N

 

OAK RIDGE NATIONAL LABORATORY
operated by

UNION CARBIDE CORPORATION
for the

U.5. ATOMIC ENERGY COMMISSION

ORNL- TM- 1129
copYNo. - 7C

DATE - May 7, 1965

OXIDE CHEMISTRY AND THERMODYNAMICS OF MOLTEN
LITHIUM FLUORIDE-BERYLLIUM FLUORIDE BY EQUILIBRATION WITH
GASEQUS WATER-HYDROGEN FLUCRIDE MIXTURES

A. L. Mathews*
C. F. Baes, Jr.

*Present address: Western Carolina College, Cullowhee, North Carolina.

A dissertation submitted to the Faculty of The University of Mississippi in
partial fulfillment of the requirements for the Degree of Doctor of Philosophy
in the Department of Chemistry.
 

LEGAL NOTICE —— - — —— e = —-

This report was prepared os an account of Government sponsored work. Neither the United States,

nor the Commission, nor any person acting on behalf of the Commission:

A. Mokes any warranty or representation, expressed or implied, with respect to the accuracy,
completeness, or usefulness of the information contained in this report, or that the use of
any informetion, apperatus, method, or process disclosed in this report may not infringe
privately owned rights; or

B. Assumes any liabilities with respect to the use of, or for damages resulting from the use of
any information, apparatus, method, or process disclosed in this report,

As used in the cbove, ‘'person acting on behalf of the Commission’* includes any employee or

contractor of the Commission, or employee of such contractor, to the sxtent that such employee

or contractar of the Commission, or employes of such contractor prepares, disseminates, or
provides access to, any information pursuant to his employment or controct with the Commission,

or his employment with such controctor.

 
iii
ACKNCOWLEDGMENTS

This report is based upon a dissertation submitted to the University
of Mississippi in partial fulfillment of the requirements for the doctoral
degree. The report describes research carried out in the Reactor Chemistry
Division of the Oak Ridge National Laboratory, which is operated by the
Union Carbide Corporaticn for the Atomic Energy Commission. The research
was supported by the Oak Ridge Graduate Fellowship Program of the OCak Ridge
Institute of Nuclear Studies and was directed by a committee appointed by
Dean Lewis Nobles of the University of Mississippi Graduate School which
was composed of Dr. George Vaughan and Dr. Allen Cahill of the Department
of Chemistry at the University of Mississippi and Dr. C. F. Bases, Jr., and
Dr. C. H. Secoy of the Reactor Chemistry Division of the Osk Ridge National

Laborsgtory.
iv

CONTENTS

ACKNOWLEDGMENTS ¢ « ¢ o o o o o « o o o o o s o o o s

LIST OF FIGURES « « « + « o o o o o o s o s s o o o

LIST OF TABIIES - * . . . . . - . . - . - . - - . * .

ABSTRACT . - . . . - . * . . . » - - . . * . . L . .

I.

IT.

I:NITRODUCT ION . - . * e ® * . . » - . . . . . . .

Physical Properties of the LiF-BeF, System . .

Thermodynamic Properties of the Various Possible
SPeCieS . . . . -* . . . . . . . - - * . . »

Thermodynamic Studies of Molten Salt Mixtures
Solubilities of Gases In Melts . . « « « & « & &
Determination of Oxides in Melts « « « « « « o &

Suitable Experimental Approach . « « « « « o« &
Transpiration Method .+ « ¢« ¢ o« ¢ ¢ o & &

Equilibria .« o o ¢« o ¢ o o o o o o &+ o
Saturated Melts .« ¢ ¢ ¢ o ¢« o &+ o & &

Unsaturated Melts . ¢« ¢ ¢« ¢ « o o o &

mE:RMTAL . » * » . . . * » » - . L . - . - »

Chemicals . & ¢ ¢ ¢« ¢ 4 ¢« ¢ ¢ o o o o o s o o
GaBSeS o « o o+ o o s + o & s = o s o o s e .
Melt Components « « o « o s o o s o o o o
Standard Reagents « ¢« o ¢ o o & o o o o o« &

Apparatus . o o o o 4 o s o s s 2 s s 2 s e o
Flow Control Panel . . . & v ¢ o & o o « o

Agueous HF Saturator .« « o« « ¢ ¢ o o o o &

Page
iii

vii

X

G

14
14
16
20
21
23
23
23
23
23
24
24

26
I11.

Anhydrous HF Mixing System

Reaction Vessel . .

Titration Assembly

Gas Volume Measurement

Procedure . « ¢« « ¢« . .
Measurements . . .
Titrations . .
Calculations .
Limitations .
Systematic Errors .

Measured Volume

Influent Pressure

*

L d

Hydrogen Diffusion .

Dead~volume .

Sumexry . . .

Random Exrrors . . .

Melt Composition

Melt Temperature

Titer Precision

Wet-test Meter Temperature

Endpoint Precision . .

Flow~-rate Precision

Statistical Error Analysis

mSULTS - . . - L . - »

Tabulation « « « ¢ o & @

Page
27
27
28
29
29
29
29
30
31
32
32
34
34

36
37
38
38
40
41
41
41
41
42
Saturated Melts .

Unsaturated Melts .

vi

L ] . * .

Determination of Equilibrium Quotients

Saturated Melts .

Unsaturated Melts
Validity of Results

Saturated Melts .

Unsaturated Melts

IVe DISCUSSION ¢ « o » &

Correlation of Q@ . -

Activity of BeF2 and IiF

Thermodynamics of BeFa(l) . . .

Correlation of

Y

Correlation of QO

Summaxry
BIBLIOGRAPHY
APPENDIX A . .
APPENDIX B .+

APPENDIX C . .

- . - - *

Page

45
45
46
54
71
71
72
T4
T4
75
88
92
98
104
106
111
146

177
Fig.

Fig .

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

S

10.

11.

vii

LIST OF FIGURES

Phase Diagram of the LiF-BeF, System (From Thoma,

I'ef- 2) - . . * - - . * - . . . . . . - - . . - . L] . *

Complete Flow-Diagram for Apparatus . . « + « o o o « &

BeO-saturated 0.333 BeFz Showing (a) Calculated and

Observed Partial Pressures, and (b) Linear Correlation

Of Pressures « « o o o o o o

BeO-saturated 0.300 BeFz Showing (a) Calculated and

Observed Partial Pressures, and (b) Linear Correlation

of Pressures in Applicable Reglon « « « « & ¢« + o o &

BeO-saturated 0.300 BeF; during Hz Sparging, Showing

(a) Calculated and Observed Partial Pressures, and

(b) Linear Correlation of Pressures « « « « « « « o &

(a) Dependence of x and y on
r and s with W. Run No. 303
(a) Dependence of x and y on
r and s with W. Run No. 305
(a) Dependence of x and y on
r and s with W. Run No. 306
(a) Dependence of x and y on
r and s with W Run No. 307
(a) Dependence of x and y on
r and s with W Run No. 313
(a) Dependence of x and y on

r and s with W. Run No. 501

W,

W,

and

and

* .

and

(b) Variation of

(b) Vvariation of

(b) Variation of

Page

25

49

50

51

59

60

6l

62

63

64
Fig-

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig-

Fig.

Fig.

Fig.

12.

13.

14.

15.

16.

18.

19.

20.

21.

22.

23.

25.

viii

(a) Dependence of x and y on W, and (b) Variation of
rand s with W Run No. 511 .« « ¢« & ¢ ¢« ¢ ¢ o o « + &
(a) Dependence of x and y on W, and (b) Variation of
rand s with W. Run No. 533 . « « « v v v o o o «
(a) Dependence of x and y on W, and (b) Variation of
rand s with We Run No. 535 . . ¢« . . ¢« ¢ ¢« ¢ ¢ o+ &
(a) Dependence of x and y on W, and (b) Variation of
rand s with Wo Run No. 539 .+ « ¢« ¢ v ¢ ¢ v v o o v &
(a) Dependence of x and y on W, and (b) Variation of
rand s with We Run No. 607 .+ ¢ « o o o ¢ o o o o « &
(a) Dependence of x and y on W, and (b) Variation of
rand s with We Run No. 621 . . « « ¢ « ¢« ¢ &« ¢ o .« &
Correlation of log Q as a Function of Melt Composition
and Temperature « « ¢ ¢« ¢ o ¢ o o o o o o 2 o 2 e o 4 .
Agreement between Observed Q and Value of Q from
Correlation « « + ¢« ¢ ¢ ¢ o o o o o o o o o o s o s o s
Activity Coefficients of LiF and BeFy in Mixtures . . .
Thermodynamic Activities of LiF and BeFz in Mixtures. .
Heat of Fusion of BeFs from Activities at Freezing
TemperatuUreS .+ « o « o o o o o o o o o o « o o s o o o
Correlation of log QA as a Function of Composition

and Temperature « « « « ¢ o o o o o o o o o o » o s
Correlation of log QO as a Function of Temperature

for Various Melt Compositions « « « « ¢ ¢« ¢ ¢« v o & o« &
Solubility of BeO as a Function of Temperature for

Various Melt Compositions « « ¢ ¢ ¢ ¢ ¢ o ¢ o o o o o &

Page

65

66

67

68

69

70

85
86

9

102

103
Table

Table

Table

Table

Table

Table

Table

Table

ix
LIST OF TABLES

Equilibrium Constants Predicted from Thermodynamic

Data o ¢ o o o o 4 s o 4 o o o s s o6 e o o v 2 o o o s
Activities of LiF and BeFy from Literature o+ « « o «
Equilibrium Quotients, Q and QA’ Calculated from Data
on Oxide-saturated Melts =+ o s ¢ o+ o o ¢ o ¢ o ¢ ¢ + &
Parameters for Unsaturated Melts from Least Squares
Program « » « o o = o o = o s o o s o o o« s o 4 o o o
Comparison of Calculated and Observed Partial Pressures
for Unsaturated Melts o o ¢ « o o « o o o o s o o o o
Parameters from Correlation of Q as & Function of
Temperature at Specified Compositions ¢ « ¢« + ¢ o o « &
Smoothed Parameters from Correlation of Q as a Function
of Composition and Temperature at the Specified
CompositionNs « o o o o o o o « o o o s o o o o s o o o

Solubility of BeO in Molten LiF-BeFz System « ¢ o - .« &

Page

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52

57

58

83

83

101
OXIDE CHEMISTRY AND THERMODYNAMICS OF MOLTEN
LITHIUM FLUORIDE~-BERYIIIUM FLUORIDE BY EQUILIBRATION WITH
GASEQUS WATER-HYDROGEN FLUORIDE MIXTURES

A. L. Mathews C. F. Baes, Jr.

ABSTRACT

The transpiration method was used to equilibrate dilute
gaseous mixtures of HF and H20 in hydrogen carrier gas with
molten LiF-BeF; mixtures varying in composition from 0.25 to
0.80 ReF2, both saturated and unsaturated with crystalline
BeO, in the temperature range 500 to 700°C. The partial pres-
sure data were used to evaluate the equilibrium quotient for
the reaction of HF and Hz0 with solid BeO and dissolved BeFz.
Bquilibrium quotients were also obtained for the formation of
oxide and hydroxide ions in the liquid phase.

These equilibrium gquotients were employed to determine:
(1) thermodynamic activities of LiF and BeFz in the mixtures;
(2) thermodynamics of liquid BeFa; (3) stability of hydroxide
in the melt; and (4) solubility of BeO in the LiF-BeF2 system
as a function of temperature.

 

I. INTRODUCTION

Molten mixtures of LiF and BeFz have been the subject of numerous
investigations in recent years primarily because of their suitability as
a carrier solvent for UFg in fluid fueled nuclear reactors. In addition,
these solutions are especially worthy of study because the components -
highly ionic IiF and highly associated, more covalent BeFz - represent
extreme types of fluoride salts. Although the molten LiF-BeFz system has
received considerable attention from both a practical and a theoretical
point of view, the study of its chemistry is still far from complete.
According to Everest,l many of the investigations of beryllium fluoride
systems did not take into account the role of moisture and the resulting
hydrolysis products. If this information were available, future investi-

gators could make appropriate experimental adjustments and corrections.
The purpose of the present investigation was to study heterogeneous
reactions of the type
Hao0(g) + fluoride species(soln)’=t HF(g) + oxygen species(soln)
in the molten LiF-Bel, system. From such a study information could in
principle be obtained about: (1) the thermodynamic activities of LiF and
BeF2, (2) the solubilities and stabilities of oxides, and (3) the inter-
action of oxide with the proton and perheps other cations in this molten
fluoride system. Information about the chemical reactivity of the compo-
nents in the molten LiF-BeF; system could be obtained from the thermodynamic
activities of LiF and Belz. The oxide chemistry of this system is of
interest because oxide is a principal impurity to be dealt with in prepara-
tive work and because metal oxides are known to be only sparingly soluble
in LiF-Bel'z mixtures.

The presence of oxide species in the molten IiF-BeF; system, which
is currently being used as the solvent in the Molten-Salt Reactor Experi-
ment at ORNL, constitutes an undesirable impurity since inadvertent pre-
cipitation of sparingly soluble uranium (and other) oxides might result
in unstable reactor operation. One of the steps in the purification of
melts for reactor operation is sparging with a mixture of HF and Hp to
remove oxide. The present study of the equilibria involved would yield
additional guidelines for this treatment.

The reactivity of oxide with beryllium and other cations has been
investigated as a possible means of removal of reactor products, or of
uranium to be reprocessed for later use. In order for proper evaluation
of these methods to be carried out, a thorough understanding of the inter-

actions occurring in melts would be desirable. For example, the use of
H20 as the source of reactive oxygen for oxide precipitating schemes and
the use of HF for removal of oxide require that the stability of the inter-
mediate hydroxide be evaluated in the melts.

In the present study the transpiration method was used to equilibrate
dilute gaseous mixtures of HF and H20 in hydrogen carrier gas with molten
LiF-BeF, mixtures varying in composition from 0.25 to 0.80 BeFz, both sat-
urated and unsaturated with crystalline BeO, in the temperature range 500
to 700°C. The primary data from the measurements were used to evaluate
the equilibrium quotient for the reaction of HF and H20 with solid BeO and
dissolved BeFz. Equilibrium quotients were also obtained for the formation
of oxide and hydroxide ions in the liquid phase. These quantities in turn
could be used to obtain the thermodynamic activities of LiF and BeFy as
well as the solubility of BeO and the stability of hydroxide. Use of the
HF-H20 equilibria as a much needed analytical tool for the determination

of oxide in such melts was also indicated.
Physical Properties of the LiF-BeFz System

Beryllium fluoride is frequently found in the form of a glass rather
than a crystalline solid. The beryllium fluoride glass consists of a ran-
dom network structure in which the beryllium atoms are surrounded tetra-
hedrally by four fluorine atoms and each fluorine atom by two beryllium
atoms.l Iiquid beryliium fluoride retains the polymeric character of the
glass as indicated by its high viscosity. In contrast to the covalent
nature of beryllium fluoride, lithium fluoride is a highly ionic salt.

The addition of LiF to liquid BeFz causes a breaking down of the polymeric

structure, but apparently the tetrahedral BeF42™ groups are retained.
Although it isn't proof of structure in the liquid phase, the fact that
a compound LipBeF,; can be precipitated from the melt may be some indica-
tion of the short range order in the liquid phase.

Phase behavior of the LiF-BeF; system has been studied extensively
by Thomsa., gg_gl.z A copy of their published diagram.(Figure 1) is included
here to illustrate the major characteristics of the system.

The melting point of BeFz is 548°C; the melting point of LiF is 848°cC.
The liquidus temperatures for the BeFz-rich region have been difficult to
obtain because of the high viscosity of these solu.‘bions-3 A brief summary
of the phase studies of various BeF; systems is included in reference l.
Many of these systems parallel those of the much higher melting silicate
glasses.

Studies of the LiF-BeF; system in the temperature range of the pres-
ent work (500 to 700°C) are restricted to the region between the high
ligquidus temperatures at low BeF2 concentrations and high viscosity at

high BeF concentrations.
TEMPERATURE (°C)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

650 \ | F
600 | B
\ LIQUID
550 \ . 548
LiF + LIQUID \
500 | 72LiF :Bef, o
450 — ~ / .
\t\ / . BeF, +LIQUID

400 - _— \

LiF + 2LiF -BeF, J 360.3
350 | |

2LiF -BeF, + BeF»
300 | | |
LIF 10 20 30 40 50 60 70 80 90 Bef,

BeF, (mole %)

Fig. 1. Phase Diagram of the LiF-BeF, System (From Thoma, ref. 2).
Thermodynamic Properties of the Various Possible Species

From previous studies of LiF, BeF2, and the other possible species
present, some information can be drawn about the expected behavior of the
system. The thermochemical data for BeF; are summarized in the JANAF
Tables.* There is considerable uncertainty in aH,” of BeFa(1), which vas
derived from the AH_.°

£ 298.15
capacity functions for both the solid and liquid phases. Two sources

for the crystal and the appropriate heat

of error were cited in JANAF. The heat capacity studies were made on
samples of BeF2 which contained BeO and Hz0. Also, the heat of fusion

is uncertain. The value of 2 kecal/mole was used in the tabulation (be-
cause of the similarity of BeFz glass to B203 and Si02) even though a
value of 12.9 kcal/mole was determined from the vapor pressures over solid
and liquid BeFs. Determination of AH%O of Bng(l) would help resolve same
of these difficulties.

The thermochemical properties of BeFa(g) have been based on proper-
ties of the liquid and the heat of vaporization of BeF2(1l) except for the
work of Greenbaum, EE,EQ‘5 who determined equilibrium constants for the
reaction
BeO(s) + 2HF(g) = BeFa(g) + Ha20(g)
over the temperature range 670 to 970°¢. They report that a @lot of log
K vs 1/T yields a least squares slope corresponding to 20.5 * 1.7 keal/mole
for AH} over the temperature range studied, and that a plot of AF} vs T
gives a value of 6.0 * 0.3 cal deg™* mole™* for ASr by a least squares
analysis. If the calculated line for log K vs 1/T using these parameters
were drawn and the reported equilibrium quotients plotted, the line would

fall on the same side of all points. A least squares analysis using all
published data, with equal weighting for all points, gave values of Afii =
20.28 * 0.84 kcal/mole and 85 = 6.67 £ 0.77 cal deg™! mole™*. From their
values Greenbaum, et g_]___.5 reported the AHfo 208 of BeFa(g) as -191.3 +

2.0 kecal/mole and 50298 of BeFa(g) as 52.4 % 0.3 cal deg™! mole™!. Based

cn the recalculation, the values would be -191.5 % 1.1 and 53.1 % 0.8,

respectively.
The vapor pressure of BeFa(i) has been studied extensively.é'lo Sense,
93_25-6’7 studied the vapor pressure from 745 to 1021°C. Two Russian groups8’9

have reported vapor pressure studies. All of these are in general agreement
but have slight differences. The most extensive, and probably the best,
study (550 to 950°C) was that of Greenbaum, g&_g&.lo Since the enthalpy
and entropy of vaporization are reasonably well known from these measure-
ments, a combination of this information with independently determined
entropy and enthalpy of formation of Ber(;) should provide a new means

for evaluating the thermodynamic properties of BeFa(g).

The thermodynamic values of Hz0(g), HF(g), and BeO(s) are well char-
acterized throughout the temperature range of the present measurements
(see reference 4). Thus, if the AHr can be determined for the reaction
H20(g) + BeF2(1) = 2HF(g) + BeO(s) ,
then AH%O of BeFa(1l) can be calculated. The greatest uncertainty in AHfO
for HF(g) is the correction which should be applied for the imperfection
at room temperature. Several recent publications have dealt with the sub-
ject- 1117 Franck and Spalthoff'’ reported that the enthalpy of vaporiza-
tion rises from 89.5 cal/g at 19.4°C to a max of 146 cal/g at 130°C and

decreases at higher temperature. Armitage, g§_§£-12 show that the various

thermodynamic properties can best be explained by assuming that HF exists
in the gas phase principally as monomers and hexamers, but no actual indi=-
cation of the average molecular weight as a function of temperature or
pressure is given. Yabroff, gg.gi-lB have summarized most past work in
their report. They conclude that HF molecules are strongly associated
into polymeric forms and that dissociation is accompanied by large changes
in enthalpy-. Armstrong14 and Feder, g§.§£-l5 have considered the effect
of this association on the heat of formation of HF(g). The average molec-
ular weight of HF(g) at 1 atm and 25°C is 54, at 0.4 atm and 25°¢ is 22,
and at 1 atm and 80°C is 20.16 For pressures as low as a few hundredths
of an atmosphere both HF and Hz0 are reasonably ideal at 25°C and undoubt-
edly are ideal at melt temperatures.

From the thermodynamic gquantities tabulated in JANAF, equilibriuvm
constants were calculated for several conceivable reactions involving HF,

H20, BeFz, BeO, and LiF. These are presented in Table 1 along with the

Table 1. Equilibrium Constants Predicted from Thermodynamic Data

 

 

Reactio K at K at

1on 800°K 1000°K  keal
BeO(s) + 2LiF(s) == Liz0(s) + BeFa(1) 3 x1071% 2 x1071 52.1
BeO(s) + Hx0(g) == Be(0H)2(s) 5x10°% 1 x107% -12.5

BeF2(1) + 2H20(g) = Be(OH)a(s) + 2HF(g) 1 x10™° 6 x10"°  12.8

2Be0(s) + 2HF(g) == BeFz(1) + Be(OH)2(s) 2 x107% 2 x107™% -37.9

Be(OH)2(s) + 21iF(s) == 2Li0OH(1) + BeFa(l) 1x107% 3x10°% 46.2
BeFa(1l) + H20(g) == BeO(s) + 2HF(g) 2x107% 6 x10°!  25.4
BeFa(g) + Ha0(g) == Be0(s) + 2HF(g) 5x10° 1x10°  -21.7
BeO(s) + Hz0(g) == Be(0H)2(g) 2 x1071° 2x10"% 41.6
BeF2(1) == BeFa(g) 1x1078 2x1074 47.1

 
calculated heats of reaction. Although the equilibrium constants refer to

reactants and products which are pure solids or liquids, they could be ap-

plied to reactions in solution if appropriate activities were used. From
these data the following predictions are made:

(1) Oxygen containing compounds of Li should react to form Be compounds.
If Lip0 were added to an ILiF-BeF2 melt, the Liz0 should react almost
quantitatively to form BeO and LiF. If IiOH were added to an LiF-BeFp
melt, the LiOH should react almost quantitatively to form Be(OH)2 and
IiF.

(2) The formation of Be(OH)2 as a separate solid phase at temperatures as
high as 800%K is very unlikely.

(3) A11 of the stable campounds have low volatilities at the temperatures
of interest.

A more precise determination of the AH. of BeF2(1) and of the activ-

ities of BeFz2 and LiF in the melt would allow more gquantitative predictions

of reactions in the LiF-BeFp system.
Thermodynamic Studies of Molten Salt Mixtures

The determination of thermodynamic activities of melt components in
molten salts has received considerable attention. Blander has swmarized
much of the work through 1962.%7

The relationships between activities and activity coefficients depend
on the choice of concentration units. The most frequent unit for expressing
concentration of mixed solvents is the mole fraction. In molten salts the
ion fraction is frequently used. TFor systems in which all salts contain the

same anion, mole fraction and ion fraction are equal. The term "mole frac-

tion" will be used in the text.
10

According to the Temkin model,l8 in which salts are considered to be
completely ionic, the ideal activity of a component is equal to the product
of ion fractions of its constituents (aij = Xixj)' For a solution which
contains only one anion, j, the ion fraction,Xj, equals one. The ion frac-
tion of each cation is equal to the mole fraction of that component. The
activities of components are usually referred to the pure liguid (super-
cooled if necessary) as the standard state. Occasionally, the activities
are referred to the pure crystalline solid for experimental convenience.

The activities of components in solution have been measured by the fol-
lowing methods: +vapor pressures, freezing point depression, electrode
potentials, and heterogeneous equilibria. The vapor pressure method is
compllicated by the formation of complex species in the vapor phase. Deter-
mination of activities from freezing point depressions requires that the
heat of fusion and the qu for the pure solid and liquid solvent be known.
Electrode potential measurements of activities are often made in cells with
liguid Jjunction. OSuch measurements are limited to dilute solutions, which
are expected to give small liquid junction potentials.

The use of heterogeneous equilibria has thus far been limited. The

19,20 in mixtures with KC1 and NaCl

activity of MgClz has been determined
by use of the equilibrium

MgCla(soln) + 302(g) = Mgo(s) + C1la(g) -

Blood, g§_§£.21 determined the activities of various metal fluorides in
LiF-BeF; mixtures using the eguilibrium

M(s) + xHF(g) == MF_(soln) + (x/2)Ha(g) -

In studies of this type it is important that the solid present be well

characterized and relatively insoluble and, of course, that all phases are

in equilibrium.
11

If the activity of one of the components of a binary mixture is known
as a function of camposition, the other one can be determined by integration
of the Gibbs-Duhem equation. From the activities, such properties as molar
heats of mixing, excess chemical potential, vapor pressure, and phase behav-
ior can be derived.

At present, a general theory of the behavior of melts has not been
developed to the point that activities can be predicted for a system such
as LiF-BeF».

The activities of LiF and BeFz have been reported for a limited number
of cases. Berkowitz and Chupks in 1960 reported the activities in an equi-
molar mixture from relative ion intensities during mass-spectral ana];ysis.22
Recently, Buchler has reported determinations by a more careful mass-spectral
analysis and emf measurements. The emf measurements were conducted at two
temperatures in a concentration cell containing pure BeF2 in one compart-
ment and an LiF-BeFs mixture in the other-23 Blichler used a twin crucible
assembly in his determination of activities with the mass spectrometer to
facilitate comparison of pure compound and mixture-24 The results of these

experiments are compiled in Table 2.
12

Table 2. Activities of IiF and BeF, from Literature

 

 

*
ggzga ?ggg aBer* 7BeF2 aLiF ZLiF
0.50% 627 0.443 0.89 0.0246 0.049
0.25° 633 0.027 0.11
0.25° 692 0.039 0.16
0.26° 604 0.016 0.06 1
0.67° 604 0.86 1.3 0.076 0.23

 

*

Activities referred to BeF2(1l) and LiF(s), respectively.
®From Berkowitz and Chupka, mass spectrometry.
bFrom Bichler, emf.

“From Blichler, mass spectrometry.

Solubilities of Gases in Melts

In addition to the studies of activities in melts, the solubilities
of gases have also been of interest. Watson, g}_§£.25 have studied the
solubility of the inert gases in molten fluorides, including the LiF-BeFa
system. All solubilities obey Henry's law and increase with increasing
temperature and with decreasing atomic weight of gas.

Burkhard and Corbett26 reported the solubility 6f water in molten
LiCl-KCl mixtures. Apparently Henry's law was obeyed for low pressures,
with the deviations above a few millimeters attributed to hydrolysis. How-
ever, no analyses were reported on the gases to determine the amount of
H,0 and HC1l in the gas phase in equilibrium with the melt.

Shaffer, et al. have studied the solubility of HF in molten fluo=-

ride mixtures. In the LiF-BeF2 system28 solubility of HF increases with
13

decreasing temperature and with decreasing BeF2 concentration. The Henry's
law constants indicate that the solubility of HF in the LiF~-BeFp system
should be less than 150 ppm per atm HF above the melt. Thus, for the pres-
ent studies with partial pressures less than 0.02 atm HF, the solubility

should be less than 3 ppm.
Determination of Oxides in Melts

Since the presence of oxide in molten halides affects many physical
and chemical properties, quantitative procedures for determination of the
amount of oxide present have been widely sought. Goldberg, et §£.29 PLro=-
posed high-temperature fluorination with KBrFs; with liberated 02 measured
tensimetrically. This method works reasonably well, but the greatest un-
certalnties were found with fluoride melts and with samples containing less
than 300 ppm.

Porter and BrownBO used an inert-gas fusion technique (described by
Banks, g§_§£.3l) in determining oxide concentrations in molten fluorides.
Samples of the melt were withdrawn through graphite filters and the entire
sample was used in the analysis. The reported analyses indicated the rela-
tive precision was * 10% for oxide concentrations of about 0.5%. No
indication was made of applicability to lower concentrations.

32,33 has determined relative oxide solubilities in ILiCl-KCl

Delarue
melts electrochemically. The concentration of oxide was determined in the
melt with Pt-C electrodes vs a Pt-PtClz reference electrode. These results
permitted identification of a variety of reactions involving oxide.

None of the methods cited are adequate for determining oxide in the

LiF-BeFs system. From studies of oxide solubility by Baes, gE_§£.34 in
14

which weighed samples of BeQ were added to fluoride melts containing uran-
ium and zirconium, it was estimated that the solubility of BeO was less than
1000 ppm. Determination of oxide content in filtered samples by the Goldberg

mfithod,zg however, gave very inconclusive results.
Suitable Experimental Approach

The molten salt production facility at the Oak Ridge Y-12 Plant has
made use of HF-sparging to remove oxide from solution in the form of water.35
Since the production procedure parallels the transpiration method for deter-
mining vapor pressures of liquids, the feasibility of transpiration techniques
for an equilibrium study of the LiF-BeF2 system was considered. Much of the
feasibility study was conducted by M. K. Kemp who determined partial pres-
sures over the ZrOz-saturated LiF-BeFa-ZrF,; system and was able to estimate
the activity of ZrF4 in solution-36
Transpiration Method
The transpiration method for determining vapor pressures of liquids is

well esta‘blished-37 In order for the trenspiration method to work satisfac-
torily in studies of heterogeneous equilibria, the following conditions
should be met:
(1) Reactions must be fast enough and flow rates must be slow enough to

allow equilibration between gas and condensed phases.
(2) Adequate stirring of liquid phases must be maintained to provide uni-

form concentrations of reactants.
(3) The vapor pressures of condensed phases must be low enough to prevent

significant loss by transport in the carrier gas.

(4) Reacting gases should be unassociated.
15

(5) An adequate means of removal and measurement of reactive gases from
the flowing gas stream must be available.

The best evidence that these conditions have been met in the present
system is described in Chapter III. The variation in flow rates and in
the amount of reaction necessary to maintain equilibrium was used to test
the validity of the first two conditions. The vapor pressure data for
BnglO and LiF-Bel'z mixtures38 indicated that very little BeFz would be
vaporized. The vapor pressure of BeO at the experimental temperatures is
insignificant.Bg Although both H20 and HF are at least partially associ-
ated at room temperature, the dilute gases at melt temperatures are
expected to be ideal.

Determinations of the partial pressures of HF and Hp0 over aqueous
hydrofluoric acid solutions have been made by means of the transpiration
m.ethod.40 Measurements were made over solutions of 10, 20, 30, 50, and
70% hydrofluoric acid, at temperatures from O to 70°C. The HF in the car-
rier gas stream was absorbed by an agueous KOH solution. The difference
between weight lost by the saturator and weight of HF found in gas stream
was assumed to be the ambunt of water removed from the saturator. Since
this difference could not be used in the present studies, a suitable
method for measuring water was needed. Xemp investigated several methods
of analysis. Condensation of samples in a cold trap with subsequent weigh-
ing and analysis for per cent HF was not satisfactory primarily because of
the small size of the samples. Adsorption of the water by a suitable des-

sicant in a weighed drying tube was not satisfactory because HF was also

adsorbed.
16

Finally, it was observed that a mixture of methanol and pyridine was
suitable for removal of water from a flowing stream even in the presence
of HF. Titration of the water with Karl Fischer Reagent could be performed
in the vessel and since Karl Fischer Reagent contains excess methanol and
pyridine, several successive titrations could be performed. Apparently the
HF reacted with excess pyridine to form a fairly soluble pyridinium hydro-
fluoride which did not interfere with the titration.

Karl Fischer Reagent consists of Iz and S0z dissolved in pyridine and
methanol (actually the "stabilized reagent" contains methylcellosolve in-

41

stead of methanol). Although the titration is straightforward, — the

reaction occurs in two steps:

502
- 7~
Hz0 + CsHsN + CsHsN'S02 + C5HsN'Iz » 2C5HsNH'I™ + CsHsN, |
0
/802 -
C5HsN | + CH30H — CsHsNHOSO20CH3 .
0

When titrating H20 with Karl Fischer Reagent the endpoint corresponds
to the first appearance of Iz. For macrotitrations the reagent serves as
its own indicator; however, for microtitrations a more precise method is
needed. Several authors have reported suitable circuits for the amperomet-
ric determination of the endpoint. The one actually used was quite similar
to the one described by Nérnitz.42
Equilibria

If the molten LiF-BeF, system comes into contact with water vapor,
hydrolysis occurs releasing some HF into the gas space and leaving some
oxygen-containing species dissolved in the melt. For a closed system at
equilibrium, the amount of HF and H20 in the gas phase will depend on (1)

the amounts of HF and H20 initially introduced, (2) the solubility of HF
17

and Hz0 in the melt, (3) the concentration of oxide in the melt, (4) the
concentration of hydroxide, a reactive intermediete (in the sense that it
can exist only in the presence of HF and H20), in the melt, and (5) the
amount of HF and Hz20 consumed in side reactions which do not influence the
oxide reaction scheme.

If the above quantities are properly controlled or measured, useful
equilibrium data can be obtained. The reaction of HF and H20 at high tem-
peratures with the structural metal used (nickel) can be suppressed by the
presence of Ha. Side reactions are essentially eliminated if the purity
of melts is sufficiently high. The solubility of HF in melts in the absence
of oxygen species has been mentioned and is small compared with the best
estimates of oxide solubility. It seems reasonable to assume that water
solubility would be of the same order of magnitude as that of HF and the
experimental results supported this. One method of controlling the oxide
concentration would be saturation of the melt with a sparingly soluble
oxide such as BeO. With the above conditions set, transpiration experi-
ments can be used to control the amounts of HF and H20 introduced and to
measure the hydroxide concentration indirectly through the material differ-
ence between influent and effluent gas streams.

For a BeO-saturated, LiF-BeFz melt with excess solid BeO present the
following equilibrium is valid:

H20(g) + BeFa(soln) = 2HF(g) + BeO(s) .
If both HF and H20 are assumed to be ideal gases and if the thermodynamic
activities of the condensed species are represented by "a", the equilibrium

constant for the reaction would be

K, = (Ppp) *8peo/ P o%Ber,
18

Since 800 is 1 by definition,

Ky = (Ppp) /Py, Ppep, = Yopey, -

This equilibrium is independent of the presence or absence of hydroxide in
the melt.

The quantity (PHF)z/PHZO for BeO saturated melts, defined above as Q,
can be obtained from determination of partial pressures in the gas phase
alone. Thus Q, which is proportional to the activity of BeFz, would be
equal to Ké for the equilibriwm involving pure liquid BeFs at the same tem-
perature. Determination of Q for various temperatures and compositions of
BeF provides the data necessary for thermodynamic calculations involving
the melts.

The following additional equilibria involving oxide and hydroxide ions
in the melt should also be considered. (The corresponding equilibrium quo-
tients, which are shown, may be considered constant for a given LiF-BeF;
composition and temperature since at the low concentrations of oxide and
hydroxide involved, the activity of F and the activity coefficients 702-
and 7.~ can reasonably be assumed constant.) Since [F ] is reasonably
constant for a given melt composition, [F~ ] is incorporated into the equi~
librium quotients.

H20(g) + 2F (soln) = 2HF(g) + 02 (soln)

Q = (Pyp) 1071/ FH20

For oxide saturated melts [0°7] is constant, hence
QO/[OZ-]sat = (PHF)zfiPfizo = Q.

There are three reactions involving hydroxide in solution.
H20(g) + F (soln) = HF(g) + OH (soln)

Qy = (Py) [0 /Py
19

Ha0(g) + 02~ (soln) == 20H (soln)

Q, = [oH"1%/(py ) [0*7]

and for a melt saturated with oxide where [0%~] is constant,
Q = [OH-]a/PHao .

Hr(g) + 0%7(soln) == OH (soln) + F (soln)

Q, = [on"1/(py) [0%7]

and for a melt saturated with oxide,

Qg = [OH ) /P, -

Note that not all of the equilibrium quotients are independent. Since
QO is independent of [OH™ ] and QA is independent of [0%“], these two equi-
librium quotients are the most conveniently employed. Both Qb and Qc can
be expressed as functions of QO and QA-

Q, = (q,)%/q, and Q, = Q,/q,
The relationships for BeO saturated melts are given by
q, = (q,)2/a and Qe = Q,/Q -

Stoichiometric relationships show that the number of protons in a given
volume of effluent gas will be less than the number in the influent gas by
the amount that has appeared as OH added to the melt. If the proton level
in the effluent gas stream exceeds the level in the influent stream, OH
is being removed from the melt. The difference in Hz0 content between the
influent and effluent gas streams corresponds to the total amount of oxide
plus hydroxide being added to or removed from the melt. Iikewise, the dif-
ference in HF content between the influent and effluent gas streams corre-
sponds to the amount of fluoride being added to or removed from the melt.
For all experiments conducted, the change in fluoride was small enough so
that the LiF-BeFz concentration in the melt was assumed to be constant

throughout a given experiment.
20

For simplicity in handling equations the following notation will be
used:
wt of melt = w(kg)
vol of gas (measured at T) through melt = V(liter)
V/wRT = W(mole kg™t atm™1)
P =28 + bW and Py,o = ¢ *d¥ (atm) for influent pressures
(NOTE: When the agueous HF saturator was employed b and 4
were always O. When gas mixing was employed b and d were
small negative numbers because small opening in valve tended
to gradually close.)
Pom = X and Py,0 =Y (atm) for effluent partial pressures
[0*"] =

[OH"] = s

1§

The equilibrium quotients may now be expressed as

Q= x*/y, Q = X°r/y, and Q = xs/y -

Saturated Melts

 

For constant. influent partial pressures of Hz20, HF, or both there will
be an ultimate steady state condition in which the effluent partial pres-
sures are not changing, hence r and s are constant. In fact r will be
constant at all times in a given experiment unless rate of reaction to form
hydroxide and water exceeds the dissolving rate of solid BeO. The speed
with which x and y approach a steady state is controlled primarily by Q and
QA' According to the equations described earlier, the difference in proton
level of influent and effluent streams is equal to the change in hydroxide
concentration. Thus,

ds/aw = (a + 2¢) - (x + 2y) .
21

Both ds and y may be eliminated by using the relationships Q = xz/y and.

