the C_ field entirely and end as four solids: D_, A_, H, and I. The region between paths DP3 and DP, will give only D, H, and I, and that between the path DP, and the corner K only D_ and I. On the A_ field the outermost layer of solid solution continually increases in A content while L is still on the surface. For the region between A and the fractionation path Gm, the solid deposited continues to in A content while L moves on the curve m > e,, ending as a mixture of B and A_. For the region between the paths Gm and GP, the depositing solid reverses its direction (of composition change) and moves toward G as L travels on the boundary curves m > P, » P, > P, The liquid then follows the increase 90 curves Py » P, 5 ey, and finally leaves a mixture of all six solids of the subsystem (counting C_, which, however, may have decomposed). For the region between Py and the path GP,, L crosses the curve p P, but ultimately reaches either P,P, or P,eq, to approach, in either case, eg as the fimit of the process; the final mixture consists of A, H_ solid solution, I, and D_. Subsolidus Reactions Involving Compounds A, H, and J The two- and three-solid regions left on complete solidification in the two subsystems so far con- sidered, below the temperatures of all the phase reactions discussed, are shown in Fig. 14.17. There are also two single-phase regions ss near points G and K. At T, (Fig. 9.1), the compound A of the system Y—U (atter changing from A_to A, at T”) decom- poses on cooling into Y and B. £cau5e A forms ternary solid solution (A_, with G), the decompo- sition temperature is lowered in the ternary system. This decompesition involves changes in the upper part of Fig. 14.17, and the pertinent isotherms are shown in Fig. 14.18: (&) just below T ,; (b) at a four-solid invariant of type B, where B+S]4Y+52_ on cooling; and (c) below this invariant. UNCLASSIFIED ORNt - LR-DWG 25630 o * E'TDS fecva.+ B4 A Ly ~ 4 e ) /45 +D§ Hylssi+ D, / Y+ A Ach Dot Hy = o (55)\ i - ),-;ss\: Ye oM . . . i G #H / Holss)+ 0.+ / At Hy O 5 Fig. 1417 UNCLASSIFIED ORNL- LR-DWG 25634 0 D 45 Fig 4418 At T’ (Fig. 14.1), H_ undergoes transition to H 5, which is a pure solid instead of a binary solid solution, and the binary transition temperature is lowered to T". Since the solid solution is not ternary, these temperatures are not changed in the ternary system. Figure 14.19 shows the ac- companying changes in the solid phase combi- nations: (a) above T’ (b) between T’ and T”, (c) below T". At T, (Fig. 14.1), the compound ] of system Y—Z appears on cooling, forming from I and K, (the binary solid solution composition for K at the temperature of T.,). Because K forms ternary solid solution (D, with D), the formation temper- ature is lowered in the ternary system. The changes affecting Fig. 14.17 are shown in the isotherms of Fig. 14.20: (a) just at T,, where the point | appears as pure | in equilibrium with I and K].; and (b) below Ty With decreasing temperature the three-phase equilibrium of I + | + D_ moves into the diagram as the triangle IJK". The two- phase equilibrium between ] and K, (Fig. 14.1) becomes the two-phase tie-line bancf Jo + D_ of Fig. 14.20(6), with tie lines running from the binary solid J—]” to the ternary solid K" —K" The solids | and K’ vary with temperature ac- cording to the miscibility gap in the J—K solid solutions shown in Fig. 14.1. 