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University

 

This is to certify that the

thesis entitled
HIGH TEMPERATURE MASS SPECTROMETRY:
SAMARIUM DICARBIDE AND
NEODYMIUM(III) MONOTELLURO OXIDE

presented by

Philip A. Pilate

has been accepted towards fulfillment
of the requirements for

A degree in W

7&2” y i/

#jor professor

 

Date February 22, 1968

0-169

ABSTRACT
HIGH TEMPERATURE MASS SPECTROMETRY:
SAMARIUM DICARBIDE AND NEODYMIUM(III) MONOTELLURO OXIDE

by Philip A. Pilato

I. Samarium Dicarbide

 

Samarium dicarbide was prepared from stoichiometric
mixtures of samarium metal and graphite powder by heating
in a sealed tantalum bomb. Analysis on three different
preparations gave the following mole percentages: samarium,
32.72 i 0.57% (calc., 33.33%); bound carbon, 67.28 i 0.57%
(calc., 66.67%). In a separate analysis 99.53% of the
total sample weight was accounted for. X-ray powder dif-
fraction analysis gave the tetragonal lattice parameters:
a0 = 3.776 r 0.004 R; Co = 6.319 i 0.008 R. The lattice
parameters did not change detectably after a portion of the
sample had been vaporized.

The mode of vaporization of SmCz, investigated over
the temperature range 1431-20580K using both graphite-lined
molybdenum and tungsten Knudsen effusion cells, was found

to be

 

SmC2(s) > Sm(g) +2C(gr). (a)

Absolute pressures of Sm(g) in equilibrium with SmC2(s)

were obtained by calibrating the mass spectrometer with:

(1) the vapor pressure of samarium metal or with, (2) the
loss in weight of SmC2(s) at a fixed temperature for a given

time. This equilibrium vapor pressure is described as a

1

 

A —, ’_.————4—__4‘

 

 

.
P‘ 7'-
T.;€-.

dynar
hith 4
and c
AOI re

 

2 Philip A. Pilato

function of temperature by the empirical least squares

equation:

 

-58,600 i 2.100) + 13.7 i 1.8

2.303R log PSm = ( T (b)

Thermodynamic data calculated for reaction (a) are AH:745 =
58.6 i 2.1 kcal/gfw and 852745 = 13.7 i 1.8 cal/gfw-deg.
These data were reduced to 298°K by use of the thermo—
dynamic data of CaCz, corrected for replacement of calcium
with samarium, and resulted in AHggs = 64.2 i 2.6 kcal/gfw
and A8393 = 22.1 i 2.3 cal/gfw-deg. The third law enthalpy
for reaction (a) calculated with an eStimated free energy
function for SmC2(s) is AHggs = 66.9 i 1.7 kcal/gfw. A
combination of the average enthalpy value with literature
data yielded for SmC2(s): AHggs f = -14.6 i 2.8kcal/gfw,
Asgga'f = 5.0 i 2.8 cal/gfw—deg, S293 = 24.4 i 2.4 cal/gfw-

deg.
II. NeodymiumfiIII) Monotelluro Oxide

The purity of samples prepared by passing tellurium
vapor over Nd203 using hydrogen as the carrier gas was. 99.6,
98.3 and 100.3% according to mass uptake data. X-ray pow-
der diffraction analyses of the residues after vaporization
indicated the compound vaporized incongruently to the ses—
quioxide. Mass spectrometric analysis of the effusing vapor
indicated that (1) the vaporization species are Nd(g), Nd0(g),

Te(g) and that 0(g) is also a product at higher temperature;

3 Philip A.Pilato
and (2) the ratio of partial pressures of NdO(g) to Nd(g)
is temperature dependent changing from less than to greater
than unity azabout 2150°K.
These observations are consistent with the hypothesis
that several simultaneous equilibria are occurring in the

vaporization of NdZOZTe. The probable reactions are:

 

2K3Nd2o3(s)+ 2/3 Nd(g) + Te(g) (c)

V

NdzOzTe (S )

 

 

 

Nd202T9(S) + o<g> > Nd203(5) + Te(g) (d)
Nd203(8) > 2Nd0(9) + 0(9) (e)
NdZOZTe(s) > 2Ndo(g) + Te(g) (f)

Reaction (c) is postulated to predominate at lower tempera-
ture while reactions (e) and (f) become favorable at higher
temperatures and this temperature dependence is consistent
with calculated equilibria constants for the reactions in
which the free energy function and standard enthalpy of

formation of NdZOZTe(s) were estimated.

HIGH TEMPERATURE MASS SPECTROMETRY:

SAMARIUM DICARBIDE AND NEODYMIUM(III) MONOTELLURO OXIDE

BY

‘ “5.
I |
7:.

Philip AffiPilato

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Department of Chemistry

1968

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1

 

 

 

 

5’ 2‘ Dig/9%

ACKNOWLEDGMENTS

The author wishes to express his sincere appreciation
to Dr. Harry A. Eick for the suggestions, encouragement and
friendship which he generously extended throughout the course
of this investigation.

Thanks are also due to my colleague, Mr. John Haschke,
for many helpful and lively discussions during the course
of this work.

The help extended by Mr. Russel Geyer who constructed
some of the effusion cells and by Mr. James Grumblatt for
aiding the author in re-wiring the mass spectrometer is
acknowledged.

A lasting sense of gratitude and appreciation is ex—
tended to the author's wife, Fran, and daughter, Paulette,
for their patience, understanding and unselfishness which
they expressed throughout this study.

Financial support from the Atomic Energy Commission

under Contract AT(11—1)-716 is gratefully noted.

ii

 

 

 

 

 

II.

III .

 

II.

III.

IV.

TABLE OF CONTENTS

Page
INTRODUCTION . . . . . 2
HISTORICAL . . . .-. . . . . . . . . 4
2.1. Reported Work on Lanthanon-Dicarbide Systems 4
2.1.1. Preparation and Characterization 4
2.1.2. Vaporization Studies . . . . . . 8
2.2. Reported Work on Lanthanon Chalcogen
Oxide Systems . . . . . . . . . 13
2.2.1. Preparation and Characterization 13
2.2.2. Vaporization Studies . . 14
THEORETICAL CONSIDERATIONS . . . . . . . . . . . 16
3.1. General Introduction . . . . . . . . . . . 16
3.2. Thermodynamic Relationships in Vaporiza-
tion Studies . . . . . . . . . . . . . . . 18
3.2.1. Second Law Relationships . . 18
3.2.2. Third Law Relationships . . . . . 24
3.3. The Knudsen Effusion Method . . . . . 26
3.3.1. General Introduction . . . . . . . 26
3.3.2. Restrictions and Constraints . . 27
3.3.2.1. Limitations Arising from
Mathematical Formulation 28
3.3.2.2. Limitations Arising from
the Sample . . . . . . . 29
3.3.2.3. Limitations Arising from
External Geometry. . 32
3.4. Measurement of Partial Pressures with a
Mall Spectrometer . . . . . . . . . . 34
3.4.1. General Introduction . . . . . . 34
3.4.2. Absolute Pressures with a Mass
Spectrometer . . . . . . . . . . . 34
3.4.3. Geometry Considerations in
Calibration . . . . . . . . . . . 40
3.5. Temperature Corrections . . . . . . . . 41
EXPERIMENTAL EQUIPMENT AND MATERIALS . . . . . 43
4.1. General Description of Experimental
Equipment . . . . . . . . . . . . . . . . 43
4.2. Detailed Description of the Apparatus . 43

iii

TABLE OF CONTENTS (Cont.)

VI.

Page

4.2.1. The High Temperature Mass
Spectrometer . . . . . . . . . . . 43
4.2.2. The Vacuum Preparation System . . 47

4.3. Chemical Materials . . . . . . . . . . . . 48
4.4. :Knudsen Cell Design . . . . . . . . . . . 48
4.5. Heliarc Apparatus . . . . . . . . . . . . 50
EXPERIMENTAL METHODS . . . . . . . . . . . . . . 53
5.1. Preparation of Samples . . . . . . . . . . 53
5.1.1. Samarium Dicarbide . . . . . . . . 53
5.1.2. Neodymium(III) Monotelluro Oxide . 54
5.2. Methods of Analysis . . . . . . . . . . . 54
5.2.1. Samarium Dicarbide . . . . . . . . 54
5.2.2. Neodymium(III) Monotelluro Oxide . 55
5. . Temperature Measurements . . . . . . . . . 55
. Vaporization Experiment Procedure . . . . 57
. Congruency Tests on Neodymium(III)
Monotelluro Oxide . . . . . . . . . . . . 58
5.6. Calibration of the Mass Spectrometer
for Samarium Dicarbide . . . . . . . . . . 59
5.6.1. Transmission Coefficient . . . . . 59
5.6.2. Calibration with Elemental
Samarium . . . . . . . . . . . . . 60
5.6.3. Calibration with Elemental Silver. 61
5.6.4. Calibration with Samarium Dicarbide 62
5.7. Appearance Potential Measurements . . . . 63
5.8. Treatment of the Vaporization Data . . . . 64
RESULTS . . . . . . . . . . . . . . . . . . . . 67
6.1. Analysis on Samarium Dicarbide . . . . . . 67
6.2. Analysis on Neodymium(III) Monotelluro
Oxide . . . . . . . . . . . . . . . . . . 68
6.3. Vaporization Mode of Samarium Dicarbide . 68
6.4. Vaporization Mode of Neodymium(III)
Monotelluro Oxide . . . . . . . . . . . . 69
6.5. Transmission Coefficient of the Effusion
Cell . . . . . . . . . . . . . . . . . . . 69
6.6 Calibration of the Spectrometer for

Absolute Pressure . . . . . . . . . . . . 72

iv

TABLE OF CONTENTS (Cont.)

VII.

VIII.

6.7.

6.10.
6.11.

6.12.

Thermodynamics of Vaporization for

Samarium Dicarbide . . . . .

6.7.1. Enthalpy of Reaction

Temperature . . . . . .

6.7.2. Entropy of Reaction . .

6.7.3. Formation Energetics . . .

6.7.4. Standard EntrOpy of Samarium
Dicarbide . . . . . . .

6.7.5. The Vapor Pressure as a Function

of

Page

74

74
80
84
85

85

Congruency of Vaporization of Neodymium(III)

Monotelluro Oxide . . . . . . .

Thermodynamics of Vaporization for
Neodymium(III) Monotelluro Oxide .

Appearance Potentials . . . . .

Sensitivity of the Spectrometer with

Relative Abundance . . . . . . .

Free Energy Functions of Reaction for

Samarium Dicarbide Vaporization

DISCUSSION . . . . . . . . . . . . .

7.1.

7.2.

Comparison of Samarium Dicarbide with

other Lanthanon Dicarbides . . .

Evaluation and Conclusions on the Vapori-

zation of Neodymium(III) Monotelluro Oxide

ERROR ANALYSIS . . . . . . . . . . . .

8.1.

8.2.

8.3.

General Discussion of Errors in High

Temperature Mass Spectrometry .

Error in Enthalpy and Entropy of

Vaporization of Samarium Dicarbide

Error in Other Thermodynamic Values

REFERENCES . . . . . . . . . . . . . .

APPENDICES . . . . . . . . . . . . .

85

86
88

88

93

95

95

106

109

109

115
116
117

124

 

 

III .
IV.
"II .
XI.

i

 

 

 

 

u Ml F. . u

S U G.

XII.

TABLE

II.

III.

IV.

V.

VI.

VII.

VIII.

X.

XI.

XII.

LIST OF TABLES

The samarium-carbon system . . . . . . . . . .

Lattice parameters for samarium dicarbide . . .
Pr0portionality constant of P = kIT . . . . . .
Vaporization data for samarium dicarbide . . . .

Summary of samarium dicarbide vaporization data.
Free energy functions . . . . . . . . . . . . .

Vaporization of neodymium(III) monotelluro oxide
in the mass spectrometer . . . . . . . . . . . .

Appearance potentials of ions from vaporization
of samarium dicarbide and neodymium(III) mono—

telluro oxide . . . . . . . . . . . . . . . . .
Thermodynamic comparison of the dicarbides . . .
Predicted values of AH398,V for MC2(s) . . . .

The vapor pressure of the samarium dicarbide
system . . . . . . . . . . . . . . . . . . . . .

Uncertamtks in calcium dicarbide vaporization
quantities . O O O O O O O O C I O O O O O O C 0

vi

Page
11
67
73
76
78

81

87

89

96

101

104

116

FIGURE

2.

3.

10.

11.

12.

13.

LIST OF FIGURES

Schematic: Time-of—flight mass spectrometer
Knudsen effusion cell . . . . . . . . . . . . .
Evacuable heliarc apparatus . . .

Mass spectrum of Sm+ . . . . . . . . . .

Ions from neodymium(III) monotelluro oxide
vaporization . . . . . .. .. . . . . . .

Samarium calibration Experiment 1162 . . . . .

+ . . .
Vapor pressure of Sm from samarium dicarbide
Experiment 1134 . . . . . . . . . . . . .

Afef for SmC2(s) -—> Sm(g) + 2C(gr) . . .

Absolute PSm over SmC2(s) . . . . . . . . . .

. . . . + +
Ionization effic1ency curves for Xe , Nd ,
NdO and Te . . . . . . . . . . . . . . . . .

+

. . . . + +
Ionization effiCiency curves for Xe , N2, and Sm

Sensitivity of the multiplier-effects of
abundance and machine parameters . . . . . .

correlation Of AH2981V(MC2) With log P1500(M).

Analysis of error in Sm-152 of Experiment II34

vii

Page
44
49
51

7O

71

75

79
82

83

90

91

92
100

113

LIST OF APPENDICES

APPENDIX Page
A. Third Law AHggs: SmC2(s) —-¢ Sm(g) + 2C(gr) . . 125
B. Mass Spectrometric Vaporization of Copper . . . 128
C. Mass Spectrometric Vaporization of Samarium . . 131
D. NBS Calibration Tables for L & N Pyrometer

#1619073 . . . . . . . . . . . . . . . . . . . . 133
E. Computer Program for Clausius-Clapeyron Plot . . 135
F. Physical Constants Used . . . . . . . . . . . . 141
G. Second Law Data for Samarium Dicarbide Vapori-

zation . . . . . . . . . . . . . . . . . . . . . 142
H. Congruency Data for Neodymium(III) Monotelluro

Oxide . . . . . . . . . . . . . . . . . . . . . 145
I. Mass Spectrometer Data for Neodymium(III)

Monotelluro Oxide . . . . . . . . . . . . . . . 148

viii

CHAPTER I
INTRODUCTION

Research efforts into the field of high temperature
thermodynamics hardly need justification in this age in
which two of the most significant technological advances
of man--atomic energy and space travel—-were derived
largely from this very field. The practical need to de-
velop new refractory building metals and alloys which
possess such combinations of properties as high tensile
strength, oxidative resistance, low density, and mallea—
bility requires thermal data which may guide the scientist
in his synthetic work. This need alone would be sufficient
to justify a project whose aim was to obtain high tempera-
ture thermodynamic data. But aside from this reason, an-
other is the elucidation, clarification and formulation of
ideas in chemical bonding and structure. As stated by
Ackermann and Thorn (1): "The rapid accumulation of high
temperature properties makes it possible to begin a syn-
thesis of the systematic behavior of ~-- phases in order to
discover the fundamental concepts which determine the
strength of bonding ---"

The general plan of work for this thesis was to char-
acterize both qualitatively and quantitatively the vapori-

zation process of samarium dicarbide (SmCz) and neodymium(III)

monotelluro oxide (NdZOZTe). The principal procedure was

2

3

to use Knudsen effusion—mass spectrometry. Using this
method the enthalpy of vaporization was obtained directly
from the ion intensity—temperature data, and the entropy

of vaporization was derived from absolute pressures ob-
tained by calibration of the mass spectrometer. The choice
of these compounds was based partially on the fact that
samarium dicarbide may be a potential core moderator mater—
ial since samarium has a high neutron capture cross-section
and that NdZOZTe is the homologue of neodymium sesquioxide
--thus comparisons of thermodynamic data could be correlated
to the effect of a one atom substitution. Furthermore in
the dicarbide, samarium is believed to be in the +2 oxida-
tion state and this study would allow a comparison of its
thermal properties with ytterbium and eur0pium dicarbide
and with the various alkaline earth dicarbides to which it

might be similar.

CHAPTER II

HISTORICAL

 

2.1. Reported Work on the Lanthanon—Dicarbide Systems

2.1.1. Preparation and Characterization

 

In the past seventeen years there has been a wideSpread
and intensified interest in the lanthanide and actinide
carbides. Various techniques have been developed for their
preparation. DeVillelume (2) reduced lanthanum sesquioxide
with carbon at 20000 and obtained the dicarbide. In 1958,
Chupka and coworkers (3) first prepared lanthanum dicarbide
(in_§i£u_in a mass spectrometer by reaction of lanthanum
metal with the graphite liner of a Knudsen cell, then ex—
amined the vapor effusing from the cell.

In 1958, Spedding, Gschneidner and Daane (4) studied
the lanthanon—carbon systems extensively, reporting carbides
of three generalized types: Ln3C, Ln2C3, LnC2. They
also reported lattice parameters for the various phases in—
cluding all the lanthanon dicarbides except promethium.
Their preparative technique depended on the volatility of
the lanthanon metal. Thus, for those lanthanon metals
with a boiling point in excess of 20000 mixed powders of
the element and graphite were pressed into pellets and arc
melted under an atmosphere of helium or argon, while for
the metals whose boiling point is less than 20000 (Sm, Tm,
Yb) the reaction between the elements was constrained in a

tantalum bomb.

5

Subsequent to the work of Spedding,gt_§1,(4) a series
of articles by Vikery, Sedlacek and Ruben was published in
which the preparation of a series of lanthanon carbides (5)
and both their magneto—chemistry (6) and their X-ray ab-
sorption characteristics (7) were presented. In their
work the authors prepared all the lanthanon dicarbides,
except those of europium, promethium, lutetium and thulium
by the reduction of the sesquioxide with carbon under a
low pressure of argon. In their second paper the authors
conclude that both samarium and ytterbium are in the +2
oxidation state in the dicarbide because their experiment-
ally observed values of the Bohr magneton numbers differ
from the values calculated for the +3 oxidation states of
the respective ions.

Pollard,g§_al, (8) also prepared a number of the di—
carbides using the method described by Vikery (5) but at
the maximum temperature of their equipment, 19000, they
were unable to prepare samarium dicarbide. They noted
that at this temperature dysprosium dicarbide formed very
slowly. Other work on the hydrolysis of lanthanon di—
carbides has been performed by Palenik and Warf (9) and
DeVillelume (2). In addition, the hydrolysis products of
lanthanon sesquicarbides as well as the dicarbides have

1. (10), Greenwood and

been characterized by Svec, g;
Osborn (11) and by Spedding and coworkers (4) who in addi-
tion studied the hydrolysis products of the tri-lanthanon

carbides. Svec, gt 31. (10), who hydrolyzed many of the

12,

 

 

.x A. . . .C .x ; 1. L. t) .C It 1.. c; Ax L. Te a. J
t l 2 .. .3 S cL n E C . a .. .C E C .C E E - a.
v. C l r. . . . a F. P: 8 O E T. .l e C t at .Q
2. .c . o X S I a a c . I DO 1 E a t I . o a A. ., e a-.. .3 I
C. A. .. ... .. -. : n}. r 3 3 t a I Z .1 x:
.-u . . .au :14 1 Yu an; n C a S "in: bye C 1» ~ kUs

ill, ll}

 

 

 
 

6
carbide samples which had been examined by Gschneidner (4,
12,13), indicated that the three principal hydrolysis
products obtained with samarium dicarbide in 1M hydrochloric
acid were ethyne (62.2%), hydrogen (16.6%) and ethene
(12.5%)-—no methane was observed. Their observation sup-
ports Vikery's (6) conclusion that samarium is in the +2
oxidation state in the dicarbide and that this dicarbide
is similar to the alkaline earth dicarbides in its behavior.

However, this theme has been challenged by Jensen and
Hoffman (14) who also prepared the compound by the reduc-
tion of the sesquioxide with graphite. The most significant
difference between the two studies is the values obtained
for the room temperature paramagnetic susceptibility:

1288 x 10_6 emu/mole obtained by Jensen and Hoffman; 2306
x 10-6 emu/mole by Vikery and coworkers.

The lanthanon dicarbide preparatory procedure used by
Greenwood and Osborn (11), although a standard method, had
not been used previously for lanthanum dicarbide. They
formed lanthanum dihydride first and then reacted it with
stoichiometric amounts of graphite under vacuum at ele-
vated temperatures. This is probably the best preparative
procedure for lanthanon dicarbides which are low in oxygen
contamination and free of excess graphite.

In 1964 the previously missing phase, europium dicar-
bide, was prepared by Gebelt and Eick (15) and its lattice

parameters and some physical properties characterized.

7
The crystal structures of the lanthanon dicarbides
have been characterized reproducibly many times. Spedding,

l. (4) using both Debye—Scherrer diffraction and

_e_t_
symmetrical focusing back reflection cameras report the
lattice parameters for most of the lanthanon dicarbides,
as well as the sesquicarbides. The values they obtained
are probably the best reported to date since they used
specially prepared, highly purified metals. Atojii, g;
‘al. (12) performed room temperature neutron diffraction
studies on lanthanum di- and sesqui-carbides while Atojii
(16) undertook a similar study on the dicarbides of lan—
thanum, cerium, terbium, yttrium, ytterbium and lutetium,
as well as those of calcium and uranium. He found all
of them to exhibit the I4/mmm calcium dicarbide structure
with all metals, except Ca(+2), Yb (possible +2.8) and
U (possible +4), in the +3 oxidation state. Recently
Atojii and Williams (17) determined the magnetic and
crystal structures of five lanthanon dicarbides at low
temperatures (to 20K). The sesquicarbides of four selected
lanthanon metals have also been studied by neutron dif-
fraction at room temperature (18).