Qy = xs/y. Rearrangement of the former gives y = x°/Q. Rearrangement and
substitution into the latter gives s = QAX/Q, which may be differentiated
to give ds = (QA/Q)dx. Thus

dx/aW = (Q/QA)[(a + 2c) - (x + 2x%/Q)].

Separation of variables gives

dx
(a +2¢) - x - (2/Q)x?

 

= (Q/Q,) aw .

Defining (a + 2c) as A, this equation may be integrated to give

1 1n (4/Q)x + 1 + [1 + (84/Q)]
[1+ (88/Q)1F (4/Q)x + 1 - [1 + (8A/Q)]

 

 

= (Q/QA)W + constant .

nj- O

The correlation of experimental measurements with this eguation is described
in Chapter III. The computer program for this correlation was written by
R. J. McNamee, Operations Analysis Division, ORGDP.

Unsaturated Melts

 

For unsaturated melts the change in r and s can be determined by mate-
rial balance. The difference between influent and effluent partial pressures
of Ha20 corresponds to the change in total oxide concentration
(dr + ds)/aWw = (¢ - y) .

The difference in proton levels corresponds to the change in hydroxide con-
centration just as in saturated melts

ds/daW = (a - x) + 2(c - y) .

By difference

dr/aW = (x = a) + (y - ¢) .

Combination of these equations with Q, = xs/y and Qy = x?r/y could, in
22

principle, yield integral equations expressing QA and QO as a function of
the measured quantities. However, the resulting pair of simultaneous dif=-
ferential equations could not be integrated. The following simultaneous
differential equations were obtained by elimination of x and y from the
expressions for dr/dW and ds/dW:

as/aw = (a + 2¢) - (Qys/Q,r)(1 + 2s/Q,)

and

dr/aw

il

(QOS/QAr)(l + s/QA) -(a+e)
These equations could be solved in the differential form to obtain values
of r and s as a function of W for specified values of QO and QA' If r,
S, QG and QA are specified at a given W, values for x and y may be calcu-
lated.

The method of solution of the equations and the correlation of experi-
mental data by this method are described in Chapter III. The computer
program for this correlation, "FIASCO", was written by M. T. Harkrider,

ORNL Mathematics Division.
23
II. EXPERIMENTAL
Chemicals

Gases

Commercial Hz was purified before use by passage through a deoxo unit,
a magnesium perchlorate drying tube and, finally, a liquid Nz trap. Com-
mercial He was passed through an ascarite trap, a magnesium perchlorate
drying tube and, finally, a liquid N2 trap. Anhydrous HF was used directly
from a commercial cylinder without further purification. B & A reagent
grade 48% hydrofluoric acid was used as the source of HF(g) and Ho0(g).
Melt Components

Beryllium fluoride was from Brush Beryllium Company (material to be
used in preparing the Molten-Salt Reactor Experiment fuel salt). Iithium
fluoride was B & A reagent grade. Various mixtures were prepared by melt-
ing together weighed samples of the two components. Samples of the mixtures
were withdrawn in filter sticks and analyzed for Be, Li, F and impurities
(Fe, Cr, Ni, Cu and S). High purity BeO from Brush Beryllium Company was
added to the melts which were used in studies of oxide saturated melts.

Standard Reagents

 

Reagent grade KOH was used in the preparation of 0.1 N base which was
standardized with potassium acid phthalate. Karl Fischer Reagent from
Fisher Chemical Company (So-K-3) was standardized by direct addition of

weighed aliquots of water.
24
Apparatus

Experiments were carried out by means of a transpiration method. The

stepwise sequence of processes was as follows:

Control of flow of
Hy carrier gas
Addition of HF(g), Equilibration with
Hao(g), or both z///, melt
Removal of HF or H20 in
standardized reagent
Measurement of volume of

H, carrier gas

A complete flow diagram of the apparatus is shown in Figure 2.
Flow Control Panel

The menifold gas pressures (Hp and He) were not constant but varied,
generally, between 5 and 10 1b gauge. A pressure relief valve (Moore
Products Campany differential type flow controller, Model 63BD, modified
form) was used to reduce this pressure to & constant value of 3.0 1b gauge.
The gas next passed through a Fisher-Porter Rotameter which was used only
as & visual check of the flow rate. The pressure was measured with a 4=-in.
Asheroft gauge graduated in 1/4-lb divisions from O to 15 1b above atmos-
pheric pressure. The brass needle valve with micrometer handle was from

Nuclear Products Company as was the 1/3-1b check valve which was used to
 

25

VAC. j{NHYD. HF
——i —
- §

X ANHYD. HF ‘

|

 

MIXING

 

 

 

 

AQUEOQUS HF SATURATION
iN CONSTANT TEMP BATH FLOW CONTROL PANEL

——

 

 

 

 

D><F— EXHAUST

   

 

L"‘:x:

 

EXHAUST

 

i
o

  

T
:llj

|

|

WET TEST

METER BUBBLE-O-

KARL FiSCHER KOH METER
SOLUTION SOLUTION

  

 

 

 

 

REACTION VESSEL IN
TUBE FURNACE

Fig. 2. Complete Flow-Diagram for Apparatus.
26

prevent back flow of gas. The Hz line to the agueous HF saturator was also
connected to a water filled manometer from which the pressure immediately
upstream of the saturator could be determined. The various pieces on the
panel were connected by 1/4-in. Cu tubing using mechanical Swagelok fittings.

An alternate flow control system, identical with the above except for
the H20 manometer, was used to control the carrier gas for the anhydrous HF
system.

Agueous HF Saturator

 

When HF and H20 were both desired in the influent gas, agueous solu-
tions of HF were employed. The Hz from the flow control panel passed first
through a dry bottle, next the filled saturator, and then another dry bottle
which acted as a trap for liquid droplets. Both the bottles and the satu-
rator were machined from Teflon bar stock. The two bottles were 2%—in-
diemeter with a capacity of 300 mi. The saturator was a two-piece spiral
gas-washing bottle (3-in. outside diameter top, 2-in. bottom) with approx-
imately the same volume as the dry bottles. Iids for the three were screw-
type with 45° shoulders which made pressure seals. The tube openings were
threaded for compression-type nuts which sealed the tubes in place when
tightened. The connecting line from the flow control panel and between the
bottles was of 1/4-in. Teflon tubing.

The saturator and dry bottles were in a constant temperature bath, the
temperature of which was used to control the partial pressures of HF and
H20. The temperature could be controlled % 0.1°C from 15 to 25°C. The bath
was continuously cooled by a water coil while heating was controlled by a

mercury-mercury contact thermostat and an electronic relay.
Anhydrous HF Mixing System
For studies reguiring anhydrous HF(g), controlled gas mixing was
employed. The manifold HF pressure was controlled by regulating the tem-
perature of the HF supply cylinder. The flow of HF was controlled by a
small-orifice Monél diaphragm valve. The HF flowed from the valve through
a 6-mil capillary to the mixing chamber, a 1/4-in. Cu tube about 3 in.
long. The HF entered at one end of the mixing chamber; the Hz entered at
the other end through a 1/8-in. Cu tube which extended the length of the
chamber to the point where the HF capillary ended. The mixed gases flowed
out through a sidearm. This system was adapted from one designed by
G. Long which was suitable for HF pressures from about 3 X 10°2 atm down-
43

ward.

Reaction Vessel

 

The melts were contained in cylindrical vessels (2-in. diam, 15-in.
long; or 4~-in. diam, 15-in. long) constructed of Grade A nickel. Fach
vessel was equipped with the following: & thermocouple well and a gas-
inlet tube (1/4-in. tubing) each of which reached to within 1/2 in. of
the bottom of the vessel; a cover gas line (1/4-in. tubing) with an at-
tached 6-in. Ashceroft Duragasuge graduated from 30-in. vac to 30-1b gauge;
and a sampling port (a 3/8-in. pipe with the end closed by a 1/2-in.
Worcester ball valve). A sidearm on the sampling port of 1/4-in. tubing
served as the gas-outlet line.

The sampling port could be connected to either a sampling apparatus
or an addition apparatus. These apparatus (developed and in common use
)

in molten salt studies at ORNL allow removal of samples from the melt

in Cu filter sticks with subsequent transfer to a dry box under He
28

atmosphere, and addition of weighed salt samples to the melt under a dry
He atmosphere.

The reaction vessel was located inside an upright tube furnace, the
temperature of which was controlled by an L & N Speedomax H Temperature
Controller with Model S Recorder and a Chromel-Alumel thermocouple. The
temperature was checked periodically with a calibrated Pt vs Pt-10% Rh
thermocouple and an L & N K-2 Potentiometer.

The gas lines from the saturator and the HF mixing chamber to the
reaction vessel and from the vessel to the titration assembly were of
l/4-in- Cu tubing. Monel sealed-diaphragm valves were comnected by means
of silver-soldered Jjoints. Both the lines and valves were heated to about
100°C with heating tape as precaution against condensation or surface ad-
sorption of the HF or Hz0.

Titration Assembly

 

The Karl Fischer titration vessel was a 300-ml round-bottom flask
with the following additions: two Pt wires fused through the bottom of
the flask about 3/4 in. apart; a sidearm added to the bottom to allow
drainage of the flask; two buret tips (for 5-ml Koch microburets with 150-
ml reservoir) fused through the top of the vessel about 3 in. apart. The
solution was stirred by a small bar magnet under the Pt wires. Teflon
gas~inlet and gas-outlet lines were fitted through a rubber stopper.

The endpoint was determined by an amperometric method using the "dead-
stop" technique-45 The indicator circuit consisted of the following:
1.5-v dc source, & 10* ohm variable resistor, a 500 ohm variable resistor,
the Pt electrodes, and a microammeter (all connected in series). With

excess Karl Fischer Reagent present the variable resistors were adjusted
29

so that a current of more than 100 pa was observed. With excess water
present the current was less than 2 pa. The endpoint was taken as the
point at which the current was 50 pa.

The KOH titration vessel was a 175-ml test tube. Teflon gas~inlet
and gas-outlet lines, and the tip of a 10-ml ILab-Crest microburet were
fitted through a rubber stopper. Phenolphthalein indicator was used.

Gas Volume Measurement

 

The carrier gas from the titration assembly was bubbled through a
bottle containing KOH solution (to remove acidic vapors from the Karl
Fischer Apparatus) and. then through a bottle containing H20 [to saturate
with HzO(g) at room temperature] before its volume was measured in a
Precision Wet Test Meter. The gas-exit line from the Wet Test Meter was

connected to a Bubble-0O-Meter which was used to measure flow rates.
Procedure

Measurements
The primary experimental quantities needed were the partial pressures
of HF and Hz0 over the melt.
Titrations.--Measurements for determination of partial pressures were
made as follows:
(1) A measured volume of standardized reagent was added to a titration
vessel.
(2) The time required for the flowing gas to neutralize the reagent
was determined.
(3) The flow rate of gas was determined at room temperature by timing

a soap bubble for 100 ml. Since diffusion of Hpz through the bubble
(4)

(5)

(6)

30

would lead to lower indicated flow rates than the true flow
rates, at least one bubble before and one bubble after the one
being timed were employed to help decrease diffusion of Haz.
Usually, at least three successive titrations were carried

out with a given reagent and then the gas flow was switched to
the other titration vessel for a similar number of titrations.
The initial volume for a series of titrations was recorded from
the wet-test meter, which indicated continuously the total gas
volume which had passed through the reaction vessel during an
experiment. The meter could be read only to the nearest 10 ml,
which was a precise enough reading for total volume but not for
individual titrations. The gas volumes titrated were calculated
from the flow rate and time of titration.

The temperature of the wet-test meter, which was the temperature
of the gas as it was being measured, was recorded.

Calculations.--The required calculations to evaluate the partial

pressures were carried out as follows:

(1)

(2)

(3)

The measured volume of gas was calculated by

(Time of titration)/(Time per 100 ml) x 100 = ml of gas.

The number of millimoles of the component removed from the gas
stream by the titration was calculated by

(ml reagent)(conc reagent) = millimoles component {HF or Hz0).

The partial pressure of the component was calculated from ideal
gas law by

P = (millimoles component)(0.08206)(temp wet-test meter)/

component
(ml gas) -
31

Limitations.--The apparatus as employed did pose some limitations
on the procedure. The aqueous HF saturator as designed could not accom-
modate flow rates greater than 200 ml/min without bumping. For consis-
tency, comparable flow rates were used with the anhydrous HF sysien.

Under operating conditions both the Karl Fischer titration vessel
and the KOH titration vessel were checked to verify that they were able
to remove quantitatively the H20 and HF, respectively, from the flowing
gas stream. In both instances two vessels were set up in series and the
leak-through from the first determined the second. The amounts of HF and
Ho0 titrated in the downstream vessels were less than 0.1% of the amounts
measured in the upstream vessels.

The Karl Fischer titration vessel was also checked against in-leakage
of moisture from the atmosphere. The amount of Karl Fischer Reagent needed
to maintain the endpoint with no gas flowing through the vessel was about
0.07 ml/hr. This correction was applied to pressures below 1 x 10”2 atm
when it altered the observed results by as much as 1%.

Since the titration vessels were operated at room temperature, in
order to avoid condensation, the max pressures of HF and H20 were limited
to the vapor pressures above agqueous HF solutions at the same temperature.

Even for pressures below these limits some surface adsorption was
encountered. When the flowing gas stream was switched through the Karl
Fischer apparatus, the PH;O determined for the first few tenths of a liter
would be lower than the following determination. Therefore, the first
titration of about 0.3 ml Karl Fischer Reagent was not recorded after the
switch was made. Dehydrdtion of the Teflon was observed after the flow-

ing gas was stopped. Additional Karl Fischer Reagent was necessary to
32

maintain the endpoint. (This was much in excess of the amount due to in-
leakage discussed above and due to the untitrated gaseous water in the dip-

line.) The same problem was not observed with P._, measurements, but usually

HF
a small aliquot of KOH was added to vessel during switching to allow stabi-
lization of flow before titrations were begun.

Systematic Errors

 

The preceding method of calculating partial pressures included +the
assumption that the pressure in the apparatus from the saturator to the
wet-test meter was constant and that the amount of material was the same
at every stage. The assumption was also made that the measured volume
was equal to the volume of carrier gas plus reactive components, HF and
H20. These assumptions were not completely valid, but it will be shown
in the following sections that the resulting systematic errors were small.

The following notation will be used in the discussion of systematic

errors:

T_ = temperature of melt, K

TW = temperature of wet-test meter, %k
Pw = total pressure at wet-test meter
p, = vapor pressure of water at Tw

X and y = partial pressures of HF and H20, respectively, at titrator

Nym and anD = moles of HF and H,0 as measured at Tw’ Pw

V,; = measured volume on wet-test meter
Va = volume of dry carrier gas going through system measured at Tw’ Pw
Vb = volume of gas entering titration assembly at TW, Pw-

Measured Volume.--The measured gas volume, Vw, was of the carrier

 

gas which had been saturated with water at Tw’ immediately prior to
33

entering the wet-test meter. The volume which should have been used in

the pressure calculations was Vb' The volume of carrier gas corresponding

to the measured volume is given by

Vg = VW(PW " PW)/EW *

The volume of HF and H20 entering the titration assembly may be calculated
from the gas laws to bhe

(nH20RTW)/PW " ('HF}TW)/PW.

(The effect of any non-ideality of HF or H20 at the low partial pressures
involved here is expected to be negligible.)

From Dalton's law of partial pressures

¥y X Pw-(x+y)

—
= -

(nHzoRTW)/Pw (MHEBTW)/PW Va
Substituting the value of Va from the above equation,

[PW - (x +y)] PwanoRTw

y = ( ) ’
VP - PRy

 

note that PW cancels, and by a parallel method

_ [PW - (x +y)] Ny RT
vfi(Pw - Pw)

 

X

According to these calculations, the x and y values calculated in
the preceding section should be multiplied by the factor f, where
P -(x+y)
=,
P - Py
The maex and min values for f can be estimated. PW = atmospheric pressure;

(x + y) varies from O to 0.033 atm, but generally is between 0.013 and
34

0.020 atm; p, is between 0.029 and 0.035 depending on T The maximum
value for f would be 1.00/0.965 = 1.037. The minimum value for f would
be 0.967/0.971 = 0.996. For the majority of measurements,

0.980/0.970 < £ < 0.987/0.970 ; 1.013 < £ < 1.0196 .

Thus the calculated partial pressures are too low by 1.0 to 2.0% due to
the removal of HF and H»0 and subsequent saturation with H20 vapor before
the volume of carrier was measured.

Another effect, which exerts a minor influence on pressure measure-
ments, is the pressure drop, between the gas space above the melt and
atmospheric pressure, required to maintain bubbling through the titrator
and wet-test meter. This drop was less than 0.01 atm, and would cause
the measured values to be low by as much as 1.0%.

Influent Pressure.--The influent partial pressures were measured

 

with the gas bypassing the reaction vessel. The influent partial pressures
are controlled by the saturator temperature and are independent of the
total pressure. The total pressure in the saturator was less during the
measurements of the influent gas camposition than when the gas was pass-
ing through the melt by the pressure drop required to maintain bubbling,
which was about 0.015 atm. This pressure drop results in an expansion

of the gas as it enters the reaction vessel, hence the actual influent
partial pressures of HF and H20 are less than the measured influent par-
tial pressures by 1.5%.

Hydrogen Diffusion.--According to published diffusion coefficient346

 

the diffusion of Hz out of the Ni vessel could be a few milliliters per
minute at the elevated temperature of the vessel. Only the reaction ves-

sel was sufficiently hot to allow diffusion of hydrogen.
35

The rate of diffusion was measured experimentally by pressurizing
an empty vessel to 5 1b gauge and following the decrease in pressure as
a function of time. The pressures were measured down to 10 in. vacuum.

A control experiment with He was used to check against leakage. The fol-
lowing rates of diffusion (expressed as the volume of gas per second
which would be measured at the wet-test meter; i.e. at 'I'W and PW) were
determined; 700°C, 0.035 ml/sec; 650°C, 0.025 ml/sec; 600°C, 0.015 mi/
sec. The rate of diffusion of Hz out of a vessel containing salt should
be no greater and probably not much less than for an empty vessel.

The influent partial pressures from the aqueous saturator were deter-
mined without loss of Hz by diffusion since the gas bypassed the vessel.
If the influent gas were passed through a veseel with no salt present,
the measured partial pressures would be greater due to this effect, by
an amount dependent on the temperature and flow rate.

Most experiments were conducted with flow rates between 2.0 and 2.5
ml/sec. This means the apparent influent pressures would be from 1.4 to
1.75% higher at 700°C; 1.0 to 1.25% higher at 650°C; and 0.60 to 0.75%
higher at 600°C then the measured influent pressures. The difference
would be less at lower temperatures.

Hydrogen diffusion did not play the same role when the anhydrous HF
supply system was used. The flow of HF through the control valve was
independent of the flow rate of Hz, hence the amount of HF was determined
as a function of time and the influent PHF was calculated from this value
and the effluent flow rate.

The effect of diffusion of Hz out of the reaction vessel need not

have been as great as indicated above. The mixing of the effluent gas,
36

primarily through turbulence, could have permitted re-equilibration of
the gas with the melt. This would reduce the error caused by loss of hy-
drogen from the system by diffusion.

Dead-volume.~-~-The preceding errors reflect the variations in pressure
and mass of flowing gas. There is one additional error in the pressure
determination at a given volume. This is the lag in measured pressures
because of the volume of the gas space above the melt. The following addi-
tional notation will be used:

T = temperature of gas above the melt, °k

Vm = volume of gas space above the melt
P = partial pressure of HF or Hz0 leaving the melt
P2 = measured partial pressure

dV = increment of gas flowing through system as measured at Tw, Pw .

From the mixing process,

moles of substance entering V, = (PldV)/(RTW)

moles of substance leaving V_ = (Png)/(RTW)

change of moles in Vm = (YmdPg)/(RZm) .

Thus,

(vap2)/(RT_ ) = (P1av)/(RT,) - (P2aV)/(RT )

and rearranging,

P = Vm(Tw/Tm)(dPg/dV) + P2 e

For most experiments, V= 0.400 liters and T_ = 300°K. When T = 773°K,
— — — O —— ——

(/T ) = (300/773) = 0.388 and when T = 973°K, (T /T ) = (300/973) =

0.308.

Therefore, at 500°C

Py = 0.1552(dP,/dv) + Pa
37

and at 700°C
Py = 0.1232(dPa/dv) + Pa

The most dramatic change in P2 occurred in the experiments when water
was introduced into melts which contained very little oxide. The maximum
rate of pressure change noted was 0.01 atm/liter. Therefore,

Py =1.55 x 10"% + P2 .

This large change occurred only during the first liter and only in the HF
measurements. During this time P2 increased to about 1 x 10"2 atm so that
the error in these unusual circumstances was only about 10%. At all other
times the chenge was less than 1 x 10™% atm/liter and often less than 1 x
10-2 atm/liter. For all of these conditions the error would be much smaller
than 1.0%.

This treatment assumes no further equilibration after the bubble leaves
the melt. If any did occur then application of the above equation would be
an overcorrection.

Summary .--The combined effect of these systematic errors on the over-
all accuracy of the results will now be considered.

Due t0 the measured~volume error all cbserved partial pressures were
1.0 to 2.0% low. The other errors do not affect the observed partial pres-
sures but do affect the material balance relationships used in treating the
data.

The calculated values of Q (i.e., x%/y) are 1.0 to 2.0% low for all
cases. This range is within the experimental scatter of the data. No
bias is introduced in calculation of activities because of the extrapola-
tion to pure BelFa2. The extrapolated thermodynamic values for BeFa(l) are

well within the precision of literature data. No comparison of influent
38

and effluent pressures is required and diffusion of H, should not influence
results.

The expected effects on Q,, (x/y)[0H"], are within the scatter of
the data. The quantity, (x/y), will not be affected by any of the errors.
The hydroxide concentration is based on proton material balance between
influent and effluent gas. Thus, due to the error in measured influent
pressures, the hydroxide concentration should be decreased by 1.5%. Due
to the error caused by diffusion of hydrogen, the hydroxide concentration
should be increased by 0.5 to 1.75% depending on temperature and flow rate.
Since the hydroxide concentration is proportional to QA’ the calculated
values for Q, could range from 1.0% high to 0.25% low. This range is
well within the indicated scatter of data, with QA generally known only
to * 10%.

For unsaturated melts, QO is based on the difference between oxygen
material balance and proton material balance. QO is subject to the same
corrections as QA, hence it is from 1.0% high to 0.25% low. The quanti-
ties QB and QC are derived from QA and Q, hence they are in error in the
same manner.

Random Errors

In order to give a satisfactory estimate of the expected precision
of the experimental measurements, the various random errors and their
probable magnitudes are considered.

Melt Composition.--The melts were prepared by adding weighed samples

 

of BeFa and LiF to the reaction vessel. The precision of weighing and
transferring samples to the vessel was about * 0.2%. The weight per cent of

Li, Be and F was determined chemically on filtered samples. The variation
39

in analyses of successive samples from the same melt was generally * 4%
for each constituent, which was clearly greater than the uncertainty based
on weights of components. Since both LiF and BeFz are hygroscopic, small
amounts of water were included in the weighed samples. Determination of
moisture content of typical samples by the thermogravimetric method indi-
cated 0.1 and 0.4% moisture, respectively. Thus, on the basis of the
above uncertainties in weight and moisture content, the melt compositions,
expressed as mole fraction BeFz, were probably known within % 0.5%.

The amounts of the impurities Cr, Cu, Fe, Ni and S were determined
in the starting materials, in filtered samples of the melt after it had
been sparged with Hz for more than 48 hr, and again immediately after
sparging for 6 hr with a dilute mixture of HF and H20 in Hz. All analyses
were within the following range: Cr always less than 20 ppm, Cu always
less than 100 ppm, Fe usually between 100 and 200 ppm, Ni usually less
than 20 ppm, and S always less than 5 ppm. Total measured impurities only
amount to about 350 ppm which is not significant in terms of melt composi-
tion.

The impurities could, however, cause some uncertainty in the partial
pressure measurements if the impurities reacted to liberate or consume HF
or Hp0 during an experiment. Consumption of HF would have occurred if
sulfide had been present in concentrations greater than 5 ppm by the reac-
tion of S%” with HF in a manner analogous to the reaction of oxide with HF.'Z*'7
Since the impurity levels were not appreciably decreased during the Haz
sparging, the impurities apparently were not reduced to the metallic state.

The results of Blood's study on the stability of the difluorides of nickel,

iron and chromium21 indicate they should eventually be reduced. However,
40

most of the reactions he studied required several days for equilibration.
His results indicate that: the Ni reaction vessel would not react with
HF to produce NiF, concentrations greater than 0.1 ppm with the highest
(PHF)z/PHg ratios employed here; the Cr would have been in the CrFz state
for all (PHF)z/PH2 ratios above 1 x 10”8 (true at all times except for
extended stripping with Ha); the FeFs concentration could have veried be-
tween the time when Hp was used and when (PHF)z/PHg = 4 x 10~* atm.

The Fe probably did not react rapidly enough to interfere (or the
analyses were in error) as indicated by the following experiment. Anhy-
drous HF-Hz mixtures (approximately 0.01 atm HF) were employed to remove
oxide and hydroxide from melt. After the melt was essentially free of

oxide, the effluent P, equaled the influent PHF' The HF was then stopped

HF
and Hz continued. The total amount of HF stripped out was about 5 ppm and

was probably due to HF solubility. If the Fe had been appreciably reduced,
more HF would have been detectable in the stripping gas.

Melt Temperature.--The temperature of the melt varied about * 0.5°

 

during the furnace heating and cooling cycle. The observed temperature
with the thermocouple at different depths in the melt did not vary more
than * 1.0°. Overall, the temperature of a melt was known and constant
to = 1.5°. One exception to the low temperature variation with dept oc-
curred when large amounts of solid IiF were in the melt. In this case
the temperature read about 15 to 20° lower at complete insertion of the
thermocouple than when the themmocouple was withdrawn about 1 in. from
the bottom. Even in this case the temperature varied no more than * 2°

when the thermocouple was withdrawn further. Apparently the solid LiF

settled to the bottom and was not stirred by the bubbling, and as a
41

result, loss of heat out of the end of the vessel was faster than the
transfer of heat from the liquid to unstirred solid.

Titer Precision.-=A 25-1iter reservoir of KOH was standardized with

 

potassium acid phthalate before initial use and again approximately 3 and
6 months later. All values agreed with the average value * 0.1%.

The 150-ml reservoir of the Karl Fischer apparatus was filled as
needed from quart bottles of Karl Fischer Reagent. The reagent was stan-
dardized each time the reservoir was filled and frequently thereafter.
Water (0.050 to 0.080 g) was added directly to the titration wvessel from
a weighing buret and the Karl Fischer titer determined. Successive titra-
tions agreed within #* 0.3%. Usually the concentration change from one
standardization to the next would not exceed 1%. The precision in measur-
ing the concentration of Karl Fischer Reagent was * 0.5%.

The volumes of both KOH and Karl Fischer Reagent used in standardiza-
tions were large enough so that the uncertainties in reading the burets
could be ignored. However, the much smaller volumes used during experi-
mental titrations were known only to % 1.0%.

Wet-test Meter Temperature.--The wet-test meter temperature, which

 

was the temperature of the gas as its volume was being measured, varied

no more than * 0.5° during a given experiment. Due to the variation in

temperature, the variation in measured volume is about * 0.2%, including
the effect due to the change in vapor pressure of water.

Endpoint Precision.--The precision in the timing of endpoints was

 

constant at * 0.5% of the measured value.

Flow-rate Precision.-~The precision in the timing of flow rates was

 

0.1 second per 100 ml. For a typical value of 50 seconds per 100 ml, this

would amount to 0.2%.
42

Statistical Erroxr Analysis

 

The probable error in the calculated quantities can be determined from
the magnitude of random errors in the various measurements. If the contri-
bution of each observable, a5 to the calculated function, Q, is known and
expressed as

a b m
Q=f(Q1:q.‘2: cevene ’qn) 2

and (AQ/Q) x 100 is % probable error in Q and (qu/qi) x 100 is % probable
error in s the contribution of errors can be calculated. If the errors
follow a normal distribution, it can be shown48 that the following equa-
tion allows for partial cancellation of errors of opposite sign:

(AQ/Q)Z = aa(éql/ql)z - bz(éqz/Q2)2 + ceenes + mz(éqn/qn)2 .

Evaluating the above equation numerically for each observable and taking
the square root of both sides will give the probable error in the calcu-
lated quantity.

Volume of Gas Titrated.--

 

ml of gas = f(time of titration, time of flow measurement )
(ml gas/ml gas)? = (0.005)2 + (0.002)% = 29 x 10™°
% probable error in vol of gas = 0.54%.

Millimoles H20 Titrated by Aligquot.-=-

 

millimoles Hp0 = f{conec Karl Fischer Reagent, vol Karl Fischer Reagent)
(Amillimoles Hp0/millimoles H20)2 = (0.005)% + (0.010)2 = 125 x 107
% probable error in millimoles Hp0 = l.ll%-

Millimoles HF Titrated by Aliquot.--

 

millimoles HF = f(conc KOH, vol KOH)
(Amillimoles HF/millimoles HF)? = (0.001)2 + (0.010)? = 101 x 10~

% probable error in millimoles HF = 1.00%-
43

Pressure HpO.--
PHgO = f(vol gas, millimoles Hz0, wet-test meter temp)

(aPHZO/PHZO)?' = (0.0054)2 + (0.0111)? + (0.002)? = 154 x 1076
% probable error in pressure Ha0 = 1.24%.

Pressure HF ==
P = f(vol gas, millimoles HF, wet-test meter temp)
(APHF/PHF)2 = (0.0054)2 + (0.010)2 + (0.002)% = 133 x 10~6

% probable error in P, = 1.15%.

HF
Bquilibrium Quotients.--The exact relationship of Q, QA and QO to

 

all of the variables cannot be expressed in the proper form to calculate
the expected uncertainty. However, use of only the dependence on the
pressure measurements would lead to 2.5, 4.0 and 4.7%, respectively, as
the most precise possible determinations. Both QA and QO depend on inte-
gral relationships between influent and effluent gas which increase the

uncertainty still further.
bty
ITT. RESULTS
Tabulation

Saturated Melts

Appendix A contains the data from each experiment performed on a
saturated melt. The experiments are arranged according to a three digit
"Run No." which indicates chronological order. Here, and throughout the
text, numbers preceding "BeF2" denote mole fraction. In the 100 series
the first experiments (101-123) were run in a 2-in.-diam vessel on 305 g
of 0.316 BeFs and 6 g BeO, whereas, for the later experiments (125-129),
enough BeF> was added to give 0.333 BeFa.

In the 200 series a 4-in.-diam vessel was charged with 1522 g of
0.80 BeFz and 10 g BeO for the first experiments (201-213). After this
composition was studied, enough LiF was added to give 0.70 (215-223),
0.60 (225-233), 0.50 (235-241), 0.40 (245-255) and 0.333 BeFa (257-273).

In the 400 series the first experiments (401-409) were run on 0.30
BeFy obtained by adding 44 g LiF and 3.0 g BeO to the melt used in the
300 series. For the later experiments (413-423) 87 g additional LiF was
added to give 0.25 BeFj.

The parameters listed in Appendix A are:

w = wt of melt, kg

T = temperature of wet-test meter, %k
a = influent P, atm x 107
= i 3
¢ = influvent PHQO, atm x 10”7 .
The effluent partial pressures, Py = x and PHgO =y, are tabulated (atm

x 10%) with the corresponding initial and final values of W. Note that
45

the use of W allows consistent comparison of experiments independent of
the weight of melt or temperature of gas-measurement.

Unsaturated Melts

 

Appendix B contains the data from each experiment performed on an
unsaturated melt. These experiments are also arranged according to a
three digit "Run No." In the 300 series a 2-in.-diam vessel was charged
with 500 g of 0.333 BeFz and anhydrous HF was used to remove oxide from
the melt. Measurements then were made while an aqueous-HF gas stream
was being passed through the melt.

In the 500 series the first experiments (501-527) were run in a 2-in.-
diam vessel containing 500 g of 0.333 BeFz. For the later experiments
(529-539) enough LiF was added to give 0.273 BeFz. Measurements were made
both while anhydrous HF was being used to remove oxide from solution and
while an aqueous~-HF gas stream was being used to add oxide to solution.

In the 600 series a 2-~in.-diam vessel was charged with 424 g of 0.60
BeF2 for the first experiments (601-615). For the later experiments (617-
627) LiF was added to give 567 g of 0.40 BeFa. Measurements were made
during both the removal and addition of oxide.

The format of Appendix B is identical to that of Appendix A except
that influent pressures are reported as P, =a + bW and P = ¢ + dW

HE H20
when gas-mixing method was employed.

Determination of Equilibrium Quotients

The experimental data were correlated according to the model presented

in Chapter I. Computer methods were developed for these correlations.
Saturated Melts

The experiments fall into the following three groups:

Case I. Measurements were made while both PHF and PHgO were still chang-

ing but were stopped before steady state was reached.

Case ITI. Partial pressure measurements were made only after PHF and PHgO

had reached steady state.

Case I1I. Measurements were made in both the changing- and steady-state

regions.

The program was designed to handle all three cases with only Case I
requiring additional input information. In all cases, since x and y were
determined alternately, direct calcuwlation of Q would require interpola-
tion, which was not very satisfactory where x and y were volume dependent.

The procedure of solution is outlined in the following steps:

1. For Case I, Q was specified as part of input information. For Cases
IT and III, Q was not specified; the camputer started with the largest
value of W and compiled average x and y as it moved to successively
lower values of W until the partial pressures became lower than the
average to that point by a specified amount (usually 4%). Safeguards
were build in to prevent the computer prematurely terminating this
process because of unusual scatter.

2. Using all of the partial pressures selected above, the average value
of x and the average value of y were calculated and their standard
deviations were expressed at the 99% confidence level. The best Q
was calculated from these averaged partial pressures and its standard

deviation was calculated from the deviation of its component parts.
&7

3. Using the Q calculated (or Q provided if Case I), each observed y was
1
converted to a corresponding x using the relationship x = (Qy)g, for
the initial region not used in the determination of Q.

4. Next, for each x (observed or calculated from observed y) the quantity

(4/Q)x +1 + [1 + (8A/Q)]%
log = £(w)

(4/Q)x +1 - [1 + (8A/Q) ]%

 

(this relationship was derived in Chapter I) was determined and tabu-
lated along with the midpoint, W,, for each observation.
5. These f(W) were now correlated according to the equation

£(w) = [1 -+ (SA/Q)I% Q (1/
24303

QA)W + constant
to obtain the best value of QA' The standard deviation in QA was cal-
culated by normal method for slope in a straight line correlation.

6. At this point a consistency check was made - the deviations from the
best fit were determined to see if the observed values of x were con-
sistently on one side of the line and values of x calculated from
observed values of y on the other side. If a difference had occurred,
Q could be readjusted or QA determined from x and y separately.

Steps 1 and 2 complete the calculation for Case IIT. Steps 1 through ©
complete the calculation for each experiment.
Several examples of the various cases are given in Figures 3, 4, and 5.

An example of Case I is given in Figure 3a, with the observed values of

x and y indicated by short bars. The line is generated by using the values

for Q and Q, determined by the correlation. Figure 3b is a plot of £(W)

vs W, indicating the linearity of the relationship. TFigure 4a gives an

example of Case III. The flat portion was used to determine Q. QA wa.s
48

determined from the initial region by holding Q constant. A plot of £(w)
vs W is given in Figure 4b for the applicable region of the above run.
Another example of Case I is given in Figure 5a showing the decrease in
x and y when influent HF and Hz0 were stopped and hydrogen sparging con-
tinued. Figure 5b gives a plot of £(W) vs W showing that the function
also holds when influent pressures are zero.