14.4. SUBSYSTEM D..U-.Z_.K Equilibrium Crystallization Along Curves The relations for complete equilibrium solidi- fication in the subsystem D—-U—Z—~K are shown, schematically, in Fig. 14.21, and Fig. 14.22 shows approximate temperature contours for this region. There are three primary phase fields: one for the D~K solid solution D_, one for the U-Z solid solution U_, and one for the incongruently melting, pure compound M. The reaction on the curve eP. is L » D, + Ug, the three-phase triangle starting as the line De U and ending as the triangle DgP Uc. This curve is reached from the D_ field for total composition x in the region De P D, and from the U field for x in e UU,P.. Solidification is complete on the curve for x in DUUSDS' The third part of Fig. 14.6 shows the vertical T vs c¢ section through this part of the system. It is similar to the middle part of Fig. 14.6 except that the solid solutions are strictly on vertical lines, D_ being on a vertical line through DK and U_ on a vertical line through UZ, On the curve p1Ps from py, to t, the reaction is one of transition, L+US—’M I with U_ ranging from pure Z at p,, to U, at t. For the section of the curve from ! to P, the reaction is even: L—>M+US (ranging from U, to Ug). The three-phase triangle L-M-U_ starts as the line p, MZ ond ends as P .MU, The sign of the reaction changes at point t, where the L—M leg of the triangle is tangent to the curve. The odd-reaction section of the curve, p,.¢, is reached only from the U_ field, for x in the region ?11tU,Z, by liquids precipitating U as primary crystallization product. Then if x is in the region p11tM, U, is consumed while L is traveling on the curve, between p,, and #, and the liquid leaves the curve to traverse the M field, on a straight line from M. Compositions for x in p, ,yM (y being on the line P_M) then reach the curve P.e , while those for x in ytM reach the curve (P, where U, 91 UNCLASSIFIED ORNL—-LR—-DWG 25632 Fig. 14 .49. now richer in U, appears again as a secondary crystallization product mixed with M. The even portion of the curve, tPS, is reached from either side: from the U_ field directly for x in the region 1P U.U, and from the M field for x in MP ¢z, either directly or after the crossing of the yt curve. Liquids for x in the region MU.Z solidify completely while traveling on this curve, somewhere between p., and P, when x comes to be swept by the M—U_ leg of the three-phase triangle. The point P is therefore reached only for x in the quadrangle D U MP, and, with the reaction L+U5->D5+M , 92 it is the incongruent crystallization end point for x in the triangle DgUgM, to leave the three solids D¢, Ug, and M. For xin P.D M, Ug is consumed, and L travels down the curve P e, to solidify completely, before reaching e, into M and D_ solid solution between D, and K. The curve Pe, o along which IL-M+D 5 I is reached from the D_ field directly for x in KD Pge,, and from the M field for x in e P M, either directly or after the crossing of the p |y curve. The compositions of points D, U, and U, are 5' hypothetical. UNCLASSIFIED ORNL-LR-DWG 25634 UNCLASSIFIED ORNL-LR-DWG 25633 Fig. 14.20. 154 UNCLASSIFIED ORNL-LR-DWG 25635 Fig. 14.22. 93 The minimum m” of the U—Z binary system is not involved in any of these considerations, for the points U, and U, involve temperatures and compositions not on the solidus curve of Fig. 14.2. Point a: For liquid with original composition at point a in Fig. 14.21, the first solid on cooling is D_, with composition between D and D.. The liquid reaches curve e P, where L+D_+U, (between Uand U,). At P, L +U5~>D5+M . The solid Ug is consumed; the liquid moves onto curve Pe, o and vanishes to leave M and D_on a line through a. Point b: The first solid is U_ (below U.). The liquid reaches curve 0115 where L-»M+US . The solid U, now moves up to reach U, when L reaches P, Thereafter, the solidification occurs as for point a. Point c: The first solid is U_ (below U). The liquid reaches curve p,,P.. As L follows this curve, the quantity of U_ first diminishes — until L. reaches ¢t — and then increases as L moves from ¢ to P.. But all the while the composition of U_ is moving toward U.. At P, the liquid is consumed to leave D, U, and M. Point d: (This point is not shown on the diagram; it is in the area between M and curve p, P, between the lines MP_ and MD..) The first solid is U_, near Z. The liquid reaches curve p, Py, and U_ is now entirely consumed in the reaction L+U oM 5 I while L is moving on the curve, before it reaches point t. The liquid then leaves