THE pmmnon AND THERMODYNAMICS or“ 1'4 f-{;--‘

EUROPILIM DICARBIDE

TIME“?! ’59 Beam quh. m _ _ ‘

MICHIGAN STATE UNIVERSITY
I Robert E GebeIf
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This is to certify that the

thesis entitled

The Vaporization and Thermodynamics of Europium
Dicarbide

presented by

Robert E. Gebelt

has been accepted towards fulfillment
of the requirements for

Ph. D. degree in Chemistry

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(2/67; 2121f} (1 Z C(‘é

Majoiyprofessor

Date December 17, “lgfih

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THE PREPARATION AND THERMODYNAMICS
OF EUROPIUM DICARBIDE
By

Robert E. Gebelt

A THESIS

Submitted to
Michigan State University

in partial fulfillment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY
Department of Chemistry

1964

ABSTRACT

THE PREPARATION AND THERMDDYNAMICS
OF EUROPIUM DICARBIDE

by Robert E. Gebelt

Europium dicarbide was prepared by the reaction of europium metal
and graphite in a stainless steel bomb. Chemical analysis indicated

an average composition of EuC X-ray powder diffraction

1.87_.i 0.07:

analysis showed the compound to be of body-centered tetragonal symmetry,

space group D17
4h

Co = 6.645 2. Vapor phase chromatographic analysis indicated that

- I4/mmm, with lattice parameters: 30 = 4.045 2;

ninetyfeight per cent of the product of acid hydrolysis of europium
dicarbide was the hydrocarbon, acetylene. hThe analytical data lead

to the conclusion that europium dicarbide resembles the alkaline earth
dicarbides more than the other lanthanon dicarbides.

The vaporization of europium dicarbide over the temperature range
11500 to 16000 K was investigated by the Knudsen effusion method. The
effusate was either collected and analyzed chemically or observed with
a time-of-flight mass spectrometer. The method involving chemical
analysis of the effusate did not yield as precise data as did the method
utilizing the mass spectrometer.

Gaseous europium and europium dicarbide were both found in equilib-
rium with solid europium dicarbide.in concentrations of 99% and 1%
respectively. Instrumental limitations prevented determination of the
concentration of the gaseous dicarbide as a function of temperature.

Calibration of the mass spectrometer with silver permitted the calculation

Robert E. Gebelt
of the pressures corresponding to the observed ion intensities. An
empirical equation, fitted to the data for europium by the method of

least squares, gave:

='.- i ' i
1ne P(atm) ( 23709 715)/T + 9.270 0.886.

By means of the second law of thermodynamics the following values were
found:

For the reaction

E“02(5) “ Eu(g) + 2C(graphite)

AH298 = 51.09 i 1.42 kcal./mole
A3298 = 18.43 i 1.75 e.u.

Values of the free energy function for EuC2(s) were estimated
and combined with published data to yield, for the same reaction, the

following value calculated from the third law of thermodynamics:

AH = 51.22 i 0.80 kcal./mole.

o
298

The enthalpies obtained for the dissociation reaction were combined
with published data on the enthalpy of vaporization of europium to
yield the following value for the standard enthalpy of formation of

EuCZ:

A = -9.17 i 1.15 kca1./mole.

0
H298

ACKNOWLEDGMENTS

The author wishes to express his sincere gratitude to Dr. Harry A.
Eick for his guidance, encouragement and friendship throughout the
course of these investigations.

Appreciation is also extended to my colleagues Dr. Richard A. Kent,
Dr. George D. Sturgeon and Mrs. Rebecca Jacobs for their many helpful
discussions during the course of this study.

Special thanks are due to Mr. Frank Betts of the Chemistry Department
shop for his help in the construction of the mass spectrometer and to
Mr. Norman Fishel who assembled most of the electronic apparatus used
in this study.

A deep sense of gratitude and appreciation is extended to the
author's wife, Judy, whose help and encouragement made this thesis
possible.

Financial support from the Atomic Energy Commission under Contract

AT(11-1)716 is gratefully acknowledged.

ii

TABLE OF CONTENTS

PAGE

I 0 INTRODUCTION 0 O O O O O O O O O 0 O O O O O O O O O O O O O 1

A. Incentives for this Research . . . . . . . . . . . l
B. Previous Investigations of Lanthanon-Carbon

Systems . . . . . . . . . . . . . . . . . . . . . 1

1. Preparations and Properties . . . . . . I

2. Crystal Structure of the Lanthanon
Dicarbides . . . . . . . . . . . . . .
3. Vapor Pressure Studies . . . . . . . . 8
4. Vaporization Studies Utilizing the
Mass Spectrometer . . . . . . . . . . . 10
C. This Research . . . . . . . . . . . . . . . . . . 11

0\

II. THEORETICAL CONSIDERATIONS . . . . . . . . . . . . . . . . . 12

A. General . . . . . . . . . . . . . . . . . . . . . 12
B. Thermodynamic Relationships in Vaporization . . . 13
C. The Knudsen Effusion Method . . . . . . . . . . . 16
l. Mathematic Relationships . . . . . . . . 16
2. Practical Requirements . . . . . . .-. . 18
D. The Mass Spectrometric Method . . . . . . . . . . 20

III 0 EXPERIWNTAL 0 O O O O O O O O O O O O O O O O O O O O O C O 23

A. Introduction . . . . . . . . . . . . . . . . . . . 23
B. Summary . . . . . . . . . . . . . . . . . . . . . 23
C. Preparation of Compounds . . . . . . . . . . . . . 24
1. Materials . . . . . . . . . . . . . . . 24

2. Reaction of Europium Sesquioxide with
Graphite . . . . . . . . . . . . . . . 24
3. Reaction of Europium with Carbon . . . . 25
4. Preparation of Praseodymium Dicarbide . 27
D. Methods of Analysis . . . . . . . . . . . . . . . 27
1. X-ray Analysis . . . . . . . . . . . . . 27
2. Chemical Analysis . . . . . . . . . . . 28
3. Hydrolysis Product Analysis . . . . . . 31
E. Temperature Measurement . . . . . . . . . . . . . 31
F. The Mass Spectrometer . . . . . . . . . . . . . . 35
1. The Instrument . . . . . . . . . . . . . 35
2. Experimental Procedure . . . . . . . . . 37
3. Treatment of Data . . . . . . . . . . . 41
G. Effusion EXperiments . . . . . . . . . . . . . . . 41
1. Apparatus . . . . . . . . . . . . . . . 41
2. Preparation of Targets . . . . . . . . . 42
3. Procedure for Effusion Measurements . . 43

IV. RESULTS AND DISCUSSION . . . . . . . . . . . . . . . . . . . 45

iii

TABLE OF CONTENTS - Cont.

A. The Preparation and Some Physical Properties of

Europium Dicarbide

1.
20

3.

Experiments Involving Europium
Sesquioxide and Carbon

9 o o o o

o p o o o

The Preparation of Praseodymium
Dicarbide .
Experiments Involving Europium and

Carbon

B. X-ray Analysis .

C. Knudsen Effusion Experiments Involving

Collection

1.
2.
3.
D. Mass
12
2.
3.
4.
5.

LITERATURE CITED

9

General

Q

0

C .

O

0

Preliminary Experiment .
Individual Experiments .

Introduction .

Conventions for Treatment of

O

9

Individual Experiments .

Treatment of Data

Analysis of errors .
E. Suggestions for Further Research .

iv

0

9

Spectrometric Studies of Europium

O O O O O

O O O O

O C 0

Target

0 Q C O O

Dicarbide

C O 9

Data . .

O O O O 0

PAGE

45

45

48

48
52

55
55
57
59
66
66
67
68
83
90
92

94

TABLE

II.
III.

IV.

VI.

VII.

VIII.

IX.

XI.
XII.
XIII.
XIV.
XV.
XVI.

XVII.

LIST OF TABLES

Lattice parameters for some tetragonal dicarbides . . . . .
EurOpium concentrations in standard solution . . . . . . .
Temperature profile of the Knudsen cell . . . . . . . . . .
Data for Eu 0

2 3

Europium dicarbide preparations . . . . . . . . . . . . .

-carbon experiments . . . . . . . . . . . . .

Interplanar d-spacings for EuC sample l-24P . . . . . . .

2
Radii of the lanthanons in the dicarbide phase (A) . . . .
Effusion data for sample l-35P . . . . . . . . . . . . . .
Analytical data for targets from experiment E-l . . . . . .
Data for experiment E-l . . . . . . . . . . . . . . . . .

Data for experiment E-2 . . . . . . . . . . . . . . . . . .
Summary of experiment MS—l . . . . . . . . . . . . . . .

Summary of experiment MS-Z . . . . . . . . . . . . . . . .
Data on the ion intensity of mass 151 as a function
Free energy function for EuC2 . . . . . . . . . . . . . .

Third law values of the enthalpy of vaporization for EuC

Third law values of the enthalpy of vaporization for EuC
calculated from experiment E-l . . . . . . . . . . . .