The values obtained for Q and QA fraom all of the saturated-melt ex-
periments are presented in Table 3. The values are arranged according to
composition and temperature of melt. Run numbers are provided for cross

reference with original data in Appendix A.
{atm}

x AND y

49

 

 

 

 

 

 

 

0.010
RUN NO. 273

Xger, =0.333 1= 600°

0.008 g =500 X102 atm
c=5.20 X 10”3 atm

—+ =510 X 10 ¥ otm

Q4=4.02 X 10”2 mole kg~

0.006

 

 

 

 

 

 

0.004 | e /“_‘z-.-"b" —"
— "

/ ,.a—'b"b'

0.002 |~ /

(@)

 

 

 

 

 

 

 

 

 

 

 

 

 

0 0.25 0.50 0.75 1.00 {.25
W (mote kg~! atm™!)

3.5

 

 

3.0

 

2.5

 

2.0

f W)

 

 

 

L~
10 Pz

 

0.5

{(b)

 

 

 

 

 

 

 

 

 

 

 

 

0 OA 0.2 C.3 0.4 0.5 06 o7 0.8 09 1.0
W (mole kg™ atm™1)

Fig. 3. BeO-saturated 0.333 BeF2 Showing (a) Calculated and
Observed Partial Pressures, and (b) Iinear Correlation of Pressures.
X AND ¥ (atm)

50

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.014 : . |
RUN NO. 407 i
o0 Xger,=0.300 #=700° l
' a=567x10 3 atm ‘ .
£=6.53 x10" 3 atm ‘ i
@=165x10"2 atm |
0.010 G =1.61x10"% mole kg~* ‘
4 _ _ - L o
0.008 // ;
0.006 f f %
. JI_____ — == St +
: "l"+r T+
0.004 —{ " 7 |
/ — ¥
/N *
0.002 1
[ 7
{o)
0 - .
0 0.50 {100 150 200 250 300 350 400 450 500 550 600 650
W (mole kg~ atm™)
4.0 ’ | T
- i
0.3
‘g —_
= 77
0.2 - 77
. J, /
-~
: ’/’ _i7/
! -
| T AT
G
s~
’ -
0.1 . "—// i
/...../f . i
,/42’ . l . |
0 040 020 030 040 050 060 070 080 090 {00 410 120 .30
w (mole kg~' atm™)

Fig. 4. BeO-saturated 0.300 BeFs Showing (a) Calculated and
Observed Partial Pressures, and (b) Linear Correlation of Pressures

in Applicable Region.
51

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.010
0.008 \
= - RUN NO. 408
© 0.006 Xger, =0.300 #=700°
—x g=0.0
; \ -y ¢=0.0
2 0.004 \ Q=165 x 10~ 2amm
> \ N @,=1.56 x40~ 2mole, kg ™"
= |
|
0.002 +. %h~\~
-
(@ NG| o —
0
0 050 100 450 200 250 300 350 400 450 500 550 600 6.50
w (mote kg~! atm™")
3.0
x
.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0 040 0.20 0.30 0.40 0.50 0.60 070 0.80 0.90 1.00 140 1.2C $.30
W (mote kg™ atm™)

Fig. 5. BeO-saturated 0.300 BeFp during Hp Sparging, Showing (a)
Calculated and Observed Partial Pressures, and ?b) Linear Correlation of
Pressures.
Table 3.

Equilibrium Quotients, Q and Qps Calculated from Data on

Oxide-Saturated Melts

 

 

g:?g ?%gg gg? * ¢ (atm) Qy + g-(mole/kg)
0.250 520 4192 ( % 0.26) x 10-% (2.77 £ 0.30) x 10-3
0.250 543 4232 0.02) x 10~3 (3.94 0.76) x 10°3
0.250 607 132 0.05) x 10~3 (6.08 1.10) x 10-3
0.250 655 421 (4. 0.09) x 10-3 (9.37  3.00) x 10~3
0.250 702 415 (9. 0.22) x 1072  (1.14 0.28) x 10°?
0.300 500 409 (4.19 % 0.07) x 10-% (3.82 * 0.29) x 10~3
0.300 540 403 ( 0.27) x 10~% (4.86 0.57) x 10™3
0.300 601 405 (3. 0.07) x 1073 (8.34 2.60) x 10-3
0.300 601 406 ( ) x 10-3 (7.04 0.78) x 10™3
0.300 652 401 ( 0.17) x 10°3 (1.35 0.16) x 10~?
0.300 652 402 (7. ) x 10-3 (1.23  0.15) x 10~
0.300 700 407 ( 0.03) x 10~2 (L.61 0.32) x 10°%
0.300 700 408 ( ) x 10~2 (1.59 0.21) x 1072
0.316 500 113 (6. 0.43) x 10~%

0.316 500 117 (6. 0.26) x 10-%

0.316 550 115 (1. 0.08) x 10™3

0.316 600 105 (4. 0.27) x 1073

0.316 600 107 (4 0.20) x 1073

0.316 600 109 (4 0.22) x 10~3

0.316 600 111 . 0.16) x 10~3

0.316 650 119 0.43) x 10™3

0.316 650 121 0.55) x 1073

0.316 700 101 0.14) x 1072

0.316 700 103 0.17) x 10~2

0.316 700 123 0.04) x 102

0.333 500 129 + 0.39) x 10~%

0.333 500 261 0.42) x 1074

0.333 550 127 0.09) x 10-3

0.333 550 263 0.06) x 103

0.333 550 264 ) x 10-3 + 10~ 3
0.333 600 125 0.16) x 1073

0.333 600 259 0.12) x 1073

0.333 600 265 ) x 10°3 x 10~3
0.333 600 269 0.20) x 10-3 x 1072
0.333 600 270 ) x 1073 x 10™3
0.333 600 273 ) x 10~3 x 10-2
0.333 650 267 0.04) x 10™%

0.333 650 268 ) x 1072 1072
0.333 700 257 ) x 10™2

0.333 700 271 ) x 1072 10~2
0.333 700 272 ) x 102 x 103

(continued)
53

Table 3. (continued)

 

 

gZ?E ?ggg gg? Q * o (atm) QA i:v(mole/kg)
0400 500 251 (2.07 £ 0.08) x 10~

0.400 550 252 (5.76  0.46) x 10-3

0.400 600 249 (1.47 0.04) x 10™3

0.400 650 253 (3.27 0.12) x 10~

0.400 700 245  (6.15° ) x 1072 (3.71 * 0.57) x 1072
0.400 700 2477 (5.00 ) x 10™2 (2.37  0.22) x 10-2
0.400 700 255 (6.15 0.21) x 10™%

0.400 700 256  (6.15° ) x 1072 (2.43 0.59) x 10”2
0.500 500 239 (4.80 % 0.20) x 1073 (2.85 £ 0.21) x 1072
0.500 550 241 (1.49 0.05) x 102

0.500 600 237 (3.27  0.11) x 10~?

0.500 650 244 (7.00° ) x 1072 {(2.9%6 0.82) x 1072
0.500 700 235 (1.40 0.15) x 10~ (8.50 1.00) x 1072
0.600 500 229 (8.07 £ 0.69) x 10-3 (3.99  0.40) x 10°%
0.600 550 231  (2.22. 0.12) x 1072 (8.05 2.00) x 1072
0.600 550 232 (2.22° ) x 1072 (2.71  1.20) x 1072
0.600 600 227 (5.10 0.43) x 10-2 (7.77 0.50) x 10™2
0.600 650 233 (1.05 0.10) x 10~ (1.14 0.13) x107%
0.600 650 234  (1.05P ) x 10°1 (8.03 3.70) x 1072
0.600 700 225 (2.1 0.09) x 1071

0.600 700 226  (2.05° ) x 10°r  (1.43 0.10) x 10~}
0.700 550 221 (2.78 £ 0.09) x 10™%

0.700 550 222  (2.78P x 102 (3.47 £ 2.30) x 102
0.700 600 217 (5.81 0.19) x 10~ (3.30 1.10) x 10°%
0.700 600 218 (5.81° ) x 1072 (6.78 3.90) x 1072
0.700 650 223 (.16 0.16) x 10~%

0.700 700 215 (2.15 0.10) x 10~% (2.22 0.21) x 1071
0.800 550 211 (2.98 + 0.11) x 10°*  (1.65 % 0.93) x 107t
0.800 600 200 (6.68 0.36) x 1072  (2.56 1.90) x 1071
0.800 600 209 (5.91  0.23) x 10~% (3.30 1.50) x 1071
0800 650 203 (1.40. 0.18) x 1071 (5.79 1.90) x 10~1
0.800 650 204  (1.40° ) x 107  (1.85 1.30) x 10°%
0.800 650 213 (1.25 0.05) x 10"1

0.800 700 207 (2.20 0.15) x 10”1 (6.15 2.10) x 10°1
0.800 700 208  (2.35° ) x 107 (2.08 0.68) x 107}

 

8501id LiF present, mole fraction BeFz actually higher than
indicated.

bCase I, Q value specified for QA determination.
54

Unsaturated Melts

 

Determinations of equilibrium quotients involving oxide and hydroxide
were based on material balance between influent and effluent gas. The
differential equations needed for this correlation were developed in Chapter

I. These equations were:

dr/dW = (QOS/QAr)(l +5Q,) -[a +e + (b + a)wl
and
ds/dW = a + 2 + (b + 24)W - (QOS/QAr)(l + 2S/QA) .

A computer program was developed for the similtaneous solution of
these differential equations using the Runge-Cutta method of solution.49
This caleculation required that the adjustable parameters, QO, QA, Ty and
8,9 and the fixed parameters, a, b, c, and d, be specified. With all of
these quantities chosen, the change in r and s with respect to W was calcu-
lated and new values estimated for r and s after the increment AW. The
cycle was then repeated stepwise and the process continued until a value
of W larger than a specified limit, wfiax’ was reached. In order to deter=-
mine r and s precisely without significant accumulative errors the step
size, AW, had to be restricted so that neither r nor s could change by
more than 10% for any step. Values for r and s were tabulated at the var-
ious values of W corresponding to the end of each step.

With both r and s known, both x and y could be calculated using the
equilibrium relationships. If the relationships
Qy = xs/y and A = xr [y
are solved simultaneously,

X = QOS/QAr and v = Qosz/QAzr .
55

These calculated values of x and y form smooth continuous curves al-
though exact equations for the curves could not be expressed. The deviation
of the observed x and y values from the calculated values was determined.

A general least squares method was used to improve the fit. The partial
derivatives of the x and y curves were determined numerically by making
slight changes in each adjustable parameter (QO, QA, T so) successively.
From the deviations and partial derivatives the adjustments in the param-
eters needed to minimize the squares of the deviations were determined.

With new values for QO, QA’ s and 8, the new values for x and y
were calculated. The least-square subroutine was repeated until the values

for Qo, QA’ r , and s, were essentially constant as indicated by their he-

O,
ing changed less than a preset limit (usually 1%) in successive steps.

The method would not work when the initial guesses were not reasonably
close to the correct values. Upper and lower limits were preset for the
value of each parameter. If these limits were reached the calculation was
terminated and the data resubmitted with different first guesses.

The '"best" values for the parameters Qys Qs T,» and s are reported
in Teble 4. The indirect method for detexrmining these values did not per-
mit calculation of the standard deviatiors of these parameters. Since a
large number of runs are reported for 0.333 BeF,, the spread in the Q and
QA values may be used as an indication of the uncertainties with which
these are known. The values for T, and sO represent concentrations of
oxide and hydroxide at the start of an experiment, hence their variations
are mainly the result of differing histories of the melts. The runs are

arranged according to composition and temperature with run numbers given

for cross reference with the original data in Appendix B.
56

A measure of the goodness of fit is given in Table 5. The mean of
the calculated x curve is given with the standard deviation of the observed
values of x from the calculated values along with the number of cbserved
x points. The corresponding information is also given for y. This tabular
information does not give a complete picture of the correlation, hence the
following figures are included to further show the relationships. ZEach
figure consists of two plots: one showing the calculated values of x and
v as a function of W with the pressure data indicated by short bars, the
other showing the values of oxide and hydroxide (r and s) at the same val-
ues of W needed to obtain the calculated values of x and y for the parameters
specified on each.

Figures 6 through 12 are all for 0.333 BeFz. Figures © and 7 (Runs
303 and 305) show similar conditions (60000) except for the initial oxide
concentration in the melt. Figure 8 (Run 306) shows the decrease in x and
y when the influent HF and H20O were stopped at the end of Run 305 and Ha
sparging continued. Figures 9 and 10 (Runs 307 and 313) are for 700 and
5OOOC, respectively. Figures 11 and 12 (Runs 501 and 511} show the behavior
during higher-temperature (650°C) and lower-temperature (550°C) removal of
oxide from the melt.

Figures 13 through 15 are for 0.273 BeFz. Addition of oxide is shown
in Figure 13 (Run 533) and removal of oxide is shown in Figures 14 and 15
(Runs 535 and 539). Figure 16 (Run 607) shows removal of oxide from 0.600
BeF2 which is near the upper limit of this technique. Figure 17 (Run 621)

shows the addition of oxide to 0.400 BeFgz.
Table 4.

Parameters for Unsaturated Melts from Least Squares Program

 

 

Temp Run { QA Ty 54

%BeFs (°C) No. (atm moles kg™%) (moles/kg) (moles/xe) (moles/kg)

0.273 600 529 3.23 x 10™7 4.11 x 1073 2.23 x 10*  1.00 x 10-%
0.273 600 539 2.57 x 1072 6.08 x 1073  1.56 x 102 1.00 x 107%
0.273 650 535 8.38 x 10~3 9.36 x 1072  1.59 x 102  3.66 x 1074
0.273 650 537 8.54 % 10™7 9.22 x 1073 4.53 x 1073 1.11 x 1077
0.273 700 533 2.72 x 10~4 1.08 x 1072  2.66 x 1073 1.92 x 1074
0.333 500 313 5.11 x 1076 5.23 x 1072 7.76 x 10™% 1.20 x 10™3
0.333 500 314 1.94 x 10°° 7.78 x 1072  3.31 x 1073 3.89 x 107%
0.333 500 503 4.39 x 107 6.34 x 1073 8.46 x 1073 2.87 x 1073
0.333 544 509 1.12 x 1077 8.69 x 1072 8.25 x 1074 1.7¢ x 1072
0.333 550 315 1.58 x 1072 1.02 x 1078 7.23 x10°% 7.99 x 10”4
0.333 550 316 1.11 x 10°° 8.53 x 1072 7.11 x 10°3 2.79 x 10°%
0.333 550 511 1.84 x 1077 6.77 x 1072  1.08 x 107% 7.52 x 10 %
0.333 550 525 2.55 x 1077 6.89 x 10°2 2.69 x 10~% 1.07 x 1072
0.333 600 301 5.15 x 1077 1.34 x 107%  6.85 x 10°% 1.23 x 107%
0.333 600 302 3.90 x 10°° 1.34 x 10 6.27 x 10”3  1.57 x 102
0.333 600 303 6.39 x 10~7 1.50 x 10™% 1.3l x 10™%  4.82 x 1073
0.333 600 305 6.05 x 1073 1.06 x 1072  7.08 x 10~% 8.73 x 107’
0.333 600 306 3.93 x 10~° 1.15 x 1072 8.10 x 1072  1.55 x 1072
0.333 600 309 6.33 x 1077 1.16 x 1072  1.04 x 1073  2.41 x 10°%
0.333 600 310 473 x 1077 1.10 x 1072 1.29 x 1072 1.34 x 107%
0.333 650 319 2.63 x 10™% 2.76 x 107% 1.0l x 103 1.00 x 1074
0.333 650 501 2.05 x 10™% 1.27 x 1072  2.01 x 1072 6.61 x 1074
0.333 650 513 2.55 x 10™%4 9.78 x 10”3 2.35 x 103 1.56 x 10”4
0.333 650 514 1.00 x 1074 1.93 x 1072  8.00 x 1072 1.36 x 1072
0.333 651 527 2.53 x 107% 1.62 x 1072 5.42 x 10-3 1.11 x 10773
0.333 700 307 6.82 x 1074 2.92 x 1072 1.29 x 10"? 5.37 x 10°¢
0.333 700 311 9.87 x 10™% 2.90 x 10"% 2.10 x 10”2 2.24 x 10”4
0.333 700 @ 523 7.24 x 107% 1.57 x 107%  3.07 x 10°% 8.28 x 1077
0.333 700 524 6.00 x 10™% 2.15 x 2072  1.80 x 10”% 8.00 x 10”3
0.400 550 619 1.48 x 1074 2.27 x 2072 1.36 x 107% 1.6l x 107%
0.400 550 625 9.10 % 10°° 1.55 x 1072 9,20 x 1074 3.37 x 1074
0.400 604 621 4.94 x 1074 1.58 x 1072  3.84 x 1073  4.49 x 1074
0.400 702 627 6.00 x 10”7 3.0l x 1072  1.50 x 107°® 1.65 x 1074
0.600 500 607 1.96 x 1074 2.39 x 107®  2.09 x10"% 1.83 x 10°°
0.600 600 611 1.14 x 1073 6.97 x 1072 2.66 x 10°2 5.79 x 10 %

 
58

Table 5. Comparison of Calculated and Observed Partial
Pressures for Unsaturated Melts

 

Run (Mean of x *¢) x 10° DNo. of (Mean of y *¢°) x 10> No. of

 

No. (atm) Points (atm) Points
301 10.252 * 0.309 35 5.979 * 0.128 26
302 4 442 0.634 10 3.906 1.189 7
303 6.325 0.247 30 7.571 0.208 25
305 9.726 0.285 42 6.843 0.230 38
306 3.030 0.155 13 4.109 0.383 10
307 15.177 0.355 47 4. 478 0.454 32
309 6.974 0.260 39 4.559 0.141 33
310 2.908 0.29% 10 3.157 0.381 12
311 11.307 0.302 60 2.866 0.258 39
313 6.296 0.267 33 11.434 0.497 32
314 1.207 0.170 8 6.469 0.929 12
315 9.490 0.462 4y 12 .455 0.679 36
316 2.728 C.273 18 16.710 1
319 16.884 0.915 40 7. 747 1.404 33
501 5.076 * 0.126 36 2.181 £ 0.192 26
503 2.149 0.095 22 1.596 0.117 20
509 7.031 0.387 47 5.474 0.422 38
511 5.921 0.298 39 2.554 0.298 39
513 11.164 0.349 41 3.939 0.264 30
514 4 .988 0.462 15 2.568 0.333 10
523 12.871 0.362 49 2.895 0.138 34
524 5.921 1.143 15 1.848 0.956 8
525 3.302 0.198 51 3.124 0.268 47
527 10.085 0.247 40 4.089 0.305 33
529 7.953 £ 0.557 40 5.582 + 0.993 40
533 11..392 0.207 3% 3.416 0.182 31
535 7471 0.330 23 3.599 0.282 25
537 7.911 0.159 40 5.034% 0.287 40
539 7.975 0.286 46 3.372 0.335 4ds
607 9.400 * 0.300 21 5.760 * 0.359 23
611 12.910 0.709 46 1.600 0.326 31
619 10.520 + 0.236 17 6.902 * 0.249 12
621 11.745 0.700 32 2.320 0.178 22
625 10.366 0.523 41 2.907 0.159 33

627 14.812 0.651 33 1.131 0.210 18

 
59

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(x1073)
@ g T e
| enmmm—— .
. /__ 4 -+ -+ . ]
E - *‘—,Mh — e X
: . '/
5 it :
o RUN NO. 303 :
< !
. Xger, = 0.333 £+ 600°
a=3.82 x10™° atm
c=405x10"2 gtm
Qo =16.35x107° atm mole kg™*
2 // Q=150 x10" 2 mole kg~! -
0
(x10™3) s
18 /
/
16 /

 

A/

 

 

r AND s {mole kg—i)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 45 50
w (mole kg™ otm™")

Fig. 6. {a) Dependence of x and y on W, and (b) Variation of r and
s with W. Run No. 303.
60

 

(x10™%)
o I\ -

\ ! RUN NO. 305
'-\ Xaer, = 0.333 #=8600°
12 a=3.82 x 10”3 atm

\ ; ¢=1.05x10"2 atm

\ Gp=6.05 x10"~5 atm mole kg~
Q,=1.06 x10™2 mole kg™ ___

Q

 

 

 

 

 

 

 

3

 

 

 

 

el e |tk - e’

‘ \
i —
-—-—.__
/w‘)‘J | T T T e—— X
{
o -

@

 

 

X AND ¥ (atm)

 

 

 

 

 

 

 

 

 

 

 

(5)

 

 

 

 

 

 

 

\

 

o

 

10 -

r AND s (mole kg~ ')

\m
\

 

 

 

 

4///

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

o 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 60 6.5 7.0
w (mole kg'i atm™')

Fig. 7. {a) Dependence of x and y on W, and (b) Variation of r and
s with W. Run No. 305.
61

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(a) :
(xt0~3) |
RUN NO. 306
L XBan =0.333 +F=600°
6 o=0.0
- c=0.0
‘E Gp=3.93 x%o“5cfm mole kg~' |
A - -2 -1
- OA—HSHO le? kg 1
% 4
Ty
3¢
2 N
\\
\ X
0 Y
{£)
-
(x10~3) "
//
14 \; /
12
1o
i \
o
=
@
°
£ \
8
n
z
I
- \\\\
5 \
4 \
\S
2
C
0 0.5 1.0 .5 2.0 2.5 3.0

W (mole kg™! atm™')

Fig. 8. (a) Dependence of x and y on W, and (b) Variation of r and
s with W. Run No. 306.
62

(x1073%)

i
RUN NO. 307
12 Xger, = 0.333  +=700°
0=3.95x10"°> atm
c=1.05 x 10" % atm

@, =6.82 x10™% atm mole kg™
@ = 2.92 1072 mole kg™'

x AND y (otm)
S

 

 

{x107>) T , \ )
” (6) | | /"

 

 

 

 

 

 

 

 

 

 

 

r AND 5 {(mole kg“)
o

 

 

 

 

 

 

 

 

 

0 A 1 ; 5 i
0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 55 6.0 6.5 7.0
w (mole kg~ ' atm™")

 

 

 

 

 

 

 

 

 

 

 

Fig. 9. (a) Dependence of x and y on W, and (b) Variation of r and
s With I‘I- RUI]. NO- 307.
63

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(x10) | - T
(o)} 4 fiu___—-l——y
! +++-——'—+-
i -“ie-)
[ P™
10 / i
T / RUN NO. 313
5, L Xger, = 0.333  #=500°
> H . a=00
2 U/# | c=163x10" atm
< ) Qo = 5.1 x107° atm mole kg™
x \\.;  §,=523x10">mole kg™’
.\ — .
4 -_"'-'—---_._‘ X
2
O 1
(x4073)
(5}
18
s
16 /’/
14 v

 

 

 

 

rAND s {mole kg™")
n

 

 

 

 

//

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 50
w {mole kg~ ! atm™')

 

 

 

 

 

 

 

 

 

 

 

 

™Mg. 10. (s.) Dependence of x and y on W, and (b) Variation of r and
s with We Run No. 313
64

_3)

 

{x10

 

 

 

 

 

-
{a) | o L _ X
e - N
T
©
~ 4 - :
\
O
=z
< +
- } - ++ bty

 

 

 

 

 

 

 

 

 

(x107%)
(b)
18 |
RUN NO. 50!
Xger, = 0-333 1 =650°
N | a=975 x 10" ° otm \

 

6 i b=-2.4x10" Y atm W’
\ ' c=6.50x10"* atm

| d=-95x10"% atm w ™

14 \ @;=2.05 x 10~ % atm mole kg~

\ Gy =127 xlO_zmole kg~

 

 

 

 

 

 

r AND 5 (mole kg™ ")

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

10 \r
8 + ‘r
6
—— ;
\
\\—
a /
‘ s
2 / *
|
1
o |
0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
W (mole kg ' atm™")

Fig. 11. (a) Dependence of x and y on W, and (b) Variation of r and
s with W Run No. 501.
65

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

_3 T
(K 10 ) (a) |
10 ! i I
i ! - l —— —-——— X
4 -— -
s e %
- RUN NO. 51l
g , - XgeF, = 0.3323 #=550°
~ 6 f T ¢=1.03 x10" < atm
o | - ; b=-1.0x10"Yatm w™'
i s | ¢= 400 x10"% atm
x - | ‘ d=-40x10"%atm w™!
4 - ' Q.= 1.84 x10”5 atm mote kg™!
o : 0 ¢
< ++M#HH | 4= 6.77x10~3 mole kg~!
| +y-
6 =/ ; { ..'"l-.___\: +
- ! \“M:t
l ¥
0
{(x107®
{b)
10
|
® |
T |
x !
-é 6 N | p—— ‘ '
- ‘
s / \\
<1 |
L 4 \
\\ i
\\
]\"-‘-—-__ -—-._.___I—-—._.__‘ s
;
1
0
0 0.5 .0 15 2.0 2.5 3.0 35 40 45 5.0 55 6.0

W (mole kg~! atm™")

Fig. 12. (a) Dependence of x and y on W, and (b) Variation of r and
s with W. Run No. 511.
66

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(x 10_5) __ T ; ‘ T
{g) _ -
.
12 \ |
| |
| | = |
10 . 1} ' "-,.__;L-_—fi-_ Afl
RUN NO. 533 ' X
XgeF,=0.273  #=700° ;
Eq | 0 =4.47x107> atm 5 f
s ’ c=763x10"° atm f !
= Q=272 10~ % atm mote kg ! ‘
g &y =1.08x10 2 mate kg-'
x © ! J
| ! l
' |
44 e |/
el
4 s . 24
M
+
2 ..I.LA }
O i
(x10™%) ! I T
(5) -
14 e
I //
12 e

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

10
]U'i i
. e
E /
. !
O
Z 6 —
v .
e S
/
//
4 —
/ /
2
é
5 |
o 0.5 1.0 .5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

W (mole kg~! atm™1}

Fig. 13. (a) Dependence of x and y on W, and (b) Variation of r and
s with W. Run No. 533.
67

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

{(x 10_3)
(o] // x
10 ; g™
//
/,/ RUN NO. 535
8 - XBeF, = 0-271 * = 650°
€ A‘ g=¢50x10"“ atm
E - _ -4 -9
° b=-24x10 " otm W
~ = c=55x10" *atm
e 6 =60 x10 % otm w!
< §y=18.38x 107° atm mote kg™
- / T 9, =9.36 x10”> mote kg™
4 R P —
fo
%_ \"'-...}’
2 {
0 |
|
{8 ‘1
(x10"3) t
14
12
-"fi 10
o
x
°@
o
E
w 8 N
o
z
<
k \
6 z \\\
4 \ \
%"-—.S
2 “~r
0
0 0.5 1.0 1.5 2.0 2.5 3.0 35 4.0 4.2 5.0

w (mole kg" atm™")

Fig. 14. (a) Dependence of x and y on W, and (b) Variation of r and
s with W. Run No. 535.
68

 

 

 

 

 

 

 

 

 

 

 

(x107) T
{a}
’/.""—'—'._-_ X
12 _ ,/’
/ RUN NO. 539
/ Xgep, = 0-273  #=600°
10 a=1.45x10"2 atm i
b=-2.0x10"*atm ™
- c=5.50x10""% atm
d=-6.0x10"%atm w™!
@n=12.57 x107 7 atm mole kq_' ]

G, = 6.08 x10™> mole kg~

 

 

x AND y (otm)
©

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

r AND 5 (mole kg™ 1)
® S

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

a
2 \
\>‘"‘—— $
° 0 05 1.0 1.5 2.0 2.5 3.0 3.5 40 4.5 5.0 5.5 6.0
W (mole kg™* otm™*)
Fig. 15. (a) Dependence of x and y on W, and (b) Variation of r and
s with W. Run No. 539.
69

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(x10™3)
X (a)
10 ) e —
X
/f
L -~ -
- T :
E Ho it ++ :
:_6' 6 7 + \*tf - —-= - T T ———— - .- -
N RUN NO. 607 i ‘
2 Xger, = 0.600 #=500° k\-fi:" '
S a a=2.00x10*23atm P
=—1145x10" " otm W' \
c=1.36x10"% atm | —,
d=-44x10 atmw ™ | !
2 — Qp=1.96 x 10™* atm mole kg™’ fi‘ e —
@y =2.39 x1072 mole kg™ |
0 | | | | |
1073 ‘
(x (6) 1
18 \--\\ T -
{6 \ \\ ‘
[
14 |
T2 ,L \ N
2 ! N \
% \ i
E
“ 10 N .,
a \ \
N
8 S ‘
S
1
6 \br
4
2
0
o 0.5 1.0 (5 2.0 2.5 3.0 35 4.0 45 5.0 5.5 6.0

W (mole kg~! atm™ )

Fig. 16. (a) Dependence of x and y on W, and (b) Variation of r and
s with W. Run No. 607.
70

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(x1073 g T
(a) - -
- I
. - S L
| - |
i -.‘__._"_l——.__..____.
. \h X
0 t
RUN NO. 62t
I Xgep, = 0400  £=604°
€ g 7=6.45x10"2 otm
s c=5.90x10" > atm
; Gy =494 x40~ % atm mole kqg™!
Z ! Q,=1.58 x107% mole kg™
x 6 ) i
4 _
s}
_—-—# s ‘
e T
2 fi } S
//fiffl ¥ |
0 ; ‘ |
(x10 ) T }
(6)
14 F— - - i + —_—
12 — —
/
=0 -t ' ——— —
1 i |
2 / =
= .
2 .
£ e
8 - — — e —— e} -
«»
o /
z
<
[ /
6 — —— L .
.___—-5
—l-'_—_-
/ /
4 / —_-_;"'"
|
|
2 i
o i i . |
0O 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 50 55 6.0

W (mote kg™' otm™!)

Fig. 17. (a) Dependence of x and y on W, and (v) Variation of r and
s with W. Run No. 621.
71

Validity of Results

The general agreement between the calculated and observed effluent
partial pressures of HF and Hp0, in view of the variely of experimental
conditions, supports the method of measurement and indicates that the equi-
libria assumed were correct and sufficient. OSome specific examples which
support these equilibria are given below.

Saturated Melts

 

The first clearcut indication of the formation of hydroxide in mea-
surable amounts came from the variation of effluent pressures with respect
to volume of carrier gas. VWhen a mixture of HF and Ha0 was introduced into
a BeO-saturated melt containing little or no hydroxide, the effluent par-
tial pressures of HF and Hz0 (x and y) increased with the increase in
volume of gas passed in such a manner that x2/y remained constant, vhile
x/y decreased. Since Q = x®r/y and Q = xs/y, the quantity x*/y would
be constant when r is constant (fixed by Be0 saturation) and x/y would
decrease as s increases.

The influent partial pressures of HF and Ha0 were varied and the
resulting Q's compared. Rums 101, 103, and 123 for 0.316 BeF2 at 700°C
(with reported Q values of 2.18 x 1072, 2.47 x 1072, and 2.13 x 10™2,
respectively) had influent pressures such that influent (PHF)a/(PHQO)
were 4.36 x 1072, 4.46 x 1072, and 4.25 x 10”2, respectively. Runs 105,
107, 109, and 111 for 0.316 BeFp at 600°C (with reported @ values of
4,61 x 1073, 4.07 x 1073, 4.09 x 1073, and 4.69 x 10”3, respectively)
also indicated that the cbserved Q's were independent of the influent
pressures, with influent (PHF)z/(PHaO) values being 6.52 x 1072, 2.28 x

1072, 5.54 x 10™2, and 4.98 x 10”2, respectively.
72

These runs include cases where the influent and effluent pressures
were nearly identical and also where quite a bit of HF was required to
react with oxide to form water and the reverse (Hz0 reacting with fluoride
to form HF). All three gave Q's in agreement. In the early runs, the
flow rate of carrier gas was varied from 50 to 150 ml/min and no variation
in the effluent pressures was observed.

The QA values determined using saturated melts were similarly found
to be independent of the ratios of HF and Hp0 in the influent stream. Also,
QA was shown to be independent of whether hydroxide was being added or re-
moved by the gas stream. For example, see the odd-even pairs 401-402,
405-406, and 407-408 in Teble 3 for 0.300 BeFa at 652, 601 and 700°C,
respectively.

The proton balance between influent and effluent gas streams, after
the initial region where hydroxide was being formed, alsc attests toc the
vallidity of the measurement.

After completion of the 200 series the melt was transferred from the
vessel through a sintered nickel filter and the material on the filter
examined by x-ray diffraction. The characteristic peaks for LiF-BeFz and
BeO were observed. There was no indication of compound formation between
BeO and the fluoride melt or of other constituents [such as Lia0 or Be(OH)a]-

Unsaturated Melts

 

In addition to the tests performed with saturated melts, the validity
of Qo was checked by conducting experiments in which oxide was being added
and a8lso when oxide was being removed. The former, more precise results,

and the latter were in reasonable agreement.
73

The total pressure of the reactive gases was varied by changing the
termperature of the saturator with no noticeable effect on the QO and QA

values.
7
IV. DISCUSSION

The measured equilibrium quotients, Q, QA’ and QO, were correlated
with temperature and melt composition in terms of simple algebraic expres-
sions. In the case of Q, wherein Ka = Q/aBer, the resulting correlation
can be used to derive a considerable amount of thermodynamic information
about the LiF-BeFp solutions and, by extrapolation, about pure BeF, liquid.
Combination of Q and QO can be used to obtain the concentration of oxide
at BeO saturation. The variation of QA with melt composition and tempera-

ture reflects the stability of hydroxide in LiF-BeF; melts.
Correlation of Q

For each composition, the Q values were correlated according to the
equation log Q = slope(1/T) + constant. The Q's were weighted by an amount
inversely proportional to their variance since all measurements did not
follow the same parent distribution. The values of the parameters are
presented in Table 6.

Since one of the primary objectives was determination of thermodynamic
properties of Bng(i), extrapolation of these data as a function of XBng
to the pure liquid BeF; was desirable. For a given temperature,
log (Q/XBng) Vs (XLiF)2
forms a parabola for the composition range 0.30 to 0.80 BeFz, thus the Q
values at various compositions were correlated by the function
log (9/Xg p,) =k + (X p)? + m(x, )% -

From definition in Chapter I, log Ka = k, therefore, correlation of k as
a function of 1/T will yield the thermodynamics of the desired reaction.

Both 1 and m also show linear dependence upon l/T- For the coefficients
75

expressed according to k = k° + k'(1/T), etc.

¥° =  3.900 * 0.019 k' = 4418 £ 17
1° = 7.819 % 0.225 1! = =5440 = 218
m° = -12.66 * 0.60 m! = 5262 + 513 .

From the above parameters, equations were generated for each experimental
composition as a function of (l/T). The smoothed parameters obtained are
tabulated in Table 7. The lines generated by the smoothed parameters for
the various experimental compositions are shown in Figure 18 along with
log K, vs (1/T) for pure BeF2(l) based on the extrapolation. Figure 19
provides a measure of this correlation. The quantity des/Qcalc is shown
for each experimental run. The standard deviation for each point is rep-
resented by a vertical bar.
Activity of BeFp and LiF

Since Q is equal to Ké(aBer),
log (Q/¥p.p,) = log K lap p )/(Xpg) = Tog K + 1og (ap p /Xpp,)
By definition, aBng is unity for pure liquid BeF; (XBer = l), therefore,
log (aBer/l) = Q0. Since XiiF = 0 at this point,
log K, = k® + k'(1/T)
In order to solve for log (aBer/Xéer), which is log 7fieF2’ at any com=-

position the value of log K  must be subtracted from log (Q/XBer) leaving

- O L, 11 2 0 1 4
log Yo, = 17 + 11 (/D) IXP 0 + [ + (/M 1% 0
At a specified temperature, the variation in ZBng with composition
is given by

- ox® 4 pxh .
10g Yo, = Kpip X p

Values for the parameters at three temperatures are presented below:
76

 

(¢ a o B %o

500 0.783 % 0.380 -5.85 £ 0.89
600 1.589 0.356 ~-6.66 0.85
700 2.229 0.338 -7.25 0.80

The quoted uncertainties in ¢ and B lead to an average uncertainty of

* 0.10 units in log 7. From these uncertainties the values 100°

BeFp'
apart would overlap within the quoted uncertainty, but the values for
500 and 700°C definitely do not overlap.

According to the Gibbs-Duhem Equation, if the activity (or activity
coefficient) of one component is known as a function of composition, the
other can be determined by integration of the equation
d 1n (72) = -X1/%X2 4 1n (71) .

From the equations given for log 7EeF2 as a Tunction of composition

at specified temperatures, integration was carried out as follows:

2 4
108 Ypep, = Fpip * PX sy

— 3
d 1og Ypop, = (200, g0 + 4BX°, ) Ay p

(1 - XLiF) (
Xar

d1n yup=-

2.303)(2axLiF + 46X3IiF) S

- _ 2 3

In 7, p = (2.303) jfi(-za + 20K o= ABXA Lo+ ABXPL L) AXL o
_ 2 3 4 i

log Y p = =20% .o + OXA o (4/3)BX gt Pt C

Twvo methods for evaluating C for various temperatures were considered.
For a given temperature, if NiF is known for one composition, C can be

determined and, hence, 1T determined for all compositions. First,
77

7LiF was calculated from the reported composition at LiF liquidus at
various temperatures vhere a, .. £ 1 and ¥ o = l/XLiF' The values for
7LiF at the various temperatures were determined from the published phase
diagram2 which was presented in Chapter I. The second method involved

the use of the Q values for BeO=-saturated melts in contact with solid IiF

to determine the XiiF at saturation. (The measured Q's are tebulated in
Teble 3 and the parameters for smoothed fit are given in Table 6.) The
equations for log aBng as a function of composition and log aBng at

IiF saturation were solved simultaneously to obtain XiiF' With the con-
centration of LiF at Bap = 1 known, Yr 4T could be evaluated. The following
values for C were obtained by the two methods.