the curve, travels across the M field precipitating more M, and reaches the same curve again near P, Here LM+ U s (now near U; in composition). At P, U, is consumed; the liquid moves onto curve P_e. and 5710 vanishes to leave M and D_ on a line through point d. Fractionation Processes in the Subsystem D-U-Z-K Figure 14.23 shows schematic fractionation paths in the subsystem D—U—-Z-K. These are hypothetical, for we have no information on the 94 UNCLASSIFIED ORNL-LR-DWG 25636 Fig. 14.23. liquid-solid tie-line directions for points on the surfaces (and we can make only uncertain infer- ences for the directions of tie lines at the boundary curves). However, we shall assume the relations shown schematically in Fig. 14.23 and discuss them along the lines followed under Figs. 6.1 fo 6.4. The paths on the M field are simply straight lines originating by extension from point M. Those on the D_ surface originate from the maximum D and diverge from the straight line DK, always convex with respect to K. This means that when a liquid is traveling over this surface, whether in complete equilibrium with the whole solid phase or in a fractionation process, the solid solution is always changing in composition toward K. More- over, the same direction of change in the solid continues here when either of the boundary curves is reached: e P or Peey. The U_ surface, with two maxima (U and Z), has two families of fractionation paths, separated by a limiting fractionation path originating at the binary minimum m*% This path, m'N, must reach one of the two boundary curves, e P, or p P We assume that it reaches the curve p, P. at the point N between P, and ¢, and that it is convex with respect to the corner Z. Accordingly, the paths on the U side of m "N are convex with respect to Z through their entire length, but some of those on the Z side, while starting out as convex with respect to U, pass through a point of inflection and become convex with respect to Z before reaching the boundary curve. The dashed curve m’R is the locus of these inflection points, and R is assumed to be between N and ¢. The paths between ZR and Zp,, have no inflection point and are simply convex with respect to U, For further orientation we note that the line PgUg of Fig.14.21 is tangent at P to the fraction- ation path UP,, Nr is tangent at N to the path m ‘N, and Rv is tangent at R to the path ZR, Point y is on the line P M, The sequence of changes in the fractionation process varies according to the regions into which the U, surface is divided by the lines and curves just defined. The outermost layer of U_ solid solution being deposited will be referred to as “*solid."”’ 1. Region e UP . (meaning between e, and the fractionation path UP.): While L is still on the U_ surface, the ‘*solid’’ increases in Z content to a limit given by the tangent to the particular fractionation path involved at the curve ecPe. At the same point of the curve, the tangent to the D_ fractionation path gives the initial composition of the D_ **solid’” precipitated, together with U, while L follows the curve e, + P.. Then, as L travels on the curve, the ‘‘solids’’ reach Dg and Ug when L reaches P.. Then L follows curve Pgey, towards e, as limit, depositing M and D ranging from D to an outermost layer approaching pure K. 2. Region between paths UP. and m'N: The ““solid’ increases in Z while L is on the surface, reaching a point between U and r when L reaches the curve between P_ and N. Then, as the liquid moves toward P, precipitating M and U, the outermost ‘‘solid'’ reverses its direction, reaching Ug when L reaches P Thereafter the solidi- fication occurs as for region 1. (Note: Once L reaches PS in fractionation, it continues onfo curve Pe, .) 