In 1967, a high temperature neutron diffraction study
of lanthanum and yttrium dicarbides was undertaken by Bow-

1. (19). These authors reported tetragonal lattice

man, gt;
parameters which are in agreement with the room temperature
data of Atojii (16) and, in addition they observed the

tetragonal to cubic transition temperatures to be in agreement

7,,br‘

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with the previously reported values (10600 for LaCz; 13200
for YC2) observed in thermal analysis studies. For
lanthanum dicarbide the lattice parameters obtained were:
tetragonal at 9000, a0 = 4.00 R and c0 = 6.58 8; cubic at
11500, a0 = 6.02 R.

For a knowledge of the work done on the lanthanon—
carbon systems prior to 1950 the reader is referred to
several reviews (20,21), to the references contained in (5)

and to Gebelt (22).

2.1.2. Vaporization Studies

 

The species which vaporize from lanthanon dicarbides
have proven to be unusual and varied. Previous work in—
dicated that lanthanon dicarbide vaporizations occur ac-
cording to one or more of the following modes

>M(g) + 2C(s) (1)
> MC2(9) (2)

(g) (3)-

3), in their mass spajnnmetric study of

 

MC2(S

)
C2(S)
)
.(

 

MC2(s + 2c(s )

         

Chupka,“
various dicarbides, observed for lanthanum dicarbide modes
(1) and (2). They measured the LaC2/La pressure ratio and
at 2500°K they calculated the value of the ratio to be 16.
However, Jackson and co-workers (23) obtained, for
lanthanum dicarbide, a LaC2+/La+ ratio of 0.45 at 2500°K
using a Langmuir vaporization technique. The latter
workers also studied the vaporization behavior of cerium,

praseodymium, gadolinium and lutetium dicarbides. They

9

observed (23) that the ion intensity ratio LaC2+/La+ in-
creased from 0.17 to 0.45 as the temperature was increased
——this observation appears to be an example of Brewer's
law (24) that at higher temperatures the formation of the
less dominant species (usually polymeric or more complex)
will be favored in a vaporization process.

The vaporization pressure of holmium dicarbide was
measured using the Knudsen effusion weight loss method by
Wakefield, Daane and Spedding (25). Gadolinium dicarbide

l. (26) with a mass

has been studied by Jackson, 3:

Spectrometer. They found GdC2(g) and Gd(g) to be the minor

and major species, respectively. The minor component

varied from 1% of the gas at 2000°K to 5.8% at 24220K.
DeMaria and co-workers at the University of Rome have

studied the vaporization of a series of lanthanon-carbon

systems (27—29). An unexpected result of their studies

was vaporization according to mode (3), and observation of

the tetracarbide species, HoC4 and CeC4, in the effusate.

Additionally,the PrC4 molecule was identified tentatively.

In all these studies the carbides were prepared in situ.

Various data such as relative intensities of the various

species, their dissociation energies and heat of reaction

are also presented (27). Both the yttrium-carbon (28) and

the neodymium-carbon system (29) were observed to vaporize

according to both mode (1) and (2). A tabulated comparison

of the enthalpies of vaporization will be made in Chapter\nflh

page 95.

10

The vapor pressure of europium dicarbide was studied
both by target collection and a mass Spectrometric tech-
nique (30). The principal mode of vaporization was accord-
ing to equation (1).

Since lanthanon—dicarbides are often compared to the
alkaline earth dicarbides, two recent alkaline earth di—
carbide studies will be mentioned. Flowers and Rauh (31)
studied the vaporization of strontium and barium dicarbides
by both target collection and mass Spectrometry. They
used extreme precautions to obtain pure specimens. Dif-
fusion effects were experimentally determined and mini-
mized by variation of orifice sizes. Flowers and co—
workers (32) also studied the vaporization of calcium di-
carbide. They used target collection to sample the effusing
beam and analyzed the deposits with an integrating flame
photometer. Their absolute accuracy is quoted to be within
10%.

The vaporization energy for graphite may be needed if
one wishes to undertake energy calculations of the Born-
Haber cycle type on equations (1), (2) or (3). Both Hoch,
.EE.§L- (33), using Langmuir vaporization, and Chupka and
Inghram (34), using a mass spectrometer, determined the
heat of sublimation of graphite to the monomeric Species
and agree on the value of 171 kcal/mole. Graphite has been
found to vaporize in more than one mode giving C2, C3 and
C4 molecules in the effusate, and a dissociation energy of

150 kcal/mole has been calculated for the C2 Species (34).

11

A generalized conclusion concerning the vaporization
of the lanthanon dicarbides was made by Wakefield, g: 31.
(25) who state that "the stability of the rare earth di—
carbides is related to the volatility of the metals, in
that the more volatile rare earths have the less stable
dicarbides."

In the course of the writing of this thesis the author
became aware from the references in an article by Avery,
.EE.2£- (96) that others were working on the samarium carbon
system. These references have appeared in the literature
(105, 106, 107). A tabulation of the results obtained is
shown in Table I. The first column lists the literature
reference and the second column lists the vapor pressure
equation in the form such that the first number is As; and
the second number is AHO for the vaporization process:

T
> Sm(g) + 2C(grj evaluated at the mideLnt

 

SmC2(S)
of the temperature range shown in column three. The general
method used by Avery and coworkers (105) and by Cuthbert,

.2E.§l; (106) to study the SmC2 vaporization was mass spectro-

l. (107) used Knudsen effusion

metric while Faircloth, 33

collection techniques.

Table I. The samarium - carbon system

 

 

Ref 2.303R log P(atm) Range, 9K
105 18.7 - 65,200/T 1300-2051
106 15.5 — 61,500/T 1400-2000

107 16.5 - 63,300/T 1400-2080

 

€25

«F‘
$.3—

AY "7 ’-
u-e'*“

.easurc

8‘3.

SECCLC
-

nrxr'.’ I
LV‘J.} e: N

:- “
5.6.635

C

an“

N...

C 2
at

Sctgr y?

CL

h .

RES

‘
«x.

I

v, .
‘VL C'-
‘N‘ie

'VA

12

The calibration procedure employed by Avery to obtain
absolute pressures of samarium from the mass spectrometric
intensity data consisted of a method which had been used
previously (96). This method utilizes an effective cross-
section for samarium vapor, which is calculated from a
measured sensitivity of the instrument for argon gas and
converts this sensitivity to that for samarium using the
ratio of ionization cross-sections as derived by Otvos and
Stevenson (69). For a series of experiments, using the
calculated absolute pressures, the total weight loss of

samarium, w, was computed by integrating the expression

1/2

dw _ wdz 1000M 273(8RT)

(EE)T ‘ 4 22400 T PM

 

P —1
‘4 mg sec

in which d is the orifice diameter in cm, M is the
molecular weight of the effusate, R is the gas constant
in ergs-deg/deg—mole, and P is the pressure in atmOsphereS.
The calculated total weight loss was then compared with the
actual measured weight loss and for each sample a correction
factor was obtained by which all calculated pressures were
multiplied to bring the calculated and measured weight
losses in agreement. The factors thus obtained (0.183 and
0.171) indicate their calculated pressures were about 5.7
times higher than the pressures based on weight loss. The
error quoted by these authors is "of a factor of about 5.“
Cuthbert, 3; El. (106) determined the vapor pressure

of samarium dicarbide using both a magnetic sector spec—.

trometer and the target collection technique. They performed

13
twenty-one experiments on two samples of the dicarbide using
tungsten cells with 0.025 cm diameter orifices. The tempera-
ture range covered in any one experiments was 400°. Absolute
pressures of Sm(g) were calculated from the measured weight
loss of material which left the cell during an entire run,
and the uncertainty in absolute pressures is estimated to
be i30%.

l. (107) studied the dicarbides of

Faircloth,-g;
lanthanum, cerium, neodynium, samarium and europium and
measured their vapor pressures in the temperature range 1300-
2400°K using target collection effusion techniques. Exposed
targets were analyzed by neutron activation analysis and
y—ray spectrometry. The measured pressures are said to be

reproducible to within i10%.

2.2. Reported Work on the Lanthanon Oxide Chalcogenide
Systems

 

2.2.1. Preparation and Characterization

 

In 1949 Zachariasen (35) prepared an impure sample of
lanthanum oxide sulfide (mixed with 30% La2S3) by heating
gently in air lanthanum sesquisulfide. From an X-ray
powder diffraction study he determined the structures of
LaZOZS, CSZOZS and Pu2028. These structures were de-
rivable from those of the corresponding sesquioxide by
substitution of a sulfur atom for a unique oxygen atom.

In 1958, Eick (36) reported the preparation of thirteen

lanthanon mono-thio oxides (Ce, Pm excepted) and determined

 

 

 

 

 

prepared
hydrogen
the latt.
The meth:
rest of t
that user
crystal 8
has been
One
Of a new
tYPe Ln2C

pared by

 

 

14

their lattice parameters. The basic procedure used in the
preparation was to convert the sesquioxides to the monothio
oxide using carbon disulfide, and then to remove the solvent
impurities by heating in an atmosphere of flowing hydrogen.
The monoseleno oxide phases of some of the lanthanons were
prepared by a solid—vapor reaction of the sesquioxide with
hydrogen selenide gas diluted by hydrogen and helium (37);
the lattice parameters and structure were also determined.
The method of preparation used by Kent and Eick (38) for
most of the lanthanon monotelluro oxides was analogous to
that used in preparing the monoseleno oxides. Recently the
crystal structure of the neodymium (III) monotelluro oxide
has been determined (39).

One report on the preparation and crystal structure

of a new series of lanthanon oxide-chalcogenides of the
type anozsz was reported (40). These compounds were pre-

pared by reaction of sulfur vapor with anozs or with a
mixture of 2Ln203 + Ln283. The crystal symmetry of the

three phases prepared was tetragonal and the lattice para—
meters (in 8 units) were: La, a0 = 4.197, co = 13.28; Pr,

30 = 4.127, C0 = 12.88; Nd, 30 = 4.11, CO = 12.80.

2.2.2. Vaporization Studies

The author knows of no published studies on the vapor-
ization behavior of any lanthanon oxide Chalcogenide. Two
unpublished investigations are known, however. These are
by Jacobs on Ndzozs (41) and by Wiedemeier on Cezozs (42).

'Both of these studies used mass spectrometers and each

15
system was observed to produce MO and S as the volatile
Species.

The vaporization behavior of the lanthanon sesquioxides
has been studied extensively and only a few selected refer-
ences are listed. White, 33 al. (43,44) studied the vapori-
zation of five lanthanon sesquioxides and yttrium sesqui-
oxide as well as the thermodynamics of certain exchange

reactions of the type

 

LnO( +Ln.( > Ln'O(

g) g)

g) + Ln(g)°

These studies permit calculation of the dissociation ener-
gies of gaseous molecules of the type LnO. Panish has also
studied the vaporization of almost all the lanthanon ses-
quioxides (45,46) and he points out several trends: (1)

the vaporization process shifts from one giving MO(g) and
0(9) to one giving M(g) + 0(g) with increasing atomic
number of the metal; (2) the vaporization behavior may be
subdivided into two groups which are the same as the cerium
and yttrium groups, and (3) within each group the trend

indicated previously is followed.

CHAPTER III

THEORETICAL CONSIDERATIONS

3.1. General Introduction

 

Several gross prerequisites must be observed if re-
liable thermodynamic data are to be obtained by monitor-
ing, with a mass Spectrometer as a function of temperature,
the vapor effusing from a Knudsen crucible containing a
refractory phase. These restrictions are: Gibbs' Phase
Rule, existence of equilibrium between the condensed re-
fractory and its vapor, a means of sampling the equilibrium
vapor with the mass Spectrometer and, if absolute pres-
sures are to be computed, a means of standardizing (cali-
brating) the sensitivity of the mass Spectrometer with
regard to the particular species in question.

These restrictions will be illustrated further in this
section. According to Gibbs' Phase Rule, (eq. 4)

V=C-P+2 (4)
where y_is the variance (degrees of freedom) of the system
--the number of variables which must be fixed to define
uniquely the state of the system; 9.18 the number of com-
ponents (smallest number of independent variable constitu-
ents participating in an equilibrium process); and g is
the number of phases (homogeneous, distinct and mechanically

separable portions). The plausibility of this form of the
16

 

 

libriur

9Iessure

( I .
_
—
—
—

which he

that the

..

L

"h .

“Inst ay-
Vl‘

“Oh

N‘J“ Of

”6"“

Au q.zlr‘c:
J‘

 

17

Phase Rule may be seen from the following examples which
are based on the usual case that the state of a single
phase of a pure substance is specified by two variables,
temperature and pressure. For a one component system of
a pure substance the temperature and the pressure must be
specified in order to determine (fix) a single phase; for
two phases of such a substance constrained to be in equi-
librium the state of the system is Specified if either the
pressure or temperature is defined; for three phases of a
pure substance in mutual equilibrium the state of the sys-
tem is uniquely determined at only one set of temperature
and pressure parameters and no variation from these
parameters is possible, i;e; the system is invariant.

Applying the Phase Rule to a vaporization process of

the type

 

AB (5) > A(g) + 118(8) (5)

Y

which has three phases and two components, results in a
variance of one for the equilibrium system. This means
that the equilibrium vapor pressure of A(g) is a unique

function of temperature, i.e. at a specific temperature

 

the system is invariant with respect to pressure (or any
other thermodynamic variable) providing that the composi-
tion of ABy is also invariant. Thus{ for such a system
meaningful vapor pressure measurements may be obtained as

a function of temperature.

13

For a phase vaporizing congruently as

 

ABY(S) > ABY(9) (5a)

the variance is also unity since there are two phases with
only one component. Hence, when one component systems
vaporize congruently, unique equilibrium vapor pressure
measurements may be made as a function of temperature.

The question of congruence of vaporization must be
established by performing apprOpriate analyses, e.g. X-
ray and chemical analyses, to confirm that the composi-
tion remains invariant as vaporization proceeds. The re-
maining two general prerequisites previously mentioned,
equilibrium and sampling of the effusing beam with the mass
spectrometer, as well as others which these restrictions

imply will be discussed subsequently in this Chapter.
3.2 Thermodynamic Relationships in Vaporization Studies

3.2.1. Second Law Relationships

Let us consider in more detail equation (5)

 

ABy(S) > A(g) + yB(s) (5).

If this reaction is constrained such that equilibrium

exists then at any Specified temperature T

0 _ 0 _ 0
AGT AHT TAST (6)
and
o -
AGT - -RTln Kp (7).

Combining equations (6) and (7) with the value of Kp gives for

equation (5)

 

 

 

 

 

 

‘
Wfiere

cal it;

react'cr
tempera:

extent :

 

 

O 0
in P = AHT + 35—1 (8)
Me) RT R

where R, the universal gas constant, is in units of
cal/deg/mole. The last three equations are obtained from
rigorously derived thermodynamic functions by making the
approximations (a) that the activities of all the solid
phases are unity, (b) that the fugacity of the gaseous
species equals its vapor pressure, and (c) that AC; for
reaction (5) is approximately zero over the experimental
temperature range. The first assumption (a) is good to the
extent that Raoult's Law holds for ABy(s) in the actual
eXperiment: for pure ABy(s) the activity is unity but for
ABy(s) in a solid solution with another substance such as
B(s‘ the activity will deviate from unity, though this
deviation may be very small. Recently, an experimental
method was described by Belton and Fruehan (47) for deter-
mination of activities of molten systems in a mass spec-
trometer. This method may be used, in certain cases, to
measure the activities of solid systems. The second as-
sumption (b) is almost always valid under the experimental
conditions of temperature and pressure in the range of
1000—25000 and 10-8 to 10-3 torr, respectively--Since under
these conditions the vapor behaves as an ideal gas. Pro-
viding that there is no composition change in ABy(s) during
the vaporization process and that the mutual solubility of
B(s) and ABy(s) is negligible, the third assumption (c) may

be justified sometimes a posteriori by observing a linear

 

 

.,
/—
_'————‘
__————

\o

 

 

 

XOR-Zero ~C

Capacity (15
Air-

tea» tants a

33‘: lf ;_C0
5r1l' ”

””1 Que t6
““hsti‘ll‘.

E"
\A

n .
UV glx'e eel;

 

 

20
plot of 1n PA 1:3 1/T.

Curvature in a Clausius-Clapeyron plot indicates that
other processes which were either unaccounted for or as-
sumed negligible in deriving the Clausius-Clapeyron equation
are occurring. These processes may arise from Ac; of the
reaction not being negligible, from polymer formation (e.g.
A2(g), A3(g)) or from stoichiometric variation in ABy with
vaporization or as a function of temperature. If curvature
is evident in the Clausius—Clapeyron graph it is necessary
to perform a "Z-plot" in order to take into account the
non-zero Ac; term. To undertake such a treatment heat
capacity data or estimates of them are necessary for all
reactants and products. Hopefully, AC; may be eXpressed
as a function of temperature by an equation of the form

ACE = Aa + AbT + ACT-2 (9)

But if Acg is a constant, equation (9) would simplify to
only one term, (the Aa term). The heat capacity may be
substituted into equation (10) which then may be integrated

to give equation (11)

AH0 = A O dT 10
f Cp ( )

Ab Ac
AH AHI + AaT + 2 T T (11)

where AH? is the constant of integration. Equation (13)
results by substituting equation (11) into equation (12)

and then integrating (12) and combining the result with

(7)

 

.4

 

 

 

‘
-3" Re A
all M v,
o
.-I‘. +F~
..“‘S' 5.
s ‘ g
' Q
'5' 0*..-
"b- “- .
.
Ah

“I
'(’

 

 

0
6(9-3-4 - AHO
5T T2 '
AHO
I = _ _AP_ .42 -2
T+§D Ranp+AalnT 2T+2T (13)

In this equation T is the integration constant. Repre-
senting the right hand terms of (13) by 2 produces the
equation
0
z =-——; + m (14)
T
which should produce a straight line when "2" is graphed
against 1/T. The two integration constants AH; and T
may be obtained from the slope and intercept, respectively.
Thus, the value of AH0 at any temperature in the interval
over which the heat capacity equations are valid may be
obtained from equation (11), AG; using (13) and then As;
from equation (6). Cubicciotti (48) has presented a re-
‘vised Z-plot treatment which utilizes tablular thermody—
Iiamic values to give the entropy and enthalpy change

€33§plicitly at the reference temperature. In his method the

tzeerm 2' is defined according to equation (15)

 

 

 

A( 0 ‘ H398)
2' s -R In K - HT T + A(sg - 8398) (15)
Es:ane
o o 0
AGT AHgss A(HT ' H298) 0 0
'——"T 3 T + T "’ A8298 - A(ST - $298) (16)

jut is apparent that

 

 

 

 

sass spt
vapor p:
case the
P. is re
icnizati

T: by th

 

 

22

0
AH298 0

2' " T- - A8298 (17)

This technique has the advantage of linearity even if a
transition state (S‘g. melting, polymorphic change) occurs
in the experimental temperature range.

In this work experimental utilization of equation (8)

was achieved by obtaining pressure in one of two ways. The

effusate, A(g), which vaporized from a Knudsen cell was

either collected (pf, Section 3.3) or monitored with a

mass Spectrometer, and from these data the equilibrium

vapor pressure was calculated. In the mass spectrometric

case the partial pressure of the specific vapor Species,
P, is related to the ion current intensity, I, produced by
ionization of the i Species and the absolute temperature,
T, by the equation

P = km (18)
The proportionality constant, k, is related to the sensi-
tivity of the spajzometer to the species being examined.

IWethods for evaluating it are discussed in Section 3.4.
Combining equations (8) and (18) produces the follow—
:irag relationship between ln IT and the enthalpy and entrOpy

O :6 reaction

 

ln IT =

 

0
was, AST
T + - ln k (19)

R R

331315 equation (which is linear only if the conditions de-
£3ignated previously are satisfied) permits the enthalpy of
3rsaaction to be obtained when the product ln IT is graphed

algainst 1/T. From such a plot AH; may be obtained directly

 

 

 

fer reac:

the seas:

‘ .,0 .
n .h cote
T
a'Seccnd

In C:

:ezperatu :

whereQ :
ite refere
be 298.160
“113?. pr:
3: 3393 he
ERRI eitl
fliCtign C
*"lCh 3:18
it is yer}.

C'IeI L.
' I." L.
..e L:

. .
". N
I?“
N
th'W‘l
Q
nail”

 

23

for reaction (5), but the entropy, As;, is a function of

the sensitivity k_and the intercept as follows

As; = R(a + 1n k) (20)

.A.AH% obtained in this manner is commonly referred to as
a "Second LaW'Enthalpy".
In order to relate AH; and AS% to a standard reference

-temperature use is made of the relationship

A0,; = me + gT(&_—)P dT (21)
vvhere Q may be any thermodynamic state property, and 6 is
tihe reference temperature which in this work is chosen to
l>e 298.160K. Equation (21) implies that Ac; for the vapori-
2:ation process be either known or estimated so that AHg98
c>1rA5398 be obtained. In the range 2980K to T°K ACD may
eacqual either zero or a non-zero constant, or may‘be a

.iSIJnction of temperature. For a vaporization process, in
'vvluich one or more products is always in the gaseous state,
lirt: is very improbable, if not impossible, that AC; be zero
CD‘lfar the temperature interval 298°K to TOK since, in gen—
EBITEil, Cg for gases are quite different from C3 for solid

Eihléises. Thus this possibility will be ignored. When Ac;

143 a.constant integration of equation (21) produces

Eng = Anggs + Acg(T - 298) (22)
and
A8; = A5398 + AC; ln(§%§) (23)

1?:111a11y, if AC3 is a known function of temperature, the

 

 

 

 

apprspri
will IGS'
Neel
majsrity
:navailak
trspy cha
22‘ and
;q’estim
In one 0
CaCZ 5"
xund of j
tsequati"

EXPressicr

.
:5.“
5‘ ‘
K‘U h
. we
.
’A
, A
~t\~“-
“be r:
'4‘
‘a

 

 

24
appropriate substitution and integration of equation (21)
will result in a..AHg98 and A8398.