 

 

 

 

 

 

 

 

 

From Thoma's Phase Diagram From Solution of Equations
%Egg "er,  TLiF ¢ "BeF2  I4F C
500 0.329 1.490 -0.299 0.321 1.473 -0.328
600 0.280 1.389 +0.083 0.281 1.391 +0.086
700 0.208 1.263 +0.283 0.256 1.344 0451

Agreement of values of C determined by both methods is very good at 500
and 600 but not at 700°C. Although ILiF saturation at 700°C oceurs at
0.208 BeFa, the value of C corresponding to a calculated saturation value
of 0.256 BeFa was considered more acceptable because the parabolic func-
tion does not fit the data well below 0.30 BeFz. In fact, at 0.25 BeFa
(data at 650 and 700°C) the fit is very poor.

Other empirical expressions were tried in an attempt to improve the
fit in this region. No improvement was obtained using expressions con-
taining additional odd-powers of XLiF’ but a very good fit was obtained

from 0.25 to 0.50 BeFa by using an equation containing X%, X%, and X
78

terms. Correlation of the data at 700°C gave the following equation:

6
7 P + 12.51X LiF

This equation should be compared with the correlation using only X? and

log (q/xBeF2) = =0.723 + 4.094X . o - 16.64X4Li
X% terms:
log (@/Xp.p ) = -0.640 + 2.220%% . o - 7.25%% L

Both fit equally well between 0.33 and 0.50 BeFp, but the former fits
better for concentrations below 0.33 BeFs and the latter fits better for
concentrations above 0.50 BeFz. In order to obtain values for ZBeFa from
the former equation, the constant term was adjusted to yield the same vale-
ue of 7Bng (at 0.40 Bng) as was given by the simpler expression used to
express activities above 0.30 BeFz. The expression obtained for log ZBeFa
was given by:

= ewije . 2 -~ . . 6
108 Ygep, = =0 0382 + 4.094X% 1 = 16 64X4LiF + 12.51x8_,

F IiF

The Gibbs-Duhem integration was carried out on this equation in order to

obtain the expression for log 7iiF:

= wmQo . 2 . 3
= -8 188XLiF + 4.094X g * 22.20X°_

5
F 14T 15.01X7. .

1og F IiF

4
7i,iF 16.64X Li
6 _
+ 12.51X I4F + C

If this equation is solved simultaneously with the equation for log aBng
at LiF saturation, the concentration equals 0.208 BeF; (the same as re-
ported by Thome) and the value of C equals 1.124.

Figure 20 shows a plot of log 7.

BeF»
composition at 500, 600, and 700°C. The dashed lines indicate the values

and log 7LiF as a function of

at 700°¢C (below 0.30 BeFz) when the equation with the x6 term was used.

LiF

(The overall fit was not improved by using the extra term, hence the sim-
pler form was used for the more general correlation.) The dotted line

indicates the values of log 7

IiF at which the solid LiF phase would appear
79

and the values of log 7 at which the pure ligquid BeFs phase would

BeFs
appear.

The (-*-+-) line shows the predicted behavior of log Tper, o0 the
basis of a simple model in which, for the region 0.33 - 1.0 BeFz, the
components are redefined as BeFz and LipBeF, and the activity of Belz is

1 > -
BeFy " The value of X BeFa is re
lated to XBer, the mole fraction in IiF-Befy mixtures, by

! = - .
X oer, = (pep, = 1)/ 2%pep,

3 — t * . LIS
Since aBng = X BeF as defined above, the activity coefficient of BeF;

assumed equal to the mole fraction X'

in ILiF-BeF; mixtures is given by
ZBer = (BXBng - l)/ZXaBeFa ’

This procedure of redefining components is similar to the method of
Flood and Urnes;50 however, the assumed proportionality of aBeFa to its
mole fraction is purely arbitrary and the resulting correlation, which is
rather good, is, therefore, entirely empirical. It might be more reason=-

able in this model to expect to be proportional to the product of

aBeFa

the cation fraction of Be?" and the anion fraction of (F ) squared [i.e.,
s 1 3 . . .

®per, proportional to (X Ber) ], the melt being considered to be a simple

mixture of the four ions Li+, Be2+, F, and BeF42'. In order to rationalize

. * 1 -

the proportionality of aBng to X BeFa it seems necessary to adopt one of

the following unattractive models for the components

IiBeF,; (undissociated) + BeFa (undissociated)

or

Liz?t BeF,2™ + Be?t BeF,2" .

A more realistic approach to an interpretation of the behavior of

aBng and arsp con perhaps be made in terms of models such as have been
80

proposed by F‘drland-5l According to this model BeFa(%) is assumed to be
a three-dimensional polymer of BeF4°~ tetrahedra with common corners, and
the addition of LiF is assumed to break the Be-~F-Be bonds. However, no
such correlation will be attempted here.
Two features of the observed variation of aBng are especially note-
worthy:
(1) The rapid drop in Tger, &5 Xpep, 8PProaches 0.33, at all temperatures,
suggests the formation of BeF4%~ ion.

(2) The temperature coefficient of 7 indicates increasing positive

BeF2

deviations from Raoult's law with increasing temperature at high
XBer values.

The activities of BeFz and IiF were calculated from the activity
coefficients as a function of composition and temperature. The activities
at 500, 600, and 700°C are shown in Figure 21. The plot of activities,
which should be proportional to the partial pressures of BeFz and LiF,
corresponds to the predicted behavior of a system showing incomplete mis-
cibility.52 Since the positive deviations increase with temperature,
these data seem to indicate that the system has a lower consolute temper=-
ature near 700°C and 0.80 BeFp. Although the number of determinations of
Q in this area is not extensive enough to definitely show the formation
of two liquid phases, the indication is strong enough to warrant further
investigation of this possibility. To date there is no clearcut evidence
of partial immiscibility in the LiF-BeFz system although various investi-
gators have considered the possibility of such occurrence.53'55 The MgO-
5102 system, which has frequently been compared with the LiF-BeFz system,l

indeed does show a miscibility gap. At least one case has been reported
81

for a similar fluoride melt. At low LiF concentrations in the system,
LiF-BeF,~-ZrFs;, evidence was obtained from quenched samples that two immis-
cible liquids were formed above the ZrF, primary phase field.56

The IiF activity exhibits large positive deviations at low BeFp con-
centrations; however, it should be kept in mind that these activities are
referred to the solid rather than the supercoocled liquid (if the latter
were used as the reference state, all of the activities would be lower).
The activities reported in the present work are in general agreement with
previous measurements (surmerized in Teble 2). The largest discrepancy
is in the value for LiF at 0.50 BeFz reported by Berkowitz and Chupka-22
The value for IiF by Bfichler24 is in reasonable agreement. Also, Biichler
obtained greater activities for BeFz at higher temperatures.23 Special
attention should be given to the value reported for 0.67 BeFz (displaying
very large positive deviations) which corresponds very closely to present
values. This agreement is particularly gratifying since three completely
different techniques have been used to obtain the values. Also, the pre~
vious studies were performed with melts which did not have BeO present.
The presence of BeO would not be expected to affect the activities since
BeO is only slightly soluble. Beryllium oxide could not have affected
the Gibbs~Duhem integration since BeO was always present as a saturating
phase, thereby restricting its activity to unity.

The expression for the relative partial molal heat content is given

by:
3ln 7 (H; - Hlo)
3T RT?

From the expression for log ZBng’ the appropriate differentiation may
be carried out to obtain

9 log xBer

= - t2 tyéh 2,
= - (1'x + m' x4 ) (1/T)

3 I4F

Therefore,

1y 2 tvh = (" - .
(1182 4+ m' X p) = (Bpep, Hper,)/2+ 303R
and

H - - . - i 2 -t 4 .
(HBeF2 HpBer) 2.303R [(-5440 * 218)X gt (5262 % 513)X g

Values for the relative partial molal heat contents at various composi-

tions are tabulated below:

 

 

 

'(EéeFa " HPBng) (fiéng - HpBeFa)
XBer cal/mole XfieFa cal/mole
0.80 - 961 £ 40 0.40 -5839 * 471
0.70 -2045 = 92 0.333 -6309 * 640
0.60 ~3363 + 224 0.30 ~6420 * 745
0.50 ~4718 = 228

Since the activity coefficient of BeFz is given by an analytical
expression, the excess chemical potential of BeFz can be directly cal=-
culated from

E = RI1n ¥

H BeFas Bel's

Since 1n yBng is a function of temperature, this equation does not lend
itself to easy tabular or graphic presention (unless in a plot similar
to Figure 20); however, the analytical expression should be useful for

further calculations involving the excess chemical potential.
83

Table 6. Parameters from Correlation of Q as a Function of Temperature
at Specified Compositions

 

 

Xper, (slope o) x 1073 constant * ¢
(IiF saturation) -3.662 0,184 1.534  0.549
0.25 -6.025 0.365 4o 147 0.384
0.30 ~-6.173 0.136 4e565 04147
0.316 -5.832 0.075 4.322 0.083
0.333 -5.674  0.116 44233  0.133
0.40 =5.565 0.101 4.528 0.114
0.50 =5.529  0.257 4.857 0.309
0.60 =5.274  0.046 4745 0.052
0.70 =4 740 0.050 44199  0.057
0.80 =4.667 0.215 4.140  0.249

 

Table 7. Smoothed Parameters from Correlatiom of Q as a Function of
Composition and Temperature at the Specified Compositions

 

 

XBng slope x 10~ constant
0.25 -5.813 3.690
0.30 -5.821 4.168
0.316 ~5.812 4.288
0.333 -5.797 4.396
0.40 ~5.694 4,076
0.50 -5 449 4,763
0.60 -5.153 4605
0.70 -4« 805 44346

0.80 =4 o 628 44096

 
84

TEMPERATURE (°C)
100 700 650 600 550 500
5
2
10~
5

 

£
o 2
O
o
QF g2
N
Au.
QI
~ S
[
<
2
10>
5
2
1o
1.00 1.05 {10 {45 1.20 1.25 1.30 1.35
19997 o)
Fig. 18. Correlation of log Q as a Function of Melt Composition

and Temperature.
 

Il

 

 

T
T ®

i
11

}

1

1

AL

|

1

 

et
|
|
|
|
|
_

 

£

Q0L
069
009
0G4

004
069
008
066G

00.Z
069
009
0G¢g
Q0%

00L
049
009
0S¢
004

004
0g9
009
06g
004

004
0G9
009
ojete
00s

004
069
009
066
00¢

004

OO0
owoO W
W0 W

 

$.20 —

110 —

(.00

91v9,, \axu 0

0.90 [—

0.80
TEMPERATURE (°C)

0.30 0.316 0.333 0.40 0.850 0.60 0.70 0.80

XBeFZ =

Agreement between Observed Q and Value of Q from Correlation.

Figo .19.
ACTIVITY COEFFICIENT OF BeF, AND LiF

0.5

0.2

0.4

0.05

0.02

0.0¢
0.2

Fig. 20.

86

LiF SOLID

500
P60y ..--1"

-
-
“~

rLiF

0.3 0.4 0.5

MOLE FRACTION BeF,

0.6

BeF, LIQUID

0.7

0.8

 

0.9

Activity Coefficients of LiF and BeF; in Mixtures.

{.0
ACTIVITY

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1.0
a.if
0.8
500
o 600
: 700
0.4
/
0.2 7
' /
) /
7
V4
0 ¥
LiF 0.2 0.4 0.6 0.8 BeF,

Mg. 21.

MOLE FRACTION

Thermodynamic Activities of IiF and BeFp in Mixtures.
88

Thermodynamics of BeFa(1)

 

From the correlation of Q as a function of temperature and composition
for the reaction
BeF2(1) + H20(g) = Beo(s) + 2HF(g)
involving pure liquid BeFa, the equation expressing equilibrium constant
values is
log K, = (3.900 * 0.019) = (4418 * 17)(1/T)
or
OF = -(17.85 * 0.09)T + (20,217 *+78) .

From this equation, the AH are 20.22 keal/mole BeFa

reaction’ 2 “Sreaction
and 17.85 eu/mole BeFa2, respectively. As indicated in Chapter I, the ther-
modynemic values of Ha0(g), HF(g), and BeO(s) are fairly well established.
Thus, by using these values and the relationships from the above reaction,
new values for Apr, Aflpf, Asof, and S° of BeFa(l) can be calculated. These

are tabulated below along with the reported values from JANAF-4

 

 

BeFo(1) at  800°K 800°K 1000°K 1000°K
JANAF Fresent Work JANAK Fresent Work

Ampf ~213.57 ~213.60 -207.08 ~208.46

. ~240.11 -234 049 ~238.92 ~234.,26

£s%p -33.18 -26.11 -31.84 -25.80

S@ 30.66 37.74 35,36 41.35

While the present values are not in close agreement with the published
values, they provide the most direct experimental method of evaluating the
thermodynamic properties of BeF2(1). If these values for BeFa(l) are com-
bined with the data of Greenbaum, gglgi-lo for the vapor pressures of
Bng(é), new values for the thermodynamics of Ber(g) can be obtained.

These are tabulated below along with the values reported in JANAF.
89

 

BeFa(g) at 800°K 800°K 1000°K 1000°K
JANAF Present Work JANAF Present Work
AFC o ~192.02 ~191.31 -192.92 ~193.91
LHO -192.29 ~181.24 ~192.63 ~181.01
£SPs ~0e34 1.25 -0.71 1.29
s° 63.50 76 .4 66.49 80.1

The values of Aflpf and S° of Ber(g) reflect significant difference between
these results and those of Greenbaum, EE_§£.5 for the reaction
BeO(s) + 2HF(g) = BeFa(g) + Ha0(g) .

Since the velues of AF°. from the two methods are in reasonable agreement,

£
the greatest source of difference must be in the temperature dependence of

the equilibrium quotients.
In addition to the thermodynamic properties of BeFa(l) and BeFa(g),
the present study provides a means of determining thermodynamic properties

of BeFa(s) through determination of the heat of fusion, AH If pure

fusion’

solid BeFz separates upon cooling the LiF-BeF; system, the relation between

a and the freezing temperature T at a given concentration XBer in the

BeFs
liguid is given by

d(1n aBeFa) =4 1n (XseF27éeF2) = (AH /RT?) ar .

fusion

1t AHi"usion

1n (XBeryser) = (e, o /RI(L/T - 1/1°)

with TO as the melting point of pure BeFa2. The values of T for various

is independent of T, then

compositions XfieF@ were tabulated from the published phase diagram-2 The
values of 7BeF2 were calculated for the specified temperatures and compo=-
sitions from the derived expression given earlier. A plot of

log (Xpop, Ypep,) V8 1/T

is given in Figure 22. The slope of this correlation leads to a value
90

of 11 * 3 keal/mole for Aflfusion' The other lines presented in the figure
include: +the line obtained if Aflfusion = 1.6 kcal/mole; the line obtained
if TBeF, = 1 (i.e., log Rers VS 1/T); the line obtained if Mo ion =

7.5 keal/mole.

The value of 1.6 kcal/mole for AH was included for comparison

fusion
because this value was recently reported57 from comparison of AHSUbl with
éigap- Both measurements were from the variation of vapor pressures with
temperature over solid and liquid, respectively. One discrepancy in these
data, which is not mentioned in the article, is that the vapor pressures
reported for the solid near the melting point are greater than the extrap-
olated wvapor pressures of the liquid by a factor of three. The faet that
the reported vapor pressures for the solid and liquid do not intersect even
near the melting point is indicative of a systematic error in one or the
other sets of measurements since both sets seem internally consistent.

The value of 7.5 keal/mole for AH was included for camparison

fusion

because this is the value obtained if aflfusion is determined to be the dif-

ference between Afipf of BeFa(1l) calculated here and Aflpf of BeFa(s) reported
in JANAF.” The AHOf of BeFa(s) is based on the heat of solution measure-
ments on BeO and BeFz in agqueous HF by Kolesov, gg.gi.58 Since there is
some question regarding the accuracy of the reported results, the value of
Mo oo, 1s about 7.5 & 6 keal/mole. Although the present results do not
definitely establish the value of AH, . . of BeFa(s), they do tend to sup-
port the value of 12 kcal/mole reported in JANAF rather then that of 2
keal/mole used in the JANAF tabulation or the more recently reported value

of 1.6 keal/mole.
91

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0 \\\i\m..___‘ |
S
\3\\ ~~— | SLOPE FOR AHfygion =
e
W\ ~ 4< 1.6 kcal /mole
~ 0.10 "o
s N\
Q
. N
° X
T 0.20 N N
o AR
g N\,
m
x \ \
8 Ls0|_ SOLID LINE: N o
. 1 v cal/mole
log Xger, Vs /7 \
POINTS: \\
1
09 TBefy VS T - N\ 11 kcal /mole
0.40 | ‘
1.20 1.25 1.30 1.35 .40 1.45 1.50
1000/7’(0}()

Fig. 22. Heat of Fusion of BeF, from Activities at Freezing Temperatures.
92

Correlation of QA

The vaelues of Q, reported in Tables 3 and 4 were correlated with

respect to temperature and composition. Visual inspection indicated that

the values exhibited linear dependence on both temperature and composition.

The general equation for the correlation was obtained in the following

manner.

(1)

(2)

(3)

The values at each temperature were grouped to determine the slope of
the line

log Q, = (slope)XEer + constant

The least-square slopes at the five experimental temperatures were as

follows:
Temp (°c) Slope No. of Values
500 2.695 * 0.473 6
550 2.480 = 0.357 11
600 3.123 % 0.174 22
650 2.847 * 0.207 16
700 2.775 £ 0.175 20

Using weights equal to the number of data points for each line, the
average slope was determined to be 2.843. All of the values agree
with this slope within the quoted standard deviations except the wvalue
at 600° which is slightly larger.

With the slope of all lines set at 2.843, the value of log QA at the
composition intercept (XBer = 0) was determined at each temperature

to give best fit to data as shown below:
23

 

 

Temp (°C)  1log @, Temp (°C)  log Q,
500 -3.138 650 ~2.757
550 -3.056 700 -2,638
600 "'"2 .893

(4) These end values were used to calculate the function of log QA vs l/T,
vhich is log Q, = -2085(1/T) - 0.503. Thus, the best smoothed velues
for QA over the experimental range are given by
log Q, = 2‘843XBeF2 - 2085(1/T) - 0.503 .

The observed values of QA and the calculated values based on the above
function are shown in Figure 23. Since the data at the various temperatures
overlap, the coordinates are specified for each line independently. The
standard deviations of the points are not shown in the figure, but most
points agree within the quoted standard deviations in Table 3. The values
determined in BeO-saturated melts are shown by closed symbols and those in
unsaturated melts by open symbols.

The concentration of hydroxide present at equilibrium for known par-
tial pressures of HF and Hz0 above a melt of known composition could be
calculated using the relationship for QA,

Q, = (PHF/PHzo)[OH"] = mole/kg ,

derived from the reaction

H20(g) + F (soln) = HF(g) + OH (soln) .

Other equilibria involving hydroxide were also introduced in Chapter
I. One reaction is
Hz0(g) + 0%27(soln) = 20H (soln)
from which

Q = [OH”]a/'PH20 = (QA)z/Q
%

for a BeO-saturated melt. Since expressions for both Q and QA are known,
the values of QB can be derived. If the equation given earlier for
log (Q/XBer) 18 rearranged in terms of Xz .. rather then X ;p, the follow-
ing equation is obtained
log (Q/XBeFa) = ~0.940 - 4596(1/T) + [35.00 - 10168(1/T)])<'BeF2
2 - 3
+ [-68.14 + 26132(1/T) IX Ber, [50.64 - 21048(1/T)]X e

Fa
+ [-12.66 + 5262(1/T)]x4BeF2 .

If this equation is combined with the expression for QA, the following

holds:

log Qp =2 log Q, - log Q = -0.066 + 426(1/7) + [-29.31 + 10168(1/T)]X‘Ber

+ [68.14 - 26132(1/T)]X2Be , [-50.64 + 21.048(1/T)]x3

F BeF2

4 -
+ [12.66 - 5262(1/T) X BeFs log XBeF2
The parameters of the equation
log Qp = slope(1/T) + constant

are tabulated below for various experimental compositions:

 

 

 

XBer Slope Constant XBeF2 Slope Constant
0.333 1629 -3.513 0.70 695 -1370
0.40 1524 3415 0.80 456 -0e571
0.50 1279 -2e925

Another reaction involving hydroxide is

IF(g) + 0% (soln) == OH (soln) + F (soln)

from which

Qy = [0 ]/PHF = QA/Q for a BeO-saturated melt.

Therefore,
95

log Qy = log Q, - log Q = 0.437 + 2511(1/T) + [-32.16 + 10168(1/T)]X'Ber
2 3
+ [68.14 - 26132(1/T) 1% Ber, [-50.64 + 21048(1/T)]X el
- 4 - .
+ [12.66 - 5262(1/T)]X Bery log Xp.p,
The parameters of the equation

log Q = slope(1/T) + constant

are tabulated below for various experimental compositions:

 

 

XBng Slope Constant XBeFa Slope Constant
0.30 3734 -3.819 0.60 3068 -3 404
0.333 3714 ~3.960 0.70 2780 -2.862
0.40 3609 ~4.052 0.80 2541 -2.348

If the above functions are used to evaluate equilibrium quotients
for 0.333 BeFp, the values obtained and Afli based on integration of the

van't Hoff equation are given below:

Equilibrium Afi?
Quotients Q at 800°K Q at 1000°K (kcal/mole)

 

Qy 6.90 x 10™3 2.29 x 107% 9.5
Qg 3.33 x 1072 1.30 x 10™2 7.5
Q 4 .80 5.70 x 10”1 -17.0

Fach of these equilibrium quotients is in terms of moles of hydroxide per

kilogram of melt due to experimental expediency, but they could be converted
to the mole fraction scale by dividing each by moles of solvent per kilogram
of melt. This conversion would not affect the Aflf values. The above values
of equilibrium quotients involving hydroxide may not provide enough informa-

tion to establish the complete nature of hydroxide in the IiF-BeF2 systemn,
96

but they do allow quantitative prediction of the extent of conversion of
oxide to hydroxide, which is the principal controlling step in the removal

of oxide by HF-sparging.
 

0.2 0.3 0.4 0.5 0.6 0.7

XLiF

Fig. 23. Correlation of log Qy a5 2 Function of Composition and
Temperature.
98
Correlation of Q0

The vealues of QO reported in Table 4 were correlated as a function of
temperature at each composition. The parameters of the equation
log Qg = slope(1/T) + constant

are given below:

 

XBng slope * O constant * o No. of Points
0.333 -8637 £ 349 5.673 = 0.401 24
0.400 -9032 + 706 7.026 * 0.812 4

The values of QO and the corresponding correlations as a function of
temperature are shown in Figure 24. Since the two values for 0.60 BeFz
would not yield a line with slope or intercept similsr to the others, a
line was drawn parallel to the line at 0.40 BeFz so as to be equidistant
between the two values at 0.60 BeFz.

Measurement of QO at high BeFz compositions is limited because the
rete of change in P, and P with respect to W approaches the precision

HF Ha0

of measurements of the low PHgO and high PHF encountered. Although addi-
tional experiments were performed on 0.60 BeFp, convergence in the solution

of equations to obtain QO’ QA’ r , and 8, was not reached due to the exper-

0)
imental limitation mentioned above.
The data on unsaturated melts were neither extensive nor preclse
enough to permit a meaningful correlation with respect to melt composition.

However, the solubility of BeO could be determined by comparison of these

measurements with those of BeO-saturated melts.
99

As described in Chapter I,
= 21n2"
0y = (B 21037 /Ry
and since for a BeO-saturated melt
2 -_—
(Pyp) /PHQO Q
2= =
o ]sat - QO/Q .
The value of Q at BeO saturation was established in the earlier work. Divi-
sion of QO by Q for the same melt composition and temperature would provide
the concentration of oxide at saturation.
The values of Q needed to determine BeO solubility are given by the

following parameters for the equation

log Q = slope(1/T) + constant:

 

XBng Slope Constant

0.273 -5900 44150
0.333 -5674 4a233
0.400 -5565 4.528
0.600 =524 4745

The solubilities in moles per kilogram of oxide in the various experiments,
as determined from QO/Q using observed QO values and smoothed Q values
from the above relation, are given in Table 8. Since

[0*7] = o,/ ,

log [0°7] = log Q; - log & ,

and as both log QO and log Q show linear dependence with (l/T), log [027]
should also show linear dependence. Combination of the parameters for QO
and Q leads to

log [0%7] = slope(1/T) + constant:
100

 

f@i@& Slope Constant
0.273 -2258 0.641
0.333 -2963 1.440
0.400 - 3467 2.498

Each of the observed solubilities is shown in Figure 25 along with the
calculated expressions for the three compositions tabulated above.

Since many more experiments were performed on 0.333 BeFz, the range
of measured solubilities at each temperature provides a rough measure of
just how well these are known. A clear trend of solubility with tempera-

ture is shown:

500°C (2.5 -~ 6.0) x 10~3 moles/kg
600 (7.2 - 11.8) x 103
700 (2.3 - 3.8) x 107%

The other values indicate that BeQO solubility may be increasing slightly

with BeFz, but the increase 1is not very great.
101

 

 

Table 8. Solubility of BeO in Molten IiF-BeF2 System
“per, o R [0%, Tpep, Tgk Run (0%
(mole/kg) (mole/kg)

0.273 600 529 1.30 x 1072 0.333 600 309 1.16 x 1072
0.273 600 539 1.04 x 102 0.333 600 310 8.70 x 1073
0.273 650 535 1.46 x 102 0.333 650 319 2.14 x 1072
0.273 650 537 1.48 x 10 2 0.333 650 501 1.68 x 1072
0.273 700 533 2.13 x 1077 0.333 650 513 2.08 x 1072
0.333 500 313 6.67 x 102 0.333 650 514 8.16 x 1073
0.333 500 314 2.53 x 102 0.333 651 527 1.98 x 102
0.333 500 503 5.72 x 1073 0.333 700 307 2.61 x 102
0.333 544 509 5.85 x 1077 0.333 700 311 3.78 x 1072
0.333 550 315 7.25 x 1073 0.333 1700 523 2.77 x 1072
0.333 550 316 5.09 x 1073 0.333 700 524 2.30 x 1072
0.333 550 511 8.45 x 1073 0.400 550 619 2.53 x 1072
0.333 550 525 1.17 x 1072 0.400 550 625 1.56 x 102
0.333 600 301 9.47 x 1073 0.400 604 621 3.23 x 1072
0.333 600 302 7.18 x 1073 0.400 702 627 9.02 x 107%
0.333 600 303 1.18 x 10°% 0.600 500 607 2.39 x 1072
0.333 600 305 1.11 x 1072 0.600 600 611 1.78 x 102
0.333 600 306 7.23 x 102

 

 
102

TEMPERATURE (°C)

. 700 650 600 550 500
Toka

OI
W n

O,

(PH,:)2 [02_] /PHZO (atm mole kg*‘)
o

 

I 2
QO
10 °
5
C
0.333
>
0.273
10°©
1.00 {05 110 145 1.20 125 130  {.35

1000/7 (ox)

Fige. 24. Correlation of log QO as a Function of Temperature for
Various Melt Compositions.
103

TEMPERATURE (°C)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

700 650 600 550 500
I [ I | l
A 0.60 BefFsp
iy 0 0.40
10 vV 0.333
—t— 0 0.273
040 __|
T 5 N
2 N
— v
o \
g
c 0.333 \ 0 A
a 92 N
QL
£ o
= v
-2
c 10 0=
- v v NGV
> g %
S% 5 O ‘\\\\L
O
1}
m
v
2
1073
1.00 .10 .20 1.30
1000 /7 (ok)
Fig. 25. Solubility of Be0O as a Function of Temperature for Various

Melt Compositions.
104

Summary

These studies of equilibria between HF, H20, and molten LiF-BeF2 had
a twofold purpose: (1) to determine as much as possible about the thermo-
dynemics of the 1iF-BeF system, and (2) to determine as mch as possible
about the oxide chemistry of the system.

The thermodynamic activities of LiF and BeF2 were determined as a
function of temperature and composition. The major characteristics of
the system include:

(1) Positive deviations from ideality at high BeF, concentrations.

(2) Increasing positive deviations of the activity with temperature indi-
cating the probability of a miscibility gaep near 700°C.

(3) Combination of activities with previously published phase diagram
indicate a higher value for Aflfusion of BeFz than currently used in
thermodynamic compilations.

(4) Activities determined with BeO present are in agreement with limited
previous data.

Extrapolation of data to pure liquid BeF,, which is inaccessible
experimentally because of high viscosity, provides a means of determining
thermodynamic properties of BeFa(l).

The equilibria between Hp0, HF, and dissolved hydroxide were studied
by estimating, from material balance calculations on the gas phase, the
amount of OH formed in or removed fram the melt upon reaction. The re-
sults from measurements on both BeO-saturated and unsaturated melts were
consistent. The results indicate that significant amounts of hydroxide

were formed in the presence of 0.0l atm HF, but OH could not exist in

the absence of HF and Hz0-
105

The equilibria between Hp0, HF, and dissolved oxide were also evalu-
ated with melts not saturated with BeO. The solubility of BeO was estimated
by combination of these results with those for BeO-saturated melts.

These results suggest methods to attack at least two allied problems:
(1) Determination of thermodynanmic activities of other fluorides dissolved

in the LiF-BeFp system; and
(2) Determination of the amount of oxide in fluoride melts.

The procedure used here to determine activities of BeO-saturated melts
could be applied to melts saturated with other sparingly soluble oxides.
Variation in Q with amount of corresponding fluoride dissolved in melt would
provide information necessary to calculate change in activities.

The experiments performed here on unsaturated melts required determi-
nation of the concentration of oxide present at the start of an experiment
in addition to the equilibrium quotients. If oxide analyses were required
on similar melts, the equilibrium quotients could be evaluated and treated
as fixed parameters, thus the variation in effluent PHF and. PHgO to a small
value of W (about 1.0) could be used to calculate the amount of oxide in
the sample prior to treatment. In principle, this should work no matter
whether oxide were being added or removed. The presence of saturating
solid oxide would complicate the analysis, but the total amount of oxide
present could be determined by treatment with anhydrous HF and measurement

of the evolved H0.
10-

11.
12.

13«

106

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111

APPENDIX A

Partial Pressures from Studies on BeO=Saturated Melts

The experiments are arranged according to & three digit "Run No."
which indicates chronological order. There are three series (100, 200,
400) included. A brief history of each series is given in Chapter III.

The information provided for each experiment includes:

Run No.
Composition of melt (expressed as mole fraction Bng)

Temperature of melt, °c

w = weight of melt, kg

T = temperature of wet-test meter, °k

a = influent Pr, atm x 103
- 3 3
¢ = influent PHgO’ atm x 10
The effluent partial pressures, PHF = x and PHao =y, are tabulated (atm

x 103) with the corresponding initial and final values of W (V/WRT). Note
that the use of W allows consistent comparison of experiments independent
of the weight of melt or temperature of gas-measurement. The equilibrium

quotients evaluated from each experiment are presented in Table 3.
112

 

 

 

 

 

 

 

 

Run No. 101
0.316 BeFp at 700°C, w = 0.305, T = 300K, a = 15.45, ¢ = 5.48

0.000 0.075 8.22 0.935 1.030 6.51
0.075 0.103 11.32 1.030 1.119 7.03
0.181 0.253 12.76 1.203 1.286 749
0.253 0.325 12.88 1.286  1.374 7.09
0.325 0.39% 13.38 1.374  1.457 7.54
0.394 0.462 13.78 1.457 1.538 7.67
0.462 0.526 14.34 1.545 1.641 12.88
0.526 0.589 14.64 1.641 1.712 13.00
0.589 0.655 14.20 1.712 1.787 12.42
0.733 0.836 6.00 1.787 1.859 12.88
0.836 0.935 6.28

Run No. 103
0.316 BeFz at 700°C, w = 0.305, T = 300°9K, a = 15.15, ¢ = 5.14
Wi We X N Wy We X Yy
0.000 (0.203 457 1.838 2.046 6.59
0.203 0.343 6.63 2.046  2.234 6.60
0.343  0.437 9.87 2:234 2414 6.93
0-437 0.531. 9.87 2.414 2.596 6.86
0.531 0.600 10.68 2.596  2.772 7.09
0.600 0.677 12.00 2.772 2.916 6.93
0.677 0.758 11.50 2.916 3.061 6.87
0.758 0.862 11.90 3.130 3.177 13.25
0.862 0.938 12.09 3.177 3.248 13.00
0.938 1.016 12.00 3.248 3.342 13.16
1.016 1.092 12.20 3.342 3.415 12.76
1.092 1.170 12.20 3415  3.485 13.25

Run No. 105

0.316 BeFa2 at 600°C,

w = 0.305, T = 301°K,

a = 17063, Cc = 4.77

 

 

Wi We X y Wy Wf X Yy
0.929 1.002 8.50 1.709 1.805 6.45

1.002 1.075 8.53 1.805 1.902 6.37

1.075 1.148 8.82 1.902 1.995 6.63

1.148  1.219 8.91 2.190 2.39 9.32
1.219 1.287 9.10 2.390 2.458 9.20
1.327  1.517 6.53 2.458 2.526 9.10
1.517 1.613 6.40 2.526 2.650 0.04
1.613 1.709 6.45

 

 
113

 

 

 

 

 

 

 

 

 

 

Run No. 107
0.316 BeFz at 600°C, w = 0.305, T = 300°K, a = 11.58, ¢ = 5.87
Wy We X y Wi We X Yy
0.866 0.943 8.12 2.162 2.379 5.70
0.943 1.016 8.50 2:379 2.543 5.63
1.016 1.169 8.12 2543  2.706 5.68
1.169  1.323 8.13 2.706 2.872 5.60
1.323  1.398 8.22 2.872  3.037 5.59
1.398 1.546 8.45 3,170 3.284 7.68
1.546 1.695 8.34 3.284  3.442 7.88
1.732  1.891 5.80 3442  3.599 7.91
1.891 2.052 5.75 3.599 3.759 7.79
2-052 2‘162 5064
Run No. 109
Oo3.16 BEFQ at 6OOOC, W = 00305, T = BOOOK, a = 6055, c = 7-75
Wi Wf X Yy Ws We X Yy
0.866 1.012 6.36 2.531 2.677 9.26
1.012  1.149 6.72 2.677 2.79% 9.71
1.149 1.286 6.75 2.7%  2.918 10.04
1.399  1.547 8.41 2.918 3.040 10.18
1.547 1.688 g.80 3.064 3.163 6.20
1.688 1.855 9.00 3.163 3.262 0.24%
1.898 2.044 6.37 3.262 3.362 6.20
2.044  2.142 6.26 3.59%  3.729 9.42
2142  2.241 6.26 3.729  3.857 9.72
2e24). 2342 6.14% 3.857 3.986 9.64
Run No. 111
0.316 BeFa at 600°C, w = 0.305, T = 300°K, a = 6.78, ¢ = 2.23
Wi We X Yy Wy We X Yy
0.799 0.943 6.45 2.205 2.302 6.4l
0.943 1.037 6.54 2.302 2.399 6.33
1.037 1.135 6.34 2.464 2600 9.14
1.135 1.230 040 2.600 2.737 9.10
1265 1.403 2.07 2.737 2.875 9.08
1.403 1.541 9.03 2.875 3.010 9.22
1e541  1.675 9.28 3.010 3.146 9.13
1.675 1.810 9.26 3.146  3.282 9.21
1.926 2.019 6.63 34463  3.555 6.75
2.019 2.111 6.72 3.555 3.648 6.59
2.111  2.205 6.57 3.648  3.742 6.59

 

 
114

 

 

 

 

 

 

 

 

 

 