3. Region p,,Zy: The ‘'solid"’ increases in U content while L is on the surface, to a limit, fixed by the tangent to the fractionation path, when L reaches the curve between p,, and y. The liquid crosses the curve at once in a straight line from 5€1g+ Ihere- after the solidification occurs as for region 1. M, precipitating M, to reach curve P e 4. Region between paths Zy and Z:: The “*solid'’ increases in U for L on the surface, to a limit, fixed by the fractionation path, when L reaches the curve between y and ¢, The liquid crosses the curve at once on a straight line from M, precipitating M, to reach the curve again along tP . This curve is followed to P, with the liquid precipitating M and U again, the *‘solid’’ starting at a higher U content than when its precipitation ceased on the curve yt, lts composition reaches U5 when L reaches P ¢; thereafter the solidification occurs as for region 1. 5. Region between paths Zt and ZR: The “‘solid"’ increases in U both before and after L reaches the curve. The limit is U, at P There- after the solidification occurs as for region 1. 6. Region between paths ZR and m’N: The ““solid’’ increases in U until the inflection point of the fractionation path is reached (intersection of path with curve m”R), and the ‘‘solid’’ at that point is given by the tangent to the path at its inflection point. Now the ‘‘solid’’ begins to decrease in U content, to a limit, given by the tangent to the end of the fractionation path at the boundary curve, reached between N and R. Then, as L follows the curve to P, the ‘‘solid” again moves to higher U content, reaching U, for L at P.. Thereafter the solidification occurs as for region 1. 7. Path m’N: For a liquid on the path m’N itself, the ‘‘solid’’ increases in Z (between the limits m” > ), and then moves, in reverse, to U, as L moves on the curve from N to P.. Thereafter the solidification occurs as for region 1. Equilibrium Crystallization in the U_ Field We finally consider the behavior of liquid on the U_ surface under conditions of complete equilibrium with the whole of the solid phase. For such crystallization with complete equilibrium, involving equilibrium paths crossing the fraction- ation paths, the behavior for the various regions would be as follows (all entirely analogous to the discussion of the regions in Fig. 6.4). When the liquid reaches a boundary curve, of liquid in equilibrium with two solids, it proceeds according to the equilibrium relations already considered above for Fig. 14.21. We are here dealing only with L on the surface itself. 1. Region between e_. and the fractionation path UP.: The equilibrium solid always increases in Z content. The equilibrium path does not 95 cross the line Pl boundary curve el . The liquid reaches the (It reaches it at a point where the L—U_ leg of the three-phase triangle for L on the curve passes through the total original composition x.) 2. Region between path UP, and line UgPg: The solid always increases in Z. The equilibrium path crosses the line U P on its way to the boundary curve, which is reached between ¢_ and P and path m’N: The solid always increases in Z. The equilibrium path does not cross the fractionation path m’N, and it reaches the boundary curve between P, and N. 4. Region between p,, and the path ZR: The solid always increases in U content. The equi- librium path does not cross the line Rv, and it reaches the boundary curve between Rand p, . 5. Region between the path ZR and the line Ru: The solid always increases in U. The equilibrium path crosses the line Rv, and it reaches the boundary curve between R and p,,. 6. Region between line Rv and line Nr: The equilibrium path does not cross the path m’N, and it ends on the curve between N and R. (¢) Region rvRd: The solid increases in U until the equilibrium path crosses the curve m'R; then the solid increases in Z content until L reaches the boundary curve. (b)) Region dNR: The solid always increases in U content for L on the surface. 7. Region between path m’N and The equilibrium path crosses the fractionation path m“N, to reach the boundary curve on the left of N, between N and a point ¢, where cm” is the L-U_ leg of the three-phase triangle for the curve with U_ at composition m" The behavior above and below the curve m’R differs as under region 6. 