2
Data for experiments MS-Z and MS-3 . . . . . . . . . . . .
Data for experiment m'A‘Ag o o o o o a o o o o o o o o e 0

Data for eXPeriment Ms-S o o o o o o a o o o o o o o c o 0

PAGE

30

34

46

50

54

56

58

61

62

65

7O

71

73

85

87

89

109

111

112

LIST OF FIGURES

FIGURE PAGE
1. The Carbon-Lined Melybdenum Effusion Cell . . . . . . . . 38

2. Vapor Phase Chromatogram of the Hydrolysis Product of
Europium Dicarbide . . . . . . . . . . . . . . . . . . . 51

3. The Vapor Pressure of Europium Dicarbide as a Function
of Reciprocal Temperature . . . . . . . . . . . . . . . . 63

4. The Temperature Dependence of the Europium Ion Intensity . 79
5. Appearance Potential Curves . . . . . . . . . . . . . . . 80
6. The Mass Spectrum of Europium-Europium Dicarbide . . . . . 82
7. A fef for Europium Dicarbide as a Function of Temperature 86
8-1. The Mass Spectrometer Knudsen Source Assembly . . . . . . 100
C-1. Electron Bombardment Power Supply - Power Circuit . . . . 103

Cu2. Electron Bombardment Power Supply ~ Control Circuit . . . 104

vi

LIST OF APPENDICES

APPENDIX 4 PAGE

A. Correction for Leeds and Northrup Pyrometer
Serial No. 1619073 . . . . . . . . . . . . . . . . . . . 98

B. The Mass Spectrometer Knudsen Source . . . . . . . . . . . 99
C. The Electron Bombardment Power Supply . . . . . . . . . . 102
D. Computer Program for Least Squares Data Fitting . . . . . 106

E. Compilation of Mass Spectrometric Data . . . . . . . . . . 109

vii

I. INTRODUCTION

A. Incentives for this Research

In recent years, mass spectrometric and thermochemical studies
have demonstrated the existence of unsuspected gaseous molecules con-
’taining heavy metal atoms in the vapor phase above refractory compounds.
These findings require new theories of bonding which can be tested only
by the examination of other compounds.

A study of vaporization processes not only provides for the
measurement of vapor pressure and the preparation of new compounds,
but also helps to establish the nature and kinetics of high temperature
reactions. Good thermochemical measurements on a large number of
refractory compounds are necessary to provide the information needed
to elucidate the nature of these high temperature reactions. To date,
much of the necessary information has not been obtained, and in addition,
much of the available data are unreliable.

While no single study can hope to provide more than a small contri-
bution, each investigation of a particular compound provides more useful
information. The study of the preparation and vaporization of europium
dicarbide was undertaken with these interests in mind.

B. Previous Investigations of Lanthanon-Carbon Systems

 

1. Preparations and Properties

 

Compounds of the type MC in which M is a lanthanon, have been

2’
known for some time. Pattersson (1) reported the preparation of the
dicarbides of lanthanum, yttrium and cerium in 1895. His method of

preparation was to melt a powdered mixture of the oxide and carbon in

a high current electric arc. Chemical analysis gave the formulas YC1 87

and Lacl.85; no data were given for cerium. This low metal to carbon
ratio was probably the result of oxide contamination of the sample.
However, it is possible that an actual non-stoichiometric compound was
present. About this same time, Moissan (2,3) and Mbissan and Etard
(4) also reported the preparation of, and hydrolytic studies on,
lanthanum, neodymium and praseodymium dicarbides.

Sometime later, Damiens (5,6) prepared the dicarbides of lanthanum,
cerium, praseodymium, neodymium and samarium by reacting the oxide with
carbon. He then studied the hydrolysis of these compounds.

In 1930, von Stackelberg (7,8) reported studies on the crystal
structure of a number of carbides, among them several of the lighter
lanthanon dicarbides. His investigations showed the crystal structure
of these compounds to be face-centered tetragonal (Di; - I 4/mmm)-
Later work, which will be discussed shortly, Showed von Stackelberg's
work to be correct; his was the first good structural investigation of
these compounds.

In 1946, Frevel, Rinn and Anderson (9) tabulated the structural
data of a large number of tetragonal compounds. These authors list
the data for both the alkaline earth and the lanthanon dicarbides known
at the time. In 1951, Villelume (10) prepared lanthanum dicarbide by
reduction of the oxide with carbon at 20000 and then studied the
hydrolysis of the product.

Gaume-Mahn (ll) summarizes the data of a number of lanthanon
borides, nitrides, sulfides and carbides. The data presented are
similar to those presented by previous authors. Gaume-Mahn, however,
suggests the addition of hydrogen to the oxide-carbon reaction mixture

to promote the reduction.

Atoji and co-workers (12) report structural data for lanthanum
.dicarbide and sesquicarbide. The use of both x-ray and neutron diffrac-
tion-in their investigations allowed determination of both metal and
carbon positions in the crystal lattice. These authors give complete
structural data including atomic positions in the unit cell and the
carbon-carbon bond distance.

In 1959, Spedding, Gschneidner and Daane (13) reported a phase
study of the lanthanumrcarbon system. They varied the carbon concentra-
tion from zero to twenty-four weight per cent, preparing their Specimen
by melting massive mixtures of the metal and carbon in an inert atmos-
phere. Along with the phase composition data, they Show that the
electrical conductivity of the dicarbide is near that of the metal,
indicating a compound of the type La+3CE2 in which the third electron
on the metal is in the conduction band of the crystal.

These same authors (14) report the preparation of a large number
of lanthanon carbides of three different types: MEG, M203 and MCZ'
These compounds were prepared by reaction of the elements at high
temperature.

The trinlanthanon carbides are facemcentered cubic and are reported
to exist only for the heavier lanthanon metals (samarium to lutetium)
and for yttrium. The lighter lanthanons are probably too large to
permit the formation of this type of compound. In the tri~lanthanon

carbide series, tri-yttrium carbide was investigated most thoroughly.

The composition of this phase ranges from YC to YC

0.25 0.40' Here: °ne

is probably dealing with an intenfiitial compound in which the carbon
atom occupies some of the octahedral holes in the metal lattice. No

attempts were made to find the composition range for the similar

lanthanon compounds, but the authors feel that the range of composition
would be similar to that of the yttrium compound.

The lanthanon sesquicarbides are body-centered cubic for the series
lanthanum to dysprosium. Holmium shows both a body-centered cubic phase
and a phase of lower symmetry. Erbium, thulium, lutetium and yttrium
also form this lower symmetry phase, the structure of which was not
determined.

All of the lanthanons form a dicarbide phase of tetragonal symmetry,

17
4h

appear in this series except that no mention of any europium-carbon

the space group being D u I 4/mmm. No unexpected results or trends
compound is made.

Hydrolytic studies on these lanthanon-carbon compounds led Spedding,
Gschneidner and Daane to state that the M3C compounds are methanides
since only methane and hydrogen result from the hydrolysis. The M'2C3
and MC2 compounds are classed as acetylides since the principal hydroly-
sis product is acetylene. However, a number of hydrocarbons are pro-
duced in hydrolysis of these compounds since the free electron in the
conduction band can participate in the reaction. Ytterbium produced
somewhat more acetylene, according to these authors, and had larger than
expected lattice parameters, indicating that it was more like an alkaline
earth dicarbide. This behavior might be expected since ytterbium
frequently forms a +2 ion.

Shortly after the work just discussed appeared, Vickery, Sedlacek
and Ruben (15,16,17) published independently a series of papers dealing
with the preparation and properties of most of the lanthanon dicarbides.

Their work agrees well with that of Spedding and coaworkers. They

prepared the dicarbides by reduction of the oxide with carbon. In this

study some of the oxide-carbon samples were quenched and examined just
after melting occurred. These quenched samples were found to contain
the free lanthanon metals. This is probably one of a very few instances
in which reduction occurs via the metal.

Vickery and co~workers (16) studied the magnetochemistry of the
carbides and found that the correct formula for most of the dicarbides

3C.2 as expected. Samarium and ytterbium tended to be divalent.

2 3

Europium.was not studied.

+
is M

Recently, Greenwood and Osborn (18) proposed a new method for
obtaining very pure lanthanum dicarbide. They first formed lanthanum
hydride which was then mixed with carbon and heated under high vacuum to
give the dicarbide. It was felt that this method would give a very pure
product with low oxygen contamination. This method could probably be
utilized for the formation of most of the other lanthanon dicarbides.

Samsonov and couworkers (19) have reported preparative work
involving scandium,yttrium and lanthanum carbides. The most interest»
ing and original part of this research is the preparation of compounds
of the formula SCZCZO and YZCZO° This type of compound should exist
for the other lanthanons, but has not been reported.

Another lanthanon carbide phase was reported by Dancy, Everett
and McCabe in 1962 (20). These workers studied the system Ml-H-CH4 in
which leas cerium or praseodymium. They present evidence, from x~ray
and hydrolysis data, for a carbide of formula MC. These compounds
exhibit a faceucentered cubic structure. To date, no other lanthanon
monocarbides have been reported.

There is some question about the existence of lanthanon monocarbides.

Spedding, Gschneidner and Daane (13) were unable to prepare cerium or

praseodymium monocarbide by direct combination of the elements. In
addition, Dancy, Everett and MbCabe (20) found that their monocarbides
decomposed in an argon-filled dry box containing minute amounts of
oxygen. If these authors were actually dealing with an MCH compound,
extreme sensitivity to oxygen might be more easily understood since a
lanthanon monocarbide would not be expected to react with oxygen at the

rapid rate reported.

2. _Crystal Structure of the Lanthanon Dicarbides

The dicarbides, which were of interest in this study, will be dis-
cussed in more detail in this section. I

Most of the authors cited previously give some structural data
for the lanthanon carbides; however, Spedding, Gschneidner and Daane
(14) give the most recent and most complete listing of lattice parameters.
These data, which are in agreement with previous work are probably the
most accurate reported since high purity lanthanon metals were used as
reactants. Atoji (21) has studied the neutron diffraction patterns of
some of the lanthanon dicarbides and has determined the carbon-carbon
bond distance in each dicarbide, as well as the metalucarbon distance.
A compilation of lattice constants for the lanthanon dicarbides and
several of the alkaline earth dicarbides is given in Table 1.