Run No. 113
0.316 BeF, at 500°C, w = 0.305, T = 300°K, a = 6.54, ¢ = 9.33
Wy Wf X Yy Wy We X Yy
0.799 0.862 9.95 2.168 2.284 10.83
0.862 0.99 9.26 2.331  2.449 2.60
0.996 1.129 9.38 2.449  2.567 2.63
1.258 1.383 9.96 2.683 2.798 2.67
1.432 1.674 2.55 R.824  2.943 10443
L1674  1.7%  2.57 2.943  3.060 10.70
1.812 1.931 10.46 3.060 3.175 10.83
2.050 2.168 10.60
Run No. 115
0.316 BeFa at 550°C, w = 0.305, T = 300°%K, a = 6.50, ¢ = 9.58
Wi We X Yy Wi We X y
0.932 1.090 3.92 2.398  2.546 4,17
1.090 1.246 3.96 2.546  2.695 4.13
1.246 1.401 3.99 2.695  2.847 .07
1.401 1.551 4e12 2.847 3.014 4 .08
1.551 1.705 400 3.014 3.151 b s O
1.732  1.862 9.57 3.197 3.325 9.70
1.862 1.990 9.72 3.325 3.451 9.95
1.990 2.116 9.91 3.451  3.573 10.21
2.116 2.242 9.88 3.573  3.701 9.79
2.242 2.368 9.90 3.7010  3.825 10.05
Run No. 117
0.316 BeFz at 500°C, w = 0.305, T = 300°%K, a = 6.25, c = 9.22
Wy We X ¥y Wy We X Yy
1.452 1.572 2.57 2.437 2.551 10.93
1.572 1.815 2.54 2.551 2.677 10.85
1.815 1.935 257 2.731 2.848 2.63
1.935 2.058 2450 2.848 2.969 2.54
2.091 2.205 10.92 2.969  3.090 2.55
2.205 2.322 10.64

 

 
115

 

 

 

 

 

 

 

 

 

 

Run No. 119
0.316 BeFp at 650°C, w = 0.305, T = 300°K, a = 6.20, ¢ = 8.98
Wy Wy X Yy Wi We X ¥
1.798  1.869  8.75 2.890 2.996  8.82
1.869 1.939  8.83 2.996  3.099  8.92
1.939 2.009  8.82 3.130 3.29% 7.59
2.009 2.080  8.68 3.294 3.373 7.92
2.398 2.551 8.13 3.373  3.453 7.76
2.551 2.709 7.90 3.453  3.615 7 .67
2.709 2.865 7.95
Run No. 121
0.316 BeFz at 650°C, W = 0.305, T = 3009K, a = 6.04, ¢ = 9.24
Wi We X Y Wi Ve X ¥
0799  0.968 7.38 2.065 2.219 8.08
0.968 1.180 7.66 2.219 2.391 8.03
1.180 1.338 7.86 2.391 2.545 8.08
1.338  1.495 7.95 2.571 2.641  8.82
1.495 1.651 7.99 2.641  2.747 8.70
1.665 1.735  8.83 2.747 2.857  8.49
1.735 1.809  8.36 2.857 2.965  8.54
1.809 2.036  8.17 2.965 3.109 8.60
Run No. 123
0.316 BeFz at 700°C, w = 0.305, T = 3019, a = 6.23, ¢ = 9.14
Wy We X v Wi We X Y
1.328  1.424 Al 2.838 2.917 11.72
1.424  1.519 6.50 2,917 2.996 11.66
1.519 1.710 6.47 3.053 3.245 6.45
1.710 1.805 6.53 36245  3.438 6.41
2.522 2.601 11.82 3.448  3.530 11.72
2,601 2.680 11.66 3.530 3.609 11.83
2.680 2.759 11.71 3.609 3.688 11.63
2.759 2.838 11.79 3.688 3.768 11.63

 

 
116

 

 

 

 

 

 

 

 

 

 

Run No. 125
0.333 BeFz at 600°C, w = 0.316, T = 300°K, a = 5.93, ¢ = 9.14
Wy We X Y Wi We X Yy
0.900 1.035 8.68 1.671 1.760 6.68
1.035 1.166 8.88 1.760 1.895 6.63
1.166 1.301 8.70 1.895 1.984 6.63
1.301 1.433 8.86 1.993 2.131 8.62
1.446 1.582 6.60 2,131 2.265 8.78
1.582 10671 6.70
Run No. 127
0.333 BeFz at 550°C, w = 0.316, T = 300°K, a = 6.00, ¢ = 9.10
Wy We X N Wi We X Yy
0.900 0.970 4e22 1.832 1.975 417
0.970 1.113 4.18 1.975 2.1313 4.32
1.113 1.253 4.25 2.113 2.184 4.18
1.286 1.416 9.12 2.250 2.382 .04
1.416  1.549 9.00 2.382 2.512 9.13
1.549 1.680 9.09 2.512 2.643 9.12
1.680 1.810 9.20
Run No. 129
0.333 BeFa at 500°C, w = 0.316, T = 300%K, a = 6.04, ¢ = 8.97
Ws We X Yy Wi We X Y
0.064  0.174 2.71 2.186 2.305 9.72
0.174 0.283 2.72 2.305 2.423 9.87
0.283 0393 2.71 2.423  2.537 10.10
0.450 0.585 8.57 2.537 2.655 9.84
0.585 0.719 8.70 2.655 2.772 9.97
1.157 1.283 9.18 2.828 2.933 2.84
1.283 1.408 9.33 2.933 3.035 2.91
1543  1.649 2.80 3.035 3.139 2.87
1.649 1.753 2.88 3.214 3329 10.07
1.753 1.967 2.78 3.329 3.446 9.96
1.967 2.071 2.86 3.446 3.562 9.99

 

 
117

 

 

 

 

 

 

 

 

 

 

Run No. 201
0.800 BeFs at 600°C, w = 1.522, T = 301K, a = 18.20, ¢ = 4.62
Wi Wf X Y Wi Wf X Y
0.057 0.072 12.25 0.788 0.822 3.55
0.077 0.092 13.07 0.822 0.859 3.32
0.367 0.388 14.55 0.859 0.895 3.37
0.388 0.412 14.28 0.895 0.931 3.30
0412 04431 1441 0.931 0.964 3.60
0.431  0.453  14.50 0.964  0.999 3.46
0.468  0.507 3.10 1.005 1.026 15.22
0.507 0.544 3.22 1.026 1.046 14.95
0.544  0.579 3.46 1.046  1.067 14.97
0.612 0.635 13.33 1.067 1.088 14.84
0.635 0.655 15.79 1.088 1.109 15.03
0.655 0.674 15.72 1.112  1.151 3.10
0.674 0.695 15.07 1.151 1.187 3.29
0.718 0.755 3.28
Run No. 203
0.800 BeFa at 600°C, w = 1.522, T = 300°K, a = 17.10, ¢ = 5.00
Wy We X Yy Wy We X Yy
0.155 0.174 16.03 0.648 0.667 16.83
Q.174 0.193 16.55 Q.97  1.032 2.06
0.193 0.212 16.67 1.032 1.085 2.27
0.400 0.419 16.7L. 1.085 1.140 221
0.419 0.438 16.59 1.140 1.196 2.13
0.443 0.480 1.89 le214 1.232 17.95
0.480 0.539 2.04 1.232 1.249 17.95
0.539 0.598 2.02 1249 1.266 17.82
Run No. 204
0.800 BeF2 at 6000C, w = 1.522, T = 300°K, a = 0.000, ¢ = 0.00
Wi Wf X Y Wi Wf X Y
0.000 0.000 17.89 0.121 0.164 2.95
0.013 0.027 9.09 0.164 0.209 2.75
0.027 0.049 5.76 0.209 0.255 2.70
0.081 0.101 3.20 0.413 0.463 2.48
0.101 0.121 3.01 0.463 0.514 2.42

 

 
118

 

 

 

 

 

 

 

 

 

 

Run No. 207
0.800 BeFa at 700°C, w = 1.522, T = 300°K, a = 15.80, ¢ = 5.26
Wy We X Yy W5 We X y
0.003 0.020 7 .24 0.814 0.831 18.46
0.020 0.030 12.71 0.831 0.847 18.67
0.122 0.200 1.42 0.847 0.864 18.76
0.214 0.231 17.51 0.864 0.880 18.72
0.231 0.248 17.72 0.880 0.897 18.67
0.494 0.511 18.32 0.934 1.009 1.60
0.511 0.528 18.03 1.009 1.082 1.66
0.528 0.545 18.05 1.082 1.158 1.59
0.545 0.562 18.32 1.158 1.234 1.59
0.647 0.729 1.46 1.257 1.273 19.49
0.729 0.810 1.52
Run No. 208
0.800 BeFa at 700°C, w = 1.522, T = 300°%K, a = 0.0, ¢ = 0.0
Wy We X y Wi Ve X Yy
0.000 0.000 19.61 1.61 0.200 0.241 3.00
0.001 0.008 18.18 0.241 0.284 2.92
0.008 0.018 12.39 0.284  0.327 2+84
0.018 0.033 8.06 0.327  0.347 3.12
0.033 0.058 5.07 0.347 0.396 2453
0.058 0.089 4.03 0.396  0.448 2.38
00089 00124 3-49 004‘48 00503 2-24‘
0.124  0.160 3.28 0.503 0.617 2.18
04160  0.200 3.16
Run No. 209
0.800 BeFp at 600°C, w = 1.522, T = 3009K, a = 15.40, ¢ = 5.26
Wy We X y Wy We X Yy
0.053 0.063 12.74 0.448 0.488 3.08
0.063 0.073 13.03 0.488 0.527 3.09
0.073 0.09 13.11 0527 0566 3.09
0.096 0.120 12.83 0566  0.604 3.16
0.347 0.370 13.26 0.604  0.642 3.18
0.370 0.393 13.42 0.642  0.680 3.17
0393 0.416 13.38 0.686 0.708 13.72
0.416 0.440 13.45 0.708 0.731 13.86

 

(continued)
Run No. 209 (continued)

119

 

 

 

 

 

 

 

 

 

 

Wi We X ¥y Wi We X ¥y
0.731 0.753 13.71 0.881 0.903 13.86

0.753 0.776 13.71 0.903 0.930 13.80

0.801 0.839 3.12 0.930 0.952 13.99

0.839 0.877 3.17

Run No. 211

0.800 BeF2 at 5500C, w = 1.522, T = 300%K, a = 15.00, ¢ = 5.46
Wi We X Yy Wy We X Y
0.029 0.072 2.83 0.558 0.585 11.41

0.075 0.081L 10.04 0.585 0.612 11.66

0.081 0.093 10.33 0.745  0.772 4.38
0.093 0.111 10.32 0.785 0.812 11.51

0.111 0.135 10.43 0.812 0.838 11.57

0.139 0.170 3.93 0.841 0.868 4ol
0.170 0.197 4ol 0.868 0.8% 4.62
0.197 0.224 445 0.89% 0.921 4450
0.419 0.446 4,46 1.028 1.054 4 .50
0.446 0.472 4.66 1.094 1.21 11.71

0.472 0.498 4. 55 1.121 1.147  11.78

0.504 0.531 11.67 1.147  1.174 11.57

0.531 0.558 11.30

Run No. 213

0-800 BEFa at 65OOC, = 10522, T = BOOOK, a = l4o40, c = 5-53
Wy We X Yy W3 We X Yy
0.128 0.185 2.14 0.750 0.769 16.67
0.187 0.207 16.08 0.782 0.836 2.18
0.207 0.225 15.97 0.836 0.893 2.18
0.534 0.591 2.12 0.893 0.952 2.08
0.591 0.647 2.16 0.961 0.980 16.59

0.69%4 0.713 16.59 0.980 0.998 16.43
0.713 0.732 16.43 0.998 1.018 16.68
0.732 0.750 16.45

 

 
120

 

 

 

 

 

 

 

 

 

 

Run No. 215
0.700 BeFz at 700°C, w = 1.650, T = 300°K, a = 14.00, ¢ = 5.46
0.094 0.117 11.97 0.643  0.660 16.61
0.117 0.141 12.13 0.660 0.677 16480
0.313 0.333 14.33 0.677 04694 17.20
0.333 0.352 14.58 0.702 0.813 1.39
0.352 0.372 14.49 0.813  0.890 1.44
0.379 0.483 1.07 0.890 0.965 1.48
0-483  0.584 1.10 0.965  1.040 1.49
0.591 0.608 16.26 1.040 1.056 18.43
0.626 0.643 16.66 1.071 1.087 18.20
Run No. 217
0.700 BeF, at 600°C, w = 1.650, T = 300°K, a = 13.80, ¢ = 5.80
0.081 0.107 10.97 1.225 1.246  13.37
0.166  0.205 2.76 1.280 1.317 3.01
0.566 0.591 11.39 1.317 1.353 3.07
0.739 0.762 12.33 1.353  1.389 3.09
0.762 0.784 12.55 1.389  1.425 3.04
0.788 0.829 2.68 1.435 1.456  13.66
0.829 0.870 2.72 1.456  1.477 13.58
0.911 0.933 13.00 1.732  1.759 3.10
0.933 0.954 13.34 1.759  1.795 3.09
1.182 1.203 13.17 1.802 1.823 13.37
1.203 1.225 13.17 1.823  1.845 13.42
Run No. 218
0.700 BeFp at 600°C, w = 1.650, T = 300°K, a = 0.000, ¢ = 0.00
W We X y Wy We X Yy
0.000 0.000 13.42 3.09 0.077 0.102  4.54
0.000 0.010 11.66 0.102 0.128  4.47
0.010 0.024  8.10 0.128 0.153  4.45
0.024 0.043  6.08 0.153  0.179  4.38
0.043  0.054 5.16 0.179 0.206  4.32
0.054 0.065  4.93 0.206 0.232  4.26
0.065 0.077 4 84

 

 
121

Run No. 221

0.700 BeFz at 550°C, w = 1.650, T = 300°%K, a = 13.20, ¢ = 6.00

 

 

 

 

0.368 0,39 10.18 0.652 0.680 4.12
0.396 0.424 10.26 0.680 0706 4.26
0.429  0.455 4e28 0.706  0.732 4.18
0.455 0.481 4« 40 0.732 0.758 4.28
0.481.  0.507 4.16 0.758 0.784 4430
0. 507 0.534 4.12 0.785 0.810 10.03

0.540 0.566 10.80 0.810 0.837 10.79

0.566 0.592 10.82 0.837 0.863 10.83

0.592 0.619 10.74 0.863 0.890 10.83

0.619 0.645  10.67

Run No. 222

0.700 BeFs at 550°C,

w = 1.650, T = 300°K,

a = 0.000, ¢ = 0.00

 

 

 

 

Wi Wf X Y wi wf X J
0.000 0.000 10.82 4.24 0.090 0.116 2.20
0.000 0.015 7.71 0.116  0.143 2.11
0.015 0.027 4T 0.143  0.171 2.05
0.044  0.065 2.63 0.229 0.262 1.96
0.065 0.090 2429

Run No. 223

0.700 BeFo at 650°0C,

a = 12.70, ¢ = 6.00

 

 

W Wf X Yy W& Wf X Yy
0.515 0.577 1.81 0.938 0.958 14.79

0.613 0.633 14.61 0.958 0.976 15.05

0.633 0.653 l4.34 0.993 1.028 1.90
0.653 0.672 14.33 1.028 1.060 2.10
0.686 0.857 1.95 1.067 1.085 15.75

0.857 0.913 2.00 1.085 1.103 15.68

0.920 0.938 15.38 1.103  1.121 15.62

 

 
122

 

 

 

 

Run No. 225
0.600 BeFz at 700°C, w = 1.827, T = 300°K, a = 12.20, ¢ = 6.05
0.004 0.014 22.36 0.489  0.535 2.18
0.014 0.022 23.37 0.535 0.582 2.16
0.022 0.032 22.90 0.582  0.628 2.19
0.032 0.040 23.07 0.634 0.646 21.43
0.111 0.120 22.46 0.646 0.658 21.12
0.120 0.129 22.67 0.658 0.670 21.12
0.194 0.235 2.45 0.670 0.682 21.00
0.236 0.245 22.29 0.682 0.737 2.10
0.245 0.254 22.41 0.737  0.783 2.21
0.254  0.266 21.67 0.783  0.829 2.17
0.266 0.278  22.00 0.829 0.875 2.18
0.309 0.335 2.07 0.878 0.898 21.40
0.335 0.382 2.15 0.898 0.902 21.08
0.382 0.429 2.16

Run No. 226

0.600 BeF; at 700°C,

w = 10820, T = BOOOK, a =290

.000, ¢ = 0.00

 

 

 

Wi We X y W, We X v
0.000 0.000 21.18 2.16 0.095 0.103 12.33
0.000 0.005 20.25 0.103 0.111 13.03
0.005 0.011 17.43 0.111 0.120 12.43
0.011 0.017 17.12 0.120 0.128 12.54
0.017 0.024 15.83 0.128 0.136 12.20
0.024 0.030 14.91 0.136 0.145 12.08
0.030 0.037 14.76 0.145 0.154 11.83
0.037 0.044 14.49 0.154 0.171 11.58
0.044  0.052 14.36 0.171 0.195 10.83
0.052 0.059 14.09 0.195 0.220 10.55
0.059 0.067 13.49 1.607 1.647 1.31
0.067 0.074 13.80 1.647 1.685 1.33
0.074 0.082 13.25 1.685 1.725 1.30
0.082 0.095 12.14

 
123

 

 

 

 

Run No. 227
0.600 BeFz at 600°C, w = 1.820, T = 300°K, a = 12.10, ¢ = 6.05

Wi Wf X ¥y wi Wf X Yy
0.000 0.000 1.30 0.986 1.054 2.97
0.011 0.085 3.51 1.056 1.078 11.86

0.085 0.097 4ol 1.078 1.099 11.83

0.288 0.308 5.20 1.099 1.121 12.05

0.308 0.316 6.25 1.121 1e142 12.05

0.316 0.332 6.59 1.183 1.214 3.24
0.332 0.348 6.54 1.214 1245 3.25
0348 0.362 7.18 1245 1.276 3.24
0.397 0.458 1.67 1.283 1.303 13.00

0.458 0.491 1.85 1.303 1.324% 12.62

0-496 0-514 8-4.1. 1-324— 1-344' 12063

Q«514 0.532 8.59 1.344 1.364  12.83

0.532 0.550 8.54 1.403 1.434% 3.36
0.550 0.568 8.82 1.434  1.463 3.38
0.781 0.796 10.67 1.463 1..493 3.45
0.796 0.810 10.68 1.495 1.515 13.36

0.810 0.825 10.61 1.515 1.534 13.46

0.830 0.914 2.49 1e534 14554 13.18

0.914 0.986 2.82

Run No. 229

0.600 BeF, at 5000C,

w = 1.820, T = 300°K,

a = 12-00, c = 6018

 

 

Wy We X Yy Wy Wf X Y
0.042 0.071 3.63 0.862 0.883 4 .59
0.071 0.098 3.83 0.883 0.905 4.63
0.098 0.125 3.88 0.915 0.941 6.13
0.134  0.203 2.92 0.941 0.966 6.09
0.203 0.236 3.03 0.966 (0.991 6.17
0.246  0.270 o2l 0.991 1.016 6.25
0.270  0.306 4 .36 1.022 1.043 4.86
0.580 0.612 5.04 1.043 1.063 5.01
0.616  0.641 4410 1.063 1.083 5.03
0.641  0.665 4.21 1.083 1.103 5.09
0.665 0.689 4.09 1.107 1.131 6.55
0.692 0.720 5.60 1.131  1.154 6.57
0.720 0.748 5.58 1.154  1.178 6.58
0.748 0.785 5.59 1.183 1.202 5.24
0.785 0.812 5.63 1.202 1.222 5.14
0.817 0.840 4446 1.228 1.251 6.57
0.840 0.862 4402 1.251 1.275 6.62

 

 
124

 

 

 

 

Run No. 231
0.600 BeFz at 550°C, w = 1.820 T = 300°K, a = 11.80, ¢ = 6.18

Wy We X Yy Wy We X ¥y
0.837 0.861 414 1.451 1.471  10.12

0.861 0.886 4413 1.471  1.492 9.99

0.886 0.911 4403 1.492 1.512 10.26

0,915 0.9%44  8.91 1.512 1.532 10.22

0.944 0.973  9.01 1.536 1.557 4.78
0.973 0.996  9.09 1.557 1.582 4.75
1.004 1.071 4.53 1.582 1.603 4. 88
1.250 1.273 4ol 1.603 1.623 4.99
1.273  1.29% 4. 67 1.625 1.644  10.59

1.299 1.320 9.97 1.644  1.664  10.49

1.320 1.341 9.95 1.664 1.684 10.41

1.341  1.361  9.95 1.687  1.709 4,75
1.363 1.384 4.80 1.709 1.729 5.05
1.384 1.405 4476 1.732 1.751 10.63

1.405  1.425 4.91 1.751  1.771  10.57

1.425  1.447 4.68

Run No. 233

0.600 BeF, at 650°C,

= 1.820, T = 2999K,

a = 11'50, C = 6'45

 

 

Wi Wf b4 Y Wi Wf X Yy
0.007 0.029 7.09 0.821 0.868 214
0.029 0.048 8.33 0.868 0.913 2.21
0.470 0.489 13.74 0.918 0.938 15.93
0.489 0.508 13.58 0.938 0.954 15.96
0.508 0.527 13.74 0.954 0.970 15.80
0.595 0.648 1.90 0.970 0.988 15.92
0.648 0.678 1.97 0.997 1.031 2.34
0.683 0.701 14.99 1.013 1.065 2.40
0.701 0.721 14.92 1.065 1.098 2.38
0.721 0.742 14.84 1l.114 1.129 16.34
0.742 0.759 14.93 1.129 1.145 16.25
0.762 0.821 2.03 1.145 1l.161 16.22

 

 
125

 

 

 

 

 

 

 

 

Run No. 235
0.030 0.051 2.11 0.707 0.721 16.28
0.051 0.072 3.30 0.721 0.735 15.87
0.147 0.234 0.61 0.758 0.789 1.75
0.237 0.242 9.17 0.789 0.818 1.84
0.242 0.251 9.75 0.818 0.845 1.92
0e425 0.439  13.00 0.845 0.900 1.95
0.439 0.456 13.30 0.901 0.914 17.04
0.473 0.493 13.62 0.917 0.941 16.87
0.494  0.551 1.24 0.948 0.988 1.83
0.551 0.618 1.58 0.988 1.014 204
0.618 0.673 l.61 1.015 1.028 17.22
0.693  0.707 16.25

Run No. 237

0.500 BeFz at 600°C, w = 2.075, T = 299°K, a = 9.74, ¢ = 5.92

Wi We X Yy Wy We X Yy
1.304 1.344 bods), 1.709 1.727 12.57
1.344 1.383 4o 54 1.727 1.745 12.13
1.387 1.405 12.58 1.745 1.764 12.13
1.405 1l.424 11.97 1.768 1.787 464
l.424 1.442 12.12 1.787 1.806 4457
1.442 1.461 12.17 1.806 1.825 4 .66
1.461 1.480 12.18 1.825 1.843 467
1.493 1.512 4.53 1.848 1.866 12.36
1.512 1.531 4.58 1.866 1.885 12.08
1.531 1.550 4.58 1.885 1.904 12.26
1.556 1.570 4455

Run No. 239

0.500 BeFz at 500°C, w = 2.075, T = 298%K, a = 10.26, ¢ = 6.97

 

 

Wy We X Yy Wy We X Yy
0.047 0.066 2.43 0.107 0.130 2.25
0.066 0.084 2.57 0.130 0.153 2.34
0.084 0.102 2.47 0.153 0.176 2.35

 

(continued)
126

Run No. 239 (continued)

 

 

 

 

 

 

W3 We X Yy Wy We X y
0.182 0.199 2.71 0.814 0.854 4.60

0.199 0.215 2.80 0.854 0.893 4.63

0.215 0.231 2.86 0.893 0.931 4.80

0.405 0.432 3.43 0.958 0.975 4.99
0.432 0.463 3.62 0.975 1.013 5.10
0.463 0.488 3.62 1.013 1.058 5.14
0.49 0.520 3.37 1.058 1.075 5.22
0.520 0.544 3.60 1.076 1.09 5.12

0.544  0.569 3.66 1.094 1.130 5.04

0.569 0.593 3.70 1.130 1.166 5.09

0.598 0.621 3.99 1.166 1.184 5.07

0.621 0.644 4.04 1.207 1.226 5.53
0.644  0.671 4.17 1.226 1.239 5.37
0.671  0.69% 4.09 1.239  1.255 5.55
0.705 0.731 4.12 1.255 1l.271 5.62
0.731 0.752 4.29 1.274 1.291 5.29

0.752 0.772 424 1.2910  1.309 5.22

0.772  0.793 4.32 1.309 1.326 5.18
0.7%  0.814 4,57

Run No. 241

0+500 BeFz at 550°C, w = 2.075, T = 2999K, a = 9.35, ¢ = 6.35
Wy We X Yy Wy We X Yy
1.439 1.454 5.67 2.391 2.405 9.50
1.454  1.463 5.75 2.465  2.477 5.93
1.463 1.472 6.09 2.477 2.488 6.30
1.472  1.481 6.09 2.488  2.499 6.18
1.483 1.492 9.93 2.499 2.511 6.33
1.492 1.501 10.05 2.514 2.528 9.50
1.501 1.510 9.92 2.528 2.553 9.32

1.510 1.519 9.88 2.553 2.567 9.32
1.528 1.537 6.10 2.567 2.582 9.54
1.537 1.545 6.45 2.614 2.626 5.93
1.545 1.553 6.68 2.626 2.638 6.17
1.553 1.566 6.64 2.638 2.649 6.41
1.567  1.577 9.63 2.649 2.660 6.43
1.577 1.586 9.92 2.662  2.672 9.68

1.586 1.595 9.47 2.672 2.681 9.79

1.595 1.605 9.57 2.681 2.690 9.74
2.354 2.363 9.85 2.700 2.712 6.38
2.363 2.377 9.92 2.712  2.723 6.33
_2.377 2.391 9.50

 

 
127

 

 

 

 

 

 

 

 

 

 

Run No. 245
0.400 BeF3 at 700°C, w = 2.432, T = 2989K, a = 8.49, ¢ = 7.89
Wy We X ¥y Wy Wy X ¥
0.013 0.025 3.22 0.370 0.384 2.17
0.037 0.047 3.68 0.397 0.410 2.37
0.067 0.102 0.87 0.410 0.438 2.64
0.102 0.109 5.72 0.439 0.459 2.97
0.109 0.122 6.08 0.460 0.466 12.13
0.122 0.134 6.41 0.466 0.472 12.13
0.134 0.146 6.68 0.472 0.485 12.08
0.329 0.337 10.41 0.49%  0.520 2.96
0.344 0.352 10.46 0.590 0.599 13.30

Run No. 247
0.400 BeFz at 700°C, w = 2.432, T = 298°K, a = 8.29, ¢ = 7.63
Wy We X Yy Wy We X y
0.180 0.188 9.26 0.499 0.511 13.38
0.188 0.197 9.21 0.511 0.528 13.30
0.197 0.205 92.13 0.528 0.540 13.51
0.218 04245 2.32 0.576  0.596 3.97
0.245 0.269 2.51 0.596 0.615 3.96
0.269 0.298 2.58 0.615 0.638 3.88
0.298 0.320 2.83 0.638 0.657 4.03
0.323 0.339 11.62 0.659 0.673 14.11
0.339 0.353 11.68 0.673 0.686 14.30
0.353 0.366 11.75 0.686 0.700 14.25
0.366 0.379 11.87 0.706  0.725 4.Q7
0.379 0.382 11.67 0.725 0.743 4.05
0.392 0.420 3.25 0.743  0.762 4.09
0.420 0.441 3.51 0.762 0.773 4.08
0.463 0.484 3.64 0.787 0.800 14.95
0.487 0.499 13.21 0.800 0.810 15.08

Run No. 249
0.400 BeFp at 600°C, w = 2.432, T = 299%K, a = 8.35, ¢ = 7.63
Wy We X Yy Wi We X Yy
0.415  0.427 6.32 0.444  0.452 2.71
0.427 0.439 6.30 0.452  0.460 9.82

 

(continued)
Run No. 249 (continued)

128

 

 

 

 

 

 

 

 

 

 

Wy We X Yy Wy We X Y
0.460 0.476 9.55 0.841 0.852 6.64
0.476  0.492 9.74 0.852 0.864 6.57
0.513 0.525 6.36 0.880 0.8%96 9.88
0.525 0.537 6.41 0.896 0.911 9.93
0.540 . 0.559 9.79 0.913 0.921 9.79
0.559 0.580 9.62 0.921 0.929 9.92
0.587 0.599 6.32 0.977 0.985 9.84
0.599 0.610 6.43 0.985 0.993 9.92
0.610 0.622 6.46 1.094 1.110 10.04
0.623  0.640 9.62 1.2110 1.126 9.76
0.640 0.656 9.66 1.144 1.155 6.63
0.656  0.672 9.57 1.155 1.166 6.76
0.672 0.688 9.57 1.170 1.186 9.86
0.830 0.841 6.75 1.186 1.201 9.86

Run No. 251

00400 Ber at 50000, W= 2-432’ T = 2990K’ a = 8-40, c = 7070

Wy We X Yy Wy We X Yy
0.000 0.022 4e32 0.294  0.302 9.41
0.022 0.041 4.28 0.369 0.386 4ed3
0.047  0.057 9.05 0.386 0.404 4.45
0.057 0.074 8.87 0.404 0.421 449
0.074 0.091 9.03 0.424  0.441 8.92
0,091  0.107 9.07 0.441  0.457 9.49
0.201 0.219 4e43 0.457 0.473 9.67
0.219 0.236 4 .46 0.473 0.488 9.60
0.236  0.253 442 0.488 0.504 9.64
0.253 0.262 4.38 0.506 0.523 4 54
0277 0.29 9.16 0.523 0.540 4455

Run No. 252

0.400 BeF2 at 550°C, w = 2.432, T = 299°K, a = 8.40, ¢ = 7.70

Wy We X y Wy We X Yy
0.671 0.689 9.79 0.733  0.747 8.25
0.689 0.704 10.55 0.747 0.761 8.21
0.704  0.719 7.67 0.788 0.803 9.97
0.719 0.733 8.24 0.803 0.817 10.72

 

(continued)
129

Run No. 252 (continued)

 

 

 

 

 

 

Wi We X Y Wy We X Yy
0.817 0.831 10.89 0.959 0.979 9.87
0.833 0.847 8.07 0.979 0.99% 92.86
0.847 0.862 8.09 0.994 1.010 9.70
0.862 0.876 7.95 1.012 1.027 7.71
0.876 0.891 7.90 1.027 1.043 7«54
0.205 0.929 9.49 1.043 1.058 747
0.944  0.959 10.05

Run No. 253

0.400 BeF2 at 650°C, w = 2.432, T = 2999%K, a = 8.40, ¢ = 7.70

Wy We X y W We X y
0.000 0.012 13.14 0.207 0.222 13.12
0.012 0.026 13.66 0.222 0.237 13.07
0.026 0.040 13.51 0.237 0.251 13.10
0.040 0.071 13.50 0.268 0.29 5.36
0.092 0.105 5.42 0.29 0.331 5.32
0.105 0.133 543 0.331 0.359 5.38
0.133 0.161 5.45 0.360 0.375 13.18
0.161 0.189 5.43 0.375 0.388 13.07
0.193 0.207 13.53

 

 

 

 

Run No. 255

0.400 BeFz at 700°C, w = 2.432, T = 299K, a = 8.40, ¢ = 7.70
Wi We X Y Wi Wf X Yy
0.000 0.023 16.87 0.299 0.332 4,67
0.025 0.067 4433 0.335 0.346 17.33
0.067 0.098 4.88 0.346 0.358 17.01
0.098 0.132 4.92 0.358 0.369 16.99
0.132 0.163 4o 84 0.369 0.383 16.95
0.168 0.178 18.00 0.383 0.394 16.95
0.178 0.190 17.20 0.419 0.452 4.63
0.190 0.201 16.84 0.452 0.485 4.60
0.201 0.213 16.55 0.486  0.497 16.92
0.235 0.267 4.67 0.497 0.509 16.32
0.267 0.299 4.66

 

 
130

 

 

Run No. 257
0.333 BeFz at 700°C, w = 2.751, T = 299%K, a = 8.40, ¢ = 7.70
Wi We X y Wy We X Yy
0.000 0.022  1.54 1.126  1.137 12.07
0.022 0.039 2.0l 1.150  1.162 5.67
0.039 0.053  2.46 1.162  1.185 5.83
0.053 0.076  3.04 1.185 1.208 5.87
0.164 0.176 5.71 1.307 1.318 12.28
0.176 0.188  6.01 1.318  1.330 12.13
0.188 0.209  6.40 1.330  1.341  12.26
0.948 0.960 12.22 1.341  1.352  12.13
0.960 0.971 12.14 1.380 1.391 5.92
0.961 0.982 12.14 1.391  1.414 5.93
1.012  1.024 5.70 1.414  1.436 5.93
1.024 1.035 5.86 1.436  1.459 5.92
1.035 1.058 5.80 1.472  1.483 11.88
1.058 1.082 5.76 1.483  1.498  11.86
1.086 1.097 12.25 1.498  1.509 12.34
1.097 1.115 12.08 1.509 1.520 12.07
1.115 1.126 12.16 1.520 1.531 12.05

 

 

 

 

Run No. 259

0.333 BeFy at 600°C, w = 2.751, T = 299°K, a = 8.40, ¢ = 7.70
Wy We X Yy Wi We X Yy
1.162 1.177 8.64 1.526 1.536 8.63
1.277 1.193 8.80 1.536 1.552 8.47
1.193  1.208 8.72 1.552  1.567 8.55
1.214  1.244 6.70 1.567 1.583 8.59
1.244 1.260 6.64 1.584 1.599 6.82
1.260 1.275 6.78 1.599 1.615 6.70
1.289 1.297 8.96 1.615 1.630 6.67
1.297 1.305 8.62 1.630 1.646 6.64
1.305 1.320 8.71 1.657 1.672 8.80
1.320 1.336 8.59 1.672 1.688 8.45
1.336 1.343 8.62 1.688 1.704 8.40
1.346  1.356 6.72 1.704 1.719 8.55
1.356 1.366 6.79 1.722  1.738 6.55
1.472 1.486 6.93 1.738 1.753 6.63
1.486 1.502 6.78 1.753 1.769 6. 74
1.502 1.517 6.72 1.769 1.784 6.62

 

 
13

 

 

 

 

 

 

 

 

 

 

Run No. 261
0.333 BeF2 at 500°C, w = 2.751, T = 2999K, a = 8.40, ¢ = 7.70
Wy We X Y Wy We X Yy
0.905 0.918 10.41 1.312  1.342 2.78
0.918 0.931 10.60 1.342  1.367 2.82
0.931 0.943 10.78 1.380 1.392 11.22
0.996 1.015 2.66 1.404  1.415 11.33
1.015 1.040 2.71 1.415  1.427 11.28
1.040 1.066 2.66 1.430 1l.454 2.88
1.066  1.092 2.64 1.454  1.478 2.88
1.097 1.109 10.67 1.478 1.501 2.91
1.1217  1.133 10.99 1.513 1.537 11.29
1.133 1.151 11.17 1.537 1.549 11.28
1.151 1.163 11.03 1.550 1.574 2.92
1.166 1.176 2.76 1.574 1.591 2.93
1.176 1.201 2.76
Run No. 263
0.333 BeFz at 5500C, w = 2.751, T = 299°K, a = 8.40, ¢ = 7.70
Wy We X ¥y Wy We X y
0.931 0.952 4.78 1.292  1.320 4.86
0.952 0.973 4.82 1.320 1.334 4.71
0.973 0.995 4.82 1.356 1.370 9.22
1.041  1.048 9.84 1.370 1.3%91 9.68
1.064 1.078 4490 1.391  1.405 9.72
1.078 1.093 4.80 1.405 1.425 9.80
10093 10107 4082 10430 11444 4082
1.107 1.121 4.80 1.444  1.472 4.87
1.134 1.148 9.46 1.472  1.501 4.82
1‘14’8 10162 9‘49 10504 1.511 9.84
1.249 1.263 4.93 1.511  1.518 9.93
1.263  1.277 4.91 1.518 1.534 9.72
1.277 1.292 4o T4 1.534 1.548 9.82
Run No. 264
Wi Vg X y Wy Weo X y
0.000 0.000 4.87 9.80 0.004  0.008 9.59
0.000 0.004 9.51 0.008 0.013 9.36

 

(continued)
Run No. 264 (continued)

132

 

 

 

 

 

 

Wi We X Y Wy We X N
0.013 0.017 9.36 0.186 0.199 2.68
0.017 0.021 8.90 0.199 0.212 2.64
0,021 0.026 8.34 0.212 0.225 2.64
0,026 0.032 7.67 0.225 0.251 2.62
0,032 0.037 7.28 0.251 0.265 2.53
0.037 0.043 7.10 0.276 0.288 3.38
0.043 0.049 6.53 0.288 0.316 3.29
0,050 0.059 4.07 0.318 0.661 2+50
0.059 0.068 3.82 0.661 0.682 1.66
00068 0'078 3-47 00682 0.704 1055
0.078 0.088 3.36 0.704 0.726 1.57
0.091 0.098 5.86 0.738 0.766 1.44
0.098 0.106 5.47 0.766  0.79% 1.32
0.106 0.122 4499 0.79% 0.828 1.25
0.122 0.138 479 0.828 0.89% 1.21
0.138  0.147 4. 66 0.894 0.921 1.29
0.147 0,183 4.43 0.921 0.949 1.24
Run No. 265
0.333 BeF, at 600°C, w = 2.751, T = 300%K, a = 8.55, ¢ = 7.76
Wy We X Y Wi We X Yy
0.022 0.039 2.08 0.422 0.444 6.00
0.039 0.054 2.26 0.444  0.466 6.20
0.061 0.079 1.45 0.466  0.488 6.21
0.190 0.207 4.07 0.498 0.519 6.07
0.207 0.222 4449 0.519 0.536 6 .04
0.222 0.237 4.55 0.536 0.564 6.00
0.237 0.251 474 0.564  0.587 6.07
0.254 0.269 425 0.587 0.609 6.14
0.269 0.311 4.75 0.609 0.631 6.22
0.311 0.330 5.16 0.633 0.653 6.78
0.334 0.353 5.28 0.653 0.672 6.97
0.353 0.366 5.42 0.672 0.691 7.10
0.366 0.378 5.40 0.691 0.700 7.07
0.378 0.391 5.58 0.704 0.715 6.45
0.3% 0.411 5.62 0.715 0.726 6.38
0.411  0.422 5.99