Necessarily for most new compounds, and for the vast
majority of refractory materials, heat capacity data are
unavailable. Consequently, reduction of enthalpy and en—
trOpy changes to standard conditions utilizing equations
(22) and (23) is formally impossible. However, heat capac-
ity estimates may be made—-the method employed in this work
was one of analogy. A similar compound of known cg
(CaC2(s)) was used to estimate the Cg value for the com—
pound of interest (SmC2(s)). SmC2(s) vaporizes according
to equation (5) with y being equal to two. Thus, the
expression used to correct both changes in enthalpy and;

entropy for this reaction to 2980K was

AQg98 = A0; - [(Q; — 0393)Ca(9) + 2(Qg ‘ 0398)C(9r)

0

T - 0398>cac2<s>1 (24)

-(0

This expression is noted to be an alternate way of eXpres—

sing equations (22) and (23).

3.2.2. Third Law Relationships

A visual inspection of equation (19) indicates that
errors in T, (and to a lesser extent in I), produce large
errors in AH; and ASg because of the logarithmic relation-
ship. The Third Law method of calculating AHgga, so—called
because of its use of absolute heat capacities which are

based on the fact that for a pure crystalline substance

25

33 - 0 (the Third Law), utilizes the free energy function,
fef. The AHggs values calculated by this technique are
rather insensitive to temperature errors. Use of this
method provides a check on the nag” value obtained from
the Second Law method. In addition it points out deter—
minate errors associated with temperature since an inde—
pendent value of AHggs is calculated for every pair of
pressure-temperature values. The free energy function,

fef. is defined as

0 0
(GO ' H398) (H ' H298)
fef = T - T — 8° (25)
.- T — T T

 

 

From equation (25) the Afef of a reaction may be deter—
mined provided Sufficient thermodynamic information is ob-
tainable for all products and reactants. The Afef of
reaction (5) may be used to obtain Aug” by using equation
(26) which results by combining equation (7) and the equa—

tion for Afef obtainable from equation (25)
0 _
--TAfef+RlP 26
AH298 [ n A(g)] ( )

BY Substituting equation (18) into (26) the following is
Obtained for the mass Spectrometric vaporization of samar-

ium dicarbide

A3398 = - T[Afef + R(ln IT + 1n k)] (27)

 

 

 

 

 

y,...§ a
L.....S::

is utilized

rapcr press

have been an
have been r
53'. The.
which is to
tail orifi
tamer is h
an eci‘dlibri
“9‘31- The
:EES‘JIing t
35.31119 thrc
35137.3

p
s.
..

experiment

»"-A1
qu"ed tar :

 

 

26

3.3. The Knudsen Effusion Method

3.3.1. General Introduction

Knudsen developed the general effusion equation which
is utilized in this work for determination of equilibrium
vapor pressures in a series of papers published in 1909
(49-51). His basic equation and its requisite conditions
have been verified by numerous experiments and recently
have been re-examined critically by Carlson (52) and Ward
(53). The method consists of confining the condensed phase
which is to be studied in a sealed container in which a
small orifice has been machined. When the charged con-
tainer is heated (under conditions discussed subsequently)
an equflibrium is established between the solid and its
vapor. The equilibrium vapor pressure is determined by
measuring the rate of mass flow of the vapor species es-
caping through the orifice in the cell. Under ideal con—
ditions (of. next Section) for a Knudsen—type vaporization
experiment in which the effusing vapor is collected on a
cooled target and then assayed, the equilibrium vapor pres—

sure is obtained from equation (28)

1/2

 

* - w 27TRT r2+d2
Peq Ate ( M ) ( r2 ) (28)

in which w is the mass of the volatile species collected,
A is the orifice area, t is the time of exposure of the ef-
fusing beam to the collection plate, 6 is the transmission

prdbability term of the orifice or "Clausing correction",

 

R is the
Tis the
:f the ef
ccllecti:
to the c:
assumes a
in equati
912.cm2

,‘_
k.

l 15 ans:
5; ‘

 

 

 

\ given by

 

3.3.2

It WE:
gerived f,- I

:Qeali

v

('1‘

V v

5
1-

“$54
t ‘ueall

A.“ ‘
‘3}; h

«LG:

 

 

27

R is the universal gas constant expressed in ergs/deg—mole,
T is the absolute temperature, M is the molecular weight
of the effusing species, r is the radius of the exposed
collection disc and d is the distance from the orifice

to the collection disc. For collection work, 6 normally
assumes a value of unity. Use of the CGS system of units
1/2

in equation (28) results in qu having the units of ergs

gl/z/cm2 sec. Recalling that 1 atm = 1,013,250 dynes/cmz

it is apparent that the pressure in atmosphers, Peq’ is
given by
P* 1/2 2 2
= eg = M? T_ r + d
Peq 1013250 '022561 Ate M) ( r2 ) (29)

For Knudsen vaporizations in which temperature-weight data

are colleCted pair-wise (e.g. mass-vacuum balance work)

r2 + d2

1.2

and 6 assumes non-unity values. In mass spectrometer work

the geometry factor term ( ) drops from equation (29),

6 assumes unity values, and the geometry factor term dis—

appears.

3.3.2. Restrictions and Constraints

 

It was mentioned that equations (28) and (29) were
derived for ideal conditions. The extent of deviation from
ideality will determine how these equations are altered.
Non-ideality factors in a Knudsen vaporization experiment

can be classed into three categories.

 

 

 

 

 

3.3.

. -
1-~a~n
F .
.u-‘vn l
——

tions in
be infin;
ex:er:al ‘
tizns are
finally

:C'A'EVQ r ,

a
\I

an, ‘ -

#5-?ng Ca
'5' I

Dililce C:

m
. 1
a:
m
(‘f
w—A
3
_

u-
‘u “h
‘a.e O-y
~‘
N
‘F,
”fefihr-A
yg,‘ ~EQ~
VA.
13v
*H‘ v
«e: ~~ Y
a “
\
IV-
‘LE pk“
'-..EAQ
k‘
1
k5‘*;
1A
‘L‘Vih
V‘QI P
V
‘.
4
":‘PE ‘
A I

 

28

3.3-2-1. Limitations Arising from Mathematical Formu—

 

lation.- Knudsen had to make certain necessary approxima—
tions in the derivation of his equations. The orifice must
be infinitesimally thin, the vapor must be ideal and the
external pressure must be negligible. The last two restric—
tions are usually satisfied, since the experiments are
normally conducted at high temperatures and low pressures.
However, a knife-edged orifice can be fabricated only with
varying degrees of success; The "channeling" effect of an
orifice of finite thickness was considered by Clausing (54)
and a table of Clausing factors, or transmission probabil-
ities, for cylindrical orifices of various length to radius
ratios have been calculated by Dushman (55). More recently
Edwards and Gilles (56) have calculated the transmission
probability for spherical orifices, and Freeman and Edwards
(57) treated the conical shaped orifice case. It must be
noted that in any type of effusion experiment in which the
collector (or sampler) is located in a plane parallel to
the orifice and directly above it, the molecules must pass
through the orifice without collision with the channel
walls of the orifice. Under such conditions the correction
for the transmission coefficient will be unity. The mass
spectrometer ionization sampling system satisfies this angu—
lar requirement of the beam and thus Clausing corrections
are unnecessary. Experiments employing total sample col-
lection, or total mass loss, however, would most certainly

have to include the transmission probability coefficient.

 

 

 

 

 

Hence, it

‘1
While The?!
the trans:

sure calc;

3.3.2
:‘ifficult
With the S
zazisn cce
:easuremer.

"1v:
m. ce or”

Vu"" l‘ i
d VL V
‘
:v-
§
'14 '7‘
"Eh: 71a 0.
h
:h
\u‘
\\;~ ‘1
q

 

29
Hence, it follows that when the mass spechnmeter is cali-
brated by determining the total weight loss of the sample
while measuring the ion intensity at constant temperature,
the transmission coefficient must be included in the pres—

sure calculations.

3.3.2.2. Limitations Arising from the Sample.- Most

 

difficult to correct are some of the limitations associated
with the sample. The most troublesome is a non-ideal vapori—
zation coefficient. For an equilibrium vapor pressure
measurement to be meaningful equilibrium must exist at the
surface of the sample. Hence the total number of particles
leaving the surface by evaporation, or by reflection, must
equal the number condensing. The condensation coefficient
is defined as the ratio of the number of grams of particles
adhering to the surface to the number hitting the surface.
Deviation of the condensation coefficient from unity results
in a measured pressure using equations (28) or (29) of less
than the equilibrium pressure. Ackermann, Thorn and Winslow
(58) treat the subject of vaporization within the phenomen-
ology of irreversible thermodynamics and formulate the

problem mathematically. They derive the equations

J (30)

m aeGs - a G.

C].

and
P

Gs - (WI/2 (31)

in which ae is the vaporization coefficient (ratio of the

 

 

 

 

 

 

 

rate flow of
:5 equation
Earring to s
aLanJmir-t
Es using a i
re obtains
Quantities C
Periment anc
fawn values
Stperficial
cerx-iensatior
in general,
particular, j

The eXE
Ct‘mtered, 1'
5131th are

.30
rates of particles leaving the sample surface per unit area
for a.Langmuir-type vaporization to those leaving an ori—
fice in a Knudsen-type vaporization), ac is the condensation
coefficient as defined previously, Gi is the total number
of particles impinging on the surface of the sample; Gs’
which is defined by equation (31), is the particle rate flow
per cm2 of surfaCe area at equilibrium, and Jm is the net
rate flow of particles away from the Surfaax the symbols
of equation (31) have their.usual significance with 3 re-
ferring to saturation (equilibrium) values. By performing
a Langmuir-type vaporization (Gi = 0) and by calculating
Gs using a P8 value determined a priori for a specific T
one obtains thavalue of Ge (using equation (30)). The
quantities Gi and Jm may be measured in a separate ex-
periment and the value of ac may be obtained using the
known values of aeGS. It must be noted, at least in a
superficial way, that at the present time the role the
condensation coefficient plays in a vaporization process
in general, and in an equilibrium vaporization process in
particular,is not easily determined experimentally.

The experimental methods, as well as the problems en—
countered, in obtaining values for the vaporization coef-
ficient are illustrated in the work of Thorn and Winslow
(50) on graphite. Commenting on this work Ackermann, g; _l.
(58) point out one inherent difficulty in trying to measure
surface temperatue--most of the thermal radiation origin—

ates in the interior of the sample and not at the outermost

 

 

 

atomic layer
:65: t6???era

X'PEIDCity dis‘

3."ka is that
:aiitain the
this necessit
szail so that
is easily ach
proximate a C
:3 practice t
sure measurem
in which all

stant. When

.emperature i

SKIES are ass

cilary deduci
izing species
Three 0t?
Lust be chose;

fig! ‘
QACEI 7")

.wlecil

 

.313 conditicc

...at the meat.

3- ieast ten ‘

 

53“ A, ‘
Mun De thE r

:1
A). ‘
U.‘
..1Q

3CCUI.

 

31
atomic layer (from which evaporation occurs); they sug-
gest temperature should be determined by measuring the
velocity distribution of all the particles in the manner
described by McFee, gt__l, (60).

Another condition required of the sample for Knudsen
work is that the vaporization rate must be sufficient to
maintain the equilibrium vapor pressure above the solid.
This necessitates that the orifice area be sufficiently
small so that replenishment of the lost or reacted vapor
is easily achieved, iLQ. the experimental conditions ap—
proximate a closed system containing the solid and vapor.
In practice this condition is verified by performing pres-
sure measurements on a series of vaporization experiments
in which all parameters; except orifice size are held con-
stant. When the absolute pressure measured at a given
temperature is independent of orifice area equilibrium pres—
sures are assumed for the particular system studied. A cor-
ollary deducible from this is that the area of the vapor-
izing species should be much greater than the orifice area.

1 Three other restraints remain. First, temperatures
must be chosen such that the vapor species will effuse
under molecular rather than hydrodynamic flow. Although
this condition is somewhat hazy, Carlson (52) indicates
that the mean free path of the vapor particles should be
at least ten times the orifice diameter. Second, no inter—
action between the vaporizing system and the container

should occur. Third, the vapor pressure measured must

 

 

4'

.‘Q F a‘
name: re

. fl

“med 1.“. we

aw small c3:

‘1' Y C
{6533.111 (1......

3.3.2.3
First Knudse:
re-exaained t
flux through
'«hich is tan;
5‘5 1339 as ef

CCZClusisn l

 

‘Zutian far Kr.
Tut Certain a
tribUtiOn ab?
tobe caused
‘L'Qfilfin

world“ C6113

‘v
:i:

.a at same

:‘11‘
“‘X

3f Parti

 

 

32

neither be affected by any solid residue product being
formed in the vaporization process nor must it vary with
any small composition change which may occur in the solid

reactant during the course of the experiment.

3.3.2.3. Limitations Arising from External Geometry.-
First Knudsen (49-51) and subsequently Carlson (52), who
re-examined the subject, concluded that the rate of particle
flux through a unit area situated on the surface of a sphere
which is tangent to an orifice plane is everywhere equal
as long as effusion flow limits are not exceeded. This
conclusion is known as the cosine law of particle distri—
bution for Knudsen effusion. Recently, Ward (53) pointed
out certain apparent anamolies occur in the cosine dis-
tribution above effusion cells. These effects were found
to be caused by the internal geometric design of the ef—
fusion cells and are a consequence of the law. The cosine

law may be formulated as

dN = ( ) Nocos 9 dw (32)

alH

where dN is the equilibrium flux of particles per unit
area at some distance from the orifice, N0 is the total
flux of particles through the orifice, 9 is the angle be-
tween the normal of the unit area plane and the conical
section of unit area of the solid angle dw. Thus, it may
be seen that (%) cos 9 dw is the fractional part of the
total flux which has a specified direction. The (%) term

results as a normalizing factor for total integration over

 

 

 

+'~e hens;
b.-

".16" inte:

on

32 it is

'Vnt R

W..-\.h up 3:

result.

r193mm ma
Mine law

r‘Eferences

 

 

 

33

the hemisphere of space above the plane of the orifice.
When integration over all.space is performed on equation
(32) it is apparent that the total flux is indeed No.
This integration may be effected by first expressing the
solid angle.in.spherical coordinates such that dw =
sin 6 d6 dQ with subsequent integration of m from 0 to v
to give

dN = N0(-}T-)(Tr) sin 9 cos 9 d9 (33)

E.

which upon integration of 9 from 0 to gives the desired

[0

result.

It is apparent that the Knudsen equation is derivable
from the postulates of the kinetic theory of gases and a
rigorous mathematical derivation and/or analysis of the
cosine law from this VieWpoint may be found in a number of
references (52,53). Rosenblatt (61) analyzes further the
effect of restrictions of molecular flow on vaporization
rates and pressures.

When the effusing vapor is condensed on cold targets,
the collection efficiency of the targets must be determined
and a correction applied for the fractional amount which i
does not adhere. Additionally, the collection efficiency
must be proven to be temperature independent or its de—
pendence on temperature measured.

Finally, the expansion of the crucible during the course
of the experiment must be considered and the proper correc-

tion made when necessary.

34

j§.4. Measurement of Partial Pressures With a Mass Speg:'

trometer

3.4.1. General Introduction

 

The utilization of the coupled Knudsen effusion—mass
spectrometer experiment in the study of refractory phase
vaporizations is now an established technique (62). Some
of the reasons for its widespread use are its advantages
of high sensitivity, a wide dynamic range of measuring
pressures, and the ability to identify uniquely all vapor
species emanating from the cell. Basically, the procedure
consists of performing Knudsen effusion vaporization ex—
periments and measuring the intensity of the effusing vapor
beam mass spectrometrically. The vapor beam is collimated
critically by a double slit system so that only those species
which have straight-through flight from the cell (i;§. no
collisbns with the orifice wall) are sampled by the instru-
ment. The intensity of the fractional part of the vapor
beam which is sampled is determined as a function of tempera-
ture. The relative intensities described in this manner
may be converted to absolute pressures when the mass spec—
trometer has been calibrated in a manner similar to that

discussed in the following Section.

3.4.2. Absolute Pressures With a Mass Spectrometer

The proportionality constant relating the absolute

pressure of a species to its ion intensity-temperature

35

product is a function of a number of parameters which may
be classified into two broad categories: (1) instrumental
parameters and (2) ionization cross-section efficiency.
Instrumental parameters arise from the variation of the
sensitivity of the ion detector with effective mass and
from the physical and electromagnetic dimensions of the
ion source and flight tube. Hence 5, the proportionality
constant for the element (or molecule) as obtained for a
specific isotOpe of the element (equation (18)) is related

to o, the ionization cross-section, by the equation

k = [ear01'1 (34)

The variable 5 is the effective multiplier gain, £_is the

isotopic abundance factor and B is the effect of any other
machine parameters. Since no Faraday cup is designed into
the time-of-flight mass spajzometer, the effective multi-

plier gain is difficult to determine and conventionally is
assigned the value of unity. The ionization cross—section
for a single ionization process (as differentiated from the
total ionization cross—section) is not readily obtainable
by ordinary methods in a mass speirometer since the concen—
trations of the species being ionized are not usually
measurable. Although many theoretical methods for calcula-
tion of ionization cross—sections have been published (g‘g,
63-68), the number of eXperimentally determined data are

considerably fewer (243, 69-73). Many of the theoretical

approaches require a knowledge of various parameters which

 

 

 

.
u,-
‘ 9
0e? " '1
...a. Y 5“
.v- -

"Ava. V

ele'e"S are

.
”an RF
“doob Vb Can

relaticn

were 3 is t
1.“. units of
:r:ss-secti:.

l.a"e been "s«

each constith

"zines rep/xi-

M l
‘51; av‘n. ;_
‘ULLIE
l? 5‘
v

 

' .
~?‘AA
V f or»
y‘VS
p'
v ,
en.e‘es* .-
L
f
,._‘
"f 1,. ‘I-
u n _
““«Yvyl’q‘! _
‘HC
3) .
. .
‘ Uc"‘ V

 

 

36

for many substances, and especially for the lanthanon
elements are either not known or not readily available to
the experimentalist. As an example, the method employed
by Lampe, §£_§l, (71) calculates the cross-section, o, in
units of cm2 with the theoretically—justified empirical
relation

0 = (1.80 x 108)a (35)
where a is the polarizability of the neutral vapor Species
in units of cm3. For most of the past decade the ionization
cross-section values calculated by Otvos and Stevenson (69)
have been used even though Lampe, gt El- (71) pointed out
that one of the main postulates on which the work was based,
gig, the additivity principle that the cross-section of a
molecule may be obtained by summing the cross-sections of
each constituent atom, was in error. Since, even the
values reported in the two most recent articles (67,68)

do not agree (e.g. for Ag, 0 is given as 5.44 x 10.16 cm2

and 11.4 x 10'16

cm2 in references (68) and (67), respec-
tively) the actual choice of ionization cross-sections seems
quite arbitrary. It should be pointed out, however, that

if the mass spectrometer is calibrated with another metal
vapor (e.g. copper or samarium) it is the error in the

ratio of cross-sections between the standard and the species
of interest that is significant and not absolute errors in
the individual cross—sections. In general, when elements

are being detected in the mass spectrometer and it is cali—

brated using a metal other than the one that is present in

 

 

 

:he effusate
whether they
1:; determir.
:2: to intrc.
effusing spe.1
przblem becsr-
A prsce;
eliminate the
rcives calib:
as that abse:
:he absolute
as a functiar
general equa:
if mass Spec:
rate of effus
tive intensi:

that t1“ais met

sPeCies a:

 

Q5
“:6 tr A
“*4 grn
:9
~‘Ls‘x
QT.“ .
e whl
Vim. .
‘t l? Net‘s
x"

37

the effusate the only requisite is that any set of 0,
whether they be theoretically calculated or experimental-

ly determined, must be internally consistent in order

 

not to introduce errors into the calibration. When the
effusing species is a molecule, however, the cross—section
problem becomes more complicated.

A procedure which may be employed in certain cases to
eliminate the whole ionization cross-section question in-
volves calibrating the instrument with the same species
as that observed in the vaporization experiment provided
the absolute vapor pressure of the metal itself is known
as a function of temperature. Cater and Thorn (74) derive
general equations and give two procedures for calibration
of mass spectrometric partial pressures using the total
rate of effusion as a function of temperature and the rela—
tive intensities of the individual species. They indicate
that this method is applicable when two or more vapor
species are present in the effusate.

To summarize, two basic methods may be employed to
calibrate a mass spejzpmeter so that absolute partial pres—
sures above a compound may be obtained from relative
measurements. These are: (1) the Knudsen vaporization
method, or the integration method (75); (2) explicit ab-
solute pressure method. The distinguishing feature of
these two groupings is that in method (1) one may use a
substance which differs from the effusate being calibrated

while in method (2) the calibrating substance is the same

 

 

 

 

:F“{
as the 6.”-

pressure is
spectromete:
to that to l
the same ceI
:erperature

tion derive

the absolute
orlated at a
perature ra:

Substituting

 

l",’_‘

;
r

 

m.
‘_ ~
:‘EJf‘Th
"Vdi arr.
‘ v
.S 1
« a
”‘6 ”Fl
“V‘eh
\.
‘h
«D ‘

38
as the effusate. The first method may be implemented ex-
perimentally in two ways. In the first and most straight-
forward procedure a known mass of the compound whose vapor
pressure is to be calibrated is vaporized in the mass
spectrometer from an effusion cell of geometry identical
to that to be used for the experiments (or, preferably,
the same cell) for a definite period of time at a fixed
temperature. Using the following form of the Knudsen equa-

tion (derived from equation (29))

_ 0.022561 w (3)1/2

eq Ate M (36)

P

the absolute partial pressure, in atmospheres, may be cal-
culated at a fixed temperature preferably within the tem—
perature range of the experiment and near its midpoint.
Substituting Peq into equation (18), k may be calculated
and the relative intensities converted into absolute par-
tial pressures. In the integration method (75) the ion
intensity of a particular species is monitored on a strip
chart recorder as a function of time at (a) fixed tempera—
ture(s). The mass of material vaporized from the cell is

related to the constant k* by the equation

1/
1 _ _M_ 2a 1/2
k* - (sz) (G) s IjTj Atj (37)

in which all quantities refer to the particular ion in
question and the units are in the CGS system. The term, M
is the molecular weight, A is the area of the orifice, G

is the weight loss, Atj is the time interval over which the

39
intensity Ij (nanoamperes) and the temperature (0K) have
been measured, and the other symbols have their usual sig—
nificance. A dimensional analysis of equation (37) shows

that k_is related to kf by the expression

k = (9.9344 x 10‘4)k* (38)
in which k_is defined by equation (18) in units of
atm/nA/OK.