Examination of these data shows a regular decrease in lattice
parameters for the lanthanon dicarbides following the lanthanide con-
traction. The increase in lattice parameters at ytterbium is probably
due to a contribution from MIZ, a species which is not found in the
other carbides. While not enough carbon-carbon bond distances are

given to establish whether or not this distance is related to the metal

Table I.

Lattice parameters for some tetragonal dicarbides

 

 

 

Metal ao cO C-C Distance
La 3.934 8 6.572 3 1.303 3
Ce 3.878 6.488 1.283
Pr 3.855 6.434 ---

Nd 3.823 6.504 -__
Sm 3.770 6.331 —--
Gd 3.718 6.275 ---
Tb 3.690 6.217 1.293
Dy 3.669 6.176 ---
Ho 3.643 6.139 ---
Er 3.620 6.094 ___
Tm 3.600 6.047 __1
Yb 3.637 6.109 1.287
Lu 3.563 5.964 1.276
r 3.664 6.169 1.275
Ca 3.89 6.38 1.191
Sra 4.11 6.68 ---
Baa 4.39 7.05 ---

 

8Data from ref. (9)

radius, any change in this distance with changing metal radius is small.
The dicarbides.1isted in Table I belong to the space group DZ; -

I 4/mmm. The metal atoms are at (000, kkk) and the carbon atoms at

(000, %%%) i (002). For lanthanum, Atoji (12) has found that Z =

0.043 i 0.002.

3. Vapor Pressure Studies

 

Although reports of high temperature vaporization studies are quite
common, very little work dealing with lanthanon carbides has appeared.
Chupka and c0uworkers (22), using a mass spectrometer, have studied
the vapor species above a number of carbides, among them lanthanum
dicarbide. These authors found two gaseous species, La and LaCZ. The

ratio of the pressures of the two species was a function of temperature

and was 1:2 at 23000 K. From their data, the enthalpy of the reaction

La + 20 -—-’* LaC (1-1)

(s) (S) 2(g)

was determined by a third law treatment to be 38 kcal/mole and by a
second law treatment to be 46 kcal/mole. The agreement of the two
numbers was considered satisfactory by the authors.

Wakefield (23) has studied the vapor pressure of holmium and the
decomposition pressure of holmium dicarbide at high temperatures. This
study utilized weight loss data; the sample was vaporized and the rate
of weight loss determined, with a balance, as a function of temperature.
The author covered a temperature range of 6500 to 17500 with correSpond-
ing vapor pressures of 10.8 torr to 10 torr. To achieve high sensia
tivity at low temperatures, a Langmuir type experiment was performed.

In order to increase the rate of weight loss, the vapor was allowed to

evaporate directly from the surface of a large sample of the material.
At high temperatures, the conventional Knudsen cell was used, and at
the highest temperatures, the Knudsen cell was fitted with a long chan-
nel orifice in order to retard the escape of the vapor. The dicarbide

was found to vaporize according to the equation:

HoC —->Ho + 20 (1-2)

2(3) (a) (graphite)'

No thermodynamic data were given in the reference consulted. In this
same study, holmium sesquicarbide was found to vaporize according to

the equation:
21-102C3(S) —-'Ho(g)+-3HOC2(S) (1-3)

In the third reported vaporization study of a lanthanon dicarbide,
Jackson, Barton, Krikorian and Newbury (24) studied gadolinium and
thorium dicarbides. The vaporization process was followed with a mass
spectrometer which was calibrated for quantitative measurement of
pressure with silver and molybdenum. The gadolinium dicarbide was
prepared by reacting a powdered mixture of the elements in the mass
spectrometer. The primary Species above the dicarbide at high tempera-
ture was gadolinium. Gadolinium dicarbide was found as a minor constit—
uent ranging from 1% of the effusate at 20000 K to 5.8% at 24220 K. No
other gadoliniumecontaining molecules were found in the vapor. The

following enthalpies were reported at 21500 K:

GdC '—~4P GdC 3 AH = 143 kcal/mole 1-4
2(a) 2<g> ( )
GdC —-% Gd + 2C ; AH = 101 kcal/mole l=-5‘

2<s> (g) (s) ( ’
Gd + 2C -—-9’GdC AH = 38 kcal/mole. (1-6)

(g) (s) 2<g> ;

10

Chupka and Inghram (25,26,27) have studied extensively the vapori-
zation of graphite. The vapor pressures and enthalpies of sublimation
were determined for C1, C2 and C3, the latter being the principal species
in the gas phase. Honig (28) has also studied the vaporization of
graphite and his data are in agreement with the results of Chupka and
Inghram. Thorn and Winslow (29) have combined Chupka and Inghram's
mass spectrometric measurements with data they obtained on the rate of
effusion of graphite. The combined data allowed Thorn and Winslow to
calculate the partial pressure of the species C1, C2 and C3 above

graphite and the corresponding enthalpies and entropies of vaporization.

4. Vaporization Studies Utilizing the Mass Spectrometer

 

A number of reports have appeared in the literature dealing with
the adaptation of the mass spectrometer to high temperature vaporization
studies. Several of these are of general interest and will be discussed
briefly.

White, Sommers, Walsh and Goldstein (30) discuss the application of
a timemof—flight mass spectrometer, similar to the one used in this
study, to the study of inorganic materials at high temperature. They
present a general treatment of the apparatus, methods and treatment of
data, and also discuss their instrument's reliability and its method
' of determination. Using this instrument, White and co-workers (31,32)
showed that the lanthanon metals vaporize as monomeric Species and that
lanthanum and neodymium sesquioxides vaporize to give the monoxides,

M0, and oxygen.
Inghram and Drowart (33) discuss the advantages and disadvantages

of the mass spectrometer in its application to the study of high

11

temperature processes. They present general requirements concerning the
sample source and the instrument itself. Finally, the authors discuss
the treatment of data obtained from the mass spectrometer and tabulate
the species observed in the gas phase over a large number of inorganic

compounds along with the enthalpy for the corresponding reactions.

C. This Research

 

In reviewing all of the work presented above concerning the lanthanon
dicarbides, only one reference (34) was found which gave any indication
of a carbide compound of eurOpium. This work, presented in the foreign
patent literature, indicated that a compound of the formula EuC was
formed in a carbide-type reactor fuel element. No information as to
how the compound was identified or how it was formed is available. The
only information given was that the presence of ZrC lowered the vapor
pressure of EuC by a factor of 106.

Since the preparation of europium dicarbide and a subsequent study
of its thermodynamic properties would be of general interest, this
research was undertaken. The general plan of attack was to first
investigate the preparation of the compound using the various methods
previously reported, and second, to study the vaporization of europium
dicarbide using the Knudsen effusion technique. Two methods of analysis
of the vapor were to be used for the second portion of the investigation.
First, the effusate from a Knudsen cell was to be analyzed chemically to
determine the vapor pressure. Second, the effusate was to be observed
in a time-of-flight mass spectrometer to determine the molecular compo-

sition of the vapor and to provide additional data on the vapor pressure.

II. THEORETICAL CONSIDERATIONS

A. General

The enthalpy and entropy changes which accompany a vaporization
process may be calculated for both the condensed and the vapor phase
from a determination of the partial pressure of the equilibrium vapor
at various temperatures. Consider a two component system consisting of

a solid and a vapor. According to the well known phase rule
F = 4 - P. (2-1)

‘3 is the number of degrees of freedom and P is the number of phases
present at equilibrium. For the state of the system to be a function
of one variable only, the phase rule implies that either of two con-
straints must be present. The system must contain the vapor and two
solid phases or the vapor and one solid and one liquid phase; or the
vapor must have the same composition as the solid phase. This latter
case, termed congruent vaporization, can be demonstrated by showing
that the composition of the solid and the vapor are identical.

For each increase in the number of components, the number of
constraints must be increased correspondingly in order that the state
of the system remain a function of temperature only.

A determination of the vapor pressure as a function of temperature,
combined with both chemical and x-ray powder diffraction analysis, both
before and after vaporization occurs, allows one to deduce the behavior
of the condensed phase and to cerrelate the thermodynamic data obtained

with the actual reactions occurring in the system.

12

13

B. .Thermodynamic Relationships in Vaporization

For the vaporization reaction

A 2 A 2-2
(s or 1) (g) ( >
the free energy is defined as:
o o 0
ACT — AHT - TAST — -RT 1n K. (2-3)

In the simple case in which only one species is present in the gas, at
low pressures K equals PA’ where PA indicates the pressure of A.

If the change in heat capacity, ACp, is considered constant for

the above reaction, then

T
AH; = AH* + f AdeT = AH* + ACp(T - T*) (2-4)
T* '
and.
O T
AsT = AS* +-f Ade 1n T (2-5)
TA

where AH* and AS* are the enthalpy and entropy at the reference tempera-
ture, T*, which is usually taken as 298.150 K. Combining equations 2-3,

2-4 and 2—5 yields:

AGT = «RT 1n PA = AH* + ACp(T - T*) 4 TAS* - TACp 1n T/T*. (2-6)

If ACp is assumed to be zero, then

RT 1n PA = -AH* + TAS* (2-7)

or

1n PA = - AH*/RT + AS*/R. (2-8)

l4

Ehuation 2-8 is the familiar Clausius-Clapeyron equation in which R is
the molar gas constant. A graph of In PA vs l/T, for the temperature

range over which P is measured as a function of T, yields AH* from the

A
slope and AS* from the intercept.

The assumption that ACp is zero, while mathematically and experis
mentally the most simple case, is probably never true in practice since
it implies the same heat capacity for the solid and gaseous phases. If

this assumption is badly in error, the ln P vs l/T plot will show

A
curvature and the more complex treatment described below is necessary.