3. Region between line UgP, line Nr: Subsolidus Compounds E and F The solid equilibria after complete solidification of liquid will be affected, with further fall of 96 temperature, by the appearance of the subsolidus compounds E and F of the system Y-U (Fig. 9.1). The pertinent isothermal relations are shown schematically in Fig. 14.24: (a) above T (temper- ature of formation of E from D and U in the binary system); (b) between TE and T g (c) below T (temperature of formation of F from E and U in the binary system)., Only the upper part of Fig. 14.21 is involved. UNCLASSIFIED ORNL-LR-CWG 25637 (a) U (&) u - F+lg ) EX& Os + g Dot £+ d & / Do+l £+ 0, {c) u far ErFtl, ’ £ L £ N Dot &+l I < Do+ £+ 0O TS Fig 14 24, 15. SYSTEM Y=WaZ: The binary system Y~W is shown schematically in Fig. 15.1, and W=Z in Fig. 15.2. We note com- pound G in Fig. 15.1, decomposing on cooling at T.. System W~Z forms continuous solid solution with a minimum at m, The diagram for the system Y-Z is used with the same lettering as shown in Fig. 11.1. It has the subsolidus compound D, solid solution in four compounds (A, B, D, and F), and transitions in two compounds (B and C). The ternary diagram, as at present reported, is that of Fig. 15.3. Despite the continuous solid solution in the W~2Z system there seems to be no solid solution formed across the diagram between the corre- sponding 2:1 compounds H and C. The phase diagram as represented in Fig. 15.3 has two principal items of uncertainty. The first is the absence of a field for compound B of system Y-Z. The field now attributed to compound C UNCLASSIFIED ORNL-LR-DWG 25638 & 1 | 1 | | Fig. 451 V = (WS) W WZ Fig. 15.2. NaF=ThF ~ZrF pertains, actually, practically entirely to the 5:2 compound B, and only a small region of the ‘*C field’’ of Fig. 15.3, near the boundary curve ¢ ,E , pertains to the 2:1 compound C. There must be another three~solid triangle in the diagram, and another invariant point between m, and E,. The second uncertainty concerns the invariant point E,, reported as eutectic, |f a temperature maxi- mum definitely exists on the curve P_Eg, then E_ must be a eutectic. This temperature maximum, however, if it does exist (and its existence seems to be experimentally uncertain, actually), will not be, as now drawn, on the line WE, for the solid phase in the large field is not pure W but a con- tinuous solid solution of W and Z. The curve P_Eg, then, may or may not have a maximum on it, and if it does, the maximum must be on the right of the line WE. The mere position of E; in the triangle EWZ does not tell us whether it is a peritectic or a eutectic, for it is necessary to know its position in relation to the particular solid solution composition saturating the liquid at EB' In Fig. 15.4 we assume, principally for the sake of clarity of discussion, that this invariont, now called F_, is a eutectic; and an additional field is introduced between those for A and E, so that both B and C are now represented with primary fields. In this schematic diagram, then, there are eleven fields and nine three-solid triangles (not all shown in Fig. 15.3) with corresponding invariant liquids. There are only two saddle points, m, between the A and the H fields, and m, between the fields for E and W_ (solid solution of W and Z)°. Because of the binary solid solutions formed by the solid phases A, B, and F, the triangles in Fig. 15.4 are not drawn for the actual compositions of the solid phases involved at the invariant so- lutions, The probable relations will be discussed separately for the two principal regions of the system, shown in Figs. 15.5 and 15.7. We shall assume that the saddle point my s exactly on the line HA, although compound A forms solid solution in the direction of B. With this assumption, the line Hm. A becomes a quasi- binary section (the only one in the system), and the region YHA an independent, simple subsystem, with two invariants, P, and E,, involving pure solid phases. The final solids are either Y, G, 97 and A or G, i, and A; but below 7' of Fig. 13.1, G decomposes into Y and H, leaving Y, H, and A for the whole corner. Some solid solution is involved at each of the other invariants of the system. The region between the section HA and roughly JE is shown in detail, in Fig. 15.5, schematically, and distorted for clarity, The reactions along the curves are as follows: 1. mPyr L > H + A, the A solid starting as pure A and ranging to A, at P . 