 

 
133

 

 

 

 

 

 

Run No. 268

0.333 BeF, at 650°C, w = 2.751, T = 300°K, a = 0.00, ¢ = 0.00
Wy We X ¥y Wi We X Yy
0.000 0.000 92.93 17.30 0.129 0.152 3.62
0.000  0.007 6.68 0.152 0.164 3.08
0.007 0.013 6.64 0.164 0.180 2.54
0.013 0.019 7.07 0.180 0.194 2.93
0.019 0.025 6.55 0.196 0.202 5.75
0.025 0.032 5.86 0.202 0.208 5.45
0.032 0.040 5.38 0.208 0.220 5.71
0.042 0.045 8.99 0.220 0.233 5.37
0.045 0.049 9.03 0.233  0.245 4.99
0.049 0.053 8.20 0.623 0.635 2.80
0.053 0.058 7.75 0.635 0.647 2.71
0.058 0.062 7.50 0.647 0.686 2.67
0.062 0.067 7.38 0.686 0.713 2.53
0.067 0.072 7 .34 0.713 0.741 2 .46
0.072 0.076 7.17 0.756  0.864 0.61
0.076 0.081 7.03 0.864 0.919 0.49
0.081 0.086 6.86 0.919 0.978 0.45
0.090 0.099 4 64 0.982 1.047 1.70
0.099 0.109 413 1.047  1.107  1.59
0.109 0.119 3.86 1.153 1.213  1.35
0.119 0.129 3.79

Run No. 269

0.333 BeF2 at 600°C, w = 2.751, T = 300°K, a = 9.75, ¢ = 10.75

Wi Wf X Yy Wi Wf X v
0.028 0.041 2.60 0.401 0.423 6.12
0.041  0.053 2.79 0.428 0.519 8.05
0.053 0.065 2.99 0.519 0.542 8.70
0.077 0.088 2.51 0.542 0.558 8.70
0.088 0.098 2.47 0.558 0.572 8.96
0.214 0.221 4 .80 0.574  0.589 6.84
0.221  0.235 .79 0.589 0.604 6.92
0.235 0.249 5.00 0.854 0.863 7.26
0.268 0.299 5.66 0.863 0.873 7.49
0.299 0.320 6.08 0.887 0.901 9.13
0.320 0.341 634 0.901 0.908 2.80
0.342 0.354 5.74 0.910 0.920 7.54
0.354 0.366 5.86 1.370  1.377 11.37
0.366 0.378 5.96 1.383 1.392 7.91
0.378 0.401 6.03 1.392  1.408 8.40

 

(continued)
Run No. 269 (continued)

134

 

 

 

 

 

 

 

 

Wi Wf X Yy Wi Wf X Y
1.408 1.425 8.46 1.617 1.625 7.83
1.425 l.441 8.18 1.748 1.759 11.46
1.441  1.458 8.05 1.759 1.771 11.64
1.497 1.509 11.67 1.771  1.782 11.86
1.509 1.521 11.66 1.783 1.801 7.92
1.521  1.532 11.79 1.801 1.819 7.67
1.532 1.544 11.93 1.819 1.827 8.14
1.548 1.564 8.43 1.827 1.836 7.96
1.564 1.581 7.95 1.836 1.853 7.79
1.581 1.599 7.87 1.853 1.867 7.75
1.599  1.617 7.80

Run No. 270

0.333 BeFz at 600°C, w = 2.751, T = 300°%K, a = 0.00, ¢ = 0.00

Wy We X Yy Wi W f X y
0.000 0.000 7.90 11.71 0.125 0.139 5.08
0.004 0.009 7.36 0.139 0.152 5.07
0.009 0.014 7.55 0.152 0.160 4.79
0.019 0.025 6.59 0.162 0.172 6.13
0.025 0.030 6 .46 0.172 0.198 5.25
0.030 0.035 6.46 0.198 0.226 4.63
0.039 0.043 8.59 0.226 0.256 4.38
0.043  0.047 10.16 0.256 0.274 3.88
0.047 0.051 10.63 0.276 0.284 4.18
0.051 0.055 10.76 0.284 0.301 4.03
0.055 0.061 10.51 0.301 0.320 3.66
0.061 0.068 9.88 0.320 0.338 3.70
0.068 0.083 g8.33 0.338 0.368 3.50
0.083 0.093 7.05 0.375 0.398 2.87
0.093 0.103 5.45 0.398 0.425 2.49
0.103 0.112 5.50 0.427  0.437 3.29
0.112 0.125 5.28 0.437 0.448 3.13

Run No. 271

0.333 BeF2 at 700°C,

w = 2.751, T = 300°K,

a = 10-90, Cc = 11050

 

 

 

Wy Wf X ¥y Wy We X Yy
0.001L 0.010 3.88 0.050 0.066 2.47
0.010 0.018 437 0.067 0.072 B4l
0.018 0.025 4.78 0.072  0.077 6.53

(continued)
135

Run No. 271 (continued)

 

 

Wi We X y Wy We X N
0.077 0.087 7.00 0.711 0.726 14.05

0.090 0.111 2.55 0.726 0.740 14.05

0.111 0.129 2.93 0.740 0.760 13.87

0.129 0.147 3.00 0.839 0.865 7.59
0.150 0.157 9.04 0.865 0.883 7.59
0.157 0.165 9.13 0.886 0.896 14.29

0.291 0.296 1l.54 0.896 0.918 13.86

0.29 0.306 11.33 1.186 1.197 15.12

0.306 0.318 11.61 1.197 1.208 15.71

0.328 0.342 . 1.208 1.217 15.67

4.79
0.342 0.352 5.63 1.217 1.229 15.12
0.353 0.386 5.99 1.229 1.237 15.57
0.386 0.418 6.29 1.237 1.246 15.72
6.60

 

 

 

 

0.418 0.438 1.260 1.279 9.08
0.440 0.451 13.16 1.279 1.293 S.47
0.451 0.461 12.92 1.293 1.307 9.21
0.461 0.475 13.08 1.307 1.325 9.29
0.475 0.491 12.83 1.325 1.339 9.41
0.578 0.59 7.24 1.339 1.367 9.40
0.596 0.618 740 1.367 1.382 9.49
0.618 0.639 7.51 1.386 1.397 15.61
0.639 0.662 7.58 1.397 1.413 15.07
0.662 0.679 7.79 1.413 1.425 15.12
0.679 0.695 7.99 1e425 1.436 15.05
0.697 0.711 14.45

Run No. 272
0.333 BeFy at 700°C, w = 2.751, T = 300°K, a = 0.00, ¢ = 0.00
Wi We X Yy Wy We X y
0.000 0.000 15.13 9.34 0.064 0.070 10.93
0.009 0.013 9.03 0.070 0.076 10.57
0.013 0.018 8.83 0.076 0.083 10.30
0.018 0.022 9.34 0.083 0.09 9.95
0.022 0.026 9.24 0.090 0.097 9.80
0.026 0.030 9.60 0.101  0.107 6.68
0.030 0.035 9.30 0.107 0.122 5.28
0.035 0.039 9.64 0.122 0.141 4.21
0.039 0.043 9.54 0.141 0.162 3.68
0.043  0.047 9.60 0.162 0.186 3.40
0.047 0.052 8.82 0.187 0.196 7.95
0.052 0.056 8.67 0.196 0.204 7.95
0.058 0.064 12.08 0.204  0.217 7.83

 

(continued)
Run No. 272 (continued)

136

 

 

 

 

 

 

 

 

 

 

Wy We X y Wy We X Y
0.217 0.231 7.63 0.332 0.376 1.53
0.231 0.255 724 0.376  0.427 1.29
0.255 0.280 6.68 0.427 0.449 4.78
0.282 0.298 2.51 0.471  0.494 455

Run No. 273

0.333 BeF2 at 600°C, w = 2.751, T = 300°K, a = 5.000, ¢ = 5.20

Wy We X Yy W We X Yy
0.006 0.017 1.53 0.417 0.441 2.74
0.017 0.028 1.54 0.441  0.463 2.93
0.037 0.055 0.73 0.463 0.485 3.00
0.074 0.082 2.10 0.546  0.580 4.01
0.082 0.091 2.07 0.580 0.613 4.13
0.187 0.200 2.66 0.613 0.663 414
0.200 0.212 2.86 0.663 (0.695 430
0.212 0.235 2.96 0.709 0.734 3.72
0.245 0.268 1.70 0.734 0.768 3.80
0.268 0.298 2.21 0.768 0.802 3.95
0.331 0.350 3.50 0.834 0.850 4.10
0.350 0.370 3.58 0.851 0.873 4.68
0.370 0.389 3.55 0.873 0.895 4057
0.389 0.408 3.63 0.895 0.903 4.53

Run No. 401

0.300 BeF, at 652°C, w = 0.544, T = 300%K, a = 5.77, ¢ = 6.40

Wy We X Y Wy We X y
0.030 0.079 1.06 0.568 0.659 3.50
0.079 0.128 1.76 0.659 0.69% 3.60
0.128 0.164 2.40 0.694 1.180 4. T4
0.198 0.246 1.32 1.180 1.216 5.22
0.246 04333 1.46 1.232 1.283 6.84
0-344 0.395 4.34 1.283 10334 6080
04395 0.421 4.60 10334 1.385 6.78
0.421 04458 4 T4 1385 14437 6.68
04523 04568 2.80 1503 1.550 5.45

 

(continued)
Run No. 401 (continued)

137

 

 

 

 

 

 

1.550 1.595 5.59 2.887 2.962 6.90

1.605 1.680 6.99 2.962 3.03% 6.75

1.680 1.782 6.82 3.039 3.0%9 6.78

1.782 1.832 6.86 3.106 3.161 5.82
1.832 1.884 6.67 3.161 3.238 5.79
1.904 1.960 5.68 3.238 3.293 5.79
1.960 2.016 5.70 3.293  3.347 5.97
2.016 2.071 5.78 3.368 3.419 6.78

2.071 2.126 5.83 3.419 3.470 6.75

2.147  2.197 6.90 3.470 3.521 6.78

2.197 2.247 6.86 4.809 4.859 6.96

2.247 2.298 6.82 4.859 4.909 6.88

2,298 2.361 6.86 4.909 4.959 6.86

2.361 2.412 6.78 5.010 5.064 6.00
2!412 2.463 6.88 5-064 5.116 600’7
2.494  2.604 5.79 5.116 5.169 6.03
2.604 2.714 5.79 5.169 5.223 5.86
2.714 2.769 5.87 5.223 5.276 6.09
2.769 2.823 5.87 5.302 5.352 6.93

2.837 2.887 7.03 5.352 5.401 7.03

Run No. 402
0.300 BeFz at 652°C, w = 0.544, T = 300°K, & = 0.00, ¢ = 0.00

Wi Wf X Yy Wi Wf X Yy
0.000 0.000 6.91 5.99 0.379 0.403 3.53

0.000 0.013 645 0.426  0.498 1.76
0.013 0.029 5.58 0.498 0.548 1.28
0.029 0.044 5.71 0.548 0.660 1.13
0.044 0.071 5.21 0.756  0.793 2.33

0.071 0.088 5.04 0.876 0.909 2.63

0.088 0.109 4 .99 0.909 0.942 2.60

0.123 0.150 4.80 0.942 0.980 2.29

0.150 0.184 3.79 0.980 1.024 1.96

0.184 0.228 2.86 1.024 1.078 1.59

0.297 0.318 4. 04 1.078  1.135 1.53

0.318 0.338 4.50 1.135 1.219 1.45

0.338 0.358 4434 1.219 1.280 1.42

0.358 0.379 4.13

 

 
138

 

 

 

 

 

 

Run No. 403
0-300 BeF2 at 54’000, w = 00544, T = 3000K, a = 5059, c = 6.33
Wy We X y Wy We X Yy
0.037 0.132 0.55 1.979 2.061 2.53
0.149 0.264 1.11 2,061 2.135 2.58
0.264 0.308 1.46 2.135 2.19% 2.60
0.308 0.345 1.72 2.194 2.265 2.46
0.362 0.411 1.41 2265 2.333 2.55
0.411  0.464 1.66 2.360 2.425 7.82
0.464  0.513 1.75 2425  2.465 7.93
0.530 0.550 3.26 2.465 2.531 7.79
0.550 0.585 3.67 2.531 2.651 7.92
0.585 1.182 5.55 2.651 2.733 7.82
1.182 1.217 6.96 2.733 2.812 8.04
1.217 1.237 6.96 2.837 2.904 2.59
1.295 1.331 2.43 2.904 2.971 2.58
1.331 1.401 2.47 2.971 3.037 2.64
1.401 1.472 2.43 3.037 3.104 2.58
1.472 1.614 2.43 3.121  3.204 .72
1.628 1.671 7.32 3.204 3.285 7.91
1.671 1.706 7.46 3.285 3.366 7.84
1,706 1.748 7.60 3.366  3.446 7.92
1.748  1.817 7.37 3.480 3.546 2.62
1.817 1.884 7.60 3.546  3.611 2.64
1.909 1.979 2+49 3.611  3.677 2.63
Run No. 405

0.300 BeF, at 601°C, w = 0.544, T = 300°K, a = 5.59, ¢ = 6.33
W3 We X Yy Wy We X Y
0.000 0.045 0.78 1.211 1.250 bob7
0.045 0.105 0.87 1.250 1.288 4¢53
0.105 0.145 1.30 1.288 1.365 4.51
0.145 0.182 1.86 1.381 1.434 6.00
0.224 0.303 1.60 1.434 1.486 6.16
0.303 0.334 2.08 1.486 1.537 6.22
0.334 0.361 2.3% 1.549 1.587 4.55
0.373 0.394 3.30 1.587 1.625 4.58
0.39%  0.425 3.38 1625 1.662 4.66
0.425  0.465 3.47 1.680 1.761 6.30
0.465 0.492 3.87 1.761 1.840 6.41
0.515 0.589 3.45 1.840 1.939 6.49
0.589 1.101 4. 96 1.939 2.017 6.54
1.101  1.146 5.75 2.031 2.106 4o 64
1.172  1.211 4049 2.106 2.180 4 .67

 

(continued)
Run No. 405 (continued)

139

 

 

 

 

 

 

2,180 2.275  4.55 3.778 3.835 6.83
2,275 2.349  4.64 3.835 3.891 6.71
2.367 2.446 6.42 3.891  3.947 6.80
2.446  2.523 6.59 3.958 4.012  4.79

2.523 2.601 6.57 4.012 4.076  4.60

2.601 2.677 6.70 5.134 5.189  4.70

2.677 2.753 6.71 5.189 5.245  4.59

2,770 2.844  4.67 5.245 5.282  4.74

2.844 2.919 4 .67 5.374 54430 6.83
2,919 2.994  4.59 5.430 5.485 6.90
2.994 3.068  4.64 5.485 54541 6.87
3.068 3.145  4.53 5.541 5.59 6.90
3.192  3.266 6.86 5.615 5.671  4.67

3.266  3.350 6.80 5.671 5.726  4.72

3.350 3.441 7.00 5.726 5.782  4.59

3.441 3.515 6.90 5.782 5.838  4.64

3.528 3.603  4.63 5.928 5.983 6.86
3.603 3.675  4.78 5.983 6.038 6.95
3.675 3.750  4.63 6.038 6.095 6.74

Run No. 406

0.300 BeF, at 601°C, w = 0.544, T = 300°K, & = 0.00, ¢ = 0.00
Wy We X Yy Wy We X y
0.000 0.000  4.67 6.84 0.433  0.497 1.99
0.022 0.040 6.68 0.497  0.573 1.67
0.040 0.059 6.7 0.573  0.660 1.46
0.059 0.082 5.53 0.720 0.763  1.62

0.082 0.106 5.28 0.763 0.806 @ 1.62

0.106 0.135 443 0.806 0.853  1.45

0.135 0.167 4,01 0.853 0.901  1.46

0.183 0.204 3.34 0.933 1.036 0.93
0.204 0.227  2.93 1.036  1.121 0.75
0.227 0.252  2.75 1.157 1.209 1.36

0.252 0.279  2.63 1.209 1.275  1.05

0.279 0.305  2.66 1.275 1.340  1.06

0.305 0.332 2.54 1.340 1.408  1.02

0.332 0.360  2.45

 

 
140

 

 

 

 

 

 

Run No. 407

0.300 BeF2 at 700°C, w = 0.544, T = 300°K, a = 5.67, ¢ = 6.53
W3 We X y Wi We X y
0.037 0.083 1.13 2.223 2.302 4.86
0.083 0.125 2.05 2.302 2.368 4.83
0.125 0.156 2.87 2.368 2.434 4.80
0.156 0.180 3.59 2.434  2.500 4.83
0.227 0.276 1.30 2.516 2.573 9.18

0.276 0.335 1.63 2.573 2.630 9.04

0.347 0.362 5.88 2.630 2.689 8.84

0.362 0.3%9 6.10 2.689 2.766 9.00

0.390 0.417 642 2.766  2.842 8.91

0.417 0.443 6.70 2.852 2.920 4470
0.443  0.468 6.95 2.920 3.152 4495
0.504 0.531 2.38 3.152 3.217 4.90
0.531 0.577 2.75 3.288 3.345 2,16

0.577 0.637 3.16 3.345 3.403 8.95

0.637 0.673 3.60 3.403 3.461 8.97

0.680 0.700 8.28 3.461 3.520 8.91

0.700 0.742 8.32 3.558 3.625 479
0.742 0.763 8.13 3.625 3.687 5.05
0.773 1.337 %429 3.687 3.751 4.99
1.337 1.377 4470 3.751 3.853 5.03
1.411  1.449 9.10 3.853 3.917 4 .95
1.449  1.487 9.05 3.917 3.980 5.04
1.487 1.526 8.93 3.995 4.051 9.18

1.526 1.565 8.93 4.051  4.109 9.05

1.598 1.653 4 .62 4.109 4.167 8.96

1.653 1.706 4.78 5.656 5.714 8.95
1.706  1.761 4470 5.714  5.772 9.00
1.761 1.815 4.70 5.847 5.909 5.07
1.815 1.868 4479 5.909 5.974 4.99
1.882 1.958 9.09 5.974  6.037 5.00
1.958 2.016 8.99 6.037 6.113 5.04
2.016 2.074 8.95 6.130 6.187 9.14
2.074 2.131 9.00 6.187 6.245 9.04

2.154 2.223 4.62 6.245 6.303 8.95

Run No. 408

0.300 BeF2 at 700°C, w = 0.544, T = 3009, a = 0.00, ¢ = 0.00
Wy We X y Wy We X Yy
0.000 0.000 9.01 5.00 0.099 0.128 7.16

0.040 0.070 6.78 0.128 0.152 7.16

0.070 0.099 7.36 0.152 0.180 6.36

 

(continued)
Run No. 408 (continued)

141

 

 

 

 

 

 

Wy We X ¥y Ws We X Y
0.180 0.206 6.32 0.598 0.628 2.91
0.206 0.236 5.87 0.628 0.658 2.82

0.288 0.346 2.21 0.680 0.752 0.88
0.346  0.380 1.83 0.752 0.862 0.58
0.380 0.430 1.28 0.862 0.927 0.49
0.444  0.490 3.80 0.952 0.999 1.86

0.490 0.514 3.58 0.999 1.072 1.67
0.514 0.541 3.24 1.072 1.128 1.54

0.541 0.569 3.08 1.128  1.187 1.45

0.569 0.598 3.00 1.187 1.252 1.34

Run No. 409

0.300 BeFz at 500°C, w = 0.544, T = 300°%K, a = 5.67, ¢ = 6.53

W4 Wf X Yy Wi We X vy
0.083 0.177 0.68 1.974  2.033 1.76
0.260 0.305 0.78 2.142 2.219 8.30
0.305 0.345 0.87 2.219 2.279 8.34
0.373 0.407 1.88 2.279 2.354 8.49
0.407 0.436 2.21 2:464  2.517 1.97
0.436 0.482 2.72 2.517 2.605 1.97
0.482 0.526 2.90 2.605 2.698 1.87
0.556 0.587 1.13 2.698 2.772 1.87

0.587 0.649 1.26 2.793 2.853 8.38
0.649 0.701 1.33 2.853 2.928 8.49
0.709 0.754 4.28 2.928 3.003 8.49
0.754 0.795 4 .64 3.003 3.077 8.51
0.820 0.845 4.90 3.196 3.288 1.87
0.866 0.912 1.51 3.288 3.362 1.88
0.912 0.958 1.50 3.362 3.436 1.88
0.958 1.490 1.63 3.436 3.510 1.86
1.490 1.528 1.83 3.536 3.596 8.38
1.576 1.610 7.29 3.596 3.704 8.29
1.610 1.644 7.63 3.704  3.764 8.40
1.644  1.677 7.60 3.778 3.834 1.88
1.677 1.710 7.75 3.834 3.888 1.88
1.710 1.775 7.72 3.909 3.955 8.22
1.792 1.855 1.67 3.955 4.000 8.51
1.855 1.914 1.74 4.000 4.046 8.25
1.914 1.974 1.74

 

 
142

 

 

 

 

 

 

Run No. 413

0.250 BeF2 at 607°C, w = 0.633, T = 299°K, a = 5.59, ¢ = 6.33
Wi Wf X Y Wi Wf X Y
0.043 0.09 0.64 1.881 1.944 7.04
0.090 0.143 1.12 1.944 2.008 7.04
0.180 0.222 1.32 2.089 2.159 4418
0.222 0.255 1.70 2.159 2.233 4,09
0.255 0.284 1.91 2.233 2.306 b o Ode
0.303 0.325 2.63 2.306 2.344 3.95
0.325 0.347 2.78 2.366 2.428 7.13
0.347 0.378 2.79 2.428 2.492 6.97
0.378 0.408 3.00 2.492 2.586 7.13
0.408 0.437 3.12 2.586 2.649 7.12
0.48% 0.509 3.43 2.672 2.708 412

0.509 0.536 4.05 2.708 2.784 3.91
0.536 0.562 4.40 2.784 2.868 &e22
0.579 0.605 3.50 2.868 2.912 4.09
0.605 0.630 3.63 2.978 3.017 7.18
0.630 0.655 3.53 3.017 3.08L 7.00
0.655 0.680 3.55 3.081 3.121 7.03
0.717 1.075 5.92 3.144  3.180 4.13
1.075  1.092 6.46 3.180 3.216 bol2
1.110  1.134 3.83 3.216 3.252 4.18
1.134  1.164 3.95 4.130 4.166 4.05
1.164 1.19 3.95 4.166  4.203 4.07
1.194 1.224 3.99 4284  4.323 7.08
1.224 1.253 4.12 4,323 4.378 7.17
1.302 1.346 6.38 4.378 4.416 7.20
1.346 1.388 6.57 4416 4.455 7.13
1.388 1.429 6.74 L.A&TT  4.514 4.08
1.429  1.485 7.05 4.514 4.588 4.01
1.497  1.526 4.07 4.588 4.661 405
1.526 1.572 3.88 4,709 4.748 7.21
1.572 1.608 414 4748  4.786 7.28
1.608 1.645 4.07 4.786 4.825 7.10
1.645 1.681 4.03 4.835 4.872 3.96
1.738 1.778 7.00 4.872 4.909 407
1.778 1.817 7.08 4.909 4.946 4 .00
1.817 1.881 7.03

Run No. 415

0.250 BeFz at 702°C, w = 0.633, T = 299K, a = 5.40, ¢ = 6.51
Wy We X y Wy We x Yy
0.029 0.057 1.05 0.080 0.112 1.82
0.057 0.080 1.33 0.145 0.200 1.01

 

(continued)
Run No. 415 (continued)

143

 

 

 

 

 

 

Wj_ Wf X y Wi Wf X vy
0.200 0.254 1.04 1.828 1.869 7.29
0.254 0.302 1.32 1.869 1.910 7.22
0.309 0.321 4.95 1.920 1.951 7.26
0.321 0.338 5.12 1.951 1.994 7.03
0.338 0.357 4,92 1.994  2.035 7.17
0.357 0.374 5.13 2.113 2.163 5.57
0.399 0.430 1.82 2.163 2.213 5.60
0.430 0.474 2.50 2.213 2.283 5.58
0.474  0.514 2.84 2.283 2.332 5.63
0.539 0.558 6.10 2.332 2.382 5.64
0.558 0.577 6.26 2.401 2442 7.34
0.577 0.596 6.36 2:442  2.491 7.20
0.634 0.668 3.25 2.491 2.542 7.01
0.668 0.698 3.80 2542 2.583 7.30
0.698 0.741 4.00 2.583 2.623 7.36
0.772 0.794 6.78 2.678 2.728 5.53
0.794 0.816 6.88 2.728 2.788 5.66
0.830 1.336 4. 96 2.788 2.836 5.74
1.336 1.388 5.40 2.836 2.885 5.72
1.400 1.420 7.34 2.885 2.934 5.66
1.420 1.441 7.17 2.948 2.989 7.29
1.441 1.482 7 .24 2.989 3.03%1 7.17
1.482 1.524 714 3.031 3.073 7.10
1.555 1.605 5.50 3.073 3.115 7.08
1.605 1.657 5.38 3.154 3.204 5.57
1.657 1.718 5.46 3.204 3.254 5.63
1.718 1.768 5.67 3.254 3.353 5.66
1.768 1.819 5.42

Run No. 419
0.250 BeFz at 5200¢, = 0.633, T = 3009K, a = 5.40, ¢ = 6.35
W We X y Wy We X ¥y
0.032 0.080 0.55 0.422 0.452 1.95
0.080 0.119 0.75 0.452 0.484% 1.89
0.119 0.150 0.96 0.507 0.530 4.72
0.150 0.178 1.05 0.530 0.551 5.41
0.209 0.258 2.21 0.551 0.569 5.76
0.258 0.293 3.20 0.569 (0.588 5.95
0.293 0.325 3.45 0.588 0.614 6.43
0.325 0.352 4.03 0.635 0.665 2.00
0.372 0.390 1.65 0.665 0.692 2.17
0.390 0.422 1.90 0.692 0.746 2.22

 

(continued)
Run No. 419 (continued)

144

 

 

 

 

 

 

 

Wi wf X y Wi Wf X y
0.746  0.773 2.23 1.960 2.016 7.87
0.789 0.814 6.62 2.016 2.086 7.82
0.814 0.838 7.08 2.086 2.156 7.87
0.838 0.869 7.08 2.156 2.212 7.84
0.869 0.899 7.21 2+.240  2.301 2.42
0.900 0.937 743 2.301 2.388 2.39
0.937 0.966 742 2.388 2.450 2442
0.990 1.017 2.23 2.450 2.510 2.48
1.017  1.447 2.35 2.510 2572 241
1.566  1.601 7. 74 2.637 2707 7.93
1.601 1.636 7.92 2.707 2777 7.82
1.636 1.664 7.75 2777 2.847 7.86
1.685 1.714 2.50 2.847 2.916 7.95
1.714 1.777 2.36 2.952  3.011 2.51
1.777 1.839 2.42 3.011 3.072 2.46
1.839 1.912 2443 3.072 3.133 2 e bs
1.932  1.960 7.75

Run No. 421

0.250 BeFp at 6550C, = 0.633, T = 300%K, a = 5.60, ¢ = 6.55
0.032 0.085 0.56 1.187 1.226 5.99
0.085 0.125 1.12 1.226 1.273 5.92
0.125 0.143 1.62 1.309 1.336 5.50
0.143 0.159 1.91 1.336 1.363 5.58
0.159 0.178 2.24 1.363 1.400 5.58
0.238 0.281 1.27 1.400 14427 5.53
0.281 0.332 1.74 1.457 1.514 5.74
0.337 0.356 3.92 1.514  1.561 5.90
0.356 0.375 3.96 1.561 1.606 6.09
0.375 Q0.392 4.25 1.606  1.667 6.30
0.392 0.410 4.10 1.667 1.710 6.34
0.410 0.428 4e21 1.733 1.760 5.47
0.475 0.498 2.41 1.760 1.787 5.55
0.498 0.841 416 1.787 1.851 5.58
0.841 0.863 5.00 1.851 1.905 5.53
0.882 0.930 4.68 1.905 1.970 5.45
0.930 0.959 5.21 2.028 2.069 6.63
0.959 0.986 5.42 2.069 2.126 6.76
0.986 1.013 5.46 2.126 2.167 6.64
1.013 1.041 5.28 2.167 2.208 6.82
1.081 1.133 5.37 2.208 2.248 6.68
1.133  1.187 5.74%

(continued)
145

Run No. 421 (continued)

 

 

 

 

2.249 2.289 6.80 2.638 2.'720 6.76
2.317 2.424 5.57 2.720 2.761 6.71
2424  2.478 5.53 2.801 2.841 5.60
2.478  2.532 5.46 2.841 2.868 5.46
2.599 2.639 6.83

Run No. 423

00250 Ber_ at 54300, W= 00633, T = 2980K, a = 5040, c = 6.35

 

 

Wi We X Y Wy We X y
0.021 0.061 0.73 1.716 1.760 7.38
0.061 0.093 0.% 1.760  1.804 7.58
0.093 0.116 1.28 1.804 1.892 7.53
0.116  0.136 1.48 1.922  1.993 3.12
0.171 0.225 2.04 1.993 2.044 2+96
0.225 0.249 2.37 2.044  2.104 2.93
0.249  0.267 2.95 2.104 2.155 2.+96
0.267 0.284 3.41 2.155 2.204 3.03
0.307 0.327 2.20 2.245  2.299 7.22
0.327 0.356 2.10 2.299 2.364 7.62
0.356 0.381 2.34 2.364  2.408 7.54
0.381 0.406 2.36 2.408 2.451 7.76
0.406  0.430 2.47 2.451 2.501 7T
0.456  0.485 3.91 2.501 2.545 7.51
0.485 0.905 6.17 2.565 2.615 2.99
0.905 0.921 6.93 2.615 2.665 2.99
0.921 0.943 7.21 2.665 2.714 3.01
0.963 0.984 2.76 2.714 2.764 2.97
0.984 1.016 2.80 2.827 2.870 7.59
1.016 1.046 2.92 2.870 2.912 "7.87
1.046  1.076 2.95 2.912 2.955 7.59
1.076 1.106 2.97 2.955 2.998 7.75
1.228 1.264 747 2.998 3.041 7.67
1.264 1.302 7.40 3.041 3.085 7.59
1.302  1.347 7.38 3.108 3.157 3.04
1.370  1.395 2.95 3.157 3.207 2.97
1.395 1.421 2.90 3.207 3.282 2.97
1.421 1.471 2.93 3.282 3.332 2.99
1.471 1.548 2.93 3.332 3.381 3.01
1.548 1.598 2.97 3.431  3.468 7.3%
1.64) 1.678 745 3.468  3.505 7.58
1.678 1.716 7.29 3.505 3.540 7.72

 

 
146

APPENDIX B
Partial Pressures from Studies on Unsaturated (with respect
to Be0) Melts
The experiments are arranged according to a three digit "Run No."
which indicates chronological order. There are three series (300, 500,
600) included. A brief history of each series is given in Chapter III.
The information provided for each experiment includes:
Run No.
Composition of melt (expressed as mole fraction BeF3)
Temperature of melt, °C
w = weight of melt, kg

T = temperature of wet~test meter, Ok

1

a + bW = influent Pi, atm x 102
7 2 3
+ N =
c + dh influent PHgO’ atm x 10
The effluent partial pressures, PHF = x and PHgO =y, are tabulated (atm
%x 103) with the corresponding initial and final values of W. Note that
the use of W allows consistent comparison of experiments independent of

the weight of melt or temperature of gas-measurement. The equilibrium

quotients evaluated from each experiment are presented in Table 4.
147

 

 

 

 

Run No. 301
0.333 BeFp at 600°C, w = 0.500, T = 2999°K, a = 3.68, ¢ = 11.00
Wi We X Y Wy We X Yy
0.000 0.000  0.107 1.700 1.753 6.51
0.000 0.030  3.72 1.753  1.807 6.46
0.030 0.053 11.55 1.814 1.852  9.71
0.053 0.080 13.92 1.852 1.89  9.93
0.080 0.106 14.39 1.890 1.930  9.53
0.106 0.133 14.36 1.930 2.011 9.3
0.133 0.159 14.26 2.038  2.090 6.72
0.249 0300 2.70 2.090 2.141 6.71
0.307 0.334 14.05 2.141 2.272 6.92
0.334 0.361 13.88 2.272  2.321 7.03
0.361 0.389 13.67 2.327 2.369  9.08
0.403  0.445 3.30 2.369 2.431  9.09
0.445  0.484 3.59 2.431 2.494  9.00
0.484  0.519 3.95 2.494  2.538  B.57
0.519 0.571 4ea 01 2.568 2.616 7.28
0.582 0.612 12.70 2.616 2.722 7.22
0.612 0.642 12.49 2.722 2.825 7 .40
0.642 0.673 12.26 2.845 2.888  8.64
0.673 0.704 12.26 2.888 2.930  9.12
0.725  0.769 475 2.930 2.995 8.71
0.769  0.812 492 2.995  3.062  8.46
0.812 0.856 4 o776 3.102  3.192 7.66
0.856  0.897 5.10 3.192  3.284 7.62
0.897 0.937 5.21 3.284  3.373 7.82
0.946 0.978 11.55 3.373 3.464 7.66
0.978 1.011 11.43 3.464  3.508 7.8%
1.492 1.528  10.41 3.509 3.579  8.14
1.528 1.565 10.28 3.579 3.648  8.09
1.565 1.601 10.20 3.648 3.719 g.03
1.610 1.645 5.99 3.719 3.814  7.88
1.645 1.700 6.32

Run No. 302

0.333 BeF, at 600°C,

W

a = 0.000, ¢ = 0.00

 

 

Wi Wf X N wi Wf X Y
0.000 0.000 7.90 7.90 0.244  0.297 3.58

0.000 0.020 7.72 0.297 0.350 3.58

0.020 0.056 5.17 0.360 0.419 2.37
0.056 0.091 5.45 0.419  0.506 1.62
0.091  0.127 5.13 0.506  0.601 1.46
0.137 0.159 6.32 0.635 0.722 2.17

0.159  0.190 4451 0.722  0.819 1.93

0.190 0.234 3.17 0.819 0.924 1.79

 

 
148

 

 

 

 

 

 

Run No. 303

0.333 BeF, at 600°C, w = 0.500, T = 299K, a = 3.82, ¢ = 10.53
W; We X N Wy We X y
0.008 0.068 1.26 2.165 2.217 7.26
0.068 0.120 2.16 2.217 2.309 7.37
0.120 0.162 2.70 2.335 2.417 8.54
0.193 0.246 2.64 2.417 2.498 8.57
0.246 0.295 2.82 2.498 2.579 8.55
0.306  0.344 4.90 2.579 2.661 8.53
0.344  0.380 5.30 2.706 2.783 7.33
0.380 0.414 5.43 2.783 2.857 7.63
0.414  0.447 5.74 2.857 2.932 7.57
0.447  0.479 5.91 2.932 3.013 6.99

0.522 0.547 5.51 3.013 3.066 7.08

0.547 0.582 5.93 3.097 3.189 8.40
0.582  0.629 5.97 3.189 3.270 8.59
0.629 0.671 6.53 3.270 3.360 8.49
0.685 0.712 6.78 3.360 3.401 8.55
0.712 0.740 ©.78 3.407 3.488 7.00
0.740 0.79 7.00 3.488 3.570 6.93
0.79%  0.821 7.00 3.712  3.793 6.97
0.844  0.892 724 3.839 3.919 8.78
0.892 0.939 742 3.919 4.008 8.54
1.492 1.542 754 4.008 4.088 8.78
1.542  1.592 7.50 4.088 4.185 8.54
1.654 1.696 8.28 4.198  4.253 6.87
1.696  1.779 8.42 4.253  4.336 6.79
1.779 1.942 8.54 4.336  4.420 6.76
1.942  2.024 8.46 4.420  4.476 6.68
2.035 2.086 7.37 4.582  4.623 8.67
2.086 2.165 7.17

Run No. 305

0.333 BeF2 at 600°C, w = 0.500, T = 299K, a = 3.82, ¢ = 10.53
Wy Vfif X y Vfii We X Y
0.000 0.023 3.22 0.263 0.290 14.32
0.023 0.042 10.09 0.290 0.316 14.00
0.042 0.065 13.30 0.337 0.404 3.08
0.065 0.090 14.63 0.404  0.462 3.63
0.090 0.116 14.49 0.469 0.497 13.39
0.116 0.143 14.26 0.497 0.526 13.13
0.156  0.200 1.60 0.526 0.569 12.91
0.200 0.232 2.16 0.569 0.599 12.76
0.236 0.263 14.09 0.621 0.669 4.38