If ACp is constant, but not zero, we have from equation 2-6,

1n PA = -AH*/RT -(ACp/RT)(T-T*) + AS*/R +(ACp/R)(ln T/T*) (2-9)

01'

ln-PA = -A/T + B 1n T + C. (2-10)

Data may be fitted to this equation by mathematical methods.

When the heat capacity is known as a function of temperature for
each species, ACp can be calculated. This ACp can then be combined
with equation 2-4, equation 2-5 and equation 2-3 to convert the measured
thermodynamic quanities to their standard states. In practice, the
heat capacity as a function of temperature is known for very few com-
pounds and either must be estimated or a simpler treatment must be
used.

Examination of equation 2-8 or equation 2-10 shows that the slope
of these lines is sensitive to the temperature. That is, small errors
in the temperature determination will produce large errors in the slope.

Therefore, whenever possible, the enthalpy determined by the second

15

law method described above should be checked by a method based on the
third law of thermodynamics since this method is less sensitive to
temperature errors. The temperature errors contribute less to this
method because an enthalpy is calculated for each pressure and these
values are then averaged. Thus, random temperature errors will tend to
cancel each other and non-random errors will result in a change in the
enthalpy with temperature.

The third law method makes use of the free energy function, fef,

which is defined as:

o o
fef — [(GT — H298)/T1. (2-11)
For the reaction in equation 2-2,

- _ o o o o _ o o
Afef — [(GT-H298)/T](g)- [(GT—H298)/T]¢;or])— ACT/T - AH298/T. (2-12)

Equation 2-3 combined with equation 2-12 yields:

A -TAfef — RT In P

A, (2-13)

0
H298 ‘
Thus, if free energy functions are available or can be calculated from

o
298

The free energy function can be evaluated from heat capacity data

available data, AH can be evaluated for each temperature-pressure set.

using the relationship:

T T
fef = 1/T f deT - f de In T - (2414)

so
0 298 298
The free energy function can also be calculated using the methods of
statistical mechanics if spectroscopic data which give the energy

states of the molecule or atom of interest are available.

Unfortunately, the data needed to evaluate the free energy function

16

are usually not available and one must make estimates using available
data for similar compounds. In such a case, the data obtained from

the slope and the intercept of the plot ln P vs l/T may be more reliable

A
and the values calculated from the third law are used only as a check on

the other method.

C. The Knudsen Effusion Method

 

 

1. Mathematical Relationships

In 1909, Knudsen (35,36,37) published a series of papers on the
effusion of gases through small orifices and tubes at low pressures. If
one considers a container at uniform temperature, located in a vacuum
and containing a gas at equilibrium, the number of particles striking a
unit area of the container wall is given by nc/4, in which n is the
number density and E'is the average Speed of the molecules. If the
container wall is thin and perforated with a small knife—edged orifice,
the number of particles passing through the orifice in a given time will
be the same as the number striking an equal area of the wall during that
same time. Thus, a determination of the number of particles passing
through the orifice permits calculation of the pressure in the container.

There are several methods by which one can determine the number of
particles passing through the orifice in a given time. Bockris, White
and Mackenzie (38) discuss these methods in detail. Of particular
interest to the work reported herein are the target collection and mass
Spectrometric techniques.

The partial pressure in atmospheres, P, can be determined from

the following equation:

1» = w/Sot' (2nRT/M)% (2-15)

 

17

where w equals weight loss in grams, M equals the molecular weight
expressed in grams, So is the orifice area in cm.2, t is time in seconds
and T is temperature, 0K. In the target collection technique, a circular
0

target of radius r, is situated at a distance, d, from the orifice and

placed coaxially to it. From the cosine law (38,39) the pressure, P, is

related to the weight of material on the target by the equation:
‘ a 2 2
P = 0.022557 w/Sot (T/M) (l + d /r ). (2-16)

The derivation of the equation for Knudsen flow assumes that the
pressure in the cell is so low that molecular collisions in the gas are
infrequent. Knudsen (35) observed that as the cell pressure rises, a
transition occurs from molecular flow to hydrodynamic flow through the
orifice, resulting in a greater mass of gas leaving the cell per unit
time than would be expected. Carlson (39) discuSses the conditions
necessary for molecular flow and concludes that a value of unity for
the ratio of mean free path,,AJ to orifice diameter is the upper limit
of molecular effusion, and thus, the limit of the effusion method.

The mean free path is the average distance a gas molecule travels

between collisions and is given by:
A = l/JE‘WnOZ (2~17)

where n,is the number of molecules per cubic centimeter and_g is the
molecular diambter. A unit ratio of mean free path to orifice diameter
indicates that the effusing molecules will have a large collision
frequency, and thus, that the flow is not molecular.

If the orifice of the Knudsen cell is not knife-edged, but has the

shape of a cone of finite length, the distribution of molecules effusing

18

from the orifice will not follow the cosine law because relfections from
the orifice wall will change the angular distribution.

Edwards (40) and Freeman and Edwards (41) have treated the conical
orifice theoretically and have calculated the transmission probabilities,
W0, for a large number of orifices of varying Shapes. Their treatment
includes the common cylindrical orifice as a special case. When the

transmission probabilities are applied, equation 2-15 becomes:
P = 0.022557 w/WOSOt (T/M)%. (2-18)

When only those molecules leaving the cell in the forward direction
are collected for analysis, this correction may be neglected, since only
those molecules emanating from the bottom of the cell are detected.
These molecules pass directly from the bottom of the cell without

collision.

2. Practical Requirements

 

There are a number of practical requirements in Knudsen effusion
experiments. Some of these apply to the method in general and others to
the particular system under study.

(a) The residual pressures in the vacuum system must be low enough
to preclude reaction of the residual molecules with the gas or scattering
of the molecular beam.

(b) The fraction of effusing molecules which strikes the target
and sticks to it must be known and the walls of the vacuum chamber must
condense all the effusing molecules which strike them.

(0) In effusion experiments in which the weight of the effusing

substance is measured, the molecular weights and relative abundance of

19

the effusing molecules must be known.

(d) The physical dimensions of the apparatus at the experimental
temperature must be known.

(e) The sample in the Knudsen cell must be large enough to maintain
equilibrium vapor pressure in the cell. In addition, the orifice size
and shape must be such that they do not alter the equilibrium pressure
of the temperature uniformity of the cell. Carlson (39) discusses these
problems.

(f) A reaction between the sample and crucible material may alter
the vapor pressure. Galloway and Eick (42) have shown that when samarium
hexaboride is heated in contact with molybdenum, molybdenum boride, MoB,
results presumably accompanied by the evolution of gaseous samarium.

Thus, in a study of the vaporization of SmB in a molybdenum crucible,

6
and anomalously high samarium pressure would be observed. Spinar and
Margrave (43) have recently shown that when nonreactive crucibles of
magnesium oxide are used to measure the vapor pressure of the alkali
hydroxides, the vapor pressures are many times higher than those reported
by early workers who had used nickel crucibles. The low vapor pressures
presumably resulted from reaction of the sample with the crucible.
Changes in the crucible material may reveal reactions between the cruci~
ble and sample. Thus, chemical and x-ray analyses should be performed
on all materials involved in the experiment.

(g) The effusion crucible and sample must be at a known, uniform
temperature. Winterbottom and Birth (44) have shown that if the t0p of
the effusion crucible is hotter than the bottom, a departure from cosine

law distribution results from surface diffusion through the orifice and

along the crucible top. In addition, if the crucible top is colder than

20

the bottom, mass transfer from the sample to the crucible top may occur,
resulting in a change of orifice shape, and possibly, total closing of

the orifice.

D. The Mass Spectrometric Method

 

Inghram, Chupka and Porter (45) give the relationship between the
measured ion intensity of a molecule in the vapor and the pressure of

that species as:

Px =(1/rik)(Cs/Ox) (TX/TS) (SW/3x) Ii (2-19)

where P is the partial pressure of Species x
r is the isotopic fraction of the ion measured
0 is the ionization cross section
T is the temperature in 0K
S is the sensitivity of the ion detector
I is the intensity of the ion measured in arbitrary units
8 indicates a standard substance
x indicates an unknown substance
k is the sensitivity of the mass spectrometer in units of ion

intensity per atmosphere of the vapor of a standard.

The isotopic fraction, r , is included in the equation, since generally

1
the intensity of one isotope is observed as a function of temperature.
The species x may contain more than one isotope; for example, eurOpium
gas contains isotopes of mass 151 and 153.

The ionization cross section is a measure of the efficiency of

ionization by the electron beam in the mass spectrometer ion source.

Otvbs and Stevenson (46) have calculated ionization cross sections for

21

a number of atoms for ionization by electron impact, but have not included
the lanthanons in their calculations. To determine the ionization cross
section, a method described by Chupka and Inghram (27) can be used. The
ionization cross section is proportional to the gas kinetic cross section,
which is, in turn, proportional to the square of the interatomic distances
in the crystal. Thus, the cross section ratio for silver to carbon is
(2.88/1.54)2, which is approximately 3.5. This is corrected to 4.0,

since the ionization potential of carbon, 11.2, is much higher than that
of silver, 7.54. The higher the ionization potential, the more diffi-
cult is ionization, and therefore, the calculated ratio is increased to
account for this. This procedure is said to produce an error in the

cross section ratio of no more than a factor of two.

The ratio of the sensitivities of the ion detector is the ratio of
the number of electrons released by each species upon impact with the
detector. Since in practice, it is usually not possible to determine
this ratio, it is considered to be unity.