The second method consists basically of graphing the
the absolute pressure of the calibrating substance (ob—
tained :flmr the literature from the eXperimental temperature)
against IT for the substance. This is a graph of equation
(18) and the slope of this graph gives k directly for the
calibrating substance. As an example, for the calibration
of Sm(g) over SmC2(s) elemental samarium would be vapor—
ized at a series of temperatures and the IT product would
be recorded at each temperature. The pressure of the ele-
ment recorded in the literature (76) would be graphed
against. IT, and the value of kSm would be determined.
This value would be used subsequently to calibrate the
Clausius-Clapeyron line for SmC2 vaporization by substi-
tution into equation (19) for a specific pair of ln IT
and 1/T values.

Should a method employ for calibration a metal other
than the one being standardized, conversion of the pro—
portionality constants will have to be effected using ioni—

zation cross-sections (77)

 

 

d... ___———_‘
_’_...— ‘

 

3.4.3

In co:
'a'CIX, geoms
A &
respect to

in the cali

O
rm.

“A. '+"’
:‘Jalbl3‘

and the va

"(3

These two 1:
the k 3.5 e
1
periment wi

ality Const.‘

7%!

(Ir
:J
Fr

 

 

40

GB
RA = kB(EX) (39)

3.4.3. Geometry Considerations in Calibration

 

In contrast to target collection Knudsen effusion
work, geometry variables, such as crucible position with
respect to the ionizing electron beam, are not critical
in the calibration procedure. Rather it is the relative
position of the crucible during the calibration experiment
and the vaporization experiment which is of importance.
These two positions should be as close as possible so that
the ki of equation (18) determined in the calibration ex-
periment will be numerically identical to the proportion-
ality constant for species i in the vaporization experi-
ment.

The Knudsen effusion weight loss method of calibrating
the mass spectometer is both geometry-independent (ori—
fice size is corrected) and has no machine parameter errors.
The truth of this statement may be demonstrated by inspec—
tion of the Knudsen equation (29). When this equation is
modified for mass spectrometric work it contains no geo-
metric-dependent variables (orifice size is excluded since
it has been considered) nor do the variables depend on any
machine parameters p§£_§g, They are only a function of the
temperature and thus a series of vaporization experiments
so calibrated are all referenced to the same absolute,

temperature-dependent value.

 

 

 

 

. 'g
.a..‘b Gaul
_ v-

L Y ’
.RF: \
:.G..b ‘

.

o ."‘ 3
ft .1431 e-

(n
r o
(D
H

1.. Km:
:ransmissior
the emitted
which the ho

in Tier. ' 5 la»

 

 

 

41

In any mass spectometric experiment it is necessary
that once machine parameters have been maximized they be
kept fixed throughout the experiments in which quanti-
tative data are being taken. In addition to being con—
stant for one experiment, these parameters must be invari—
ant from experiment to eXperiment if the same calibration

factor is to be used.

3.5. Temperature Corrections

 

The measurement of temperatures using an Optical pyrom—
eter in Knudsen effusion experiments requires that certain
transmission corrections be made for partial absorption of
the emitted radiation by various windows and/or prisms through
which the hot object is viewed. These corrections are based
on Wien's law of radiation (95):

_C2

Jh/I' = C17\—5 exp(—:A-,f) (403)

where is the energy flux per unit area at a wave-

Ja ,T
length a radiated by an object at a temperature T; C1
and C2 are the first and second radiation constants, re-

spectively. The diminuation of the energy flux in passing

through an intervening filter is given by

JK,T = Jh,T exp(—kx) (40b)

where Ta is the apparent object temperature as observed

through the filter, T is the true temperature, k is the

 

.Fnfirn ' A“ C
‘I UthAA
. u».
d-
.
. .
lebA-u 5.1
U'Ubtl

4»
3:”)‘5 1.1
5.1

from which t2

 

 

The terx

radia:

.
‘s
J-

this tEIm

 

.2 “1,

‘ :J‘Vrsheter
‘AY‘ K
stsatd‘e "f 1.,
.H ‘
§‘yl arc K
Ejv

 

42
absorption coefficient in cm.1 and x is the absorbing
path length in cm. Combining the two previous equations

results in

 

-5- _. _ _
Clh e Cz/KTa = e kx C1 h 5 e CZ/RT (40c)
from which the two following equations result
-C2 - k C2 1
m ‘"X‘fi (48)
a
1 1 —kxh
._ _.__ = —————- 41b
T Ta c2 ( )
The term Egfi- may be evaluated by measuring how much
2

the intensity of light radiated by a hot object is dimin-
ished by the filter (prism and/or window). Since Wien's
law of radiation states that the energy radiated by a given
substance is proportional to its temperature the magnitude

of this term is obtained by

) (410)

5‘:

ll
6TH
I
ti IH

f L
where Tf is the temperature of a standard lamp read with
the pyrometer sighted through the filter, TL is the tem—
perature of the standard lamp read with the pyrometer direct-
ly, and Ki is defined by equation (41c). The true temper-
ature is then obtained by using equations (41b) and (41c)

to give

1__1_
T — T K. . (41d)

 

 

. ——___

iserubly and net

 

 

.
L1. Genera-

The four
2: ssure stud
the mass spec:

3e electron l

? the vacuu:
Hator; and .
’SEd for fabr;

u:ducts.

4--.+;
2%

 

 

‘El:::sfi
u r C -
or}; L1“
.‘s
‘5‘ ‘3 Y‘ ‘
\Jsis‘dErs‘
~25?

 

CHAPTER IV
EXPERIMENTAL EQUIPMENT AND MATERIALS
4.1. General Description of Experimental Equipment

The four major pieces of equipment used for vapor,
pressure studies in the course of this work were: (1)
the mass spejnpmeter with its associated d.c. high volt—
age electron bombardment power supply and furnace as-
sembly and necessary read-out oscilloscope and recorder;
(2) the vacuum preparation system; (3) the induction gen-
erator; and (4) the glove box. Various materials were
used for fabricating crucibles and for the synthesis of

products.

4.2. Detailed Description of the Apparatus

 

4.2.1. The High Temperature Mass Spectrometer

 

The instrument used was a Model 12, Bendix T.O.F.
mass spectrometer fitted with a 167-cm long flight tube,
with a Model 107 ion source and with a M—105—G6 electron
'multiplier. Figure 1 illustrates the basic design of the
instrument and a detailed description‘may be found else-
where (78,79). This instrument had been assembled in this
laboratory from commercial components and has been modi—
fied considerably as described below: (1) a continuous.

ionization kit, purchased from the Bendix Corporation, was

43

 

 

 

 

 

 

 

 

 

 

44

 

 

numm m

 

 

mpocm mmoom
mmUOC¢ Ill

 

 

 

 

mOHmcm

 

 

 

.Hmuweonuowmm mmmE pamHHMImoumfiHe "0Humamcom .H musmHm
Emummm
0m> OB
_ F monsom GOH
HmHHmHanz quEmHHM conuomHm PH
.llerlhhlfl. .
wasu uMHHQ mommzm\\.c III?HHH UHHU Houucoo
- m “I.“ m a m
*mpwmwm mmHsmMUfiH. or U.H couuumam
\ I
H. _ \\ OmOHMHm i— . _“
c HuomHmmn
:H. . n F: _
. _ Alll
mHHum mu _.|| _ _ +
@H . \V _
m HIV—N UH .m maH GOH IN _ __ uchH
No Pi VV\ _H% .m _ mmm
mpozumo .0. p> omen: omwa r
vmwumo GOH . ;
camasm
wpocm mmnp conuome

 

 

 

_
.U.U> omH+

 

 

‘ .

'2'..." 7”qu o C

uU—‘V """u
.

rode increase

   

Changes were 1*.
electron grids
:pressed on i
been from trai.
:lte Spectrum u
justable inst:
contamination
also permits :
;:nization pr:
beam {6.9. the
'2‘ A 3.
5“ filament

:19 e 1e Ctran
‘43‘41

dbe incre

.Erge Cloud .
:3“ Tan f~1 -

 

 

 

45

added to permit the electron gun of the ion source to be
operated in either normal pulsed (10KHz) or in continuous
duty mode. Operation of the electron gun in continuous
mode increased the sensitivity by a factor of about 100.
Changes were made in the ion source such that one of the
electron grids may be either grounded or have -150 V DC
impressed on it. This alteration prevents the electron
beam from traversing the ion source and thereby turns off
the spectrum without necessitating any alteration of ad—
justable instrument parameters. Such a feature prevents
contamination of the multiplier between measurements and
also permits the detection of and correction for redidual
ionization processes which do not result from the electron
beam (e.g. thermal, potential).

(2) A 3.0 volt battery was connected to the electron
gun filament (negative terminal of battery) and to one of
the electron grids (positive side) so that the trap current
would be increased in the ion source by dissipating the
charge cloud of emission electrons on one side of the elec-
tron gun filament.

(3) A small steel plate was spot welded behind the
filament and maintained at the same potential as the fila-
ment thereby retarding electron emission in the "reverse"
direction.

(4) The anode shield was connected to a switch which
either connected it to the trap anode or to electrical

ground. Use of this switch permits critical alignment of

46

the ion source magnets thereby insuring that the electron
beam traverses the electron gun filament-trap anode region
in a linear rather than spiral trajectory.

(5) All the nickel mesh grids in the ion source and
in the electron multiplier were replaced with molybdenum
mesh grids which have a higher transparency for ions and
which interact less with potential fields than do the nic-
kel grids.

(6) A 50 liter/sec titanium sublimation gettering
pump, Varian Associates Model 922-0032, was inserted between
the Knudsen cell furnace housing and the 15 liter/sec Vac
Ion pump.

(7) A new Knudsen cell furnace assembly was designed
and constructed. The improvements incorporated in the new
design as compared to the previous one were: (a) a smaller
heat zone which thereby minimized temperature gradients and
(b) quartz discs to replace the boron nitride ones which
out-gassed excessively after they had been exposed to the
atmosphere. A more complete description of the furance as-
sembly is given by Rauh, EE.§£° (80).

(8) The analog scanner circuit was fitted with a pulse
transformer which increased the gate pulse on the electron
multiplier from about 60 nsec to 360 nsec. This alteration
allowed monitoring the sum of the integrated peak intensi-
ties of up to four isotopes instead of just one peak, there—
by increasing the sensitivity of the instrument. The pulse

transformer set was purchased from Polyphase Instrument Co.,

Bridgeport, Pa.

47

As is indicated in reference (22), the spectrum was ob-
served on a Tektronix Model 545A oscilloscope fitted with
a CA dual channel pre-amplifier and was recorded using a
Bausch and Lomb Model V.0.M.—5 strip chart recorder.

The power supply used to heat the cell in the Spec-
trometer is a well regulated electron bombardment unit and
has been described elsewhere (22). In this system the cell
is grounded and the filament assumes a negative potential.
Temperatures were measured using a Leeds and Northrup dis-
appearing-filament type optical pyrometer, serial no.
1619073 calibrated previously against the 1948 International
Scale of Temperature at the National Bureau of Standards and
by sighting through a prism and optical window into the cell
orifice. The calibration data for the pyrometer are presented

in Appendix D.

4.2.2. The Vacuum Preparation System

Either of two vacuum systems was used for the prepara-
‘tion or vaporization of samples. One was an all glass
system (81) while the other was a fast pumping station
employing a current concentrator designed for maximizing
the current flow through the crucible material (82). The
fast pumping station which employed a 45 ft3/min (1274
liters/min) forepump and a three-stage 500 liter/sec dif-
fusion pump was used in conjunction with the current con—
centrator. The induction generator was a 20 Kw, 250—450

szThermonic brand unit manufactured by Induction Heating

48
Corporation, whose input voltage was stabilized by a General
Electric Inductrol Voltage Regulator and whose current was

controlled by a saturable core reactor.
4.3. Chemical Materials

The purity and source of the materials used in the
experiment were: (1) samarium metal, 99.9%, from Lunex
Corp., Pleasant Valley, Iowa; (2) graphite powder, Acheson
Grade #38, Fisher Scientific Co., Fair Lawn, N.J.; (3)
tellurium metal chips, 99.999%, Fairmount Chemical Co.,
Newark, N.J.; (4) neodymium sesquioxide, 99.9%, Michigan
Chemical Corp., St. Louis, Mo.; (5) hydrogen gas, 99.95%,
The Matheson Co., Chicago, Ill.; (6) thin-wall, seamless
tantalum tubing from Fansteel Metallurgical Corp., North
Chicago, Ill.; (7) molybdenum stock from the Kulite Tungsten
Co., Ridgefield, N.J.; and (8) sintered tungsten rod from

Sylvania Co., Towanda, Pa..

4.4. Knudsen Cell Design

 

Effusion cells used for vapor pressure experiments
were of the basic design illustrated in Figure 2. Those
cells which were made of molybdenum and were used for the
samarium dicarbide study were fitted with a graphite cup
liner while those fabricated from tungsten metal were used
without any liner. The effusion cells were each converted
tx>a one piece assembly by heating them to such a tempera-

Une that the halves of the cells fused together.

 

rV///I/// /////W.WnWWW_I § Li V/é m.

 

49

Effusion cell

Figure 2.

» 0.080 cm

i I

 

T

7F

 

\ 1.8 cm

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

/////////////fl

 

4.!
C Liner

 

 

 

1.6 cm
Bottom

 

 

F .
7/2:
Top

 

nfiv

In:

Q
.pn

cu“

Air-f1
-v'..ul
'
o
-

\2nh‘ r

skub-.n

5.

r“ he .6
.G Li ”n
a:

:u .5 Z 4
u s. q . A 4

+.. E
«t
4H .. . A:
Q» 1 4 v 4
2» .2 .1.
I I nA

 

 

v 4 A: 5: . .
2.. .. .. 2» .. .
Hg... . . a: . s
u u. . .. . s u. . . .
:k l» is

 

50

4.5. Heliarc Apparatus

An evacuable heliarc welding apparatus was constructed
to seal small tantalum bombs charged with samarium metal
and graphite powder. This assembly is illustrated in Figure
3. The apparatus consists of a glass tube 18 in (45.6 cm)
long, 7 in (17.8 cm) in diameter, with 1/8 in (0.32 cm)
wall thickness whose ends are beaded to be 1/4 in (0.63 cm)
wide; and two 1/2 in (1.25 cm) thick bakelite blocks for
capping the ends of the glass tube. Each bakelite block
has an 1/8 in (0.32 cm) groove into which a rubber gasket
is fitted. Electrical feedthroughs in the bakelite consist
of Swagelok connectors, which serve also as gas ports.
Torr-Seal epoxy resin (Varian Associates, Palo Alto, Calif.)
was used to vacuum seal the metal feedthroughs to the
bakelite blocks. Polyethylene tubing (an insulator), was
used to connect the Swagelok fittings to the copper tubing
valve system. Entry and manipulations inside the apparatus
were executed with a rubber glove. The two bakelite blocks
were necessary to allow simultaneous evacuation (or pres—
surizing) on both sides of the glove. Hoke valves (type
309A) were situated on the c0pper tubing leading from the
apparatus to a mechanical pump so that the system could
either be filled with helium (or any purging gas) or be
evacuated. ‘An oil bubbler permitted the equalizing of
pressures when manipulations were performed with the rubber

glove. Four symmetrically—Spaced Springs applied cohesive

 

 

 

h.."‘li‘s.

 

 

 

 

 

51

.msumummmm UHmHHwQ mHQm50m>m

.m mHSmHm

 

 

\.

J-

 

v’i

52

tension to the apparatus when it had atmospheric, or higher,

internal pressure. The pressure was monitored by an aneroid—

type pressure gauge and by a McLeod mercury manometer (Kontes

Glass Co., Vineland, N.J.). An Airco Welding Products, Union,

N.J., arc welder provided the D.C. current.

CHAPTER V
EXPERIMENTAL METHODS

5.1. Preparation of Samples

5.1.1. Samarium Dicarbide

The preparative technique was an adaptation of Sped—
ding, gt 2;. (4). Tared amounts of samarium metal chips,
scraped free of oxide coating, were inserted into a 6.5 mm
diameter (about 3.5 in (8.5 cm) long) seamless tantalum
tube which had been outgassed at an observed temperature
of 20000 for about 10 hours. A stoichiometric amount of
graphite which had been outgassed at 20000 for about 5 hours
was added to the samarium metal. The ends of the tantalum
tube were crimped tightly and were sealed by heliarcing
(Cf. Section 4.5) after the tube had been evacuated to a
pressure of 0.06 torr or less and flushed with helium gas
several times. This procedure reduced the possibility of
oxygen contamination. Subsequently the tantalum was sus-
pended in a Vycor vacuum system and heated inductively at
an observed surface temperature of 15000 to 1700°_for 6 to
10 hours. Since samarium dicarbide hydrolyzes in air, the
lxxflo*was opened in a helium—filled glove box (hereafter called
"glove—box") and all subsequent manipulations were performed

in this box; the samples were stored in a vacuum desiccator.

53

54

5.1.2. Neodymium Monotelluro Oxide

 

Samples of this phase were prepared according to the
vapor transport procedure employed by Kent and Eick (38).
Calcined neodymium sesquioxide and tellurium chips were
placed in separate, adjacent quartz boats enclosed in an
open-ended Vycor tube which was located in a tube furnace.

A 1.5 mole excess of tellurium was provided to assure com—
plete conversion of the oxide. The temperature, measured
with a chromel-alumel thermocouple and potentiometer was
increased slowly to about 7000 and maintained there for about
5 hours while hydrogen gas was swept through the tube, there—

by transporting the tellurium vapor over the sesquioxide.

5.2. Methods of Analysis

 

5.2.1. Samarium Dicarbide

 

Chemical analyses were performed using the oxalate pre—
cipitation method. Tared samples were dissolved in 6‘M
hydrochloric acid, digested on a hot plate for about 4 hours,
and filtered to remove free carbon which was dried and
weighed. The pH was adjusted to 4—5 using bromcresol green
indicator, and the samarium was then precipitated as the
oxalate. The precipitate was calcined to the sesquioxide
by heating overnight at 9000 in a muffle furnace and weighed
after it had cooled. Samarium content was calculated from
the weight of the converted sesquioxide; bound carbon was
calculated from the difference between the original weight

of the sample and the sum of the free carbon and samarium

.m-
In-
....,..
. .-
‘v-\.

 

 

 

a». fire Ab» . rLs A~.\ V o u . . ;.~ . s .
2. L.“ w . 2“ Kw. a: n... . . a: 2‘ p . . .4... . s: ..
r . . . .3 A . . C. H o «C A: . . 4 c .2 flaw . . 2... . . ‘
nu. fix. .0 .5 v. I. as ... la ..» :4 a e . r ...
c . ~.v. - . 4.: .. . u v. .\~ - v .~ - . . s. ~
.1

 

 

55
weights. Duplicate analyses for carbon and samarium content
were performed on one sample by Galbraith Laboratories,
Knoxville, Tennessee.

X-ray powder diffraction photographs of the various
preparations were taken with 114.59 mm diameter Debye-
Scherrer cameras. Lattice parameters for three preparations
were determined using the Nelson-Riley least squares extra-
polation techniques which is part of a larger computer pro-

gram (83).

5.2.2. Neodymium Monotelluro Oxide

 

Three preparations of this compound were made. The
mass increase which resulted from substitution of a tellurium
atom for an oxygen atom was used as a basis for calculating
the purity of the product as well as for indicating com-
pleteness of reaction. The preparation was then heated for
several hours in a dynamic hydrogen atmosphere to purge it
of any free tellurium. The purity of the olive green pro—
duct, as well as its identification was proven further by

its characteristic X—ray powder diffraction pattern.

5.3. Temperature Measurements

 

A chromel—alumel thermocouple was used for the Nd202Te
preparatory procedure since accurate temperature measure-
ments were not required. The optical pyrometer described
previously was used for all effusion work. To reduce ran-
dom errors, each temperature value reported in this thesis

is an average of three independent readings.