 

(continued)
149

Run No. 305 (continued)

 

 

 

 

 

 

Wi Pflf X Yy W We X Yy
0.669 0.713 470 3.626  3.713 8.01
0.713 0.786 474 3.713  3.799 8.08
0.786 0.828 5.07 3.815 3.913 7.71
0.842 0.890 11.83 3.913  4.022 7.79
0.890 0.939 11.41 4,031  4.129 7.67
0.939 0.989 11.34 4,129 4,179 7.62
1.030 1.095 5.37 4.239  4.321 - 8.43
1.095 1.158 5.58 4e32]1  4.407 8.08
1.158 1.218 5.72 4407 4,493 8.16
.102.18 10278 5-84 4-493 4--602 8-29
1.292  1.344 10.83 4.630  4.706 747
1.344  1.396 10.80 4,706 4.800 7.99
2.119 2.160 9.34 4.800  4.900 7.55
2.160 2.221 9.25 4.900 5.003 7.32
2.295  2.344 7.08 5.003 5.054 7.32
2.344  2.391 7.30 5.103 5.187 8.26
2.391 2.488 7.21 5.187 5.272 8.22
2.488 2.535 7.40 5.272 5.355 8.37
2.543  2.607 8.82 5.355 5.438 8.38
2.607 2.672 8.74 5.453  5.560 7.10
2.672  2.760 8.55 5.560 5.693 7 .0
2.771 2.836 7.51 5.693 5.800 7.09
2.836  2.930 7.40 5.844  5.924 8.74
2.930 3.022 7.62 5.924  6.006 8.45
3.022 3.068 7.59 6.006 6.088 8.58
3.069 3.137 8.28 6.100 6.207 7 .04
3.137 3.229 8.20 6.207 6.289 6.83
3.229  3.322 8.09 6.289 6.372 6.86
3.322  3.416 8.01 6.407 6.490 8.43
3.448  3.538 7.71 6.490 6.572 8.47
3.538 3.626 7.91 6.572 6.654 8.4

Run No. 306

0.333 BeFz at 600°C, w = 0.500, T = 299°K, a = 0.000, ¢ = 0.00

Wy We X y W3 Wf X y
0.000 0.000 6.84 8.42 0.256  0.319 3.36
0.040 0.058 7.76 0.319 0.366 2.91
0.058 0.081 6.09 04383 0.414 3.08
0.089 0.110 470 0.414  0.447 2.84
0.110  0.130 4 .57 0.447  0.503 2.70
0.130 Q.174 434 0.503 0.546 2.60
0.188  0.220 4436 0.571  0.655 1.67
0.220 0.256 3.84 0.655 0.748 1.50

 

(continued)
150

Run No. 306 (continued)

 

 

 

 

 

 

Wi Wf X Y wi Wf X Y
0.748 0.865 1.18 1.022 1.082 1.55

0.885 0.941 1.68 1.082 1.146 1.47
0.941  1.022 1.64 1.146  1.284 1.37

Run No. 307

0.333 BeFy at 700°C, w = 0.500, T = 297°%K, a = 3.95, ¢ = 10.50
Wy We X Yy Wy We X Yy
0.000 0.031 6.08 2.288 2.388 4o 21
0.031 0.055 15.95 2.388 2.455 4ol
0.055 0.076 17.46 2.458 2.508 14.96

0.076 0.107 18.32 2.508 2.585 14.71

0.107 0.138 17.99 2.585 2.649 14.78
0.138 0.168 18.87 2.649 2.714 14.39
0.168 0.199 18.71 2.761 2.838 4o Dby
0.199 0.230 18.32 2.838 2.931 453
0.230 0.260 18.82 2.931  3.023 4459
0.260 0.290 18.41 3.023 3.112 470
0.290 0.331 18.37 3.114 3.195 13.99
0.378  0.431 2.26 3.195 3.262 14.00
0.431  0.478 2.92 3.262 3.330 13.88
0.492 0.523 18.37 3.330 3.425 13.88
0.523 0.555 17.84 3.455  3.541 4487
0.555 0.587 17.47 3.541 3.644 476
1.018 1.039 17.33 3.644 34730 4.90
1.039 1.073 16.71 3.730 3.814 4.97
1.108 1.170 3.40 3.827 3.909 13.80
1.170 1.229 3.55 3.909 3.978 13.66
1.229 1.292 3.30 3.978 4.048 13.50
1.301 1.336 15.83 4.048 4.118  13.49
1.336 1.372 15.97 4.185  4.269 5.01
1372 1431 15.92 4269 40354 4.95
1.431  1.479 15.78 4354  4.439 4.93
1479 1.525 16.22 4.439 4551 5.01
1.563 1.623 3.53 4e563  4.633 13.33
1.623 1.716 3.75 4.633 4.706 13.04
1.716 1.813 3.63 4706 4777  13.20
1.822 1.871  15.33 b 777  4.849  13.05
1.871 1.920 15.33 4.883 5.020 5.09
1.920 1.982 15.20 5.020 5.155 5.18
1.982 2.056 15.29 5.155 5.288 5.29
2.121  2.205 4o 17 5.288 5.419 5.32
2.205 2.288 4e22 5.433  5.505 1293

 

(continued)
151

Run No. 307 (continued)

 

 

 

 

Wi We X Yy Wy We X y
5.505 5.580 12.67 6.020 6.147 5.50
5.580 5.653 12.87 6.163 6.239 12.37
5.653 5.727 12.64 6.239 6.316 12.30
5.753 5.888 5.17 6.331 06.3% 5.57
5.888 6.020 5.32

Run No. 309

0.333 BeF, at 600°C,

 

 

Wy We X y Wy We X y
0.000 0.037 2+55 5.107 5.188 5.20
0.037 0.051 6.49 5.188 5.256 5.21
0.051 0.075 7.92 5.256  5.337 5.21
0.075 0.118 8.92 5.337 5.403 5.32
0.118  0.157 9.49 5.424  5.489 5.82
0.199 0.245 1.53 5.489 5.588 5.79
0.253 0.291 9.93 5.588 5.688 5.66
0.291 0.328 10.18 5.740 5.819 5.40
0.328 0.366 9.96 5.819 5.925 5.32
0.366  0.403 9.99 5.925 6.000 5.64
0.435  0.472 1.87 6.000 6.076 5.53
0.472  0.505 2.14 6.100 6.164 5.91
0.505 0.534 2.38 6.164 6.265 5.63
0.546  0.585 .62 6.265 6.368 5.51
0.585 0.664 9.53 6.368 6.464 5.95
0.664  0.747 9.03 6.502 6.577 5.60
0.780 0.835 254 6.577 6.652 5.62
0.835 0.88% 2.86 6.652 6.728 5.63
0.88 0.952 3.05 6.728 6.806 5441
0.960 1.023 8.96 6.811 6.881 5.45
1.023 1.089 8.60 7.574  7.645 5.36
1.089 1.177 8.58 7.645  7.755 5.18
1.211  1.276 3.26 7.804 7.878 5.75
1.276 2.017 3.78 7.878 7.951 5.4
2.035 2.110 7.59 7.951 8.026 5.07
2.110 2.186 7.37 g.026 8.101 5.58
2.186 2.265 7.22 8.124 8.192 5.57
2.310 2.377 417 8.192 8.261 5.54
2.377 2.428 4 .09 8.261 8.334 5.18
2.428 2.478 422 8.336 8.408 5.09
2.478 2.559 4.33 8.440 8.515 5.63
R+564  2.670 Te1l4 8.515 8.591 5454
2.670 2.750 7.04 8.596 8.671 5.08
4.879  4.973 6.05 8.671  8.745 5.08
4.973  5.036  6.01 8.764  8.827 5.66
5.036  5.099 6.00 g.827 8.89 5.57

 

 
0.333 BeF, at 600°C, w = 0.500, T = 297°K,

152

Run No. 310

a = 0.000, ¢ = 0.00

 

 

 

 

 

 

Vs We X Yy Wy We X ¥y
0.000  0.000 5.08 5.59 0.345  0.411 2.13
0.000 0.028 4.92 0.420 0.456 2.66
0.028 0.054 5443 0.456  0.494 249
0s054  0.082 4 .99 0s424  0.578 2.26
0.082 0.115 4.32 0.616 0.712 1.46
0.127 0.148 3.68 0.712 0.835 1.14
0.148 0.180 3.59 0.835 0.903 1.03
0.180 0.209 3.22 0.903 0.978 0.94
0.209 0.240 3.10 1.016 1.078 1.53
0.250 0.294 3.22 1.078 1.208 1.46
0.294  0.345 2.72

Run No. 311

0.333 BeFz at 700°C, w = 0.500, T = 300°K, a = 2.35, ¢ = 7.35

W i Wf X Y wi Wf X Y
0.016  0.029 7.29 1.637  1.707 1.99
0.029 0.054 11.37 1.773 1.818 12.70
0.054 0.083 12.88 1.818 1.878 12.45
0.083 0.111 13.49 1.878 1.939 12.46
0.111  0.139 13.49 1.939  1.969 12.57
0.255 0.311 1.35 2.017 2.124 1.96
0.317 ©0.344 1l4.14 2.124  2.225 2.05
0.344  0.370 14.09 2.236 2.281 12.49
0.370 0.398 13.76 2.281 2.344 12.04
0.398 0.425 13.68 2.344  2.406 12.12
0.425 0.481 13.58 2.406 2.468 12.08
0.481 0.508 13.80 2.504  2.605 2.07
0.556 0.667 1.25 2.605 2.700 2.18
0.667 0.793 1.66 2.700 2.796 2.17
0.812 0.885 12.95 2.811 2.874 11.86
0.885 0.914 12.99 2.874 2.938 11.82
0.914 0.943 13.03 2.938 3.003 11.70
0.943 0.972 12.82 3.003 3.066 11.84%

1.032  1.121 1.55 5.386 5.453 3.10
1.121  1.204 1.68 5.453  5.520 3.10
1.210 1.239 13.13 5.616 5.666 11.32
1.239 1.283 12.82 5.666 5.719 10.63
1.283 1.328 12.67 5.719 5.771 10.86
1.328 1.373 12.58 5.771.  5.824  10.68
1.444  1.526 1.71 5.862 5.972 3.16
1.526  1.637 1.87 5.972  6.127 3.12

 

(continued)
153

Run No. 311 (continued)

 

 

 

 

 

 

Wi We X Yy Wy We X y
6.127 6.258 3.18 9.359  9.497 3.53
6.264 6.335 10.63 9.497 9.614 3.54
6.335 6.388 10.55 9.614 9.771 3.54
6.388 6.460 10.45 9.786  9.863 9.74
6.460 6.515 10.37 9.863 9.942 9.49
6.597 6.703 3.25 9.942 10.06 9.25
6.703 6.813 3.18 10.06 10.14 9.43
6.813 6.921 3.20 10.18 10.30 3.54
6.921  7.028 3.26 10.30 10.42 3.60
7.089 7.144 10.22 10.42  10.53 3.66
7.244 7.218 10.20 10.60 11.01 9.59
7.250 7.353 3.36 11.02 11.13 3.57
7.381 7.998 3.37 11.13 11.25 3.59
7.998  8.099 3.43 11.26 11.32 9.40
8.185 8.259 10.18 11.32 11.38 9.32
8.259 8.335 9.92 11.38  1l1.44 2.16
g.335 8.410 10.00 12.05 12.13 9.38
8.410 8.487 9.84 12.13  12.21 9.10
8.530 8.655 3.34 12.21  12.29 9.22
8.655 8.775 3.46 12.33  12.45 3.59
g8.775 8.898 3.40 12.45 12.56 3.72
8.898 8.958 3.49 12.56 12.68 3.72
8.965 9.041 9.90 12.68 12.75 3.88
9.041 9.119 9.72 12.75 12.84 9.28
9.144 9.221 9.70 12.84 12.92 9.09
9.221 9.301 9.50 12.92 13.01 9.08

Run No. 313

0.333 BeFz at 500°C, w = 0.500, T = 298°K, a = 0.00, ¢ = 16.30

Wi We X y Wi We X Yy
0.023 0.051 6.70 0.501 0.542 8.79
0.051 0.071 9.51 0.542 0.580 9.17
0.071 0.089 10.20 0.593 0.641 7.83
0.08% 0.126 10.37 0.641 0.690 7.62
0.154  0.202 5.97 0.690 0.740 7 .64
0.202 0.232 6.87 0.740 0.804 734
0.232 0.263 6.88 0.830 0.898 10.39
0.270 0.310 9.26 0.898 0.965 10.66
0.310 0.351 9.30 0.965 1.029 11.07
0.351 0.393 8.95 1.039 1.067 6.60
0.393 0436 8.84% 1.067 1.096 649
0.450  0.477 775 1.096 1.155 6.42
0.477 0.501 8.80 1.174  1.205 11.13

 

(continued)
154

Run No. 313 (continued)

 

 

1.205 1.237 11.28 2.685 2.725 4,75

1.513 1.546 5.75 2.725  2.806 4« 60

1.546  1.613 5.58 2.834  2.917 12.82
1.613 1.648 5.43 2.917 2.971 13.16
1.660 1.690 11.86 2.971 3.036 13.07
1.690 1.748 12.22 3.036 3.089 13.25
1.748  1.806 12.18 3.100 3.143 4 o 40

1.806 1.864 12.18 3.143 3.187 4.28

1.864  1.923 12.03 3.187 3.233 4.10

1.947 2.021 5.07 3.233 3.321 426

2.021 2.095 5.08 3.340 3.3%9% 13.08
2.095 2.172 4 .88 3.39  3.448 13.16
2.172 2.211 4.88 3.448  3.501 13.32
2.265 2.322 12.62 3.501 3.606 13.57
2.322 2.377 12.83 3.635 3.730 3.99

2.377 2.432 12.93 3.730 3.825 3.96

2.432 2.486 12.97 3.825 3.921 3.93

2.486  2.540 13.13 3.942  4.049 13.21
2.568 2.646 4.84 4.049  4.154 13.55
2.646  2.685 4.83

 

 

 

 

Run No. 314

0.333 BeFz at 500°C, w = 0.500, T = 298°K, a = 0.00, ¢ = 0.00
Wi Wf X Yy Wi Wf X Y
0.000 0.000 2.79 14.47 0.580 0.657 3.64
0.078 0.124 7.63 0.867 0.969 0.92
0.124 0.175 6.91 1.002 1.142 2.53
0.204 0.272 1.39 l.142 1.244 2.08
0.272 0.358 1.32 1.244 1.373 1.93
0.388 0.445 497 1.399 1.511 0.67
0.509 0.580 4.00

 

 
155

Run No. 315
0.333 BeFz at 550°C, w = 0.500, T = 300°%K, a = 0.00, ¢ = 20.00

 

 

 

Wy We X y Wy We X y
0.020 0.039 10.08 1.584  1.729 7.78
0.039 0.038 14.92 1.729 1.775 8.34
0.058 0.075 16.25 1.775  1.821 8.07
0.075 0.099 15.72 1.821 1.882 9.25
0.099 0.121 17.30 1.933 1.984 13.47
0.121 0.132 16.80 1.984 2.034 13.87
0.158  0.189 4e351 2.055 2.105 7.62
0.189 0.215 5.36 2.105 2.154 7.66
0.219 0.244 15.11 2.154  2.204 749
0.244  0.270 14.96 2.252  2.317 13.89
0.270 0.295 1l4.54 2.317 2.365 1447
0.321  0.354 6.37 2,365 2.403 14.70
0.354 0.380 7.93 3.672  3.733 6.18
0.380 0.406 7.84 3.733  3.795 6.09
0.406 0.432 8.21 3.795  3.859 5.90
0.434  0.464  13.07 3.942  3.988 14.96
0.464  0.492 13.07 3.988  4.033 15.39
0.492 0.522 12.92 4.033  4.077 15.79
0.522 0.567 12.32 4.077 4.121 15.79
0.585  0.609 8.71. 4143 4.206 6.04
0.609 0.631 9.36 4.206 4.206 6.21
0.631  0.652 10.01 4.266  4.328 6.07
0.652  0.686 10.29 4.328  4.390 6.08
0.686 0.718 10.54 4440  4.506 15.76
0.731  0.764 11.51 4.506  4.570 16.26
0.764 0.798 11.12 4.570  4.633 16.42
0.798 0.833 10.63 4.633  4.697 16.34
0.833 0.887 10.55 4,716  4.780 5.91
0.975  1.007 10.84 4.780  4.845 5.78
1.007 1.040 10.62 4.845  4.909 5.88
1.040 1.070 11.30 4.909 4.993 5.60
1.070 1.101 11.21 5.017 5.082 16.00
1.113  1.151 9.80 5.082 5.145 16.38
1.150  1.212 9.37 5.145 5.221 16.39
1.212  1.285 9.05 5.221 5.283 17.04
1.285 1.348 8.93 5.313 5.358 5.12
l.411  1.453 13.07 5.358  5.479 5.43
1.453 1.491 12.80 5.479  5.525 6.16
1.491  1.528 13.29 5.325  5.59 5.46
1.528 1.580 13.18 5.5%  5.646 5.42

 
156

 

 

 

 

 

 

Run No. 316

0.333 BeF, at 550°C, w = 0.500, T = 300°K, a = 0.00, ¢ = 0.00
Wy We X Yy Wy We X ¥y
0.000 0.000 4.74 16.71 0.268 0.308 2.36

0.000 0.063 4.80 0.308 0.348 2.36

0.063 0.079 4e63 0.348  0.390 2. 24

0.079  0.103 3.96 0.390  0.477 2.17

0.103 0.131 3.29 0.477  0.574 1.95

0.131 0.162 3.01 0.574  0.676 1.82

0.162 0.195 2.87 0.676  0.796 1.58

0.195 0.232 2.55 0.796 1.674 1.31

0.232 0.268 2.62 1.674  1.808 0.84

Run No. 319

0.333 BeFa at 650°C, w = 0.500, T = 2999K, a = 0.00, ¢ = 19.90
W3 We X v Wi We X y
0.024 0.038 13.92 1.007 1.028 6.45
0.038 0.067 19.53 1.028 1.049 6.82
0.067 0.092 22.14% 1.049 1.078 7.00
0.092 0.118 22.51 1.084  1.106 17.32
0.118 0.142 23.18 1.106 1.128 16.68
0.142 0.166 23.66 1.128  1.163 16.20
0.166 0.190 23.26 1.174 1.288 6.68
0.204  0.255 2.70 1.288 1.675 8.07
0.255 0.298 3.20 1.675 1.715 8.68
0.298 0.334 3.88 1.728  1.755 1400
0.342 0.359 22.21 1.755 1.782 14.05
0.359 0.385 22.37 1.782 1.809 14.09
0.385 0.411 21.66 1.809 1.834 14.63
0.411 0.438 21.08 1.834 1.861 14.05
0.438 0.464 21.20 1.891 1.948 8.60
0.465 0.512 LN 1.948 1.984 9.50
0512  0.541 4.83 1.984 2.023 8.91
0.541  0.567 5.29 2.023 2.060 9.29
0.567 0,593 5.30 2.066 2.095 13.36
0.595 0.623 20.16 2.095 2.122 13.51
0.623 0.652 19.26 2.122 24149  14.45
0.652 0.682 18.95 2.149 2.176 13.80
0.682 0.712 18.68 2.176 2.204 13.51
0.769 0.806 5.54 2.277 2.315 8.95
0.806 0.829 6.17 2.315 2.353 9.17
0.870 0.902 17.78 2.353 2.392 8.96
0.902 0.932 18.53 2.392 2.429 9.33
0.932 0.993 18.55

 

 
157

 

 

 

 

 

 

Run No. 501
0.333 BeFz at 650°C, w = 0.500, T = 298%K, a = 9.75,
b = -0.24, ¢ = 0.65, 4 = -0.0095
Wi Wf X vy Wi Wf X ¥
0.000  0.000 0.46 2.025 2.086 6.17
0.038 0.075 1.0l 2.086 2.117 6.13
0.075 0.105 1.26 2.117 2.178 6.16
0.105 0.132 1.40 2.225 2.305 2.55
0.132 0.154 1.71 2.305 2.388 2.49
0.215 0.313 0.70 2.388 2.468 2.58
0.313 0.398 0.82 2.468  2.546 264
0.409  0.427 4.08 2.564  2.595 6.16
0.427  0.456 4.03 2.595 2.654 6.29
0.456  0.484 3.93 2.654  2.714 6.3%
0.484 0.511 422 2.714  2.774 6.32
0.511 0.536 4 o 46 2.897 2.952 2+53
0.536 0.569 4453 2.952  3.009 242
0.613 0.657 1.59 3.009 3.064 2449
0.657 0.697 1.71 3.064 3.118 2.54
0.697  0.771 1.86 3.118 3.203 242
0.771  0.841 1.95 3.203  3.289 241
0.859 0.886 5.49 3.312 3.372 6.33
0.886 0.922 5.22 3.372 3.432 6.32
0.922 0.956 5.62 3.432  3.493 6.17
0.956  0.989 5.67 3.493 3.553 6.20
0.989 1.030 5.49 3.553 3.614 6.25
1.059 1.122 2.20 3.672  3.799 2.17
1.122  1.180 2.37 3.799 3.925 2.20
1.180 1.237 2440 3.925  4.021 2.14
1.255 1.288 5.86 4.021 4.117 2.13
1.288 1.320 5.84 4,200 4.274 6.32
1.336 1.855 2.51 4274 44335 6.25
1.855 1.930 2.76 4.335 4.394 6.34
1.957  1.987 6.20 439  4.453 6.42
1.987 2.025 6.03 4.502  4.567 2.13
Run No. 503
0.333 BeFa at 500°C, w = 0.500, T = 2989%K, a = 5.15
b = -0.10, ¢ = 0.26, d = -0.0050

Wy Wp X y Wi We X ¥
0.049 0.138 0.21 0.720 0.795 0.92
0.229  0.437 0.33 0.795 0.865 0.98
0.466  0.523 0.66 0.865 0.934 1..00
0.523 0.576 0.71 0.973 1.005 1.18

 

(continued)
158

Run No. 503 (continued)

 

 

 

 

 

 

Wy Wf X Yy Wi Wf X Yy
1.005 1.070 1.17 4.098 beld2 2+54

1.070 1.157 1.29 4142 4.183 2.75

1.157 1.219 1.22 4.183  4.237 2.78

1.237 1.305 1.52 4o 237 4.292 2.78

1.305 1.373 1.52 40322 4.398 1.82
1.373 3.147 1.98 4.398 b 75 1.78
3,147 3.211 2.14 bo&75 4559 1.80
3.278 3.310 2.38 4.559 4 .637 1.77
3.310 3.341 2.37 4« 666 4.731 2.91

3.341 3.405 2.36 4.731 44796 2.88

3.434 3.497 240 4,796 4.859 2.97

3.680 3.724 2.61 4879 4,958 1.73
3.724 3.766 2.66 4.958 5.046 1.56
3.795 3.860 2.10 5.046 5.142 1.43
3.860 3.928 2.03 5.142 5232 1.53
3.928 3.997 1.99 5.261 5.319 3.20

3.997 4. 067 1.98 5.319 5.377 3.25

Run No. 509

Qs 333 Ber at 54400, W = 00470, T = 2980K, a = 4035, c = 7070
W3 Wr X y Wy We X Yy
0.000 0.018 2.26 0.611 0.647 8.18
0.018 0.034 4.92 0.674  0.717 4o22
0.034 0.058 6.75 0.717 0.748 451
0.058 0.078 7.84% 0.748 0.780 4o 54
0.078 0.104 7.83 0.780 0.810 4.62
0.1.04 0.128 8.22 0.823 0.857 8.36
0.128 0.152 8.29 0.857 0.891 8.08
0.161 0.193 2+ 24 0.891 0.927 7.91
0.193 0.220 2.67 0«927 0.963 7.80
0.220 0.24% 2.88 0.963 0.999 7.80
0.252 0.276 8.53 1.072 1.131 4.83
0.276 0.299 8.63 1.131 1.185 5.29
0.299 0.322 8.53 1.185 1.225 5.34
0.322 0.345 8.76 1.240 1.278 7.32
0.345 0.368 8.72 1.278 1.316 7.38
0.387 0.412 2.90 1.316 1.354 7.38
0.412 0.434 3.20 1.354 1.393 .25
0.434 0.474 3.60 1.393 1.432 7.28
0.474 0.511 3.88 1.493 1.543 5.71
0.518 0.541 8.63 1.543 1593 5.71
0.541 0.574 8.97 1.593 1.642 5.83
0.574 0.611 8.30 1.642 1.692 5.76

 

(continued)
159

Run No. 509 (continued)

 

 

 

 

 

 

Wi Wf X Yy Wi Wf X y
1.714 1.809 6.78 3.061 3.116 6.43
1.809 1.911 6 .67 3.137 3.184 6.37
1.951  1.997 6.16 3.184 3.231 6.33
1.997 2.044 6.05 4433  4.485 5.76
2.044  2.093 5.91 4.485  4.537 5.76
2.093 2.139 6.17 4.537  4.589 5.84
2.139 2.186 6.03 4.651  4.703 6.90
2.206 2.246 6.92 4.703 4.756 6.82
2.246  2.288 6.67 4,756 4.807 6.92
2.288 2.330 6.67 4.807 4.912 6.83
2.330 2.37 6.55 4.938 4.989 5.86
2.417  2.462 6.32 4.989 5.042 5.71
2.462  2.508 6.24 5.042 5.09% 5.70
2.508 2.553 6.30 5.094 5.148 5.62
2.553 2.644 6.29 5.214  5.265 6.99
2.662 2.723 6.60 5.265 5.368 6.99
2.723  2.796 0.63 5.368 5.468 7.13
2.79%  2.858 6.42 5.468 5.567 7.22
2.858 2.921 6.4 5.590 5.668 5.66
2.947 3.005 6.17 5.668 5.740 5.57
3.005 3.061 6.41

Run No. 511
0.333 BeFz at 550°C, w = 0.470, T = 298°K, a = 10.30,
b = -0.10, ¢ = 0.40, d = ~0.004

Wy We X Yy Wi We X v
Oo004 0-095 0044 On9‘74 10019 3021
0.161 0.263 0.35 1.035 1.066 3.90
0.274  0.309 1.70 1.066 1.097 3.96
0.309 0.340 1.95 1.097 1.145 4410
0.340 0.379 2.09 1.145  1.194 4.17
0.413 0.471 1.23 1.194 1.241 425
0.471 0.531 1.78 1.262 1.365 3.42
0.531 0.584 2.01 1.365 1.424 3.58
0.605 0.640 2.87 1.424  1.520 3.70
0.640 0.679 3.05 1.520 1.576 3.83
0.679 0.718 3.10 1.592 1.633 4 .88
0.718 0.754 3.32 1.633 1.673 5.00
0.783 0.836 2.70 1.673 1.736 5.09
0.836 0.883 3.00 1.736 1.776 5.01
0.883 0.928 3.10 1.805 1.881 3.68
0.928 0.974% 3.08 1.881  1.961 3.57

 

(continued)
160

Run No. 511 (continued)

 

 

 

 

 

 

Vfli Dflf X Yy V{i Vfif X y
1.961 2.039 3.62 3.692 3.742 8.05
2.039 2.117 3.64 3.780 3.867 247
2.117 2.195 3.62 3.867 3.958 2.32
2.219 2.254 5.62 3.958 4.055 2.20
2.254  2.290 5.67 4.061  4.107 8.60

2.290 2.358 5.88 4.107  4.154 8.66
2.358 2.425 5.95 4.154 4.209 8.99

2.450  2.543 3.05 4.209 4.244 8.59
2.543  2.608 3.26 4.285  4.341 1.90
2.608 2.676 3.1% 4.341 4.403 1.72
2.676  2.742 3.20 4.403  4.469 1.61
2.742  2.812 3.04 409  4.538 1.52
2.836 2.915 6.66 4.538  4.608 1.52
2.915 2.985 6.87 4.622  4.606 8.97

2.985 3.054 6.93 4666  4.711 9.08

3.054 3.111 7.04 4.711  4.755 9.05
3.158 3.243 2.51 4755  4.799 9.05
3.243 3.321 2.72 4.838 4.892 1.30
3.402 3.488 247 4,945  4.997 1.37
3.524  3.576 7.62 4.997  5.115 1.20
3.576  3.643 7.87 5.129 5.171 9.46
3.643  3.692 8.00 5.171 5.214 9.42

Run No. 513

0.333 BeF, at 650°C, w = 0.470, T = 298%K, a = 4.60, ¢ = 7.90
Vi We X Y W We X y
0.000 0.016 2.55 0.504  0.536 2.26
0.016 0.037 7.53 0.552 0.582 13.43
0.037 0.072 11.34 0.582 0.612 13.71
0.072 0.104 12.68 0.612 Q.656 13.39
0.104 0.137 13.20 0.656 0.702 13.18
0.137 0.167 13.39 0.781 0.832 2.79
0.187 0.220 2.18 0.832 0.878 3.10
0.220 0.253 2.13 0.878 0.922 3.20
0.270 0.298 14.22 0.941 0.989 12.66
0.298 0.326 14.00 0.989 1.050 12.43
0.326 0.356 13.79 1.050 1.102 12.30
0.356 0.385 13.71 1.136 1.181 3.18
0.405  0.440 1.99 1.181 1.222 3.41
0.440 0.473 2.17 1.222 1.262 3.54
0.473  0.504 225 1.262 1.303 3.47

 

(continued)
161

Run No. 513 (continued)

 

 

1.320 1.370 12.04 2.686 2.724 10.68

1.370 1.421 11.91 4.185  4.227 2.63

1.421 1.472  11.79 4227  4.268 9.63

1.558 1.595 3.82 4.350 4.389 543
1.595 1.629 421 4.389 4.428 5.41
1.629 1.681 407 4428 4467 5.45
1.697 1.749 11.38 bod7 4 507 5.38
1.749 1.802 11.38 4.529 4.591 9.71

1.802 1.874 1l.14 4.591  4.654 9.46

1.874 1.929 11.05 4e654  4.718 9.40

1.997 2.048 417 4,718  4.783 9.33

2.048 2.134 413 4.846  4.905 5.41
2.134 2.230 b ode2 4.905  4.953 5.88
2.253 2.307 11.25 4.953 5.005 5.49
2.307 2.363 10.82 5.005 5.055 5.63
2.363 2.419 10.66 5.073  5.137 9.40

2.458 2.505 451 5.137 5.201 9.37

2.505 2.552 4e53 5.201 5.266 9.17

2.552 2.599 4o 54 5.266 5.309 9.33

2.615 2.650 11.29 5.309 5.353 9.25

2.650 2.686 11.13

 

 

 

 

Run No. 514

0.333 BeF, at 650°C, w = 0.470, t = 298°K, a = 0.00, ¢ = 0.00
Wy We X y Wy Wf X Yy
0.000 0.000 9.34 5.59 0.287 0.343  4.26

0.000 0.010  8.38 0.343 04374  3.87

0.025 0.041  7.28 0.406  0.439 3.64

0.041 0.059  6.84 0.478  0.529 1.41
0.059 0.077  6.62 0.529 0.590 1.15
0.115 0.151 3.96 0.590  0.660 1.01
0.151 0.171 3.47 0.660 0.742 0.86
0.171  0.19% 3.09 0.761 0.814  2.30

0.19%4 0.221 2.63 0.814 0.89  2.16

0.221  0.249 2.50 0.869 0.931  1.96

0.261 0.287  4.62 0.931 0.972  1.92

 

 
162

Run No. 523
0.333 BeF, at 700°C, w = 0.470, T = 298°K, a = 4.30, ¢ = 7.65

 

 

Wi We X Yy Wy We X Y
0.000 0.016 243 2.279 2,317 13.00

0.016 0.036 8.18 2.317 2.359 12.93

0.036 0.061 11.96 2.359 2.395 12.89

0.061 0.092 13.20 2.395 2.434 12.86

0.092 0.120 13.92 2.590 2.637 3.09
0.120 0.148 14.21 2.637 2.685 3.04
0.148 0.189 14.80 2.685 2.731 3.14
0«322 0.348 15.57 2.731  2.777 3.12
0.348 0.386 15.78 2.793 2.840 12.70

0.386 0.425 15.36 2.840 2.914 12.32

0.425 0.465 15.12 2.914 2.946  12.49

0.496 0.549 1.37 2.958 3.006 12.59

0.549 0.596 1.55 3.006 3.054 12.51

0.596 0. 644 1.51 3.054 3.103 12.29

0.644 0.691 1.52 3.141 3.185 3.29
0.705 0.738 15.00 3.185 3.228 3.36
0.738 0.772  14.72 3.228 3.292 341
0.772 0.806  14.72 3.292 3.355 3.43
0.806 0.841 14.58 3.355 3.418 347
0.841 0.875 14.39 3.432 3.482 12.21

0.886 0.976 1.64 3.482 3.531 12.12

0.976 1.054 1.85 3.531 3.581 12.04

1.054 1.127 2.00 3.581 3.631 12.01

1.170 1.205 14.50 3.631 3.682 11.91

1.205 1.240 14.25 3.741  3.802 3.62
1.240 1.275 l4.14 3.802 3.862 3.60
1.275 1.311 13.88 3.862 3.941 3.67
1.311 1.347 13.95 3.941 4.020 3.70
1.432 1.496 2.28 4.020 4.097 3.7
1.496 1.556 24l 4.107 4.158 11.82

1.556 1.617 241 4158 4.209  11.79

1.617 1.675 249 4.209 4.260 11.71

1.701 1.737  13.74 4.260  4.312 11.63

1.737 1.775 13.45 4.312 4.363 11.62

1.775 1.836 13.12 %0420 4493 3.99
1.836 1.881 13.18 4493  4.566 3.96
1.965 2.019 2.68 4566 4.640 3.95
2.019 24072 2.70 o640 4.712 3.99
2.072 2.124 2 .80 4845  4.898 11.33

2.124 2.176 2.82 4.898 4.952 11.26

2.176 2.226 2.86 4,952  5.005 11.33

24240 2.279 13.14

 

 
163

Run No.