The sensitivity, k, is experimentally determined: An inert standard
material of known vapor pressure is added together with the sample, to
the cell. The ion intensity of the standard is measured at constant

temperature as a function of time. The sensitivity is then defined by:
k = I; IAtj/t](l/PS). (2-20)
J

The first term in equation 2-20 is the average ion intensity over the
time needed to vaporize all of the standard. PS is the pressure of the
standard at the temperature of measurement.

When dealing with any given species x, equation 2-19 may be rewritten

as

llb

22
Px = K (IxTx) (2-21)

since all the other terms are constant for a given experiment. Combin-

ing equations 2-8 and 2-21 yields:

1n PX = 1n K Txli = (-AH*/RT) + AS/R (2-22)
or

In IiTx = (~AH*/RT) + C. (2-23)

where C = AS/R ~ 1n K. Thus, the slope of a graph of 1n IT vs l/T is
equal to the enthalpy of reaction divided by R. The entropy may be
determined from the intercept, C, if the constant K is known. Substitu-
tion of the calculated pressures into equation 2-13 permits an independ-
ent determination of the enthalpy of the readtion.

Wiley (47) and Wiley and MtLaren (48) have described the theory of

the time—ofwflight mass Spectrometer.

III . EXPERIMENTAL

A. Introduction

An examination of previously reported preparations of the lanthanon
dicarbides indicates that two basic methods were used: the reduction of
the metal oxide with carbon at high temperature ig‘zaggg and the reaction
of the elements at high temperature. No data have been presented con-
cerning the relative merits of these different methods and it appears
that either works equally well for most of the lanthanons.

The oxalate method for the quantitative determination of the
lanthanons has been used for a number of years and needs no additional
discussion. However, methods for determining microgram quantities of
the lanthanons are relatively recent and not too numerous. The method
chosen for the analysis of europium appeared to be the best available
for use in aqueous solution.

The Knudsen effusion technique used in this study has been applied
successfully to a large number of systems. While some difficulties are
present in this method, it is currently the most accurate available for

the determination of vapor pressures at high temperature.

B. Summary

Two methods were used in the attempt to prepare europium dicarbide.
The first, the reaction of europium sesquioxide with carbon heated in
vacuo, proved unsuccessful. The second, the reaction of europium with
carbon in a closed stainless steel container, proved successful. The

reaction product was characterized by both chemical and x=ray analyses.

23

24

The dicarbide was studied by the Knudsen effusion method, using both
mass spectrometric and material collection techniques to determine the

pressure of the effusate.

C. Preparation of Compounds

1. Materials

Both the europium sesquioxide (99.8% pure) and the europium metal
(99% pure) were obtained from Michigan Chemical Corporation, St. Louis,
Michigan. The graphite, listed as graphite grade UF-4-S was obtained
from Ultra Carbon Corporation, Bay City, Michigan, and was a high density

material of spectroscopic purity.

 

2. Reaction of Europium Sesquioxide with Graphite

The sesquioxide was calcined at 9000 to remove volatile impurities
and to convert any carbonate present to the oxide. The crushed graphite
was heated under vacuum in a graphite crucible to a temperature of
18000 to remove absorbed impurities. The oxide and carbon were then

intimately mixed in proportions according to equation 3-1:

Eu203 + 7c «— 2EuC2 + 300 (3-1)

and placed in a previously outgassed graphite crucible. A slight excess
of graphite was used to insure complete reduction. The crucible had a
snug fitting lid containing an orifice to allow escape of the carbon
monoxide evolved.

The graphite crucible was then heated by induction in a vacuum
line. Heating was initiated after the residual pressure in the system
had decreased to l x 10"5 torr or less. The onset of the reaction was

evidenced by both a rapid rise in pressure due to the evolution of carbon

25

monoxide and a darkening of the walls of the Vycor condenser around the
crucible. When the pressure had decreased again to the residual value,
heating was terminated. The crucible was removed from the vacuum line
and taken into a helium filled dry box. A sample of the product was
loaded into a capillary tube for x-ray powder diffraction analysis.

The material on the walls of the vycor condenser was dissolved
in dilute hydrochloric or nitric acid. During solution, which was very
rapid, a gas with the characteristic odor of acetylene was evolved.
This gas, however, was not analyzed because of the difficulty involved
in the collecting of a sample. The resulting solution was analyzed

for europium using the oxalate method to be described.

3. Reaction of Europium with Carbon

In additional attempts to prepare europium dicarbide, the metal and
carbon were placed in a metal bomb and heated for varying lengths of
time. Initially, the bombs were fashioned from type 316 stainless steel.
However, when both halves of the bomb were constructed of the same
material, the bomb could not be Opened after heating Since the threads
seized. The combination of type 310 stainless steel for the bottom with
type 316 for the top eliminated this problem. During the course of the
experiments, a bomb was made from molybdenum as one method of determining
whether or not the sample was reacting with the bomb.

The bombs were all constructed in the following manner: A piece
of 2.54 cm. stock was reduced in diameter slightly so that the resulting
piece would fit into the tube furnace. A 0,953 cm. diameter hole was
then drilled in the bomb. This hole was enlarged at the t0p and then

tapped to provide a 5/8 - 18 thread 1.91 cm. deep. A 0.952 cm. x 1.714

26

cm. hole which contained the sample remained below the thread. The top
of the bomb was machined to give a matching thread. Flats were milled
on both the top and bottom of the bomb to provide a gripping surface
for tightening. The bomb was sealed with a 0.13 mm. thick platinum
washer.

Prior to use, the bombs were cleaned in hot nitric acid, dried at
1100 and prepared for loading in the dry box. The metal was added as a
solid piece; the carbon as a granular powder. The ratio of metal to
to EuC . The

1.5 3
top of the bomb was partially tightened in the dry box after loading.

carbon was varied to give a composition range from EuC

The top was retightened to insure a good seal after the bomb was removed
from.the dry box. The bomb was then placed in a Vycor tube through which
helium was passed. The vycor tube was placed in a tube furnace wound with
Kanthal type A-l resistance wire on an alumina tube.

After the tube had been thoroughly flushed with helium, heating
commenced. The heating time was varied from twenty to sixty hours while
the temperature was varied from 10000 to 11000. Temperature was measured
with a chromel alumel thermocouple in contact with the bomb. Since
extremely accurate temperature measurements were not necessary, room
temperature was used as reference and temperatures were corrected
appropriately.

The bomb was allowed to cool in the helium atmosphere. It was
necessary to break the gasket seal in air Since sufficient torque could
not be applied in the dry box. Immediately after the top had been
loosened the bomb was placed in the dry box where its contents were
removed with the aid of a 0.952 cm. drill ground flat on the end.

Although the material in the bomb was somewhat difficult to remove, it

27

could be ground easily with an agate mortar and pestle. Some of the
resulting product was loaded into an x-ray capillary tube for analysis;
the rest was stored in a closed vial in the dry box.

In some of the preparations, a small sample was dissolved in nitric
acid. Thiocyanate ion was added to test the sample for iron contamina-

tion since iron was the bomb constituent of greatest concentration.

4. Preparation of Praseodymium Dicarbide

 

Praseodymium dicarbide was prepared according to equation 3-2:

Pr6011 + 21 C * 6PrC2 + 900 + 02. (3-2)

Oxygen appears as a product since the Pr loses oxygen at a tempera-

6011
ture below which reduction occurs (8000). The reactants were placed in

a graphite crucible and heated by induction to 13000, at which temperature
the pressure rise in the system, indicating the initiation of the reac«
tion, began. The temperature was slowly increased to 15000. At this
temperature, the reaction was essentially over as indicated by a pressure
drop. The temperature then elevated to 17250 for one half hour. At

this temperature the pressure was 9 x 10"7 torr -- essentially background

pressure, and heating was terminated. The crucible was removed to the

dry box for x~ray powder diffraction analysis of the product.

D. Mathods of Analysis

 

l. X-Ray Analysis

 

X-ray powder diffraction photographs of the samples were taken
using either CuKa radiation (ken = 1.5418 A) or FeKa radiation (Kan =
1.9373 A) and a Debye-Scherrer x-ray powder camera of 114.59 mm. diameter.

Since copper radiation produces florescence with eurOpium specimens, iron

28

radiation is more desirable. -All samples were contained in 0.3 mm.

diameter Pyrex capillary tubes which were filled in a helium atmosphere.

2; Chemical Analysis

The diearbide samples were analyzed using standard gravimetric
techniques. The sample was dissolved in dilute hydrochloric or nitric
acid (1N) and was then digested on a hot plate to insure complete
solution. Any insoluble residue was assumed to be unreacted graphite
and was collected in a fritted glass crucible, dried at 1100 and weighed.
The remaining solution was adjusted to pH 4 to 5 with ammonium hydroxide
and excess saturated oxalic acid solution was added.

The oxalate precipitate, after digestion for a minimum of four
hours, was collected in a tared alundum filter crucible and fired at
9000 in a muffle furnace, in most cases overnight, to convert it to the
oxide. The crucible was reweighed after cooling and bound carbon was
determined by difference.

Europium deposited on the targets during a collection effusion run
was analyzed by the method of Rinehart (49) with minor modifications to
simplify the procedure. A brief description of the method follows:

The platinum discs used as targets were placed in fifty milliliter

beakers and ten milliliters of l‘N HClO were added. The samples were

4
digested on a hot plate for one hour. These solutions were then quanti-

tatively transferred to twenty-five or fifty milliliter volumetric flasks
(the volume of the flask depended on the quantity of europium thought to

be in solution) and diluted to volume with the perchloric acid. These

solutions served as the samples for the analysis. A standard solution

was prepared by dissolving calcined europium oxide in 1.N HClO4 to make

29

a solution of approximately 1 mg./m1. Portions of this solution were

analyzed by the oxalate method to determine the actual concentration.