 

«u»

"“

.‘\

‘9-
.“

v
.

r,

.‘E

 

 

 

56

Temperatures measured by optical pyrometry must be cor-
rected for absorption due to the material of the viewing
port window-prism assembly. To effect this correction, the
transmissivity term, KA. was determined for the window and
prism assembly after every experiment by measuring first
the temperature of a tungsten strip lamp whose input voltage
was regulated carefully, and then by measuring the apparent
temperature through the window-prism assembly. The window
and prism were then cleaned to remove any film deposit which
may have formed during the vaporization experiment, and the
apparent temperature of the lamp was re-measured. Subsequently
the temperature of the lamp was measured directly. For each
of these temperature measurements five independent readings
were taken and the average of each set was used. Since
the transmissivity may change over the course of an experi—
ment as a result of deposit formation on the optical window,
the average transmissivity of the “clean" and "dirty" opti-

cal assembly, KA, was used. This value was obtained from

the relation

2 1
K : —_————— - '—- (42)
A To + TD TL
where TC and TD are the observed average apparent tem—

peratures of the lamp through the "clean" and "dirty" opti—
cal assembly, respectively, and TL is the observed average
temperature of the lamp measured directly. The true tempera-

ture is obtained from the observed experimental value, Ta’

using equation (43)

-K . (43)

In all correction determinations of this type a tung-
sten lamp temperature of about 15000 was chosen since this
is the most accurate scale region of the pyrometer. It
must be noted that the pyrometer correction listed in Ap-
pendix D was applied first to the observed pyrometer read—
ings and the corrected values were used in equations (42)

and (43).
5.4. Vaporization Experiment Procedure

Samples of NdZOZTe were manipulated in air while those
of SmCz were handled only in the glove box. In both cases
samples were pulverized and were loaded into the effusion
cells through the orifice. Transfer of the effusion cell
from the glove box on to the Knudsen cell furnace assembly
and insertion of the assembly into the mass spectrometer
were performed as quickly as possible and, in general, re—
quired no more than two minutes. The mass Spectrometer was
evacuated immediately and the pressure decreased rapidly
to 5 x 10_5 torr or less. The effusion cell was then heated
slowly so that the pressure did not exceed 5 x 10_5 torr
until a heater filament current of 11 ampen§s(about 10000)
was reached. A negative D.C. voltage was then applied to
the filament, and the cell was heated to higher temperatures
by electron bombardment since the effusion crucible was at

ground potential. Although an induction period of about one

58
minute is required for the cell temperature to equilibrate
in this system after a new power setting is chosen (84), a
five minute interval was always allowed before measurements
were initiated. Temperatures were usually incremented sys-
tematically until a maximum value was reached and then de—
creased in like fashion. The viewing window for tempera-
ture measurement was protected from undue coating by the
effusate with an externally Operated, magnetic shutter. A
similar shutter positioned between the ion source and the
effusion cell was used to demonstrate that the effusing
species did, indeed, originate from the cell and was also
used to correct for background contributions to the measured
intensities. The integrated intensities were recorded in
both pulsed and continuous ionization modes by scanning all
the isotopes and/or monitoring and recording the intensity

of the most abundant isotope.
5.5. Congruency Tests on Neodymium(III)_Monotelluro Oxide

To ascertain whether NdzozTe vaporized congruently,
preliminary vaporization experiments were performed using
'tungsten and molybdenum .effusion cells. These :effusion
cells were outgassed to constant rate weight loss to be cer-
‘tain that they were clean. The outgassing data are shown
eas Table H-I in Appendix H. Subsequently a series of eleven
\faporization experiments were performed using the molybdenum
<:ell over a temperature range of 1505-18480, and from 7-81%

(of the sample vaporized in each run. Three other vaporizations

59
were performed using tungsten cells. After each experiment
the residue was examined by X-ray powder diffraction analysis.
The results are shown in Table H—II of Appendix H and are

discussed in Section 6.8.

5.6. Calibration of the Mass Spectrometer for Samarium

 

Dicarbide

 

5.6.1. Transmission Coefficient

 

Knudsen effusion crucibles used in this work Were ma-
chined from molybdenum and tungsten bar stock. The orifice
of each cell was machined in the following manner. A
tapered drill of the correct size was cut into the crucible
top inside section until 5-10 mils of metal remained. The
orifice was then formed by machining the top face until the
correct diameter hole remained. Since all the orifices
‘were made in this fashion, they should have comparable
dimensions. An attempt was made to determine the channel
thickness of one of these orifices byza"depth of field" type
Ineasurement with an 100x magnification microsc0pe. This
procedure failed, however, and the top was cleaved along
a cross-section of the orifice and mounted on edge so that
the field of vision in the microscope was along the channel
‘width of the orifice. Although in this position it was im-
possible to focus on the entire'bhannel width", continual
variation of the focus moved the field of vision along por—
tions of the "channel". Clay impressions of the cleaved

cross-section were also made.

60

5.6.2. Calibration with Elemental Samarium

Two techniques involving samarium vapor were used to
calibrate the mass spectrometer. In the first procedure
a tared Knudsen effusion cell of the same design and orifice
size as the cell used in the vaporization experiment being
calibrated was loaded with 1-2 grams of samarium metal
cleaned by abrasion to remove the oxide coating. The
charged cell was then placed into the mass spectrometer and
the system evacuated. The samarium was then vaporized and
temperature and ion current intensity data were collected
as described previously. After the experiment the cell
was reweighed to confirm that metal still remained in it
and the window-prism transmissivity was checked. Then, at
each corrected temperature the value of the total samarium
vapor pressure, P (obtained from Habermann and Daane(76)),
*was graphed against IiT’ in which Ii is the normalized in-
tensity of samarium obtained from isotOpe i. Such a graph
results in a line whose lepe is ki’ the proportionality
constant obtained from isotOpe i. Since reference (76)
expresses the pressure in a logarithmic form, equation (18)

was used in the form
log ki = log P - log IiT — 2.8808 (44)

where the reference states for k and P are in atmospheres

and torr, respectively, and the number 2.8808 arises from

conversion of torr to atmospheres.

61

The second procedure was the integration method (sf,
Section 3.4.2). In calibration experiment II 63 a tared
effusion cell was loaded with about 1-2 grams of cleaned
samarium metal and weighed accurately. After evacuation,
the temperature was elevated quickly to a pre—determined
power setting and the intensity of one isotope of samarium
was monitored as a function of time at constant temperature.
At various times background intensity readings were deter—
mined by stopping the effusing beam with the shutter.
The sample was heated for a time sufficient to cause a
significant weight loss (343; one hour at 1100°K causing
loss of 0.1 to 0.2 gram ), and the temperature was monitored
periodically. Heating was then terminated suddenly, the
time recorded and the cell re—weighed after it had cooled.
FrOm. equation (37) a sensitivity was calculated for which
k was found using equation (38). The orifice diameter was
corrected for thermal eXpansion at the weighmfl mean tempera-

ture of the calibration eXperiment using Krikorian's data

(85).
5.6.3. Calibration with Elemental Silver

In this procedure a small, known weight of silver metal
(abcmt 10 mg) was placed into the effusion cell containing
saunarium dicarbide powder and the metal was vaporized at a
fixed temperature while the intensity of the ‘10'7Ag isotOpe
‘NaS nmmitored as described in Section 5.6.2 for samarium

nuatal. The time required for the intensity of the silver

 

:5
.wu

.—»

-v-

-1.

'§

 

 

62

{maks to fall to the background level was recorded as the
end time of the calibration. The temperature was then ele-
vated and vaporization of samarium dicarbide was started
using instrumental conditions identical to those used for
the silver calibration. In a fashion analogous to that
described previously, the calculations of the integration
method were performed on the silver data. Conversion of

the proportionality constant, k, from silver to samarium

was effected using equation (39).

5.6.4. Calibration with Samarium Dicarbide

Calibration eXperiment IV 3 utilized the pressure
calculated above samarium dicarbide as obtained in a Knudsen
vaporization experiment to obtain absolute pressures. -An
effusion cell to be used subsequently for vaporization ex-
periments (after calibration) was loaded with samarium di-
carbide and weighed in the glove box. After the spectrom-
eter had reached a sufficiently low pressure (5 x 10"5 torr),
the cell was heated to a pre-selected temperature which was
in the range of the planned vaporization experiments and
the 11») current intensity was monitored. The temperature

was nmfiisured at regular intervals and the total time of the

vaporization was recorded. The cell was then removed and

weighed. Applied corrections included: background inten—
sityn ‘transmittance effects of the optical assembly on
temperature, and orifice diameter eXpansion (85). The

calculated Knudsen pressure (Cf. equation (29) without

4...

.~.

 

A: .1. A; 2.“
a.“ ,. . H... .2
:u . . :- «x.
> a new > . l

 

 

 

 

63

gwometric term) at the weifined mean temperature, T3 of the

cmlibration experiment was then used to obtain .k for

(Sm-152 and Sm-154) by using equation (18) and obtaining

the value of IT at T. from the Clausius-Clapeyron least

squares line of the vaporization experiment being calibrated.
In this calibration experiment the 360 nsec gate

pulse transformer was used. This alteration allowed simul-

taneous measurement of the sum of the ion current inten-

sities of the two most abundant isotopes. In the subsequent

vaporization experiments for which this calibration was

‘used the intensity data were collected in the same manner.

£557. Appearance Potential Measurements

The appearance potential of an ion is defined as the
ndehnum energy required to produce that ion (and any co—

appearing neutral fragments) from a given Species (ion, atom,

or nuolecule). For an ion produced from a neutral Species

arui Inesulting in only the ion and two electrons the ap-
pearance potential is the same as the ionization potential,

xmiz.., the energy required to remove an electron from the

 

sgxecjxas.
Ionization efficiency data were collected on various
*varxor' species in the mass Spectrometer with two objects in
rnirui: (1) to Show whether these were primary species coming
ciireurtly from the effusion cell or secondary Species pro-

chicemi by rupture of a bond and subsequent ionization; (2)

tc> fturther identify any species coming from the effusion

64
cell by its ionization potential. The instrument used is
not adequately equipped for highly accurate ionization
potential work, but it suffices for the two aforementioned
objectiveL Because of its simplicity and its sufficiency
the linear extrapolation method was employed. A general
discussion and appraisal of the experimental techniques
used to obtain appearance potentials may be found else-
where (91). The principal feature of the linear extrapo—
lation method is that in the ionization efficiency plot of
ion current XE electron energy the linear portion of the
curve is extrapolated to zero ion current intensity. An-
other substance, ideally isoelectronic with the first,
whose ionization potential is well known, is used to cali-
brate the energy axis and thereby correct for machine para—
meters. The calibrating substances are usually the noble

gases; krypton and xenon were used in this work.
5.8. Treatment of the Vaporization Data

All mass spectrometer data were reduced by a computer
least squares program whose logic is listed in Appendix E.
This program corrected observed intensities for background
contributions, normalized isotopic intensities using the
isotopic abundance data found in reference (91), corrected
observed temperatures for window-prism transmissivity and
applied to temperatures a pyrometer correction taken from

the table in Appendix D.

 

 

 

..v

“4-

n
I..-

.
...

v...

vu'h

..-~.

v.
r-
.v

(T)

{ )

 

..
~
‘4
-
~.
~

 

65

The computer program had a rejection criterion such
that any experimental point which varied by greater than
three standard deviations of that least squares calculated
value would be rejected and a new least squares value cal—
culated. This criterion guards against gross erratic
errors but is not very reliable for small sets (10—20 points)
of data. After each computer least squares analysis the
output data were graphed and if a point was found to ex-
hibit a large deviation from the others in the set another
rejection criterion was applied.

This second criterion was that developed by Grubbs (92)
for small sets of data. His rejection criterion for the

largest member of a set of size n(2 < n j,25) uses the

 

statistic
2 Z (x. - x )
S i=1 1 n
_13. : (44a)
52 n — 2
iéi (Xi — X)

‘where xn is the largest member; E5 and 2' are the

arithmetic averages of the set with xn excluded and xn

included, respectively, and n is the initial number of
Oints. Basically, the criterion of equation (4Lfl is the
P
Comparison of the variances of the two sets—-one with the

suspect rejected and one with it included, see equation

 

(44b)
2 2
S 0
- -2
i“ = 2 1 <:-1> (44b)
S

66
If the calculated statistic described was found to have
2.5% Significance (:.95% confidence that the point does
not belong to the set) using the percentage points tables
(92) it was rejected. An equation similar to (44a) was
used for testing the smallest observation. Of a total of

446 points 29 were rejected by this scheme.

 

n\~
2‘

1’4

.5.

.._

.“

:»

.._

 

 

CHAPTER VI

RESULTS

6.1. Analysis on Samarium Dicarbide

 

From seven analyses on three different preparations
the following mole percentages and uncertainties expressed
as standard deviations were determined: samarium, 32.7 i
0.6% (calc., 33.3%); bound carbon, 67.3 i 0.6% (calc.,
66.7%). The Galbraith Laboratories' analysis of samarium
dicarbide accounted for 99.53% of the sample weight with
samarium 86.81 weight % (theoretical 86.22%) and carbon
12.72 weight % (theoretical 13.78%). The weight percent
analysis indicates that little oxygen contamination can be
in the samples.

The lattice parameters calculated for two preparations
are shown in Table II. They agree within experimental er-
ror with those reported by Spedding E£.El; (4) for samarium
dicarbide: a0 = 3.770 8, c0 = 6.331 A. For preparation
III 1 it may be seen that the lattice parameters of SmC2

are the same before and after a vaporization experiment.

Table II. Lattice parameters for samarium dicarbide

 

 

‘;;;;i No. Film No. a0 1 0,(A) c0 i 0,(R)
I 57 A-1854II 4 3,776 i 0.004 6.319 r 0.008
III 1 A-1901III 3 3.767 i 0.003 6.312 i 0.014
III 1* A—1933111 17 3.769 i 0.002 6.318 i 0.009

M1

68

6.2.. Analysis on Neodymium(III) Monotelluro Oxide

From the mass increase data resulting from converting
the sesquioxide to the monotelluro oxide, the purity of
three preparations was calculated to be 99.6%, 98.3% and
100.3%. The interplanar d-spacings Obtained from X-ray
powder diffraction photographs agree with those reported

in the literature (38).
6.3. Vaporization Mode of Samarium Dicarbide

The sublimation of samarium dicarbide was Observed to
occur according to equation (45) in the temperature range

1431-20580K
> Sm(g) + 2C(9r) (45)*

 

SmC2(s)

Neither SmC2(g) nor SmC (g) species was observed in the
vapor above the dicarbide samples studied in the mass spec-
trometer. In each vaporization experiment the mass region
154-250 amu was examined occasionally and no peaks other
than background were noticed. A vaporization experiment
‘was performed at a low ionization energy of 10.0 volts and
the same vapor species were Observed. That samarium was
8 vapor Species observed was confirmed by its isotopic

th
abundance distribution and by its ionization potential.

 

P’

*That carbon is in the graphite allotrope is based on the
fmfi;that heating amorphous carbon at high temperatures
(>15000) in_vacuo causes it to convert to the graphite
fmmland also on the fact that in the x—ray powder diffrac—
tum photograph of the residue obtained from vaporization
omeCz strong lines attributable to graphite were present.

69
(Wpical spectra for the samarium isotopes obtained from

samarium dicarbide and those from samarium metal are prer

sented in Figure 4.

624. Vaporization Mode of Neodymium(III) Monotelluro Oxide

The ions Observed in the mass spectrum for the vapori-
. + + + +

zation of NdZOZTe were Nd , NdO , Te and O and these
. + . . . . .
(excluding O ) are shown in Figure 5. These ions were identi-

fied in the manner described previously except for 0+ whose
low intensity prevented measuring its ionization potential.
That O+ was originating from the effusion cell was shown

by its disappearance from the spectrum upon tilting the
molecular beam out of the path of the ionizing electron beam.

The four vapor species observed in the spectrum cannot be

described by a single equilibrium process. (Cf. Section 7.2).

. + .
The temperature for which the O was determined to be

coming from the cell was about 23000K. It was also Observed

that the ratio of deO/de increased with temperature and

from a plot of [(IT)NdO/(IT)Nd] y§_1/T (using experiments

III 61 and III 46) the inversion of the ratio at unity

occurred at about 21600K.
5-5. Transmission Coefficient of the Effusion Cell

Isttempts to measure the channel thickness of the Knudsen
cell's; orifice indicated the depth to be immeasurably thin,

i~e- 1ihe orifice was knife-edged within the limits of de—

‘ ~ ’

teCtifini. Furthermore, since it was impossible to focus

7O

Em mo Eouuommm mom: .3 wusmHm

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

+
Em 0>OQ< _ mUEm m>OQ<
%_
3. 1244
W I
.v W
I
9 I
0’ Q
0
E
a, w
T» 8
r7
6 I
.v w...
I) L 6.7
_ L
l.
or
A
j
I
g l
77
I
Q
I v
9
Z

391

71

 

 

 

 

 

 

 

 

 

 

 

 

W

+ +
Te+ Nd NdO

Figure 5. Ions from neodymium(III) monotelluro oxide
vaporization.

72
the microscope on the entire channel "width" and since chang—
ing the focus continuously moved the field of vision along
portions of the channel it was concluded that the orifice

"channel" was really a conical section and that no percept-

ible cylindrical channel was present. Clay impressions

 

taken along the cross—section of the orifice channel also

indicated no perceptible width. Therefore, a value of unity

was used for the transmissivity correction (Clausing factor)

 

in the Knudsen equation of pressure, £39,, the weight—loss

calibration procedure.

It should be mentioned that the effusion cells were not

rnachined with the Specific purpose of attaining knife-

eumges, but that they resulted from the machining procedure

(fibescribed in Section 5.6.1). Cells with finite, measurable

cheurnel depths are suitable for absolute pressure measure-

nmnrts since corrections for this type of geometry are very

accnxrately known quantities.

6.63. Calibration of the Spectrometer for Absolute Pressure

Values of the proportionality constant between the par-

txia]. pressure and the ion current-temperature product for
‘the:*various samarium isotOpes, as well as the method employed

tr) cflatain each value, are listed in Table III. Equation (18)

may be Obtained in the form
log P = log k + log IT + log 760 (44)

where the reference state for P and k are torr and atm,

respectively. A graph of equation (44) for the calibration

73

 

 

 

 

om.vH .mm> ammosax NoEm m >H sum mos HHH
wo.mH .dm> ammoscx NoEm m >H elm Hos HHH
Hm.mH .dm> cmmescx NOsm m >H elm Hos HHH
om.mH .dm> ammoscm Noam m >H elm no HHH
osma .umms:H am ecm .d.> sm mm HH .mo HH wma me HH .He HH
ow.mH .ummucH Em paw .m.> Em mo HH .mo HH mmH me HH .Hv HH
NV.NH OHSmwme Homm> Em No HH mvH me HH .Hv HH
mm.NH oudwmwum Homm> Em mm HH va me HH .Hv HH
sm.mH mosses aoHumummucH ma um HH emH Hm HH
>®.NH posqu COHumumwucH m4 hm HH NmH hm HH
sm.mH sesame coHumHmmucH me am HH sea an HH
I .mem wmou .mem.
2 2H coHumHnHHmo uo moms scHumHnHHmo nomH coHumNHuomm>
.HHx u.m mo ucmomcou wbHHmEoHuuomon .HHH mHQme

74
experiment II 62 is shown in Figure 6. Inspection of this
equation shows that.at log P = 0 the value of k is obtained

from the corresponding value of IT at this point.

6.7. Thermodynamics of Vaporization for Samarium Dicarbide

6.7.1. Enthalpy of Reaction

The results of the ten vaporization experiments of
samarium dicarbide are listed in Tables IV and V. Individual
data points for the experiments are presented in Appendices
.A and G. The value of AHgga was obtained using the assump-
tion that the heat content of SmC2 was equal to that of CaCz
and that the two compounds have identical phase transition
ernfloalpies and entropies in the tetragonal to cubic phase
cfloanges. The average value obtained for the Second Law
rMHgQB fOr reaction (45) was 64.2 i 2.1 kcal/gfw and the

txytal number of experimental points was 417. The uncertainty

in.zmH398 is the weighted average of Rob (R is the gas con-
steuit, Ob is the standard deviation in the slope of the
ljaast squares line) for the individual experiments as listed
iri'Table V. A typical graph of the vapor pressure of samar—
iun1 in equilibrium with Smcz is shown in Figure 7. A Z-plot
tnneatment of the data was not performed Since no curvature

vans evident in the Clausius-Clapeyron graph of the vapor

pnxessure and the absence of curvature in the temperature

raruge 1561—20300K may be seen from Figure 7.

75

 

 

 

 

.mmHH quEHHmmxo COHumunHHmu ESHHmEmm .m muomHm
EH Samoa
o.m Em 9m a; H;
H 3 _ _ . . a . _ _ q _ _ _ _ . a
1V.HI

 

D

NmH va
QVH

.0
Ned

.e

 

 

76

 

 

Table IV. Vaporization data for samarium dicarbide

Exp. Sm AHO RO NO. Ran e Md Pt T e

No. 180- (kcaT/ (kcaI/ of a a 9 Temp, CZIl
tOpe gfw) gfw) Pts OK OK

I127 147 55.8 2.4 14 20.11 0.67 1563- 1830 Mo-C
152 58.7 2.5 15 21.03 0.71 2043
154 56.8 3.2 15 20.62 0.89

1134 147 58.3 1.1 21 21.32 0.29 1561- 1796 Mo-C
149 62.2 1.7 22 22.15 0.47 2030
152 57.9 1.1 22 20.73 0.30
154 58.6 1.1 22 21.01 0.30

1141 147 56.8 1.8 15 19.51 0.48 1673- 1871. Mo-C
149 59.4 2.3 14 20.48 0.62 2058
152 57.4 2.5 17 19.54 0.67
154 56.9 2.2 17 19.53 0.61

1143 147 60.2 1.2 23 19.67 0.34 1653- 1839 Mo-C
149 59.0 1.6 20 19.69 0.43 2024
152 58.7 1.2 23 19.08 0.34
154 57.6 1.0 23 19.16 0.27

iIIIDG 147 60.5 3.1 10 21.25 0.85 1627- 1810 Mo—C

148 61.6 3.0 10 21.56 0.82 1992
149 59.3 2.8 10 20.93 0.75
150 60.1 3.2 9 21.10 0.85
152 59.5 3.1 10 20.96 0.85
154 59.1 3.1 10 20.83 0.82

77

Table IV. (Cont.)

 

Sm AHU Rob No. Md Pt
Sgp° Iso- (kcgl/ (kcal/ of a Ca Range Temp, gig:
' tOpe gfw) gfw) Pts 0K 0K

 

fi—

III16 152 59.6 3.0 16 18.29 0.81 1685- 1798 Mo-C

154 56.4 2.9 15 18.85 0.80 1911

11163 WGP 57.0 4.1 10 21.71 1.24 1431- 1646 W
1860

111701 WGP 55.5 1.7 11 20.92 0.51 1542- 1663 W
1784

111702 WGP 59.7 2.3 10 22.00 0.70 1531- 1633 W
1735

 

IEII703 WGP 61.1 4.1 13 21.69 1.25 1577- 1659 W
1741

 

 

Notes: 1. R is gas constant.

2. a, Oa’ are the ordinate intercept and standard devia—
tion of the intercept;_respectively of the Clausius-
Clapeyron least squares equation.

3. WGP means 360 nanosec gate pulse used to sum the

1528m and 154Sm current intensities.