98 UNCLASSIFIED ORNL-LR-DWG 25639 2. €9P3: L >H+I1, 3. pyoPs: L+ -1 4. p,P,i L +A > B, the A solid starting with the composition given by Fig. 11.1 at temperature p, and ranging to A, at P . 5. P,P,: L -1+ A, the A solid ranging from AB to A,. 6. P,P.: L>1+B8, the B solid starting as pure B and ranging to B.. 7. P.P,: L ] +B, the B solid ranging from Bs to B,. Fig. 8. p,P,: L + B C, the B solid starting with the composition given by Fig. 11.1 at temperature Py and ranging to B, at P,. 9. e,E,r L 5 C +E, the E solid starting with the composition given by Fig. 11.1 at temperature e, and ending at E 7) (not to be confused with the eutectic point £, }. 10. P.E,: L »] +C. (Note: the solid for the C field is C, above the isothermal curve at ¢ CB below it.) 1 ond UNCLASSIFIED ORNL-LR~-DWG 25640 15.4. 1. p Pg: L +W_ > ], the W_solid starting as pure W and ranging to Wy (of Fig. 15.7). 12, PgE,: L » ] + E, the E solid starting as pure E and ending at F,,. (But the compositions of the solids at P_ will be discussed further under Fig. 15.7.) The invariant reactions are as follows: Pyt L +H - A, + 1 incongruent crystallization end point for triangle [l (HA ;1). 99 UNCLASSIFIED ORNL-LR-DWG 25644 Fig. 15.5. P L + A‘1 R B; incongruent crystallization end point for triangle 1V (4,IB). P, L + 1 > By + ]; incongruent crystaliization end point for triangle V (BI]). P L +B, > C, +]; incongruent crystallization end point for triangle VI (B, CJ). Eyi L > Cg+ ] + E i congruent crystallization end point for triangle VI [CEJEU)]' Liquids with original compositions in the tie- line areas of Fig. 15.5 complete their crystal- lization on the various curves, leaving two-solid mixtures of one pure compound and one solid solution. The B solid involved in the liquid equilibria of Fig. 15,5 is the B form. Figure 11,1 shows this form undergoing transition to the pure Bfi between the temperatures T’ and T’ in the binary system Y-7, These temperatures are unaffected by the third component W. The changes in the solid-phase 100 combinations brought about by this transition are shown in the series of schematic isotherms of Fig. 15.6: (a) between P, and T ; (b) between T’ and O; {c) at Q; (d) between O and T""; (e) below T”. The point Q is a four-solid invariant of type B, the reaction being: I +B,(ss) - calories == ] +Bg . The two-solid equilibrium between I and B (ss) here shrinks to a line on cooling, to be replaced by the two-solid equilibrium between | and B (@ line). At T, between isotherms (d) and (ei the equilibrium between | and B (ss) shrinks to a line and vanishes. Also, at temperature T, of Fig. 11.1, below E, of Fig. 15.5, the compound D of system Y-Z7 appears, forming from C and E ,, (more exactly it forms from compound E of the composition given by Fig. 11.1 at the temperature 7). This simply divides the triangle V|| [which involves, at this temperature, C., ], and E,.] into two triangles: one for i I and D {pure D), and one for | and conjugate solid solutions of D and E, with compo- sitions given in Fig. 11.1. At ¢, of Fig. 11.1, o further changes to Cj. ’ The remaining region of the system is shown schematically in Fig. 15.7, with a temperature maximum m, assumed to occur in the curve Pato, and E_ therefore a eutectic. The point E, there- fore lies in a three-solid triangle (IX) involving the solids E, F, and a W—Z solid solution assumed The W composition in