The results of this analysis are given in Table II. This solution was

successively diluted to give standards of l, 2, 5, 10, 20, 50, 70 and

100 micrograms per milliliter.

The step by step procedure was as follows:

1)
2)

3)

4)

5)

6)

8)

9)

Add 1.0 ml. of sample to a 10 m1. volumetric flask.
Add 1 drop of 0.025% phenyl red indicator.

Add l‘N NaOH dropwise until near the color change.
Follow with 0.2 N NaOH to the color change.

Add 0.03 N HCl until color just reappears.

Add 0.5 ml. of Z‘N NH4C2H302-HC2H3O2 buffer.

Add 2.0 ml. of 0.1% sodium alizarin sulfonate.
Dilute to volume.

Using the Beckman DU Spectrophotometer read the

absorbancy at 550 mu against a reagent blank.

Determine the unknown from the standard curve.

Table II. Europium concentration in standard solutions

30

 

 

Sample Number Sample Volume

Total

Eu Concentration

Eu

Concentration

 

l 20 m1.
2 20
3 20
4 20

20.210 mg.

19.216
21.030

21.202

Average

fi—__

1.0105 mg./ml.
0.9608

1.0515

1.0601

1.0207 mg./ml.

 

31

3. ,Hydrolysis Product Analysis

 

Several samples of europium dicarbide were hydrolyzed in 3‘N HCl
in a confined system through which helium was flowing. The helium carried
the gaseous hydrolysis products through a "Drierite" filled drying column
into a liquid nitrogen covered U-tube fitted with a rubber septum and
loosely packed with Pyrex wool. The gas sample Condensed at the entrance
of the tube at the liquid nitrogen level, but wasrecondensed at the bot-
tom of the tube by gentle warming and subsequent cooling. The tube was
then evacuated for one to two seconds to remove most of the helium.

After the gas sample reached room temperature, it was analyzed
using an F &>M Model 590 flame ionization gas chromatograph using helium
as the carrier gas on an alumina column. The column was programmed
for a 4.60 per minute temperature rise. The instrument was calibrated

for each run with welding grade acetylene and natural gas.

E. Temperature Measurement

 

Temperature was measured with a Leeds and Northrup Model No. 8622-C
disappearing-filament type optical pyrometer, serial No. 1619073. The
pyrometer was calibrated at the National Bureau of Standards. Scale
readings, together with the true temperatures, as determined by the
National Bureau of Standards, are listed in Appendix A. A graph of
TOCNBS - TOGScale vs TOCScale was made for each temperature range and
was used to correct the observed temperature.

Before-and after each series of experiments, either effusion collec-
tion or mass spectrometric, the transmissivity of both the window and

prism through which the temperature was determined was measured. If

the before and after measurements differed, theaverage value of the

32

two was used. A deposit of silver formed rapidly on the window at high
temperature in the mass spectrometric experiments involving this metal.
The onset of deposition could be observed by a sudden lowering of temper-
ature with time at constant power setting. In these cases, the "before"
value of transmissivity was used with the temperature observed before

the deposit formed and the "after" value was used with successive temper-
atures. Some error resulted from this procedure, but no other method

was available.

To measure the transmissivity, the temperature of a tungsten band
lamp, heated to a temperature near 15000, was read directly with the
pyrometer and through the window and prism. The correction for trans-
missivity follows from Wien's radiation law and is defined by the
equations:

A 1/Tw

1/Tw - l/T (3-3)

and

A l/T l/T - 1/T (3-4)
P P

where TW and Tp are the observed temperature of the hot object viewed
through the window or prism and T is the observed temperature with noth-
ing in the light path. The pyrometer readings were corrected to the

true temperatures using theiNational Bureau of Standards corrections.

The total window and prism correction is:
A l/TT = A 1/Tw + A 1/Tp. (3-5)

The quantity A 1/TT is nearly constant for all temperatures, and the

relationship

l/T = l/TO - A 1/TT (3-6)

in which To is the observed temperature, was used to calculate true
temperatures from the apparent measured temperatures. In some experi-
ments, a magnifying lens was used on the optical pyrometer in lieu of
the standard lens. A correction factor, as described above, was deter-
mined for this lens and applied where necessary.

The design of the Knudsen cell used in these experiments prevents
the machining of a black body hole in the bottom of the cell. This
creates no problem in the mass spectrometric experiments Since the
temperature can be measured by sighting directly through the orifice
into the cell. In the effusion experiments, however, material was
collected on targets and it was necessary to Sight onto the bottom sure
face of the cell. Therefore, a series cf temperature measurements was
made in which the bottom surface, top surface and orifice temperatures
were determined at selected temperatures over the range of interest.
The results, which are Shown in Table III, were corrected to the true
temperature using the National Bureau of Standards corrections and the
window and prism absorption correction. Inspection of these data shows
the top-surface temperature to be higher than bottom surface temperature.
This difference, not shown in Table III, showed no temperature trend.
The average temperature difference is nine degrees. It is fortunate
that the top of the cell is hotter than the bottom since, under these
conditions, no mass transport, which could result in plugging of the
orifice, would be expected. The difference, To KBB - To KBS’ when
plotted against To KBS’ gives a line with slight upward curvature. This
curve was used to correct the observed surface temperature to the true

temperature of the Knudsen cell.

34

Table III. Temperature profile of the Knudsen cell

 

 

 

TOKBS TOKTs - TOKBB TOKBB " TOKBS
1180 1190 1243 63
1225 1238 1289 64
1265 1272 1331 66
1275 1283 1342 67
1295 1305 1364 69
1327 1336 1398 71
1360 1373 1436 76
1380 1389 1458 78
1398 1411 1478 ' 80
1431 1438 1515 84
1450 1459 1535 85
1455 1462 1542 87
1497 1505 1591 94
1515 1524 1611 96
1564 1573 1669 105
1584 1592 1689 105
1607 1618 1713 106
1637 1643 1745 109
1645 1657 1754 109
1663 1671 1779 116
1695 1707 1841 146
aTOKBS = bottom surface temperature

bTOKTS = top surface temperature ,

c o

orifice surface temperature (a black body)

TKBB

35

All temperature measurements were made in groups of at least three
to permit determination of temperature with a precision of $10. Tempera-
tures were read often enough to give a minimum of four determinations
during a target exposure. The average of all readings was taken as the
temperature of the exposure. In the experiments involving target col-
lection of the effusate, the temperature tended to drift upward with
time at the higher temperatures, probably as a result of deposits which
formed on the walls of the condenser and reflected radiation back to the
crucible. When the temperature of the Knudsen cell was decreased, this
effect was eliminated.

In the mass spectrometric experiments, the temperature remained
constant for periods of thirty minutes, within the limits of error of
the pyrometer readings at all temperatures. Thirty minutes was_the
maximum period of time any sample was held at one temperature. Since
less than thirty minutes was required to obtain the desired information

with the mass spectrometer, only two temperature readings were made.

F. The Mass Spectrometer

 

1. The Instrument

 

The mass spectrometer used in these studies was constructed in this
laboratory by Mr..Norman Fishel, Dr. Richard A. Kent and myself, from
components supplied by the Bendix Corporation. While not physically
similar to the corresponding commercial unit, the Model 12~101, electron-
ically it is identical, with one modification. The unit is equipped
with a 167 cm. driftntube instead of the normal 100 cm. tube. This
alteration required electronic circuitry modifications which were peru

formed by the Bendix Corporation.

36

The mass spectrometer was equipped with a high temperature Knudsen
inlet system described in Appendix B. The inlet system (separated from
the main vacuum system by a small slit) was evacuated by a 15 liter per
second Vac-Ion pump (Varian Associates, Palo Alto, California). Thus,a
differential pumping system was effected. The vacuum in the inlet system
was monitored by measuring the current flowing through the pump, Measured
pressures varied during an experimental run and were of the order of
10.5 to 10-6 terr. The vacuum in the ionization and drift chamber was
monitored by‘a Veeco (Vacuum Electronic Engineering Company) ionization
gauge. When the mass spectrometer was initially put into operation, a
pressure of 1 x 10'.8 torr was achieved. Under experimental operating
conditions, however, pressures of l to 6 x 10.7 torr were considered
adequate.

The output of the ion multiplier of the mass spectrometer was
observed on an oscilloscope. Two electrometers were also present. Any
portion of the mass Spectrum could be observed with these units by means
of a self-containing scanning system which pulsed a gate in the ion
multiplier to remove the electrons corresponding to the mass of interest.
The output of these electrometers was recorded on a Baush and Lomb VOM
5 strip chart recorder.

The two electrometers did not give the same ion intensity when
observing the same maSs peak. .For.quantitative work, it would have been
necessary to calibrate one against the other and to ascertain the
stability of this calibration. Since it was not necessary in this
investigation to perform quantitative observations on two species
simultaneously, only electrometer one was used. The second electrometer

was used only as an auxiliary device to observe other portions of the

spectrum.

37

Ion intensities were measured with this electrometer recorder
combination using the peak height on the chart combined with the scale
factors from the electrometer. The intensities were recorded in units

of nanoamperes.

2. Experimental Procedure

 

The Knudsen crucible used in these studies was fabricated from
molybdenum rod and spectroscopic grade graphite. It is shown in cross
section in Figure l. The cell was machined in three parts: top, bottom
and graphite liner. The top was pressed onto the bottom after the liner
had been put in place and the bottom cooled in liquid nitrogen. The
assembly was then heated to 20000 to bond the molybdenum together and
to remove anyvolatile impurities.