Table

78

V. Summary of samarium dicarbide vaporization data

 

 

 

 

Total AHO Rob AS$ ROa AH398(45) Asggs(45)
Expt. Pts (kcaT/ (kcal/ eu (kcal/gfw)
gfw) gfw) eu eu

1127 44 56.9 2.7 15.7* 1.5 60.8 24.0*

1134 87 59.3 1.2 —— - 63.1 —-

1141 63 57.6 2.2 14.3 1.2 61.6 22.6

1143 89 58.9 1 2 13.5 0.7 62.8 21.9
11106 59 60.0 3.0 -- - 63.9 —-
11116 31 58.0 2.9 -- - 61.8 —-
11163 10 57.0 4.1 12.2 1.2 60.6 20.4
111701 11 55.5 1.7 11.4 0.5 58.9 19.5
:111702 10 59.7 2.3 13.8 0.7 63.3 22.0
:111703 13 61.1 4.1 14.7 1.2 64.7 22.8
IQOtes:

1. *Included for
A8398(45)‘

comparison; not used to Obtain average

2. R.is the gas constant.

3. an

Ga,

are the ordinate intercept,

standard devia-

tions of the intercept and slope, respectively, of the

Clausius-Clapeyron least Squares equation.

79

 

 

5.0-
ln IT s
406 '-

 

 

 

 

4.9 5.2 5.5 5.8 6.1 6.4

104 0."1

T , K
.Firpire 7. Vapor pressure of Sm+ from samarium dicarbide
Experiment 1134.

80
Calculation of AHggs for reaction (45) using the Third
Law method resulted in a value of 66.9 i 1.7 kcal/gfw,
where the uncertainty is the standard deviation among the
values. A compilation of the values used to calculate the
Third Law AHggg is presented in Appendix A. Values of Afef
were interpolated from Table VI; Figure 8 illustrates

Afef y§_T.

6.7.2. Entropy of Reaction

Treatment of the data obtained from six vaporization
experiments resulted in a value of A8298 of 22.1 t 2.3 cal/
deg—gfw for reaction (45). The method employed to obtain
the expressed uncertainty associated with A8298 will be ex—
plained fully since it was not straightforward. The major
source of error is in ‘k, the calibration constant and a
minor contribution is the error in the literature data used
to reduce As; to the 2980 standard state. The following
logic was used to obtain an estimate of the uncertainty in
E. To the ln P y§_%- data (Appendix A), which are shown
in Figure 8a, was assigned the identical value of the lepe

as Obtained from the Second Law analysis. From the known

value of the lepe a value of the standard deviation of the

intercept of the absolute pressure data was calculated using

the variation equations of Youden (98). The total error in
as; using this procedure was found to be 1.8 eu and this
value is the product of the gas constant and the standard

deviation of the intercept. Additional errors arising from

 

fr";

 

81

Table VI. Free energy functions

 

 

Values of -fef in cal/deg-unit shown _Afef
, * for
0 . j
T. K Sm(g) 2C(gr) Sm(l) Ca(l) CaC2(s) Smczéfl Eq(45) v
eu

 

1400 49.279 “8.196 23.58 15.83 30.41 38.16 19.31
1500 49.676 -8.696 24.29 16.35 31.42 39.36 19.01

 

1600 50.053 9.182 24.96 16.84 32.39 40.51 18.73
1700 50.409 9.654 25.60 17.30 33.30 41.60 18.47

1800 50.748 10.110 26.21 17.73 34.17 42.65 18.21

 

1900 51.070 10.552 26.79 18.13 35.00 43.66 17.96
2000 51.376 10.980 27.33 18.50 35.80 44.63 17.73

2100 51.669 11.396 27.86 18.84 36.53 45.55~ 17.52

 

.ReIF. 87 86 88,89 88,89 89,90 88,89,90

 

Notes:

 

1. Equation (45): SmC2(s) > Sm(g) + 2C(gr)

2. fef(SmC2(s)) = fef(CaC2(s))- fef(Ca(l)) + fef(Sm(l))

82

> Sm(g) + 2C(gr)

 

Figure 8. Afef for SmC2(s)

 

 

19.0

 

18:8

—A(fef)
eu

18.6

18.4

18.2

18.0

17.8

17.6

 

 

1 I l l 1 I
1600 1800 T OK 2000 2100

 

 

83

 

.AmvmoEm Hm>o Em

 

 

. B
HIM vOH X.fl
0.5 m.® O.m m.m O.m
_ _ _ 4 L. S _ _ H . a _ . . _ _ _ a .
o l
O
O
o l
O
J
O
& 4
ed 0
o l
omoo
O U 1
O
0 WW
0 l
. a
8
o 0 A30 1
OO
O l
00
o oo 1
O OO
O 1
o
oo
00 1
cm

m opsHomQ¢ .mw owdem

 

 

84

using literature data to Obtain A8898 were estimated to be 0.53
cal/deg/gfw (Cf. Section 8.2).

The least squares intercepts used in equation (20) to
calculate, as; for the various experiments are compiled in
Table IV (p. 76); the respective calibration constants are
found in Table III (p. 73). The values of the entropy of re-
action as obtained from the individual eXperiments are summar—

ized in Table V on page 78.

6.7.3. Formation Energetics

The standard enthalpy and entropy of formation Of SmC2(s)

they be obtained by consideration of the reactions

 

SmC2(s) > Sm(g) + 2C(gr) (45)

 

Sm(s) > Sm(g) (46)
It.:is apparent that subtraction Of equation (45) from (46)

> SmC2(s) (47)

 

gives Sm(s) + 2C(gr)

fen: which the enthalpy of formation of SmC2(s) is obtained as
0 _ 0 0
AH298If(SmC2(S)) - AH298(46) - AH298(45) (43)

'Usjnng the average value obtained from the Second and Third
loam: calculation for reaction (45) and 43298 = 51.03 i 0.24
kcxal/gfw for reaction (46) (from Habermann and Daane (76))
AHggsif(SmC2(s)) = —14.6 t 2.3 kcal/gfw. Similarly the value
(of 1ihe entropy Of formation may be Obtained analogously using

1. (88) as

Asggg(46) '—' 27.1 1 0.5 eu from Hulgren, e;

15298,f(5mc2(s)) = 5.0 1 2.8 eu.

 

85

6.7.4. Standard EntrOpy of SmC2

The standard entropy Of SmC2 is found using the relation

A5398(45) : 5298(5m(9)) + 25398(C(9r)) ‘ 5298(SmC2(5)) (49)

which results in

 

o Is.

S298(SmC2(s)) : 24.4 i 2.9 en. E

Values for 8298(C(gr)) and 8298(Sm(g)) were taken from refer— A
ences (86) and (87) respectively.

6.7.5. The Vapor Pressure as a Function of Temperature '

 

The equilibrium vapor pressure of samarium over SmCz as
a function of temperature over the temperature region of

1431-20580K is

= (—58,600 i 2100)

2.303R log PSm(etm) T

+ (13.70 t 1.8).
(50)
This equation was obtained by taking a weighted mean of the

least squares values of AH and Asg. Thus the values are

t-BO

Obtained for reaction (45): AH2745 = 58.6 i 2.1 kcal/gfw

and 262745 = 13.7 i 1.8 eu. The errors expressed are the

standard deviations.
6.8. Congruency of Vaporization of NdZOZTe

Analysis of the residue remaining in the effusion cell
after vaporization experiments indicates that Nd202Te vapor—
izes incongruently with a loss Of Nd(g) and Te(g) and with
:3 shift in composition toward that of Nd203.‘ The results

of a series of vaporizations from a molybdenum crucible are

86

dumn in Table H-II of Appendix H. These effusion cells

used for the congruency tests were considered free of oc-

cflnded gases when their weight loss at constant temperature

remained invariant. The tungsten cell was observed to be

less reducing than the molybdenum cell since the X-ray
powder diffraction photograph of the residue from a vapori-
zation experiment in which 48% of the sample was vaporized
(0.3142 g sample initially) Showed only lines characteristic

of NdZOZTe. However, using the same cell and at the same

temperature, a vaporization in which 72% of the sample

(0.3198 g initially) was vaporized gave an X-ray pattern
characteristic of Nd203.

6.9. Thermodynamics of Vaporization of NdZOZTe

Reliable thermodynamic data on the vaporization of

Nd202Te was thought to be obtainable if the extent of vapor—

ization were kept sufficiently small such that the composi—

ticni'varied insignificantly from the stoichiometric value.

Witfli this viewpoint in mind three vaporization experiments

werez<conducted in the mass Spectrometer. The data are sum-

marized in Table VII and the individual experimental data

poirnxs are presented in Appendix I. These results indicated

tlme pracies observed in the vaporization upon which quanti-

‘tatiAne calculations are based are the products of several

simultaneous equilibria (Cf. Section 7.2).

 

 

87

 

 

 

 

rllll
HONN 3 h mHmNvaON mm wm.mH ov.MHH ¢VHIOUZ Hm HHH
HONN 3 h mHmNvaON mm mm.ma mw.®oH NvHIOUZ Hm HHH
HONN 3 h meNvaON mm hm.vm mw.mw vealpz Ho HHH
HONN 3 h meNvaom mm mm.mm vm.mw NVHIUZ Hm HHH
VNHN 3 m mvmmlmomfi Ne vm.MH wb.mOH omH.mNHImB mm HHH
VNHN 3 m mvmmlmcmfi NV vo.w m®.®OH «VH.NvHIOUZ mm HHH
vNHN 3 m mvmmlmomfi NV Hm.m mm.wh va.NvHIUZ mm HHH
hmHN 02 OH mmNNIHNON mm mn.w om.mmH vaIOUZ mv HHH
hmHN 02 OH mmNNIHNON NN vw.w om.omH NvHIOUZ mv HHH
bmnm 02 OH mmNNIHNON mm om.m O®.NOH vaIUZ we HHH
hmHN 02 OH mmNNIHNON NN mm.w ow.HHH NVHIUZ mv HHH
& s9 . VHo omnH Azmm A3mm
mm mm .3... 5w ammo when.

HouonHuoomm

mmmE 0:0 cH mpon OHSHkuocoe AHHHV

ESHemoomc mo :OHumNHHomm>

.HH> magma

88

6.10. .Appearance Potentials

The results of the ionization efficiency measurements

are presented in Table VIII. Figures 9 and 10 illustrate

the shape of these curves. Comparison of both the literature

and the corrected appearance potentials of the ion Species
indicates that all the species vaporizing from NdZOZTe (ex-

+ .
cept for 0 whose appearance potential was not measured)

to be primary species.

6.11. Sensitivity of the Spectrometer with Relative Abundance

During the course of this work a comparison was made

of the set of proportionality constants, k, obtained from

two different calibration experiments. The parameter ‘k

is defined by equation (18) and characterized by equation
(34) (_<_2__f_. Sections 3.2.1 and 3.4.2). The term )3 is the

prcmxmrtionality constant between the total samarium vapor

pressure and the IT product where I is the normalized

11X} current i.e., it is the ion current (corrected for back—

grcnuni) of a specific isotopic species divided by the iso—

topfix: abundance of the species. Figure 11 illustrates the

resufiLts obtained. It is apparent that for each curve 'k

decnneases with increasing isotopic abundance of a samarium
spmuzies. Assuming that ionization cross—sections vary neg-
Iligjloly between the samarium isotOpes, the mass spectrometer

(affixziency is seen to be higher for the more abundant iso—

tOpes.

 

89

VIII . Appearance potentials of ions from the vapori-
zation of SmC2 and NdzozTe

 

 

'. . Species V:lii:(:t)tlr:v segsgd Corrected value
eV eV

64 Xe+ 12.12(91), 12.08(94) 10.9 Standard(+1.2)
Nd+ 5.51(91), 6.3(94) 4.7 5.9
Nd0+ 5.7(41) 3.9 5.1
Te+ 9.01(91), 8.96(94) 10.0 11.2

11 66 Xe+ C_:_f_. above 13.4 Standard(—1.3)
Nd+ 93. above 7.1 5.8
1150+ 9;. above 6.8 5.5
N2+ 14.53(91), 15.51(94) 17.1 15.8
320+ 12.59(91), 12.56(94) 14.9 13.6

111 18-1 N: 93:. above 16.6 Standard(-1.1)
Xe+ £2, above 11.6 10.6

111 18-2 112+. 93:. above 10.2 Standard(+4.3)
Sm+ §__f_. above 2.3 6.5

 

 

 

50

90

 

 

 

 

 

 

40 ,Nd+
O
30
o
,_4
(U 0
U
U)
i?
«320
H
4..)
-H
.0
H
m
+.
14
10
0 1 1 1 I l l I; l l L l L 1
0 4 8 12 16 20 24 28
EE,V
Figure 9. Ionization efficiency curves for

Nd

+

, NdO+ and Te+.

+
Xe ,

 

nA

20

15

10

91

 

 

X

.001

Figure 10.

EE,v

and Sm+.

 

. . ' . . +
Ionization eff1c1ency curves for Xe ,

+
N2

 

 

 

92

 

x 10"5

4° ” o Exp . 1162

~ AExp. 1111i

10+~

 

 

 

2 tSm—>1s0 148 149147 154 152
1 1 1 1 J 1 J 1 L 1 1 ~11 1 3! 1 fin
.02 .10 .20 .30
Percentage Isotopic Abundance

 

Iiigure 11. Sensitivity of the multiplier-effects of
abundance and machine parameters.

 

 

93

6.12. Free Energy Function of Reaction for Samarium Dicarbide

Utilization of equation (27) implies that the Afef for
the vaporization reaction of samarium dicarbide is known.
Unfortunately, the high temperature heat capacity of samarium
dicarbide has not been measured. Since samarium dicarbide
has been shown to be alkaline earth in its behavior with
reSpect to the oxidation state of samarium in the compound
(6) and also similar in its hydrolysis products (10), CaC2
was used as a basis for comparison in order to obtain an
estimate of the fef of samarium dicarbide. This value of

fef was Obtained as
fef(SmC2(s)) = fef (CaC2(s)) — fef(Ca(l)) + fef(Sm(l)). (51)

The values Of fef(Ca(l)) and fef(Sm(l)) were chosen to cor-
rect the effect of substitution of a samarium atom for a
calcium atom in the lattice of calcium dicarbide instead of
fef(Ca(s)) and fef(Sm(s)), reSpectively because at the tem-
peratures employed for the vaporization of samarium dicar-
bide the values Of the fef Of both samarium and calcium had
to be Obtained by extrapolation since neither metal exists
as a solid in this range of temperature. It was estimated
that the extrapolation error introduced in the fef of either
metal was less if.extrapolation were made from the liquid
state, rather than the solid state, to the temperature needed.

Since samarium dicarbide was found to vaporize as (Cf. Sec—

tion 6.3)

 

94

 

SmC2(s) > Sm(g) + 2C(gr) (45)

then for this reaction

Afef = fef(Sm(g)) + 2fef(C(gr)) - fef(SmC2(s)) (52)

The sources of fef for the substances in this section are

found referenced in Table VI.

 

‘w. ‘-

CHAPTER VII

DISCUSSION

7.1. Comparison of Samarium Dicarbide with other Lanthanon

Dicarbides

 

To the present date seven lanthanon dicarbides have
been studied and characterized from a thermodynamic view—
point. The thermodynamics of vaporization Of three alkaline
earth dicarbides and of yttrium dicarbide have also been
determined. These prOperties are presented in Table IX,
and compared to the thermal prOperties and vapor pressure of
the corresponding metal. Certain explanations on the struc—
ture of Table IX are necessary. The choice Of 1500°K for
the temperature at which to tabulate the metal vapor pres-
sures was made since at a higher temperature the vapor
pressure of ytterbium rises exceedingly high while at a lower
temperature than 1500°K the metal vapor pressure of lanthanum
becomes extremely small. All thermodynamic quantities listed
were reduced to values at the standard temperature at 2980K
'whenever the values found in the reference literature were
not given at this temperature. This reduction of data to
298°K necessitated using the heat capacity change for the
calcium dicarbide vaporization reaction (Cf. Equation (24))
Since the heat capacity data of none of the compounds in

Table IX has been measured.

95

96

 

 

 

 

 

 

 

.Anmvom + Amvz A Amvmoz "mUOE GOHumuHuomm> prQHMOHQ AN
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97

 

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99

It may be seen from an inspection of Table IX that there
is a correlation between the vapor pressure of the metal
and AH293,V of the corresponding dicarbide--the AH298,V of
the dicarbide is inversely related to the volatility of the
corresponding metal. This is consistent to the conclusion
drawn by Wakefield and Daane (25) in which they state that
the more volatile elements have the less stable lanthanon)
dicarbides. Figure 12 presents this trend of AH398,V of
the dicarbides with metal vapor pressure. The dicarbides
seem to be congregate into either of two groups on the graph.
The group at the lower left portion of the graph is composed
of the dicarbides in which the metals are either known to
be in the +2 oxidation state or in which they have a strong
tendency to be divalent. The remaining group is composed
of metal dicarbides in which the metals exhibit the +3 oxida-
tion state. These two groups Of dicarbides also are dif—
ferentiated by mode of vaporization. Whereas the dicarbides
<of the predominantly +2 metals vaporize giving the gaseous
rnetal and solid carbon the +3 lanthanon dicarbides vaporize
ruyt only in this mode but also vaporize congruently, giving
«gaseous metal dicarbide molecules, at higher temperatures.

The fact that samarium dicarbide falls in the group of
+2 metal dicarbides (in its relation of the samarium vapor
pressure and 4H298,v Of the dicarbide)confirms Vikery's con-
cfihision that samarium is in the +2 oxidation state in the
<iicarbide (6) and is not in the +3 oxidation state as pro-

posed by Jensen and Hoffman (14). This a_posteriori

100

 

9.0h

‘109 P1500(atm) 0f M(S)

L

Gd

J_ 1 l l 1

KO

 

 

 

80

l
o 100
Anzgsiv OfMC2(S)

140

Figure 12. Correlation of AHggB,V(MC2) with log P1500(M).

101
conclusion shows further that the heat capacity of calcium
dicarbide may be used as an approximation for the unknown
heat capacity of samarium dicarbide in order to obtain thermo—
dynamic data at the standard reference temperature (2980K
in this work) from data at temperature.

Using Figure 12 several predictions should be possible
on the values of AHggslv for the lanthanon dicarbides which
have not yet been thermodynamically studied. Using the
values of the metal vapor pressures the predicted values of
AH398,V for the lanthanon dicarbides whose thermodynamic

rxroperties have not been characterized are given in Table X.

0
1%flole X. Predicted values of AH298’V for MC2(S)

 

 

Metal -109 P1500(M) ~ I AH(2)98,v(MCz)
(P, atm) (kcal/gfw)
Ce 8.11 (88) 125
Lu 8.08 (76) 125
Tb 6.98 (76) 103
Pr 6.24 (88) 88
Er 5.19 (76) 67

 

'The usual difficulty encountered in pressure calibra-
'ticu1 (uncertainty in the values of the ionization cross-
seuctjxans) may be overcome using a calibration procedure em-
Exloydnng the same Species to be calibrated if the vapor pres—
suane (of this species is known as a function of temperature.

TTuis Exrocedure is relatively straightforward for most metals.

102

Problems are met, however, when the Species is a complex

molecule. If another compound whose pressure—temperature

curve has been determined, is known this substance may be
used in a procedure analogous to that described previously

to calibrate the mass Spectrometer. This general technique

has the disadvantage that one must assume no sensitivity
changes occur in the instrument providing all machine para-

meters are duplicated exactly in both the calibration and

the vaporization experiment. What is needed is an lg situ

[grocedure in which the sensitivity of the mass Spectrometer
is measured just prior to and immediately after the vapori-

zuation experiment. In a T.O.F. mass spectrometer the addi-

tirni of a movable Faraday cup immediately before the elec-
trcni multiplier would measure the sensitivity Of this com-
The measurement of the partial pressure of a

ponent.

.parflzicular Species in the ion source would result in a known

seruaitivity for the ionization process performed using a

unjryie set of machine parameters. Effectively, a detector

is rueeded which is sensitive to specific vapor Species or
scmua phenomena or property characteristic Of the Species.
.Another technique which may overcome some calibration

prcflilems is the use of a double (or multiple) chamber Knud-

serieeffusion cell (108). Using this cell with the cali-

lxratjnng substance (whose vapor pressure is known as a func-
t:ion.<3f temperature) in one compartment will result in a
reference point possible at every temperature. Ideally it

would be desirable to calibrate the sensitivity of the mass

,103

spectrometer with the same species that one wishes to measure

the pressure- This may be accomplished by using an isotopically

enriched compound or metal. For illustration consider the

case of a hypothetical compound having two isotopes Ay

Ay+n The compound AB (the isotopic distribution of

and
A is natural) is placed in one chamber and in the other

chamber is placed the.metal (or compound) A which is en—

riched in Ay. For the case of dissociative vaporization of

AB, the Spectrum in the mass region Of A will consist of

the sums of the species from A (enriched in Ay) and from

AB. The fractional contribution of the standard metal A

to the Ay peak may be determined from a comparison of the

. + .
Observed abundance ratios of Ay to Ay n in the Spectrum

and the natural abundance ratios. Thus a known intensity

rnay be attributed as originating from A and the remainder

‘tO AB. In this way the intensity—temperature data of AA

HEQ/ be used in conjunction with the known vapor pressure of

A. 'to calibrate the sensitivity of the mass spectrometer for

e\mary experimental point. Of course, this procedure would

(norrxact completely any machine sensitivity fluctuations which

rnay (occur from one eXperimental point to another. One weak

Iooixrt of this technique is that the volatility of the metal
nuist; not be significantly higher than that of AB.