equilibrium with liquid at mar W, and E. Although m4, then, is a saddle point, the section Em, W to have the composition shown as W_. is, of course, on a line with m is not quasi-binary, since the point W does noBT represent liquid and solid of the same composition in equilibrium. The point Wg represents the W_ composition for triangle VI, for the peritectic point P, together with the two solids | and E. It is assumed that the solid phase E is pure for liquids along the whole length of the curve PoE,, and that the binary scolid solution of E (in the direction of C) enters only beyond P, on curve P8E7' solid phase may begin to vary in composition even before P tn this case the line W_E would end slightly to the left of E, as would also the line W myE. We assume, therefore, that the [t seems possible, however, that the FE is reached. spread inthe composition of solid F is insignificant along the curve Palig. UNCLASSIFIED ORNL-LR—-DWG 25642 .“ffi"yf‘/f"(,‘ N i I+ J+ BQ(SSF)/;’#,/‘H \ (v il . ///f/ /.‘ \ /+BB+BQ(5$) ! :" "f‘l‘w' Ilr‘I\ N 'i"w\\‘\\.\ /f"/-"'/\“ N\ [ \ H\\\'\\ i HJ+C+ B i }‘!w\‘!\\‘\\\f“f ///I + + Q(SS) TT\\TrTF | — J+BB+ Bqelss) P J+C+Ba(55) B — ¢ o / \ / // \\ 7 'y IS+ By, \ | / \ / L/ | BB c Fig.15.6. 101 UNCLASSIFIED ORNL-LR~-DWG 25644 Py ) o o o }: P2 Pses L7l £ F Fig. 45.7 We consider this region, then, on the basis of the relations as drawn in Fig. 15.7. The reaction on curve p, P is L+WS—>] ' and the three-phase triangle starts as the line p11JW and ends as p JW,. The curve is reached by liquids for original composition x in the region P WWPg. For x in JWWg, the liquid vanishes on the curve to leave J and W_. For x in p,,]P, W vanishes on the curve, and L leaves the curve to traverse the | field on a straight line from J. On the curve m P, L->-E+W_, 5 the three-phase triangle starting as Em W _ and ending as EP W, For x in the region EW W m I the liquid vanishes on the curve to leave E and w.. The curve is reached from the W field for x in P8W8Wm msy and from the E field for x in EP8m3. The point P, is reached for x in the quadrangle P JWgE; the invariant reaction is L+Wgo]+E . 102 This is the incongruent crystallization end point, then, for triangle Vil (]WBE),' but for x in EP.], L moves onto curve PBE7' Along this curve, L-]+E , with the three-phase triangle starting as JPGE and ending as ]PBE(7)’ so that for x in E(7)]E the liquid vanishes on the curve to leave | and a solid solution between E and E7ye Along curve m E, LsE+W_, the W_ solid ranging between W and W,. For x in the triangle EW _W_, the liquid vanishes on ma 9 the curve to leave P2 and W_. Along curve e E, L>sE+F . Curve p E, starts as L+W_»F, from p, to point s, where the line Fs is tangent to the curve; between s and £, L>F+W_ . S The three-phase triangle starts as the line p, FZ and ends as the triangle FE Wy, For x in FW,Z, the liquid vanishes on the curve to leave FF and W _ between Z and W,. For x in the region Fp s, W, vanishes on the curve, and L traverses the F field to reach either curve eSE or the even section of 9 the original curve, sE,, when W_ appears again, bu* as a secondary crystallization product mixed with F. The point Eg is reached only for x in triangle 1X, with the reaction L—)E+W9+F . Compositions in the region covered in Fig. 15.7, then, upon cooling in complete equilibrium, solidify either to a mixture of three solids (the corners of one of the triangles VIl, Vill, and IX) or to mix- tures of two solids, in the tie-line areas for | and W, for | and E, for E and W_, and for I7 and W_. The fractionation paths on the surface for liquid in equilibrium with W _ are sketched in Fig. 15.8, on the basis of the assumptions made in Fig. 15.7. Line WgPg is tangent to the fractionation path Wm m 3 ending at P, , is tangent to the path Wm, UNCLASSIFIED ORNL-LR-DWG 25645 Fig. 15.8. and WoE, is tangent to the path Wi . Curve mN is the ?imiting fractionation path dividing the separate families of paths originating at