The cell was heated to a similar temperature before each experiment
as a cleaning procedure. A similar cell without the graphite liner was
used for some of the experiments with silver. After outgassing, the cell
was taken into a helium filled dry box and the sample loaded into the
cell through the orifice; europium dicarbide as a finely ground powder,
silver as thin wire. The cell was weighed before and after addition of
the sample. The cell was then removedfrom the dry box and placed as
rapidly as possible in the electron bombardment heating assembly of the
mass spectrometer. The complete assembly was attached to the mass
spectrometer which was evacuated immediately. The sample was exposed
to the atmosphere for two to three minutes.

The cell was heated in the mass spectrometer by electron bombard-
ment. A brief description of the power supply is given in Appendix C.

Crucible temperatures below 8000 were obtained by radiant heat from the

38

 

 

 

 

 

 

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39‘

tungsten filament. Although 8000 is not an upper limit for radiant
heating, no reliable method of controlling the filament current exists
on the power supply and this method of heating was not used above that
temperature. To achieve higher temperatures, a D. C. potential was
applied between the hot tungsten filament and the crucible; the fila—
ment being negative and the crucible at ground potential. The electrons
that "boil” off the hot filament are accelerated by the potential field
and gain kinetic energy. When these electrons hit the crucible they
release this energy to the crucible, thus heating it. The temperature
is controlled by varying the power of the bombarding electrons. The
method by which this control is achieved is described in Appendix C.

After the pressure in the mass spectrometer had decreased to 10-6
torr, the Knudsen cell was heated slowly to 8000 to outgas both it and
the sample.‘ Outgassing was considered finished when the pressure in the
sample region had decreased to 1 x 10.5 torr or less. In no Case was
the pressure allowed to exceed 5 x 10“4 torr during outgassing.

After outgaSsing, the D. C. potential was applied to the filament
and the control unit set for automatic regulation. The desired tempera-
ture was then selected using the appropriate setting on the power supply,
In general, the power control was changed by five units or multiples
thereof for each temperature change in order to provide a convenient
number should it be necessary to return to a given temperature. Once a
given power level was set, the corresponding temperature was read with
the optical pyrometer. Once a desired setting was made, the power
supply would maintain the selected power level within the accuracy of
the meters used for measurement. This stability was further confirmed

by the temperature readings which showed no change, within the limits of

40

error of the measurement, over periods of thirty minutes.
Once temperature equilibrium was established, (ten minutes or less)
the electrometer and recorder were set to scan the region 145 to 200

+ + +

a.m.u. This mass region includes the ions Eu , EuO , EuC , EuN+and EuC +

2
which might be expected above a europium carbide sample. The ion intensi-
ty data were then determined from the recorder charts. Other mass ranges
were observed periodically to check for other species that might be signi-
ficant. During several experiments the ion intensity was also measured
as a function of the energy of the electrons used to form the ions.
These measurements were made for mass 151, europium, mass 18, and mass
28 which was used as a reference since it was always present as back-
ground in the instrument. These data were plotted according to the
method of White, £5.2l- (30) and the straight line portion of the curve
was extrapolated to give the appearance potential”

The crucible temperature was varied in two different ways. In
some exPeriments, the temperature was increased step-wise to a maximum
and then decreased in like manner. In other experiments, the temperature
was first increased about twenty degrees, then decreased ten degrees,
then increased twenty degrees, etc. -- the temperature trend being upward.
After the maximum temperature was reached, the process was reversed and
the temperature was decreased. When a sauple was observed on succeeding'
days, after being at room temperature overnight, a similar temperature
schedule was followed.

When silver was added to the europium dicarbide sample, the tempera-
ture was first raised to approximately 11000. The ion intensity of Ag107

was measured as a function of time until all of the silver had evaporated

from the cell. The measurements on the dicarbide were then carried out

41

in the usual manner.

3. Treatment of Data

 

The temperature data from the mass spectrometer were corrected as
outlined on page 31 and then combined with the corresponding intensity
data to give the product IT for eurOpium 151 and eurOpium 153. These
numbers along with the temperature, were treated by the method of least
squares on a Control Data Corporation 3600 digital computer using the

equation:
In IT = A/T + B. (3-7)

The program to accomplish this was written following the equations given
by Youden (50). This program, which is given in Appendix D, calculated
the slope and intercept of the best straight line through the data. The
standard deviation of these quantities and the standard deviation of an
individual IT value were then calculated. Calculated values of IT were
generated for each T value and were compared with the input data. If
the difference between the calculated and the input value was more than
three times the standard deviation, the point was rejected and the
parameters for the line were recalculated. Dr. George D. Sturgeon modi-
fied the program so that the datum with the maximum deviation from the

expected value was tested for reliability first.

C. Effusion Experiments

 

1. Apparatus
Kent (51) has described the apparatus used in these experiments. The
Knudsen cell used for these experiments was the same as that used in the

mass spectrometric work.

42

2. Preparation of Tar ets

 

The effusate from the Knudsen cell was collected on platinum discs,
2.48 cm. in diameter and 0.13 mm. thick. The discs were cleaned in
boiling nitric acid, washed in distilled water and heated bright red in
a hydrogen flame. The targets were individually mounted in aluminum
cassettes and held in place by a phosphor-bronze spring. Eighteen
targets were loaded into the copper magazine of the effusion apparatus.

A knowledge of three dimensions is needed to calculate the vapor
pressure. These are the crucible orifice diameter, the distance from
orifice to target collimator and the diameter of the collimator.

The orifice diameter was measured using a set of number drills. A
drill was found which fit the orifice most closely and its diameter was
measured with a micrometer.

The orifice to collimator distance was measured with a Gaertner
Scientific, Mbdel No. M911, serial No. 1585a, cathetometer. The scale
could be read with a vernier to 0.05 mm. and readings were estimated to
0.01 mm. The measurements were made after the apparatus had been assem-
bled and evacuated for a minimum of one-half hour to seat the greased
glass joints. The vacuum system was then opened to the air, the shutter
assembly was removed and the height of the collimator was determined.
The system was re-evacuated and the height of the crucible was measured
through the Vycor condenser. Each measurement was made ten times and
the average value was used.

The collimator diameter was measured using a telescoping gauge and
a micrometer. Ten readings were taken on randomly spaced diameters and

the results averaged.

43

3. Procedure for Effusion Measurements

 

The procedure used during an effusion experiment was as follows:
The sample was loaded (in the dry box) through the orifice into the
effusion crucible. The targets were put in the magazine, the sample
crucible placed on its stand and the apparatus assembled and evacuated.
This last step was carried out as rapidly as possible to minimize reac-
tion of the sample with air. Helium was continuously passed through the
system to minimize sample reaction while the distance measurements were
made. The system wastfimnire-evacuated. When the pressure had decreased
to l x 10"6 torr, the magazine Dewar was filled with liquid nitrogen
and heating was begun. After the temperature had stabilized, the shutter
was opened and target one was exposed. The time interval during which
the shutter was open was measured with a Precision Scientific Company
”Time-It” electrical timer which was graduated to read to 0.01 minutes.
The temperature was measured several times during the exposure. When
the desired time had elapsed, the shutter was closed and the target was
ejected from the magazine. A new temperature was then selected and the
cycle refléated. The series of targets was exposed, first at successively
increasing temperatures over the range of interest, then at successively
decreasing temperatures. After the run was completed and the sample had
cooled, the crucible was placed in the dry box and the sample removed
for analysis. The crucible was then returned to the vacuum line for
measurement of top versus bottom temperatures. The targets were analyzed
as described previously (pp. 28-29).

The second effusion run, as well as two sets of targets in the first

run, was designed to determine the efficiency of the collection of

44

effusate on the targets. The procedure was like that described above
except that two target cassettes held two targets back to back with a

1.58 mm. diameter hole in the center of each. The second cassette held

a solid target. The operation was as follows: The first target inter-
cepted most of the effusate beam, the third target intercepted that which
passed through the holes in the first two, and the second target collected
that material which bounced off the third target. The analytical data

for targets two and three yielded the fraction of material adhering to

the upper target.

IV. RESULTS AND DISCUSSION

A. The Preparation and Some Physical Properties of Europium Dicarbide

The two methods for the preparation of lanthanon dicarbides dis-
cussed in Chapter III gave different results with europium and will be
discussed separately in this chapter.

1. WgéperimentsflInvoTving Europium SesquioXide and'carsdn

Three similar experiments were carried out in an attempt to prepare
europium dicarbide by the reduction of the sesquioxide with carbon. The
data are summarized in Table IV.

In experiment 1, the sample was heated three times. In the first
heating, a heavy black deposit, which was thought to be an impurity and
was disgarded, was found on the walls of the vacuum chamber. In subse-
quent heatings, when this deposit was analyzed chemically, europium was
found. But since some of the effusing material had been disgarded,
quantitative calculations could not be made.

In experiments %Nand 3, all of the material deposited on the con-
denser walls was retafined so that accurate mass balance data could be
obtained. The quantity of carbon monoxide given in Table IV was calcula-
ted assuming that reduction was complete and occurred according to the
equations:

Eu203(s) + 3C(s) * Eu(g) + 300(g) (4_1)

and

EuC + 3C0 (4-2)

Eu203(s) + 70 2(3)

(3) (g)°

The values for free carbon and europium were determined as described in

Chapter III.

45

46

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m H m e am 0 oo mm. o a uwnaaz
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mudoawumaxw donumo u.m0~5m How puma .>H mHQMH

47

Table TV shows that 91.5% and 93.5% of the material put into the
crucible was accounted for in experiments 2 and 3 respectively. The
remaining material probably escaped as gaseous hydrocarbons when the
material on the condenser walls was hydrolyzed (the odor characteristic
of acetylene was evident during hydrolysis).