.A comparison of the results obtained by other workers
(11)5,2106,107) with those obtained in the present work is pre-

sented in Table XI. From the table the value of as; and AH;

are directly given in column two for which T is the midpoint

104

 

 

 

Table XI. The vapor pressure of the samarium dicarbide sys—
tem
Ref. 2.303 R 10g P(atm) Range 0K P1600 X 105 P1700 X 105
atm atm
105 18.5-65,200/T 1300-2051 1.51 5.01
106 15.5-61,500/T 1400-2000 1.00 3.05
107 16.5-63,300/T 1400-2080 .871 3.89

 

Present Work

1127 15.7-56.900/T 1563-2043 2.76 13.5

1141 14.3—57,600/T 1673-2058 . 1.82 5.50
1143 13.5-58,900/T 1653-2024 .813 2.46
11163 12.2-57,000/1 1431-1860 .776 2.09
111701. 11.4-55,500/1 1542-1784 .813 2.34
111702 13.8-59,700/1 1531-1735 .725 2.19
:r11703 14.7-61,100/T 1577—1741 .741 2.24

 

_105

value of the temperature range given in column three. Also

pressures at 1600°K and 1700°K are shown for comparison.
Of the experiments performed in this work experiment

II27 was the only one calibrated using silver metal to ob-

tain absolute pressures. InSpection of the pressures listed

shows that the pressures obtained in 1127 are from a factor
of 2 to 6 higher than the others. That the pressure given
by this calibration procedure is not in agreement with the
other pressures is not surprising if the inherent errors
of the calibration procedure using silver metal (ratio of

ionization cross-section of silver to samarium, multiplier

efficiency differences, etc.) are considered. Experiments

III63, 111701, 111702, and 111703 were calibrated by the
‘weight loss method using SmCz and show good internal consis-
tency; Experiments II41 and I143 were calibrated using the
lneasured vapor pressure of samarium metal in which the tem—
;xarature and ion current intensity were monitored and the
atmuolute pressure was found from the literature as a function
cxf temperature. This procedure is eXplained in detail in

Secfiaion 3.4. The experimental temperatures were of the or-
der'cof 8000 and some difficulty was encountered in measuring
time temperature of the orifice since the design of the heat—
irm; system of the spectrometer caused the orifice to appear
darfloer than the surrounding surface of the effusion cell
due: to reflected radiation from the heating filament.

The extent of agreement between the predicted pressures

as (given by the references in Table XI and the present work

106
are fairly good considering the different methods of esti—

mating absolute pressures from the mass Spectrometric in-

tensity data employed. The technique of target collection

used by Faircloth, g£__l, (107) is generally recognized as

being a more precise method of measuring absolute partial

pressures and it would seem that of the three reports in

the literature this is the most accurate. The pressures

given by runs 11163, 111701, 111702 and 111703, which were

calibrated by a weight loss method of SmCz agree most closely

with those of Faircloth, g£.al. (107). The higher values

of 1141 may result from temperature measurement errors.

7.2. Evaluation and Conclusions on the Vaporization of

Neodymium(III) Monotelluro Oxide

The vaporization mode occurring for NdZOZTe is not a

sinqile process. The facts upon which this conclusion is

basmxi are (1) the vaporization products are Nd(g), NdO(g),
Te(gy), O(g) and Nd203(s), and (2) the ratio of partial
prenssures of NdO(g) to Nd(g) is temperature dependent,
Charmaing from less than unity to greater than unity at about

21500K.
.All of these observations are consistent with the hypo-

theusis that several simultaneous equilibria are occurring in

tflne xlaporization of NdZOZTe. The probable reactions are

Nd202Te(S) ‘a’ g'Nd203(S) + g'Nd(g) + Te(g) (53)

Nd202Te(S) + 0(g) ——> Nd203(s) + Te(g) (54)

107

Nd203(s) —> 2NdO(g) + 0(9) (55)
NdZOZTe(s) -——> 2NdO(g) + Te(g) (56)
Reaction (53) is postulated to predominate at lower tempera—
tures while reactions (55) and (56) would become more favor-
able at higher temperatures. The fact that some O(g) coming
from reaction (55) might react with NdzozTe(s) is accounted
for by the side reaction (54). Also since Nd(g) and NdO(g)

result from different processes a different lepe would be

expected in the respective Clausius-Clapeyron log 1T 13 l/T

plots.

To show the plausibility of the above reactions and
also to demonstrate that reactions (55) and (56) are favored
over reaction (53) at higher temperatures, the values of
the equilibrium constants for all three reactions were cal-
culated at 1800, 2000, and 22000K. The method used was
based on the equation

0
AH298

T

 

- R in K = Afef +

‘whirfli is obtained from the definition of Afef for a reaction

auui the equation AG; = -RT In K. The fef of NdZOZTe(s)

was approximated as

fef(NdZOZTe(s)) = fef(NdzO3(s)) - fef(O(g)) + fef(Te(g))
anui the standard enthalpy of formation as

o _ 0 0 o
Asts(Nd202Te(S)) - AH298(Nd203(S)) + AH298(Te(g)) " AH:293(0(9))-

A.cxmnpilation of the thermodynamic quantities, the sources
of’xneference and the calculated values of the equilibrium con-

stxnrts are given in Appendix I. The results of these

108
calculations show that in going from 1800°K to 2200°K the
equilibrium constant of reaction (53) increases by a factor

of 105-1, reaction (54) stays practically constant--its

equilibrium constant changing by a factor of about 10_°57,

and reactions (55) and (56) increase by a factor of 103‘6

and 103'3, reSpectively. The magnitude of the changes in

the equilibrium constants of reaction (53) compared to those

of reactions (55) and (56) with increasing temperature sup-

porfiithe prOposed hypothesis, 'Furthermore, the calculation

supports the observed experimental fact that the ratio

(IT)NdO . .
CPI) does invert from less than unity at lower tempera-
Nd

ture tc>greater than unity at higher temperatures. It should

be nmnrtioned that the substitution of the ratios of the IT
pnxxhict in lieu of partial pressures is a valid approxima-
tfixni since according to Panish (46) the ionization cross-

sectirnns of Nd(g) and NdO(g) are approximately the same.

'The postulate that reaction (55) is the favored reac-

tjxxi at higher temperature is supported by the work of

Vflmite, t _l, (101) who show that at 2215°K the vaporization

pnxxhicts of this reaction have low but detectable pressures

(for'rnass spectrometric studies)-—the partial pressures of

NdO(g) and 0(9) being 4.951 x 10"6 and 7.900 x 10‘7 atmosheres,

respmurtively. These pressures are consistent with ascribing

the ()(g) as coming from reaction (55) since the measurement
that;()(g) was coming from the effusion cell was performed

at atxmit 2300°K, a temperature at which reaction (55) has

a pa1fi:ial pressure of O(g) of 1.35 x 10”6 atmospheres (101).

CHAPTER VIII
ERROR ANALYSIS

8.1. General Discussion of Errors in High TemperatureMass

Spectrometric Measurements

 

If a set of eXperiments, each containing many (>10)
measured points, are performed independentaly and their
average value is used as a measure of the "true" value,
this "true" value will have associated with. it an uncer—
tainty which will reflect the random statistical fluctua-
tion in each experiment as well as the inter—experimental
errors. The intra—experimental error may arise from various
uncontrollable factors such as electronic fluctuations in
the ion source, electron multiplier or read-out apparatus
(analogues, recorder) and from systematic errors such as
a slowly drifting electron energy or trap current, or a
growing metal coating on the Optical window. Systematic
errors may be found in the individual experiments and these
errors are either eliminated in succeeding measurements or
their effect is removed by appropriate correction. The re-
maining uncertainty is commonly estimated by either of two
quantities: (a) an average deviation from the mean or (b)

the standard deviation from the mean. In this work the

"unbiased" form of the equation used to calculate the stand-

ard deviation was

109

1 <57)

where o is the standard deviation, Xi is the observed

experimental value, X' is the average value of the Xi's,

and n is the number of points in the experiment. The
divisor (n — 1) in equation (57) represents the number of
degrees of freedom in the set and ensures that the estimate
made of the standard deviation using this equation (on small
sets) will have the same value as that obtained from an
experiment with a very large number of measurements.

The other error associated with an average experimental
valiua obtained from combining a series of experiments is
the Lnacertainty (or amount of difference) between experiments.
:rt is likely that this latter type contributes to the un-
cerfiuainty in the average value of Asg since it arises from

time calibration procedure which assumes identical machine

parinneters between experiments. The net effect of this

intxxr—eXperimental error should be a noticeably larger range
(or':apread) in the values of As; than in AHg. For example,
the2<data for SmCz contained in Table V show a 15% variation
between the lowest and highest value of As; (based on the
average value of As; in the set) whereas the same measure
of the range in AH; is 9.6%.

,Another consideration in the analysis of data is sys—
The absence of such an error may be shown

tematic errors .

.in 21 set of data which is fitted statistically to a straight

 

111

line by thexuethod of least squares if all (or most) of the
experimental points lie within 1: where C is the uncer:
tainty along either the ordinate or abscissa about the least
squares line. The magnitude of C is obtained from the
combined errors in the experimental measurements and hence
the errors produced in AH; should be totally accountable

by the statistical fluctuations or inherent limitations of
the measurements of temperature and the current ion intensity
of the particular isotope. The reproducibility with which
temperature may be measured using an optical pyrometer in
the range of 1500-20000 is dependent, to a large measure.

on the observer's experience but has been quoted to be of
the order of :20 (102). Since each temperature measurement
‘was made in triplicate and the average value used, an un-
certainty in the measured temperature was judged to be with—
in :50. The uncertainty in the calibration of the pyrometer
tx: the 1948 International Temperature Scale (gf. Appendix D)
is (pioted to be 14° for the experimental temperature range
The quantitative reproducibility of the mass Spec?

used.

trxxneter in measuring the ion current is quoted to be

(2-5% (103).

The contribution to the error in the ordinate made by

time estimated uncertainty of 19° in the temperature is the

displacement of A 1/T along the abscissa.
.For an actual calculation a random selected point from

thez<iata for Sm-152 of experiment 1134 is chosen. This

pchrt has a temperature of 1801°K and an ion current intensity

 

 

112
of 0.0501 nanoamperes. The error contribution of :90K at
1801°K on the abscissa of a 1n 1T y§_1/T graph (cf. Figure
13) is calculated to be 10.0555 x 10.4 The relation be-

tween the uncertainty in the abscissa and the ordinate is

Ay = Ax - slope

where Ay and Ax are the uncertainties in ln IT and

l/T reSpectively. From the least squares computer program
Cli- Appendix E) experiment 1134 has the slope of

—2.91 x 104. Hence the error in in IT is calculated to be
10.30. Examination of Figure 13 reveals that in the vi-
cinity of 104/T = 5.55 (temperature of 1801°K) most of
the points do fall within this error interval about the
calculated least squares pressure line, and hence it is con-
cluded that the error in the experimental data is free of
errors not reducible to statistical fluctuations in the
experimental design.

It should be mentioned that certain types of systematic
errors such as having a pyrometer calibration in error by a
constant number of degrees will not be revealed by the
previcms analysis. This type of possible error, however,
is checked for by the following method. It is generally
the practice in high temperature thermodynamic studies to
compare "Second Law" and "Third Law" heats of vaporization.
The agreement of the two methods coupled with an examination
of the individual values of the enthalpy obtained by the

Third Law method is indicative that there are no systematic

 

113

 

6.0

 

 

 

 

4.0
ln IT
3.0
" 1
A
- Ho
1801
2.0” K
I 4 l I l [I I I l l l 1 l l 1 L
4.9 5.5 6.0 6.5

1 -1

Ex 104, OK

Figure 13. Analysis of error in Sm—152 of Experiment 1134.

114

errors because of temperature measurement, vapor pressure
measurement or in the tabular free energy functions used
to compute the Third Law enthalpy. A critical statistical
evaluation of the random errors and other approximations
inherent in the estimation of Second and Third Law enthalpies
of sublimation are given by Horton (104) whose conclusions
may be paraphrased as:
(1) The better precision usually noted in Third Law
heats as compared to Second Law heats is a consequence due
to the difference between the two estimators of the precision;
(2) The Second Law heat is generally biased in its

calculation;

(3) The Third Law heat is not the minimum variance
unbiased estimator of the heat:

(4) The standard deviation obtained from a least
squares fitting consistently overestimates the true standard
deviation.

These conclusions are not of great practical importance,
however, since the magnitude of the effects of the dis-
crepencies is very small. Thus for the Third Law enthalpy
of tungsten the difference between the usual method of cal—
culation and the minimum-variance estimator is calculated
to be 17 calories per gram—atom or 0.008%, a difference too
small t£>be of significance. EXperimentally it was found
that there is agreement between the Second and Third Law
enthalpdes of vaporization of SmC2 (although this may be
fortuitrms) and also no observable trend of the Third Law

enthalpw'with temperature was observed (Cf. Appendix A).

115

8.2. Error in the Enthalpy and Entropy of Vaporization of

Samarium Dicarbide.

The total uncertainty in the standard enthalpy of vapor—
ization of SmC2 may be considered to arise from the statis-
tical fluctuations inherent in the measurement technique
and from the errors associated with the literature values
of the quantities necessary to reduce the enthalpy to a
standard temperature. Table IV contains the enthalpy of
vaporization as well as the associated error for the various
experiments. The following equation, which is a variation

of equation (24), was used to obtain the Second Law enthalpy

at 2980K

AH393 = AHg '[(H¥ ' H398)Ca(g)+'2(Hg‘3298)C(9r)“(H;'ngs)CaC2(S)]

(24a).
The sources used and the errors associated with each quan-
tity of equation (24a) are given in Table XII. Combining
the individual error contributions, the sum of the errors
111 (H% - H398) at 1900°K for vaporization of one mole of
CaC2(s) is found to be 503 calories. The statistical un-
certainty in the average value of AHggs is 2.11 kcal/gfw.
Tfinarefore the value of the Second Law enthalpy and its total
associated uncertainty for the vaporization of SmCz is
4H3” = 64.2 i 2.6 kcal/gfw. Similarly, the error associ-
ated with the literature values used to compute 03398 of
varxxrization for Smcz results to be 0.53 cal/deg/gfw. This
erinor, combined with the statistical variation in the aver—

agEE‘value (1.8 eu), results in a A8298 for the vaporization

(if SmCZ of 22.1 i 2.3 eu.

116

Table XII. Uncertainty in calcium dicarbide vaporization
quantities for T = 1900°K

 

 

Species Uncertainty in (Hg-H298) Uncertainty in (ea—8398)

CaC2(s) 0.1%;::29 cal/mole 0.1%;':0.034 cal/mole/deg
Ca(g) 0.1%; i 8 cal/mole 0.1%; 10.009 cal/mole/deg
C(gr) 3.0%; 1238 cal/mole 3.0%; 10.243 cal/mole/deg

 

Data taken from Kelley (89).

8.3. Error in Other Thermodynamic Values

The uncertainty associated with the enthalpy (entrOpy)
of formation of SmCz may be determined by inspection of the
errors in the quantities of equation (48) (and an analogous
one for the entropy). The enthalpy and entropy of sublima-
tion of samarium at the reference temperature of 2980K are
given as 48.59 i 0.22 kcal/gfw by Habermann and Daane (80)

l. (88), respectively.

and 27.11 i 0.50 eu by Hultgren, 23
Combining the errors of the quantities in equation (48)
results in a standard enthalpy of formation for SmC2(s) of
—14.6 i 2.8 kcal/gfw. The standard entropy of formation for
SmC2(s) and its total calculated uncertainty is 5.0 i 2.8 eu.
The error associated with 3393(SmC2(s)) may be deter-
Inined by combining the errors of the absolute entropies
found in equation (49). The absolute entropy of samarium
gas is given by Kelley and King (90) as 43.75 i 0.01 eu and
that of 2 gram-atoms of graphite is 2.71 i 0.04 eu (90).

Combining these values results in 8398(SmC2(s)) = 24.1 i 2.9 eu.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

REFERENCES

Thermodynamics, Vol. 1, International Atomic Energy
Agency, Vienna, 1966, p. 245.

 

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26.

27.

28.

29.

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31.

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W}

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H.

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G. Inghram, J. Drowart, "Mass Spectrometry Applied to

 

 

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Translated into English by the American Institute
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546 (1956).

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Impact Phenomena, Oxford University Press, Oxford,
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L. COOper, G. A. Pressley, Jr., F. E. Stafford, J.
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D. Cater, R. J. Thorn, J. Chem. Phys., 44, 1342 (1966).

Colin, P. Goldfinger, M. Jeunehomme, Nature, 187,
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121

C. E. Habermann, A. H. Daane, J. Chem. Phys., _1, 2188
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M. G. Inghram, W. A. Chupka, R. F. Porter, ibid., 23,
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W. C. Wiley, 1. H. McLaren, Rev. Sci. 1nstr., 26, 1150
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Instruction Manual for Models 1003 and 1005 (Basic
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E. G. Rauh, R. C. Sadler, R. J. Thorn, Argonne National
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R. A. Kent, Ph.D. Dissertation, Michigan State University,
1963.

 

A. D. Butherus, Ph.D. Dissertation, Michigan State
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R. E. Vogel, C. E. Kempter, Los Alamos Scientific
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1130 (1961). Re-written for the CBC 3600 computer

by H. A. Eick, 1967.

E. G. Rauh, Argonne National Laboratory, Private Com—
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O. H. Krikorian, University of California Radiation
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JANAF Thermochemical Tables, The Dow Chemical Company
Midland, Michigan, 1963

R. C. Feber, C. C. Herrick, Los Alamos Scientific
Laboratory Report LA-3184 (1965).

R. Hultgren, R. L. Orr, P. D. Anderson, K. K. Kelley,
Selected Values of Thermodynamic Properties of Metals
and Alloys, John Wiley and Sons, Inc., 1963.

 

:K. K. Kelley, Contributions to the Data on Theoretical
Metallurgy XID; Bureau of Mines Bulletin 584, 1960.

 

I<. K. Kelley, E. G. King, Contributions to the Data on
Theoretical Metallprgy XIV, Bureau of Mines Bulletin
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Iz.‘W. Kiser, Introduction to Mass Spectrometpy and Its
Applications, Prentice-Hall, Inc., Englewood Cliffs,
N. J., 1965.

 

92.

93.

94.

95.

96.

97.

98.

99.

100.

101.

102.

103.

104.

105.

106.

107.

108.

F.

122

E. Grubbs, Ann. Math. Stat., 1, 27 (1950).

W. R. Savage, D. E. Hudson, F. H. Spedding, J. Chem.

PhYSoI lg: 211 (1959).

Handbook of Chemistry and Physics, 45th Edition, Chemical

Rubber Publishing Co., Clevélgnd, Ohio, 1964-65.

Physiochemical Measurements at High Temperatures, J.

H.

P.

D.

C.

W3

D.

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O'M. Bockris, ed., Chapter 2, Butterworths Scientific
Publications, London, 1959.

F. Avery, J. Cuthbert, N. J. D. Prosser, C. Silk,
J. Sci. Instr., 43, 436 (1966).

. R. Stull, G. C. Sinke, Thermodynamic Properties of

the Elements, American Chemical Society, Washington,
D.C., 1956

 

J. Youden, Statistical Methods for Chemists, John
Wiley and Sons, Inc., New York, 1951.

H. Spedding, J. J. Hanak, A. H. Daane, Trans. AIME
212, 379 (1958).

A. Eick, J. M. Haschke, P. A. Pilato, Paper presented
at the Thermodynamics Symposium, International Union
of Pure and Applied Chemistry, Heidelberg, Germany.
Sept. 12-14, 1967.

N. Walsh, H. W. Goldstein, D. White, J. Am. Ceram.
Soc., 43, 229 (1960).

R. Lovejoy, Can. J. Phys., _6, 1397 (1958).

N. Reilley, Advances in Analytical Chemistry and
Instrumentation, Vol. 4, page 371, John Wiley and
Sons, Inc., New York, 1964.

S. Horton, J. Research of NBS, 70A, 533 (1966).

F. Avery, J. Cuthbert, C. Silk, Brit. J. Appl. Phys.,
_1_§. 1133 (1967) .

Cuthbert, R. L. Faircloth, R. H. Flowers and F. C. W.
Pummery, Proc. Brit. Ceram. Soc., 8, June (1967).

L. Faircloth, R. H. Flowers, F. C. W. Pummery, Atomic
Energy Research Establishment Report AERE-R5480,
jHarwell, England (1967).

‘V. Hackworth, Ph.D. Dissertation, University of
Cincinnati, 1967.

 

123
109. Chem. Eng. News, 39, No. 47 (1961).

110. H. W. Goldstein, E. F. Neilson, P. N. Walsh, D. White,
J. Phys. Chem., §§, 1445 (1959).

111. C. E. Wicks, F. E. Block, Thermodynamic Properties of
65 Elements - Their Oxides, Halides, Carbides and
Nitrides, Bureau of Mines Bulletin 605, 1963.

 

 

 

 

APPENDICES

124

APPENDIX A

Third Law AHggs: SmC2(s) ——> Sm(g) + 2C(gr)

The values of AHggs contained in this table were based on

a calculation using the fef of CaC2(s) (corrected for the ef—

fect of substitution of a samarium atom for calcium in the

lattice) as was described in Section 6.12. The numbers "2-4"

under the heading "Isotope" mean that the intensity measured

was the sum of Sm-152 and Sm—154 intensities. This addition

was effected using a 360 nsec wide gate pulse obtained with
a PIC #841 pulse transformer in lieu of the PIC #811 (~60 nsec
‘wide) component in the gate pulse circuit of the analogues.
WAve" under the "Isotope” column means that the average total

ithensity (as obtained by the average of the normalized iso-

topdx: ion currents measured) was used. A graph of ln P.y§

lwfir of this data is presented in Figure 8a on page 83.