525

0.333 BeF, at 550°C, w = 0.470, T = 298%K, a = 10.20,

 

 

 

b = -0.19, ¢ = 0.40, d = -0.007
Wi Wf X Yy Wy wf X Yy
0.039 0.181 0.28 3.371 3.246 3.86
0.213 0.301 0.41 3.276  3.340 3.10
0.301 0.395 0.39 3.340  3.407 3.00
0.435 0479 0.90 3.437 3.500 3.14
0479 0.519 1.00 3.500 3.565 3.13
0.519 0.553 1.18 3.585 3.662 3.75
0.553 0.586 1.24 3.662 3.738 3.80
0.653 0.715 1.16 3.738 3.813 3.88
0.715 0.762 1.53 3.813 3.886 3.96
0.762 0.808 1.58 3.920 4.048 3.42
0.808 0.870 1.76 4.04L  4.107 342
0.899 0.934 1.71 4.007 4.164 3.51
0.934 0.980 1.75 4.185 4.240 3.99
0.980 1.037 1.75 4,240  4.313 3.96
1.037 1.092 1.82 4.313 4.387 3.90
1.114 1.177 2.32 4.387 4.461 3.93
1.177 1.232 2.63 4.498 4.553 3.64
1.232 1.284 2.75 4.553  4.634 3.72
1.284 1.351 271 4.634  4.713 3.80
1.396 1446 2445 4713 4.766 3.75
1.446 1.519 2.17 4.785 4.864 3.68
1.519 1.5%94 2.16 4.864  4.943 3.66
1.594 1.665 2+26 4.943  5.024 3.59
1.679 1.747 3.20 5.024 5.105 3.60
1.747 1.809 3.50 5.105 5.187 3.55
1.809 1.871 3.5 5.207 5.280 4014
1.871 1.932 3.62 5.280 5.355 4+ 01
1.958 2.029 2.51 5.355 5.428 .12
2.029 2094 249 5.428 5.500 4.18
2.09 2.157 2+54 5.500 5.571 4.20
2.157 2249 2.62 5.595 5.684% 3.24
2275 2333 3.78 5.684 5.771 3.33
2.333 2.390 3.82 5.771 5.858 3.33
24390 2.465 3.87 5.882 5.948 454
2.465 2560 3.82 5.948 6.014 4457
2.584 2655 2.83 6.014 6.057 4o 66
24655 2.726 2.83 6.084 6.147 4.80
2726 2.799 2.75 6.166 6.241 2.91
2.799 2.869 2.84 6.241 6.312 3.08
2.869 2969 2.80 6.312 6.383 3.05
2.+984% 3.040 3.90 6.383 6.454 3.05
3.040 3.096 3.92 6.454  6.527 3.00
3.096 3.171 3.86 6.554  6.614 5.00

(continued)
Run No. 525 (con‘tinued_)

164

 

 

 

 

 

 

Wy We X Yy Vi3 We X y
6.614 6.674  4.84 7.035 7.115 2.72
6.676  6.737 5.00 7.115  7.197 2.67
6.737  6.797  4.96 7.197 7.278 2.68
6.797 6.856  5.12 7.309 7.344  5.62
6.856 6.916  5.03 7.3 7.399 5.51
6.952 7.035 2.60 7.399  7.453  5.54

Run No. 527

0.333 BeFz at 651°C, w = 0.470, T = 298%K, a = 4.30, ¢ = 7.63

W3 Wy X Yy Wy We X Y
0.017 0.037  4.08 1.481  1.536 10.96
0.037 0.058  5.88 1.536 1.592 10.82
0.058 0.085  7.20 1.592 1.655 10.79
0.085 0.135  8.04 1.718  1.773 4.01
0.135 0.169 9.38 1.773 1.827 4.05
0.169 0.203  9.64 1.827 1.879 4 e 20
0.203 0.234 10.21 1.879 1.930 4028
0.234  0.264 10.78 1.930 1.981 430
0.264 0.29%  10.78 2.019 2.075 10.59
0.294  0.322 11.17 2.075 2.133 10.42
0.402  0.438 1.99 2.133 2.192 10.21
0.438 04470 2.29 2.192 2.251 10.22
0.470  0.499 2.53 2.251 2.318 10.12
0.509 0.526 11.82 2.401  2.452 436
0.526 0.552 12.12 2.452  2.502 438
0.552  0.593 11.87 2.502 2.568 PAvAL
0.593  0.627 11.87 2.568 2.640 b 57
0.627 0.661 11.8% 2.640 2.703 4.63
0.718  0.769 2.87 2.741 2.802  9.80
0.769 0.816 3.07 2.802 2.864 9.7
0.816 0.863 3.10 2.864 2.9%7  9.70
0.912 0.947 11.51 2:.947  3.030 9.58
0.947 1.000 11.51 3.076  3.140 4455
1.000 1.052 11.46 3.140 3.203 b o 64
1.052 1.087 11.34 3.203  3.264 478
1.120 1.164 3.30 3.264  3.325 475
1.164 1.206 3.49 3.325 3.386 4480
1.206 1.268 3.54 3.386  3.447 4.83
1.268 1.326 3.78 3.459  3.541 9.67
1.326 1.383 3.79 3.541 3.625 = 9.63
1.401  1.428 11.18 3.625 3.709  9.51
1.428  1.481  11.20 3.709 3.793  9.47

 

(continued)
165

Run No. 527 {(continued)

 

 

 

 

W i W. f X Y W i Wf X Yy
3.863 3.931 4.80 4,167  4.225 5.07
3.931  3.991 4,92 4e246  4.311 9.17
3.991 4.050 4.96 4,310 4,377 9.10
4.050  4.109 4.91 4377 bbb 9.01
4109  4.167 5.00

Run No. 529

b = -0.20, ¢ = 0.70, d = -0.007

 

 

 

Wy We X Yy Vs We X N
0.056 0.088 1.05 1.647 1.690 5.84
0.088 0.115 1.24 1.690 1.734 5.88
0.161 0.203 0.76 1.734 1.776 6.10
0.203 0.231 1.09 1.832  1.947 8.14
0.253 0.272 2.62 1.947 1.986 8.01
0.272 0.299 2.54 1.986 2.025 8.01
0.299 0.354 2.82 2.025 2.064 7.97
0.383 0.404 2.92 2.089 2.137 7.16
0.404  0.431 3.50 2.137 2.185 722
0.431  0.454 4 .00 2.185 2.232 7.24
0.454  0.674 5.40 2.232 2.279 7.33
0.674  0.701 6.84 2.279 2.325 74l
0.74  0.734 4o22 2.342 2.389 6.70
0.734 0.774 4426 2.389 2.436 6.63
0.774  0.814 4.30 2.436 2.485 6.37
0.814 0.853 4443 2.485 2.536 6.04
0.853 0.891 4a51 2.554  2.593 g.79
0.943  0.985 742 2.593 2.632 8.71
0.985 1.024 7.96 2.632 2.671 8.76
1.024 1.063 7.96 2.671 2.710 8.84
1.063 1.102 8.07 2.751  2.799 5.21
1.102 1.140 8.25 2.799 2.853 459
1.145 1.179 5.09 2.853 2.911 4432
1.179  1.245 5.14 2.911 2.956 4el2
1.262  1.29% 5442 2.963 2.995 10.68
1.294  1.326 5.38 2.995  3.042 10.92
1.364  1.401 8.46 3.042 3.088 11.14
1.401 1.439 8.36 3.088 3.133 11.37
1.439  1.476 g.38 3.156  3.190 3.75
1.476  1.512 8.64 3.190 3.221 3.91
1.512 1.548 8.55 3.221  3.252 4,07
1.558 1.602 5.79 3.252 3.300 3.90
1.602  1.647 5.76 3.300 3.332 3.93

(continued)
166

Run No. 529 (continued)

 

 

 

 

 

 

Wy We X Yy Wi We X Yy
3.346  3.384 13.39 3.622 3.656 3.60
3.384 3.422 13.68 3.669 3.702 15.63
3.434 3.457  14.76 3.702 3.734 15.88
3.457 3.494 13.96 3.734  3.765 16.57
3.517 3.553 3.42 3.765 3.797 16.22
3.553 3.586 3.78 3.876  3.904 3.36
3.586 3.622 3.51 3.904 3.932 3.37

Run No. 533

0.273 BeFz at 700°C, w = 0.520, T = 298°K, a = 4.47, ¢ = 7.63

Wi Wf X Y Wi Wf X Y
0.016 0.024 4 .66 1.152  1.196 2.96
0.024 0.039 7.20 1.196 1.248 3.16
0.039 0.058 9.37 1.248 1.296 3.36
0.058 0.075 10.62 1.296  1.344 3.41
0.075 0.106 11.84 1.400 1.462 11.67
0.118 0.152 1.90 1.462 1.509 11.59
0.152 0.185 1.99 1.509 1.556 11.43
0.185 0.217 2.03 1.556 1.619 11.47
0.228 0.241 13.63 1.619 1.683 11.39
0.241 0.268 13.75 1.730 1.783 3.71
0.268 0.29%  13.55 1.783 1.836 3.70
0.294 0.321 13.71 1.836 1.904 3.82
0.321 0.348 13.43 1.904 1.954 3.96
0.393 0.425 2.07 1.954  2.004 3.90
0.425 0.453 2.28 2.005 2.070 11.21
0453  0.483 2.21 2.070 2.136 10.92
0.483 0.512 2.20 2.136 2.203 10.83
0.523 0.550 13.36 2.203 2.270 10.79
0.550 0.577 13.28 2.304 2.352 4.08
0.577 0.606 12.91 2.352 2.413 4430
0.606 0.634 12.93 2.413 2.472 bodel
0.634 0.662 12.68 Re4T72  2.531 4o 40
0.700 0.753 246 2:540 2.590 10.76
0.753 0.802 2.67 2.590 2.641 10.71
0.802 0.850 2.71 2641 2.692 10.64
0.850 0.897 2.78 2.692 2.744  10.55
0.904 0.946 12.89 2.744  2.795  10.50
0.946 0.989 12.68 2.831 2.892 4.28
0.989 1.033 12.50 2.892 2.951 bodel
1.033 1.070 12.05 2.951  3.009 4451
1.070 1.115 12.16 3.009 3.067 4 46

 

(continued)
167

Run No. 533 (continued)

 

 

 

 

3.075 3.128 10.20 3.323 3.378 470
3.128 3.182 10.16 3.378 3.434 4.67
3.182 3.236 10.04 3.441 3.498 10.12
3.264 3.323 b4obi2 3.498 3.552 10.08

Run No. 535

0.273 BeFa at 650°C, w

= 0.520, T = 298%K, a = 15.00,
b = "0'24‘, c =

 

 

 

 

 

 

0.55, & = =-0.006

Wy We X y Wy We X Y
0.098 0.121 1.63 1.712 1.788 4.30
0.121 0.158 1.95 1.788 1.864 4429
0.177 0.260 0.79 1.864  1.957 .21
0.260 0.310 1.29 1.957 2.035 4.18
0.310 0.581 264 2.045 2.108 8.59

0.581 0.616 3,67 2.108 2.192 8.60

0.629 0.665 6.09 2.226 2.284 9.30

0.665 0.709 6.16 2.312 2414 3.83
0.709 0.752 6.28 2.414  2.466 3.75
0.752 0.796 6.21 2.466  2.538 3.67
0.796 0.838 6.43 2.538 2.609 3.67
0.838 0.879 6.59 2.632 2.681 9.32

0.912 0.945 4.01 2.681 2.740 9.25

0.945 0.991 4.25 2.740  2.817 9.38

0.991 1.062 4 .58 2.817 2.875 9.43

1.062 1.134 4o 54 2.922 2.978 3.47
1.134 1.204 4.63 2.978  3.036 3.37
1.231 1.281 722 3.036 3178 3.21
1.281 1.332 7.14% 3.193 3.247 10.08
1.332  1.406 7.26 3.247 3.301 10.08

1.406 1.481 7.28 3.301 3.355 10.11
1.481 1.554 745 3.382 3.426 2.96
1.592  1.636 449 3.426  3.470 2.92
1.636 1.712 4.28 3.470 3.514 2.96
Run No. 537

0.273 BeFz at 650°0C, w = 0.520, T = 298%K, a = 4.08, ¢ = 7.63
Wy We X Yy Wy We X Yy
0.016 0.028 3.07 0.071  0.090 5.64

0.028 0.048 3.62 0.110 0.139 2.20
0.048 0.071 4.62 0.139 0.169 2.07

 

(continued)
Run No. 537 (continued)

168

 

 

Ws We X N Wy We X Y
0.169 0.198 2.17 1.958 2.010 5.51
0.216  0.259 8.42 2.010 2.075 5.34
0.259 0.299 9.05 2.075 2.131 5.63
0.299 0.339 9.03 2.159  2.226 8.10
0.339 0.379 9.20 2.220 2.2% 7.99
0.379 0.419 9.05 2.294  2.362 8.0l
0.476  0.495 3.29 2.362 2.430 7.96
0.495  0.546 3.68 2.430 2.499 7.86
0.546  0.594 3.97 2.548  2.595 5.43
0.594  0.641 4.09 2.595 2.642 5.38
0.649  0.687 9.47 2.642 2.698 5.60
0.687 0.725 9.55 2.698  2.765 5.70
0.725 0.764 9.34 2.765 2.822 5.51
0.764  0.802 9.34 2.839  2.902 7.79
0.802 0.842 9.10 2.902 2.979 7.70
0.869 0.912 4.37 2.979  3.050 7.67
0.912 0.954 4.50 3.050 3.121 7.63
0.954  0.995 e s B4 3.157 3.243 5.93
0.995 1.036 4 .66 3.243  3.309 5.76
1.036  1.075 4.83 3.309 3.374 5.79
1.093 1.133 9.14 3.374 3.440 5.74
1.133 1.173 9.03 3.440  3.506 5.83
1.173 1.214 8.84 3.593 3.692 7.36
1.214 1.255 8.84 3.692  3.766 7.36
1.255 1.297 8.64 3.766  3.840 7.32
1.317 1.356 4+ 90 3.840 3.914 7.32
1.356 1.408 4.84 3.948 4.012 5.95
1.408  1.459 4.99 4.012 4.076 2.90
1.459 1.510 5.01 4.076  4.140 5.95
1.510 1.558 5.18 4.140  4.203 6.00
1.581 1.623 8.47 4,203  4.265 6.12
1.623 1.675 8.40 4.286  4.360 7.32
1.675  1.719 8.33 4.360 4.436 7.21
1.719 1.763 8.24 4.436 4,512 7.12
1.763 1.828 8.30 4545  4.598 6.03
1.864 1.911 5.33 4,598 4.650 6.05
1.911  1.958 5.38 4.650  4.702 6.09

 

 
169

Run No. 539

0.273 BeFz at 600°C, w = 0.520, T = 298°K, a = 14.50,
-b = -0'20, c =

 

 

0.55, d = =0.006
Wi We X Yy Wi We X Yy
0.055 0.104 0.56 2.522  2.579 beodi]
0.104 0.151 0.76 2.579 2.639 4o 24
0.224  0.256 0.98 2.639  2.700 4.13
0.256  0.300 1.44% 2.721  2.761 9.10
0.300 0.338 1.66 2.761  2.809 9.01
0.350 0.384 2.12 2.854 2.893 9.17
0.384  0.425 2.67 2.893 2.953 9.10
0.425 0.465 2.74 2.980 3.034 3.53
0.465 0.502 2.90 3.034  3.087 3.62
0.523  0.547 2.66 3.087 3.140 3.55
0.547 0.576 3.26 3.140 3.213 3.46
0.576 0.614 3.29 3.224 3.278 10.04
0.614 0.649 3.63 3.278 3.332 10.09
0.649  0.681 3.99 3.332 3.386 10.12
0.696  0.729 3.84 3.386 3.438 10.34
0.729  0.766 3.88 3.438 3.490 10.51
0.766  0.812 3.99 3.507 3.578 2.67
0.812 0.856 4.08 3.578 3.649 2.68
0.909  0.947 4 .96 3.649 3.725 2.51
0.947  0.984 5.12 3.725  3.807 2.29
0.984 1.019 5.45 3.822 3.867 11.95
1.038  1.077 462 3.807 3.914 11.75
1.077  1.135 4470 3.914 3.960 11.75
1.135 1.191 4 .86 3.960 4.021 11.76
1.191  1.246 4,96 4.050 4.116 1.%1
1.266  1.302 5.22 4.116 4.190 1.72
1.302 1.349 5.40 4.190  4.269 1.60
1.349 1.393 5.76 4.269  4.35]1 1-54
1.393 1.437 5.74% 4.365 4.422 12.55
1.437 1.481 5.82 4422  4.480 12.61
1.502 1.567 5.57 4.480 44536  12.78
1.567 1.632 5.60 4.536 4.592 12.68
1.632 1.695 5.72 beb624 4670 1.37
1.695  1.756 5.90 4.670  4.720 1.29
1.756 1.816 6.10 4.720 4.773 1.18
1.848 1.870 5.64 4.785 4.827 13.13
1.870 1.916 5.59 4.827 4.869 12.89
1.916 1.961 5.64 4.869 4.912 12.68
1.961 2.008 5.37 4e912 44954  12.78
2.008 2.077 5.45 4.982 5.041 1.07
2.096  2.147 7.08 5.041 5.103 1.01
2.147 2.198 7.10 5.103 5.163 1.06
2.198 2.248 7.16 5.163 5.230 0.94
2.248 2.298 7.33 5.272 5.314 12.87
2.465  2.522 4.50 5.314 5.342 12.93

 

 
170

 

 

 

 

 

 

Run No. 601

0.600 BeFa at 600°C, w = 0.424, T = 2979K, a = 13.7, ¢ = 3.88
Wy Wp X y Wy We X Yy
0.000 0.024 5.50 0.714 0.751 2.16
0.024  0.055 A 0.760 0.789 11.36

0.055 0.091 854 0.789 0.8192 11.09
0.091 0.128 9.10 0.819 0.849 11.21

0.128 0.164 9.20 0.849 0.879 11.13
0.164 0.200 9.34% 0.879 0.908 11.13
0.266 0.312 1.73 1.027  1.09% 2.41
0.312 0.357 1.80 1.094 1.158 2.49
0.373 0.406 9.91 1.158 1.256 2.46
0.406 0.439 10.14 1.256 1.320 2+49
0.439 0.472 10.22 1.331 1.358 12.37

0.472 0.504 10.30 1.358 1.385 12.20

0.504  0.537 10.14 1.385 1.439 12.17
0.571 0.614 1.86 1.439 1.49% 12.17
0.614 0.675 1.96 1.494  1.566 12.38
0.675 0.714 2.09 1.597 1.663 2.4

Run No. 603

0.600 BeFa at 7019C, w = 424, T = 297°K, a = 13.7, ¢ = 3.88

Wy Wf X Yy Wi Wf X Yy
0.000 0.035 2.54 1.140 1.191 17.59
0.035 0.056 4.22 1.239 1.353 1.35
0.056 0.087 5.7 1.353 1.471 1.31
0.087 0.120 6 .64 1.471 1.581 1.40
0.120 0.149 7.75 1.581 1.693 1.38
0.149 0.181 8.45 1.723 1.769 19.05
0.237 0.301 1.20 1.769 1.818 18.95
0.301 0.362 1.26 1.818 1.866 18.74
0.362 0.433 1.31 1.866 1.913 18.89
0.440 0.456  14.07 1.913 1.960 18.97
0.456  0.487 14.38 2.153 2.265 1.37
0.487 0.534 14.30 2.265 2.322 1.36
0.534  0.579 14.66 2.335 2.358 19.21
0.579 0.638 15.08 2.358 2.406 18.74
0.694  0.752 1.32 2.406 2.453 18.70
0.752 0.808 1.38 2.453  2.477 18.74
0.808 0.865 1.36 2+564  2.623 1.32
0.865 0.949 1.40 2.623  2.680 1.36
0.987 1.038 17.39 2.685 2.709 19.13
1.038 1.089 17.46 2.709 2.732 19.13
1.089 1.140 17.29

 

 
0.600 BeFy at 500°C, w = 0.424, T = 2970K,

Run No. 605

a =13.7, ¢ = 3.88

 

 

 

 

 

 

Wy We X Yy Wy We v
0.010 0.046 245 2.143 2.201 3.99
0.046  0.070 3.76 2.201 2.253 4+50
0.070 0.104 3.82 2253  2.300 beo 34
0.164 0.235 1.09 2.306 2.355 470
0.235 0.304 1.12 2.400 2.483 5.34
0.304 0.372 1.15 2.483 2.563 5.58
0.372 0.434 1.24 2.563  2.657 5.66
0.434  0.494 1.27 2.657 2.734 5.74
0.494  0.548 1 obde 2.734  2.810 5.84%

0.549  1.019 1.96 2.896 2.946 4o 97
1.113  1.174 3.66 2.946  2.988 5.54
1.174 1.233 3.72 2.988 3.033 5.22
1.233 1.293 3.75 3.033 3.076 5.38
1.293 1.350 3.86 3,097 3.166
1.350 1.408 3.86 3.166 3.235
1.408  1.464 3.96 3.235 3.304
1.481 1.508 2.80 3.387 3.427 5.82
1.508 1.557 3.17 3.427  3.465 6.12
1.557 1.629 3.20 3.465  3.531 5.79
1.660 1.771 4 o240 3.531 3.607 6.12
1.771 1.867 4 .60 3.668  3.726
1.867 1.963 4.62 3.726 3.813
1.963  2.056 479 3.813 3.902
Run No. 607
0.600 BeF2 at 5000C, w = 0.424, T = 297°%K, a
b = -1.15, ¢ = 0.136, d = -0.041

Wi P{f X y Pfii Vfif Yy
0.039 0.065 5.91 0.908 1.009
0.065 0.114% 6.30 1.045  1.110 5.97
0.114 0.163 6.33 1.110 1.171 6.28
0.174  0.230 7.95 1.171  1.293 6.33
0.230 0.286 7.99 1.293 1.413 6.41
0.286 0.341 7.99 1.432 1.525
0.377 0.439 6.29 1.525 1.620
0.439  0.500 6.34% 1.620 1.713
0.500 0.572 6.38 1.713  1.805
0.572 0.631 6.54 1.858 1.948 5.97
0.648 0.726 8.54 1.948 2.038 6.03
0.726  0.804 8.54 2.038 2.218 6.00
0.804 0.908 8.58 2.218 2.401 5.91

 

{continued)
172

Run No. 607 (continued)

 

 

 

 

 

 

Wy Wp x y Wy We x y
2.419  2.527 10.29 3.452  3.564  9.90
2.551 2.662 10.03 3.564  3.677 9.91
2.662 2.77%  9.93 3.706  3.79 429
2.835 2.906 5.47 3.796  3.900 FAAY
2.906 2.978 5.34 3.900 3.978 4,95
2.978  3.127 5.18 3.978  4.060 4 .66
3.127  3.202 5.13 %0084  4.191 10.39
3.227 3.339 9.91 4 191 4.255  10.37
3.339 3.452 9.84 4.255 4.319 10.37

Run No. 611

0.600 BeFz at 600°C, w = 0.424, T = 2979%K, a = 6.45, ¢ = 5.90
Wi We X vy Wi We X Yy
0.000 0.019  2.29 1.669  1.701 13.91
0.019 0.038  7.13 1.701 1.733 13.87
0.038 0.065 10.01 1.733  1.765 13.67
0.065 0.088 11.34 1.853  1.912 1.31
0.088 0.123 11.47 1.912  1.973 1.26
0.123 0.160 12.05 1.973 2.034 1.27
0.160 0.196 12.25 2.034  2.140 1.45
0.227 0.314 1.34 2.148 2.180 14.17
0.314 0.371 1.34 2.180 2.212 13.75
0.371  0.430 1.31 2.212  2.245 13.67
0.443  0.475 13.79 2:245 2.277 13.63
0.475 0.508 13.63 2.277 2.310 13.46
0.508 0.541 13.54 2.395 2.556 1.44
0.541  0.573 13.66 2.556 2.653 1.59
0.573 0.606 13.83 2.661. 2.693 13.79
0.677  0.750 1.06 2.693 2.726 13.67
0.750 0.827 1.00 2.726 2.759 13.46
0.827 0.974 1.05 2.797  2.950 1.51
0,992 1.023 14.43 2.950  3.090 1.66
1.023  1.054 14.21 3.090 3.219 1.79
1.054 1.086 13.79 3.219  3.389 1.82
1.086 1.118 13.91 3.389 3.551 1.90
1.118  1.150 13.75 3.576  3.609 13.50
1.244  1.315 1.08 3.609 3.643 13.01
1.315 1.382 1.16 3.643 3.676 13.42
1.382  1.515 1.16 3.676 3.710 13.12
1.515 1.578 1.21 3.710 3.744  13.12
1.606 1.637 14.43 3.818 3.9 1.68
1.637 1.669 14.13 3.941  4.057 1.99

 

(continued)
Run No. 611 (continued)

173

 

 

 

 

 

 

 

 

Wy We X Yy Wy We X Yy
4.057  4.171 2.03 2.022 5.073 13.25

4171 4.282 2.09 5.073 5,123 13.25

4.297 4.348  13.07 5.123 5.174  13.07

4.399 4.451  12.86 5.250 5.354 2.21
4.451 4.504 12.71 5.354  5.456 2.28
46572 4.681 2.13 5.468 5.518 13.09

4.681  4.788 2.16 5.518 5.570 12.87

4.788  4.897 2.13 5.570  5.622 12.95

4.897 5.003 2.18

Run No. 619
0.400 BeFp at 550°C, w = 0.567, T = 2999%K, a = 21.0, ¢ = 0.68

Wi Wf X Y Wi Wf X N
0.000 0.000 7.63 5.00 0.884 0.929 11.13

0.000 0.050 8.34% 0.929 0.975 10.87

0.050 0.148 8.50 0.975 1.035 11.04

0.148 0.195 g8.83 1.035 1.095 11.11

0.294 0.337 6.66 1.169 1.210 6.99
0.337 0.379 6.90 1.230 1.266 7.18
0.379 0.419 7.17 1.266  1.314 7.25
0.431  0.481 2.96 1.366  1.477 11.93

0.481 0.531 9.96 1.477 1.545 12.29

0.531 0.582 9.92 1.545 1.613 12.17

0.582 0.632 9.99 1.694  1.746 6.57
0.742 0.782 7.28 1.746 1.799 6.64
0.782 0.819 7 .64 1.815 1.868 12.63

0.819 0.865 7.55 1.868 1.921 12.54

Run No. 621

0.400 BeFz at 604°C,

w = 0.567, T = 299°K,

a = 6.45, ¢ = 5.90

 

 

 

Wy We X vy Wy We X Yy
0.004  0.017 2.5 0.216 0.261 1.27
0.017 0.026 7.22 0.261 0.329 1.24
0.026 0.041 8.84 0.385 0.409 13.47
0.041  0.058 9.79 0.409 0.458 13.59
0.058 0.083 10.47 0.458 0.490 13.29
0.083 0.107 10.57 0.496  0.520 13.39
0.107 0.129 11.08 0.5397 0.637 1.42

(continued)
Run No. 621 (continued)

174

 

 

 

 

 

 

0.637 0.672 1.63 1.797  1.907 2.63
0.672  0.707 1.67 1.907 2.014 2.75
0.722 0.747 13.43 2.014 2.099 2.72
0.747 0.785 13.32 2.131 2.172 12.24
0.785 0.822 13.36 2.172 2.214 12.00
0.822 0.847 13.09 2.214 2.256 11.75
0.863 0.896 1.75 2.256  2.298 11.87
0.89% 0.975 1.88 2.333 2.416 2.76
0.975 1.034% 1.97 2.416  2.496 2.88
1.042 1.079 13.43 2.496  2.574 2.95
1.079  1.117 13.21 2.685 2726 11.97
1.117 1.156 12.82 2.726  2.7692  11.75
1.156 1.183 12.39 2.769 2.811 11.79
1.247 1.300 2.17 2.811 2.847 11.59
1.300 1.375 2.32 2.857 2.916 2.95
1.375  1.447 2.41 2.916 2.972 3.07
1.447 1.544 2.38 2.972  3.027 3.13
1.574 1.626 12.91 3.027 3.084 3.08
1.626 1.678 12.72 3.098 3.141 11.63
1.678  1.730 12.64 3.141  3.184 11.63
Run No. 625
0.400 BeF, at 5500C, w = 0.567, T = 299K, a = 6.45, ¢ = 5.90
Wi We X Yy Wy Ve X Yy
0.004 0.020 2.08 0.649  0.677 11.95
0.020 0.034 6.93 0.677 0.706 11.42
0.034 0.052 9.47 0.706 0.734  11..83
0.052 0.076 10.38 0.734 0.779 11.26
0.076 0.092 10.80 0.779 0.807 11.64
0.099 (0.121 11.04 0.834 0.873 2.16
0.154  0.200 1.23 0.873  0.947 2.28
0.200 0.242 1.33 0.947  0.981 247
0.242  0.284 1.36 0.981 1.014 2.51
0.297 0.317 12.38 1.035 1.065 11.22
0.317 0.337 12.47 1.065 1.094 11.28
0.337 0.365 12.04 1.094 1.125 10.91
0.365 0.392 11.92 1.125 1.155 10.80
0.392 0.421 11.59 1.186 1.231 2.51
0.464  0.501 1.52 1.231  1.271 2.75
0.501 0.533 1.72 1.271 1.324 2.64
0.533 0.563 1.88 1.324 1.361 3.09
0.563 0.609 1.83 i.361  1.396 3.13
0.622 0.649 12.01 1.402 1.431 11.20

 

(continued)
Run No. 625 (continued)

175

 

 

 

 

 

 

1.431  1.462 10.78 2.256 2.291 9.60
1.462 1.494 10.53 2.325 2.374 3.50
1.494 1.590 10.38 2.374 2.418 3.78
1.625 1.662 3.01 2.418  2.463 3.75
1.662 1.699 3.03 2.480 2.514 9.66
1.699  1.733 3.25 2.514  2.549 9.57
1.733  1.767 3.29 2.549  2.584 9.57
1.790 1.821 10.51 2.584 2.619 9.49
1.821 1.854 10.37 2.670 2.712 4a 017
1.854 1.886 10.34 2.712  2.754 3.96
1.886 1.918 10.21 2.754  2.797 3.93
1.955 1.990 3.25 2.818 2.853 9.53
1.990 2.037 3.53 2.853 2.897 9.45
2.037 2.069 3.50 2.897 2.932 9.36
2.069 2.118 3.50 2.932 2.968 9.25
2.138 2.172 10.05 2.997  3.040 3.96
2.172 2.205 9.96 3.040 3.081 4.08
2.205 2.526 9.75 3.081 3.122 i1
Run No. 627
0.400 BeFp at 702°C, w = 0.567, T = 2999K, a = 6.70, ¢ = 6.05
Wi We X y Wy We X Y
0.000 0.011 3.00 0.744  0.808 0.88
0.011 0.022 5.82 0.808 0.856 0.91
0.022 0.033 9.18 0.856  0.914 0.97
0.033 0.048 11.12 0.942 0.961 17.12
0.048 0.068 12.43 0.961 0.992 16.32
0.068 0.087 13.08 0.992 1.022 16.28
0.087 0.106 13.49 1.022 1.043 16.17
0.106 0.123 14.88 1.053  1.142 0.95
0.123 0.143 14.64 1.142 1.197 1.02
0.288 0.308 16.28 1.197 1.255 1.07
0.308 0.328 16.16 1.283 1.312 17.29
0.328 0.349 16.51 1.312 1.341 16.87
0.349 0.380 16.13 1.341 1.381 16.82
0.413  0.472 0.96 1.381  1.421 16.49
0.472 0.542 0.81 1.421  1.462 16.13
0.542  0.602 0.93 1.495 1.576 1.03
0.611 0.631 16.87 1.576 1.648 1.17
0.631 0.651 16.51 1.648  1.717 1.22
0.651 0.671 16.28 1.736 1.766 16.59
0.671 0.692 16.34 1.766  1.796  16.51
0.692 0.712 16.05 1.796  1.837 16.20

 

(continued)
Run No. 627 (continued)

176

 

 

Wy We X Yy Wy We X y
1.837 1.878 16.30 2.265 2.296 16.01
1.905 1.975 1.20 2.318 2.382 1.32
1.975  2.041 1.28 2.382 2.442 1.40
2.041  2.102 1.37 2.442  2.502 1.41
2.120 2.151 16.36 2.502 2.561 1.43
2.151 2.181 16.36 2.581 2.611 16.43
2.181 2.223 15.96 2.611 2.642 15.87
2.223 2.265 16.05 2.642 2.674 15.80

 

 
177
APPENDIX C
Glossary

a (or a + bW) - influent partial pressure of HF

A - (a + 2c)

aBer - thermodynamic activity of BeF:2

,B - parameters expressing the variation in "BeTa with composition at

a specified temperature according to the equation

- ox? 4
10g Ypep, = Kpip ¥ PX 14w

¢ (or ¢ +dW) - influent partial pressure of Hz0

C - integration constants

ACP - heat capacity change at constant pressure

PW - (x + y)
f - correction factor = ——m———

w ~ Py
AFr - free energy of reaction
Tpep, - octivity coefficient of BeFp = aBng/XBng
AHOf - standard heat of formation
Pusson heat of fusion

AH& - heat of reaction
Afiéubl - heat of sublimation
AH%ap - heat of vaporization
fiéer - partial molal heat content of BeF2 in solution
HPBer - partial molal heat content of pure liquid BeF,
K - thermodynamic equilibrium constant

2
K, = % /yaBng = Q/aBer
178

k, 1, m - parameters used in correlation of Q as a function of melt
composition according to the equation

log (@/Xpp,) = k + L p)? + mix, )%

kp, lo, m° - temperature independent portions of k, 1, and m, respectively

k', 1', m* - temperature dependent portions of k, 1, and m, respectively
Ny and anO - moles of HF and Hz20 as measured at TW, Pw
P and P - partial pressures of HF and H20, respectively.
HrF H20
p, = Vapor pressure of water at Tw
v total pressure at wet-test meter
Py - partial pressure of HF or Hz0 leaving melt
P> - measured partial pressure of HF or Hz0

Q - x°/y for BeO saturated melt
Qy - xsfy

Q, - s?/yr = (QA)Z/QO

oy - s*fy = ()3/

Q - s/x =9q,/q,

Q@ - s/x=09/Q

QO - xar/y

r - [0%7] - oxide concentration in moles per kilogram of melt

s - [0H ] - hydroxide concentration in moles per kilogram of melt
r and Sy - values of r and s at W = 0 in unsaturated experiments

S~ - standard entropy at specified temperature

ASr - entropy of reaction

O - standard deviation

t -~ degrees Centigrade (generally used to indicate melt temperatures)

T =~ degrees Kelvin (used to indicate wet-test meter temperatures)
179

Tw - temperature of wet-test meter, °k
E .
M BeF, excess chemical potential of Bel's
Vé - volume of dry carrier gas going through system measured at Tw’ PW
VE - volume of gas entering titration assembly at TW, Pw
“m - volume of gas space above the melt
Vw -~ volume of gas through melt measured at TW, PW (1iters)
dV -~ increment of gas flowing through system as measured at Tw’ PW
w - weight of melt (kg)
W - V/‘WfiRTw (mole kg™ * atm™t)
Xé - mole fraction BeF;
el
x = effluent partial pressure of HF

effluent partial pressure of Ha0
1.
2-6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.

18.
19.
20.
21.
22.
23.
2 s
25.
26.
27
28.
29-31.
32.
33.
3.
35.
36.

69.
70-84.
85.

86.
87.
88.

89.
90.

181

ORNL TM-1129

INTERNAL DISTRIBUTION
R. F. Apple 37. D. Scott
C. F. Baes, Jr. 38. D. R. Sears
J. T. Bell 39, J. H. Shaffer
C. M. Blood 40. S. H. Smiley
F. F. Blankenship 41. P. G. Smith
G. E. Boyd 42. H. H. Stone
M. A. Bredig 43. A. Taboada
R. B. Briggs 44. R. E. Thoma
D. W. Cardwell 45. G. M. Watson
G. I. Cathers 46. A. M. Weinberg
E. L. Compere 47. M. E. Whatley
J. L. Crowley 48. J. C. White
F. L. Culler 49. B. J. Youn
J. M. Dale 50. L. Brewer {(consultant)
R. B. Evans III 51. J. W. Cobble (consultant)
D. E. Ferguson 52. D. G. Hill (consultant)
R. A. Gilbert 53. H. Insley (consultant)
W. R. Grimes 54. G. Mamantov (consultant)
M. T. Harkrider 55. T. N. McVay (consultant)
B. F. Hitch 56. R. F. Newton {consultant)
S. 8. Kirslis 57. J. E. Ricci (consultant)
K. A. Kraus 58. G. Scatchard (consultant)
R. B. Lindauer 59. H. Steinfink (consultant)
D. L. Manning 60. T. F. Young (consultant)
H. F. McDuffie 61-62. Central Research Library
R. J. McNamee 63. Document Reference Section
R. L. Moore 64-66. Laboratory Records Department
K. A. Romberger 67. Iaboratory Records, ORNL R.C.
M. W. Rosenthal 68. ORNL Patent Office
H. C. Savage

EXTERNAL DISTRTIBUTION
Research and Development Division, ORO

Division of Technical Information

¥F. A. Anderson, Chemical Engineering Dept., University of Miss.,
University, Mississippi

M. J. Blander, North American Aviation Science Center,

8437 Fallbrook Avenue, Canoga Park, California

A. Buchler, Arthur D. Little, Inc., 30 Memorial Drive, Cambridge 42,
Massachusetts

S« F. Clark, University of Mississippi, University, Mississippi
P.A.D. deMaine, University of California, Santa Barbara, Calif.
G. Dirian, Commissariat a 1'Energie Atomique (CEN Saclay) 69,
Rue de Varemne, Paris, France
91.
92.
93.
e

95.

96.
9‘7.

98.
99.

100.
101.
102.

103-112.
113.
114.
115.

116.
117.
118.
119.

120.
121.
122.
123‘
124.

182

C. F. Dodson, Western Carolina College, Cullowhee, North Carolina.
F. R. Duke, Texas A and M College, College Station, Texas

J. E. Eorgan, Kawecki Chemical Co., Boyertown, Pennsylvania

H. Flood, Institute of Silicate Science, Norwegian Institute of
Technology, Trondheim, Norway

Tormod Férland, The Institute of Theoretical Chemistry, Trondheim,
Norway

R. M. Fuoss, Yale University, New Haven, Connecticut

M. A. Greenbaum, Rocket Power Inc., Research lLaboratories, Pasadena,
California

Marwin Kemp, University of Arkansas, Fayetteville, Arkansas

0. J. Kleppa, Chemistry Department, University of Chicago, Chicago,
J1linois

S. langer, General Atomics, P.0. Box 608, San Diego, California

G. Long, Chemistry Dept., UKAEA, Harwell, Didcot, Berks., England
C. R. Masson, National Research Council of Canada, Atlantic Regional
Laboratory, Halifax, Nova Scotia

A. L. Mathews, Western Carolina College, Cullowhee, North Carolina
D. A. Mathewes, Western Carolina College, Cullowhee, North Carolina
J. L. Margrave, Rice University, Houston, Texas

N. J. Meyer, Department of Chemistry, Bowling Green State University,
Bowling Green, Ohio

G. Nessle, Kawecki Chemical Co., Boyertown, Pennsylvania

S. Pizzini, BEuratom, CCR, Ispra, Italy

P. A. Reid, Western Carolina College, Cullowhee, North Carolina
Rustum Roy, Materials Research Laboratory, The Pennsylvania State
University, University Park, Pennsylvania

S. D. Squibb, Asheville-Biltmore College, Asheville, North Carolina
B. R. Sundheim, New York Univeristy, New York, New York

E. L. Topol, 19806 Gilmore Street, Woodland Hills, California

W. J. Wallace, Muskegon College, Muskegon, Michigan

J. Zarzycki, Compagnie de Saint-Gobain, 52 Bd De la Villette,

Paris 19€, France