W and at Z. The path mN is assumed to be convex with respect to Z and to end (at N) on the curve poEge The paths onthe W side of mN are convex, through- out, toward Z; the solid solution being precipitated on this surface continually increases in Z con- tent. Those on the Z side start as convex with respect to W, but some of them (nearing mN) pass through an inflection point before reaching the boundary curve between p, and N. For these paths the sclid solution precipitated by liquid traveling on the surface first increases and then decreases in W content before reaching the curve. The complete fractionation process tends toward one of the eutectics E, and E, as limit. |t must be remembered that on reaching a transition curve in such a process L. does not travel on the curve but immediately crosses it. This occurs, there- fore, in a narrow region between Z and the curve where the odd section of the curve (pbs) be crossed. Liquids reaching the boundary PyLg wou?d curves between m, and Pg all end at Eg, however, whether or not they cross the transition curve, and the final solids consist of E, F, and W_. The curves p, P, and p, P are also crossed in the fractionation process. Consequently in a narrow region between W and the beginning of the curve p P, liquids will end on the curve e P, then proceeding to E, as limit, leaving W, J, I, H, A, B, C, and E in the final nonequilibrium mixture, For liquids a little farther out from the YW side, the curve e P, will just be missed, and the solid H will not be present at the end. |if the curve p, P is just missed, then both A and I will also be absent, |f the liquid misses the curve P.P,, and ends to the right of P, then the final solids will be W_, J, C, and E; this will be the mixture obtained for liquids up to the fractionation path W . 103 INTERNAL DISTRIBUTION C. E. Center Biology Library Health Physics Library Central Research Library Reactor Experimental Engineering Library . Laboratory Records Department . Laboratory Records, ORNL R.C, . M. Weinberg . B, Emlet (K-25) . P. Murray A. Swartout . H. Taylor . D. Shipley C. Lind . L. Nelson . P. Keim H. Frye, Jr. . S. Livingston . G. MacPherson . L. Culler . H. Snell . Hollaender . T. Kelley . Z. Morgan F. Weaver . S. Householder . S, Harrill E. Winters E. Seagren . Phillips . VonderLage . Billington . Lane . Skinner . Jordan , Boyd J. Barton P. Blakely . Blander . F. Blankenship . M. Blood Cantor . B. Evans . A, Friedman . A, Gilbert WTODYONZIEONOEETCTOTOINOPOXREIFPP>PTNINCONITOmMME - > mIw“X>P»ouvn 66. 67. 68. 69. 70. 71 72. 73. 74. 75. 76. 77. 78. 79. 80. 81-90. 91. 92, 93. 94, 95. 96. 97. 98. 99. 100. 101. 102, 103, 104. 105. 106. 107. 108. 109, 110. 111, 112, 113. 114, 115, 116. 117. 118. 119. 120, W TEOFAUEP-AEAAMANC>EQAICPIOPIALIOEIAIPAZA-~~FPAO0000 ML ORNL-2396 Chemistry-General TID-4500 (14th ed.) . R. Grimes . Insley . Kertesz . Langer E. Meadows . Moore . Nessle . Newton . Overholser Redman . Shaffer . Sheil . Smith . Strehlow Sturm . Thoma . Ward . Watson . Bredig = N . Minturn Dworkin . Smith . Robinson Miller . Alexander . Dickison . Keilholtz . Manly Fraas . Mann Bruce Bettis . Milford . Charpie . Ergen . Lindaver White Meyer . Yaughn . Ferguson . Blanco T. Long . . Cathers . H. Carr, Jr, . E. Goelier MMOMUODARP>TCLOAMUIOEDOSATMIPTAmMmE-><-IVom=—m 105 106 121. 122-141. 142, 143 147. 148. 149151, 152, 153-713. J. O. Blomeke 144, H. Eyring (consultant) J. Ricci (consultant) 145. G. T. Seaborg (consultant) C. E. Larson (consultant) 146. ORNL — Y-12 Technical Library, P. H. Emmett (consultant) Document Reference Section EXTERNAL DISTRIBUTION Division of Research and Development, AEC, ORO W. W. Grigorieff, Oak Ridge Institute of Nuclear Studies University of Cincinnati (1 copy each to H. S. Green, J, W, Sausville, and T. B, Cameron) E. F. Osborn, Pennsylvania State University, University Park, Pennsylvania Given distribution as shown in TID-4500 (14th ed.) under Chemistry-General category (75 copies — OTS)