125

 

126

 

Iso- ~Afef AH 104
Expt. tope T.OK 1n 1T -ln k e.u. kcgis -fif— -ln P
gfw
11163 2-4 1431 2.304 15.56 20.15 . 66.19 6.988 13.26
11163 2-4 1519 2.398 15.56 18.96 68.51 6.583 13.16
111702 2-4 1532 2 .409 15 .04 18 .92 67 .43 65 .27 12 .63
111701 2-4 1542 2.813 15.21 18.89 67.12 6.485 13.40
11163 2—4 1546 2.687 15.56 18.88 68.75 6.468 12.87
111702 2-4 1556 2 .795 15.04 18.432 67.39 6.427 12.25
11163 2-4 1575 3.499 15.56 18.80 67.35 6.349 12.06
111703 2-4 1577 2.421 14.30 18.80 66.87 6.341 11.88
III701 2-4 1582 3.315 15.21 18.78 67.10 6.321 11.90
111702 2-4 1595 3.074 15.04 18.74 67.81 6.270 11.97
III701 2-4 1607 3.460 15.21 18.71 67.59 6.222 11.75
111703 2-4 1614 2 .548 14.30 18.70 67.87 6.196 11.75
III702' 2-4 1616 3.299 15.04 18.69 67.89 6.188 11.74
III702 2-4 1631 3.575 15.04 18.81 67.84 6.131 11.47
111701 2-4 1634 3.763 15.21 18.64 67.62 6.120 11.45
III703 2-4 1634 2.767 14.30 19.42 67.90 6.120 11.53
11163 2-4 1634 4.080 15.56 18.64 67.72 6.120 11.48
1141 ave 1639 1.874 12.65 18.63 65.64 6.101 10.78
111701 2-4 1645 3.973 15.21 18.45 67 75 6.079 11.24
111703 2-4 .1648 3.057 14.30 18.60 67.49 6.068 11.24
1143 ave 1648 1.431 12.59 18.60 67.20 6.068 11.16
III703 2-4 1650 2.960 14.30 18.60 ‘67.89 6.061 11.34
1143 ave 1653 1 .479 12 .65 18 .59 67 .43 6 .050 11 .17
111703 2-4 1653 2.954 14.30 18.59 68.02 6.050 11.35
111703 2-4 1653 2.974 14.30 18.59 67.96 6.050 11.33
1141 ave 1673 2.331 12.59 18.54 65.13 5.977 10.26
11 1703 2-4 1678 3.212 14.30 18.53 68.06 5.959 11.09
111702 2—4 1679 4.091 15.04 18.52 67 .62 5.956 10.95
111701 2-4 1688 4.376 15.21 18.50 67.57 5.924 10.83
11 I703 2-4 1698 3.594 14.30 18.73 67.94 5.889 10.71
1143 ave 1698 1 .893 12 .65 18 .47 67 .67 ’ 5 .889 10 .76
II 163 2-4 1700 4 .954 15 .56 18 .47 67 .22 5 .882 10 .61
III702 2-4 1701 4.411 15.04 18.47 67.32 5.879 10.63
1143 ave 1710 1.885 12.65 18.44 68.11 5.848 10.77
2111702 2-4 1714 4.321 15.04 18.43 68.08 5.834 10.72
111703 2-4 1715 3.867 14.30 18.43 67.17 5.831 10.43
111702 2-4 1720 4.575 15.04 18 .42 67.42 5.814 10.47
111701 2-4 1721 4.765 15.21 18.41 67.42 5.811 10.45
111703 2-4 1722 2.890 14.30 18.41 67.34 5.807 10.41
1141 ave 1726 2.833 12.59 18.40 65.23 5.794 9.76
111702 2-4 1735 4.780 15.04 18.38 67.25 5.764 10.26
1143 ave 1737 2 .307 12 .59 18 .37 67 .40 5 .757 10 .28
1143 . ave 1739 2 .439 12 .59 18 .37 67 .03 5 .750 10 . 15
111703 2-4 1741 4.046 14.30 18.36 67.45 5.744 10.25
111701 2-4 1747 5.031 15.21 18.34 67.41) 5.724 10.18
111701 2-4 1747 4.991 15.21 18.34 67.54 5.724 10.22
13143 ave 1758 2.579 12.59 18.32 67232 5.688 10.01
1141 ave 1760 3.186 12.59 18.31 65.11 5.682 9.40
1143 ave 1776 2.695 12.59 18.27 67.33 5.631 9.90
IJB43 ave 1781 2.659 12.59 18.26 67.66 5.615 9.93

 

127

 

 

Iso- -Afef AH 104
Expt. tOpe T,°K ln It -ln k e.u. keg? -—,f——- —ln P
gfw
11163 2-4 1781 5.577 15.56 18.26 67.85 5.615 9.98
11163 2—4 1783 5.695 15.56 18.25 67.50 5.609 9.87
111701 2-4 1784 5.122 15.21 18.25 68.33 5.605 10.09
1141 ave 1789 3.642 12.59 18.24 64.18 5.590 8.95
1143 ave 1807 2.968 12.59 18.19 67.40 5.534 9.62
1141 ave 1812 3.944 12.59 18.18 64.07 5.519 9.65
11163 2-4 1815 6.089 15.56 18.17 67.15 5.510 9.47
1143 ave 1817 3.179 12.59 18.17 66.99 5.504 9.41
1141 ave 1836 4.172 12.59 18.12 63.97 5.447 8.42
1143 ave 1840 3.237 12.59 18.11 67.53 5.435 9.35
1143 ave 1852 3.389 12.59 18.08 67.33 5.400 9.20
1141 ave 1859 4.421 12.59 18.06 63.76 5.379 8.17
11163 2-4 1860 6.338 15.56 18.06 67.67 5.376 9.22
1143 ave 1876 3.530 12.59 18.02 67.57 5.330 9.06
1141 ave 1886 4.555 12.59 18.00 64.06 5.302 8.04
1143 ave 1916 3.920 12.59 17.93 67.34 5.219 8.67
1143 ave 1922 3.902 12.59 17.91 67.60 5.203 8.69
1141 ave 1932 4.829 12.59 17.89 64.34 5.176 7.76
1143 ave 1932 4.263 12.59 17.89 66.52 5.176 8.33
1143 ave 1941 4062 12.59 17.87 67.58 5.152 8.53
1141 ave 1949 4.923 12.59 17.85 64.48 5.131 7.67
1143 ave 1963 4.394 12.59 17.81 66.94 5.094 8.20
1143 ave 1971 4.426 12.59 17.80 67.04 5.074 8.16
1141 ave 1971 5.154 12.59 17.79 64.30 5.074 7.44
1141. ave 1988 5.202 12.59 17.76 64.47 5.030 7.39
1143 ave 2024 4.717 12.59 17.68 67.45 4.941 7.87
1141. ave 2025 5.397 12.59 17.67 64.74 4.938 7.19
1141. ave 2045 5.310 12.59 17.63 65.42 4.890 7.28
1141. ave 2047 5.402 12.59 17.60 65.40 4.885 7.19

 

APPENDIX B
The Mass Spectrometric Vaporization of Copper

As a check on the reliability of obtaining absolute pres-
sures a sample of c0pper was vaporized in the mass spectrometer
and its pressure was measured as a function of temperature.
Both copper isotopes were used to obtain log IT y§y% graphs.
The value of k for copper was obtained from that measured
for silver by using the ionization cross-sections of Mann(68)
in equation (39) and had a value of 3.14 x 10"6 atmOSpheres

deg 1 nanoampere-l. The results obtained are presented in

0
'Table B—1, in which A81747 was obtained using equation (20).

'Table B—1. Copper vaporization.

 

 

szotope AH3747 0* a** —1n k A52747
kcal e.u.
9:?t

CHI—63 78.9 1.8 27.8 12.7 30.0

Chi—65 75.9 1.8 26.9 12.7 28.2

 

*
o is the standard deviation in the least squares slope.

**te is the intercept of the least squares line.
0
Using Kelley (89), the values of AH2747 and A81747 ob-
tajnued as the average from the two isotopes resulted in
A3398 = 83.3 i 1.8 kcallg-at and A5398 = 34.3 1 1.0 e.u.
(true uncertainties are the standard deviations). Values of

AHng calculated from the Third Law method were obtained

IisiJug'the free energy function of copper from.Hd&gren pp _L.(88)
128

 

129
in equation (27) and are presented in Table B—2. The average
value for AHggs thus obtained (with its standard deviation)
is 78.4 i 1.1 kcallg—at which may be compared to 80.86 kcal[g-at

given by Hultgren and to the mass spectrometric measured values

of 81.88 and 82.39 kcallg—at obtained by Avery §£_§1.(96)
using the Second and Third Law methods, respectively. If the
value of 482656 obtained by Avery, g; _£. (96) for the vapor-

ization of copper is reduced to A8298 using reference (88) a

value of 31.5 e.u. is obtained.

The Third Law AHggs shows a detectible temperature trend.
This decrease of AHggs with increasing temperature may have
been due to an insufficient correction for the lowering of
the observed temperature from a copper coating which developed
on the optical window. Thus, the temperatures used in the
<calculation are probably lower than the "true" temperatures

. 0 .
and.thus resulted in lower AH293 values at higher tempera-

tures.

130

 

 

 

 

Table B—2. Third Law AHggs for copper vaporization.
IsotOpe T, 0K ln IT —Afef AH298
e.u. kcal
gfat
63 1542 1.832 30.37 80.0
65 1542 2.249 30.37 78.8
63 1609 3.355 30.22 78.4
65 1609 3.109 30.22 79.2
63 1715 4.799 30.01 78.3
65 1715 4.694 30.01 78.6
63 1789 5.574 29.86 78.7
65 1789 5.572 29.86 78.7
63 1852 6.454 29.75 78.0
65 1852 6.439 29.75 78.0
63 1881 6.319 29.69 79.6
65 1881 6.218 29.69 80.0
63 1883 6.794 29.69 77.9
65 1883 6.735 29.69 78.1
63 1916 7.133 29.63 77.8
65 1916 7.135 29.63 77.8
63 1953 7.687 29.57 77.1
65 1953 7.7601 29.57 76.1
Notes:
1. Data is experiment 1126.

2.

ln k

for the table is —12.67.

APPENDIX C

Mass Spectometric Vaporization of Samarium

In the course of using samarium as a calibration substance
for the mass spectrometer partial pressures, the energetics
of its vaporization were obtained. In the temperature
range 1145 to 1218°K the current intensities of Sm-152 and
Sm—154 were measured. The average value obtained from the

least squares analysis for the isotOpes gave a Second Law

AH2181 = 47.0 + 1.9 kcallg-at which compares favorably with

Kelley‘s value of 47.7 kcallg-at (89). By plotting P_y§ T

for samarium, where the value of P was taken as a function

of the experimental "true" temperature using the vapor pres-
sure data of Stull and Sinke for samarium (97), the values
of k152 and k154 were obtained from the slopes. Using equa-

'tion (20), and reduction of the ASQ181 by Kelley's data a

[M3298 Cd’24.9 i 1.5 e.u. was obtained as the average value

frcxn the two isotopes, which may be compared to 27.5 i 1.0 e.u.

obtxeined by Kelley and King (90). The Third Law AHggs was

calrnilated using reference (88) for the free energy function

ofFEeamarium and equation (27). The values calculated are

presented in Table C—1, and the average A113“ derived is

48.S3 + 0.6 kcal|g—at (the error is the standard deviation).

_.

TTue total error in 03398 is estimated to be about R0 or

atmnrt 1.3 kcallg-at. A comparison of the AHggs obtained for

time vaporization of samarium may be seen to compare favorably

131

132

with the value of 49.56 measured by Savage pp al. (93).

 

 

 

Table C-l. Experiment III31-The vaporization of samarium
IsotOpe T, 0K 1n 11 -ln k -Afef Anggs
e.u. kcal
g-at

152 1145.0 2.7699 11.116 26.252 49.05
154 1145.0 2.7933 11.120 26.252 49.01
152 1152.6 3.4140 11.116 26.242 47.89
154 1152.6 3.3595 11.120 26.242 48.02
152 1161.5 2.8368 11.116 26.230 49.58
154 1161.5 2.7758 11.120 26.230 49.73
152 1182.5 3.5350 11.116 26.203 48.80
154 1182.5 3.4869 11.120 26.203 48.92
152 1192.2 3.6061 11.116 26.190 49.02
154 1192.2 3.5875 11.120 26.190 49.07
152 1212.0 4.1717 11.116 26.155 48.43
154 1212.0 4.1552 11.120 26.155 48.47
152 1214.4 4.2548 11.116 26.150 48.31
154 1214.4 4.1739 11.120 26.150 48.52
152 1217.5 3.6392 11.116 26.143 49.92
154 1217.5 3.6231 11.120 26.143 49.97
152 1237.2 4.5247 11.116 26.102 48.50
154 1237.2 4.5525 11.120 26.102 48.44

 

APPENDIX D

Temperature Corrections
1. The NBS Calibration Data for L & N Pyrometer #1619073.

Table D-l presents the calibration table for the pyrometer
with its internal tungsten lamp, XY85. The pyrometer was
calibrated on April 19, 1963 and was reported to have the
maximum uncertainty of 14° at 800° to about 13° at 10630

and increasing to about 15° at 28000. "True" temperatures

 

are those based on the 1948 International Temperature Scale.

 

 

 

 

Table D-1. NBS calibration data.
L Range H Rapge XH Range
Actual True Actual True Actual True
800°C 796°C 1100°c 1092°c 1500 1485
850 845 1200 1189 1600 1581
900 893 1300 1289 1700 1678
950 943 1400 1391 1800 1777
1000 994 1500 1494 1900 1876
1050 1045 1600 1598 2000 1977
1100 1097 1700 1702 2200 2183
1150 1149 1750 1753 2400 2390
1200 1201 -- —- 2600 2597
1225 1226 -- -- 2800 2804
2. Transmissivity Correction

A black body radiator emits electromagnetic energy ac-

cording to Plank's Law of Radiation

133

134
C1
= C’
A A5(e 2[7\T_.1)

 

J

where J1 is the rate of energy radiation per unit area, A
is the wavelength and C1, C2 are the first and second radia-
tion constants, respectively. Plank's equation may be con-

siderably simplified at low values of AT to

_ _5 —c2/xT
JA — CIA e

which is known as Wien's equation. Margrave (95) states that
for 1T less than 0.3 cm°K, Wien's equation fits the observed
spectral distribution within 1%. The transmissivity correc-

tion follows from Wien's Law and is given for any material as

1
K ' ' T

Sal“

where K is the transmissivity correction, To is the tem—
‘perature of the object viewed through the material and T
is the true temperature of the object (Cf. Section 3.5 for a

Inore detailed description).

APPENDIX E
Computer Program for Clausius-Clapeyron Plot

The following computer program was used to obtain the
least squares line of 1n IT y§_ l/T. The equations of the
least squares analysis were obtained from Youden (98).

All analyses were performed on a Control Data Corpora-

tion 3600 computer.

135

136

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mm

APPENDIX F

Selected Physical Constants

50
H

1.98726 cal/deg mole
W = 3.14156

1 atm = 1013250 dyne/cm2

Masses: Basis is 12C = 12.000 amu (109)

Sm = 150.35 Ag = 107.870
Nd = 144.24 Te 2 127.60
Cu : 63.54

Isotopic Abundances: Basis is reference (91)
Sm—147 = .1509 Te-128 = .3179
Sm-148 = .1135 Te-13O = .3448
Sm-149 = .1396 Ag-107 = .51817
Sm-150 = .0747 Ag-109 = .48183
Sm-152 = .2655 Cu-63 = .691
Sm-154 = .2243 Cu-65 = .309
Nd-142 = .2711
Nd-144 = .2385

141

APPENDIX G

Second Law Data for SmC2 Vaporization

The following is a compilation of a portion of the
Clausius-Clapeyron data for the vaporization of SmCz. The
remaining part of the data is not tabulated here since it

is presented (in a different form) in Appendix A.

Table G—l. Experiment IIIO6

 

 

 

 

'T,°K - ln IT

Sm-147 Sm-149 Sm-152 Sm-154
1784 4.416 4.376 4.385 4.378
1896 5.448 5.411 5.415 -—
1982 6.059 6.057 6.074 6.064
1627 2.398 2.524 2.428 2.476
1706 3.433 3.366 3.404 3.361
1839 4.689 4.723 4.685 4.667
1932 5.533 5.509 5.374 5.702
1981 5.766 5.786 5.678 5.743
1976 5.639 —- 5.631 5.635
1934 5.321 5.323 5.343 5.281
1992 -- 5.734 -— 5.732

 

142

143

Table G—2. Experiment I134

 

 

 

T 0K In IT

' Sm-147 Sm-149 Sm—152 Sm—154
2030 6.818 5.618 6.342 6.453
1578 2.609 2.211 2.342 2.213
1689 3.952 3.741 3.408 3.500
1766 4.711 4.355 4.151 4.315
1819 5.153 4.605 4.882 4.736
1878 5.846 5.648 5.387 5.482
1937 6.174 5.898 5.767 5.801
1950 6.403 6.302 5.881 6.096
1979 6.307 6.004 5.899 5.927
1981 6.302 6.194 5.832 5.928
1966 6.335 6.181 5.772 5.918
1933 6.355 6.264 5.701 5.785
1898 5.940 5.797 5.531 5.656
1859 —- 5.244 5.116 5.162
1823 5.189 4.977 4.661 4.748
1762 4.730 4.285 4.144 4.236
‘1696 3.988 3.842 3.522 3.633
1627 3.334 2.802 2.689 2.793
1801 5.029 4.849 4.502 4.632
11917 5.966 5.793 5.585 5.639
'1855 5.563 : 5.412 4.998 5.199
L1562 2.519 2.067 2.108 2.241

 

144

 

 

 

Table G-3. EXperiment IIIlG
T,°K 1n IT
Sm-152 Sm-154

1854 3.363 3.329
1873 3.534 3.496
1873 3.682 —-
1887 3.848 3.678
1911 4.100 3.888
1909 4.095 ——
1904 4.068 4.168
1904 -- 3.905
1911 4.208 4.038
1863 3.895 3.747
1844 3.724 3.541
1810 3.417 3.329
1775 3.009 2.984
1740 2.592 2.500
1686 1.919 1.910
1740 2.541 2.474
1685 1.981 2.053

 

APPENDIX H

Congruency Data for Neodymium(III) Monotelluro Oxide

 

 

 

Table H-l. Outgassing Data

72:12:? F727 H2132. 7:27.227
0C (g) (mg) (min.) X 102)

A. Tungsten effusion cell: Initial starting weight: 96.2479g
1—5 2000 96.1637 80.6 1440 5.60

6 2180 96.1528 14.5 * *

7 2200 96.1379 14.9 500 2.98

8 2200 96.1225 15.4 759 2.03

9 2200 96.1126 9.9 500 1.98
10 2200 96.1026 10.0 600 1.67
11 2200 96.0961 6.5 372 1.75
12 2200 96.0881 8.0 556 1.44
13 2200 96.0740 14.1 1107 1.27
14 2200 96.0644 9.6 642 1.33
15 2500 96.0211 43.3 223 19.4
16 2200 96.0164 4.7 327 1.44
17 2200 96.0105 5.9 575 1.03
18 2500 95.9552 55.3 374 14.8
19 2500 95.8422 113.0 * *
20 2500 95.7475 94.7 537 17.6
21 2500 95.6354 112.1 512 21.9
22 2500 95.3875 247.9 1025 24.1

B. Molybdenum effusion cell: Initial weight: 18.3287g

1 2200 27.3850 943.7 292 3.232
2 2200 26.9119 473.1 208 2.275
3 2200 26.2209 691.0 320 2.159
4 2200 24.8521 1368.8 635 2.156

 

«)6
Not available since furnace shut off during run.

145

146

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147

Table H-3. Vaporization of neodymium(III) monotelluro oxide
from tungsten cell

 

 

Initial Time X-Ray
Run Sample Wt. % LOSS A:' T Heated Residue
g. C min.
III28 0.3142 48 2000 120 NdZOZTe
11132 0.3466 >89 2190 60 N826.

III36 0.3722 72 2000 231 N826.

 

APPENDIX I
I. Calculation of Equilibrium Constants

The equilibrium constants of reactions (53),

(54) and

(55) were calculated (Cf. Section 7.2) from the data contained

in Tables I-1 and I-2 and are presented in Table I-3 below.

Table I-1. Free energy functions

 

-(G° - Hg98)/T, cal/mole-deg

 

 

 

 

 

 

T.OK
Nd203 Te 0 NdO Nd NdZOZTe
(s) (9) (9) (g) (9)

1800 63.74 48.47 43.37 68.5 51.18 68.64
2000 67.28 48.93 43.81 69.4 51.77 72.40
2200 70.14 49.35 44.22 70.1 52.31 75.27
Ref. (110) (97) (97) (43) (97) calc‘d
Table I—2. Standard enthalpies of formation

. o Nd203 Te Nao Nd Ndzo’Te
8
PM (g) (s) (g) (g) (g) (53

0

figiea’ 59,550 -432,150 46,500 -36,000 76,800 -419.1
mole
Ref. (97) (111) (97) (43) (97) calc'd

 

148

149

 

 

 

 

 

 

 

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150

 

 

 

 

 

 

 

 

 

II. The Mass Spectrometer Data for Neodymium(III) Monotelluro
Oxide:
Table I-4. Experiment 11146
1n IT (IT)NdO
T'OK Nd-142 Nd-144 142-Nd0 144-Nd0 Te-130 TIT)Nd
2293 5.025 5.036 5.330 5.407 5.938 1.403
2267 4.583 4.603 4.963 4.980 _5.531 1.460
2183 3.568 3.673 3.988 4.014 4.132 1.461
2227 4.398 4.362 4.574 4.650 4.497 1.262
2264 4.464 4.425 4.824 4.897 5.376 1.517
2194 3.891 3.968 4.030 4.067 4.460 1.126
2153 3.024 3.033 3.302 3.360 3.648 1.354
2181 3.393 3.392 3.352 3.422 4.096 0.995
2021 1.721 1.836 1.498 1.444 3.479 0.734
2188 4.005 4.103 4.216 4.296 4.088 1.223
Table I—5. Experiment 11155
0 1n IT (IT)NdO
T' K Nd-iii 122-Nae IT Nd
2333 5.074 5.414 5.760 1.405
2346 4.864 5.254 5.350 1.477
2305 4.696 4.984 4.650 1.333
2222 3.380 3.908 3.243 1.696
2203 2.844 3.779 3.291 2.547
2173 2.551 3.261 2.711 2.034
2085 1.800 2.158 1.690 1.430
2038 1.420 1.477 0.894 1.059
1978 0.721 0.905 -- 1.202

 

151

Table 1-6. Experiment 11161

 

 

 

Nd-142 Nd—144 142-Nd0 144—Nd0 (IT)Nd
2318 2.322 2.432 2.641 2.805 1.416
2293 2.284 2.398 2.449 2.610 1.209
2257 1.984 2.058 2.173 2.323 1.279
2195 1.726 1.753 1.802 1.873 1.104
2166 1.161 1.665 1.520 1.561 0.867
2123 1.171 1.185 0.857 0.884 0.735
2084 0.240 0.207 —0.133 —. 867 0.786