An extrapolation of the data of Thorn and Winslow (29) for the tri-
meric and monomeric species, C3(g) and C1(g)’ which are the principal
vapor species in equilibrium.with graphite at high temperatures, indicates
that at 16000, the partial pressure of each is about 2 x 10"13 atm. This
low pressure, substantiated by the constant weight obtained when empty
graphite crucibles were heated at 14500 to 15000 for a few hours, indi-
cates that any carbon found in the condensate when europirum sesquioxide
and graphite were heated either left the crucible as a volatile carbon
species or was produced by reaction between carbon monoxide gas (present
in the system at pressures of about 10-3 torr) and the vaporizing species,
europium. However, the presence of a volatile carbide would not be sur-
prising since Chupka and cowxmkers (22) report that lanthanum.dicarbide
is a major component in the vapor in equilibrium with solid lanthanum
dicarbide.

The disturbing variation in the europium to graphite ratio in the.
condensate may result from either differences in the heats of sublimation
of europium and.eur0pium dicarbide, from the use of different acids in
the hydrolysis technique, from different reaction rates of europium.with
carbon monoxide gas or from combinations of the three. Since precise data
could not be obtained readily by this method, additional sesquioxide-

graphite experiments were not performed. In summary, two important

48

observations can be deduced from these data: First, since carbon is
found in the condensate, some volatile europium-carbon species may be
present in the vapor. Second, if such a species exists, its vapor

pressure is much higher than that of other lanthanon dicarbides.

2. The Preparation of Praseodymium Dicarbide

In order to determine whether or not die procedure just discussed,
involving europium sesquioxide and carbon, would yield a lanthanon di-
carbide with some other lanthanon oxide, a sample of Pr6011 was reduced
with carbon.

X-ray powder diffraction analysis of the praseodymium-carbon prepara-
tion showed only lines attributable to the tetragonal praseodymium dicar-
bide. The calculated lattice constants were: a0 = 3.8352; co = 6.3912.

These values compare favorably with the data of Spedding and co-workers

(14): a0 = 3.8553; c0 = 6.4342.

3. .Experiments'Involving Europium and carbon

(a) General

Since the sesquioxide-carbon experiments indicated the probable
existence of a highly volatile europium-carbon compound, the reaction of
europium and graphite in a closed container seemed a logical method to
attempt for the isolation of that compound. Stainless steel was chosen
for the container material since it was readily obtained and easily
machined. In addition, the low melting point of europium (875°) did not
require the use of a refractory metal.’ The construction of the bomb is
discussed in Chapter III.

The results of the tests used to check for the absence of contami-

nation of the sample by the bomb are as follows:

49

The thiocyanate ion test used to check for the presence of iron, the
major component of the bomb, was negative. From.this test, it was con-
cluded that no iron dissolved in the europium sample. The x-ray powder
diffraction pattern of the sample prepared in a molybdenum bomb and those
of the samples prepared in the stainless steel bomb gave identical d-
spacings. From this observation, it was concluded that neither bomb was
reacting with the europium sample. Thus, it is evident that the stain-
less steel bomb used was a suitable container for eur0pium dicarbide pre-
parations. Table V lists the europium carbide samples that were prepared,
the starting composition and the results of the chemical analyses that
were performed on those samples which were used for futher studies.

The reaction between europium and carbon in the stainless steel
bomb produced a soft crystalline material that was easily removed with
the aid of a tool made by grinding flat the end of a 3/8" drill. This
black material was ground easily toa fine powder in an agate mortar.
When it was exposed to the air, the sample reacted rapidly with moisture.
For this reason, sample manipulation was carried out in an_inert atmos-
phere whenever possible. The analytical data gave an average sample

composition of Eu C where the errOr is the standard deviation.

l.87i0.08

(b) vapor phase chromatographic analysis
Samples 1-16P, 1-17P and l-30bP were hydrolyzed with dilute (llev/v)

hydrochloric acid and the resulting gas was collected for vapor phase
chromatographic analysis as described-in Chapter III, section D-3. The
results for sample-l-16P were inconclusive due to technical difficulties.

A Chromatogram from the successful analysis of one of the other two samples

is shown in Figure 2. The first small peak and the large peak correspond

.II
J

50

Table V. Europium dicarbide preparations

 

a , r u ——

 

 

Samplefiumberh - 'Starting Composition . Analysis
1-15P 2.04
1-16P 2.02
l-17P 2.05 EuC1.93
l-23P 2.02
1-24P 1.78 EuCI.89
1-26P 1.95 EuC2.26b
l-28P 2.00 Eucl.92
1-30bP 1.50
1.31? 2.20 Eucl.91
l-34P 3.09
l-35P 1.79 EuCl.79
1-36P 1.83
1-43P 1.91
l-44P a Eucl.89
l-62P 2.07 Eucl.70
2-19P 2.56 Eucl.94

 

aComposition unknown - prepared by the addition of carbon to
unanlyzed sample l-43P

bAnalysis data believed to be invalid

 

51

 

Apex 7.9.4.4? Y Uu/ r:

 

 

 

 

 

flG up: 2 , 144.001? pHASE CH)? 0444 rOGRAM
OF 795' HVOA’ 02. rev: 10100.0 ac 7'
OF EUR cap/UM Oxcmea/OE.

52

to methane and acetylene respectively, as determined by comparison of
the retention times with those of standard samples. The second small
peak was assigned to ethane, but may be assignable to some other C2 or
C3 hydrocarbon since no ethane or propane standards were used. It was
not possible to condense any.hydrogen resulting from the hydrolysis with
the apparatus used. Therefore, accurate values for sample composition
can not be given since hydrogen was probably present. However, if the
results are based only on the hydrocarbons detected, it is possible to
state that acetylene was present in at least 98% concentration.

Palenik and Warf (52), Svec, Capallen and Saalfeld (53) and Green-
wood and Osborn (18) have studied the hydrolysis of the lanthanon di-
carbides. While these authors differ slightly in the relative quantities
of the hydrolysis products, they all report hydrogen, ethane, ethene,
ethyne andC4 hydrocarbons as the major products formed upon hydrolysis
of the dicarbides with dilute acid. A typical analysis would be: hydro-
gen 18%; ethane 6%; ethene 8%; ethyne 60%; C4 4%; others 4%. As is evi-
dent from Figure 2, the data from the hydrolysis of europium dicarbide
bear no resemblance to these data. Greenwood and Osborn (18) also
studied the hydrolysis of calcium dicarbide and found the resulting gas
to contain 98% acetylene, some carbon dioxide and no other hydrocarbons.
Therefore, I conclude that europiumdicarbide resembles the alkaline

earth dicarbides more than the other lanthanon dicarbides.

B. Xjray Analysis
All of the solid europium dicarbide preparations were analyzed by
_x-ray powder diffraction and all gave similar powder patterns. Patterns

were similar but not identical-- the d-values were the same on every

53

film, but the relative intensities of the lines varied with sample
composition. The x-ray powder photographs were characteristic of the
body-centered tetragonal structure common to the other lanthanon dicar-
bides and the alkaline earth dicarbides. The calculated lattice params
eters were: a0 a 4.045 3; co = 6.645 3. Interplanar d-values together
with their observed intensities are listed in Table VI.

In all preparations, a second phase was apparent, as indicated by
the three unindexed lines in Table VI. This phase could be reduced to
minor proportions by extended heating at 10600, but could not be removed.
This phase could be obtained in higher concentration by using a lower
carbon to europium ratio and by heating at lower temperatures.

The extra lines observed in the x-ray powder diffraction pattern
did not correspond either to the MZC3 or M30 phase reported by Spedding
and co-workers (14) for other lanthanons. This lack of comparison is
to be expected, however, since europium dicarbide is more alkaline earth
in character. The d-values for these extra lines were also compmed to
the d-values for europium metal, europium (II) oxide, europium (III)
oxide, europium nitride and graphite with negative results in all cases.
Consequently, this second phase is assumed to be a europium carbide
with a different crystal structure.

The volume of the unit cell for europium dicarbide (107 X) is sub-
stantially larger than that of the neighboring samarium and gadolinium
dicarbides (90 3 and 86.9 8 respectively). In this respect it is
analogous to ytterbium dicarbide, which, according to Spedding (14),
is also larger than its neighbors. This behavior is indicative of a
divalent metal ion, which is to be expected for eurOpium, and it indi-

cates that the dicarbide should be similar to an alkaline earth dicarbide.

54

 

 

Table VI. Interplanar d—spacings for EuC2 sample 1-24P
Miller Indices ‘ dcalc d obs I rela
(h k 1) 8 -

101 3.450 3.450

102 3.322 3.322

-—- --- 3.070

110 2.853 2.853

--- --- 2.561

112 2.165 2.169

200 2.006 2.020

.103 1.936 1.941

_-- --- 1.h05

211 1.747 1.748

as strong; m medium; w = weak

55

The lattice parameters and volume reported (9) for strontium dicarbide
(a0 = 4.11 3; co = 6.68 R; V = 112.7 2 3) are reasonably close to-those
observed for the europium dicarbide phase. In addition, the chemical
reactivities are similar.

From the data ofAtoji (21), it is possible to calculate the radii
of the lanthanon ions in the dicarbide phase. Some of these radii are
given in Table VII with the metallic radii calculated from the data
reported by Spedding (14). The radii calculated from the dicarbide
lattice parameters compare favorably with the metallic radii of the
lanthanons, with the exception of ytterbium. This discrepancy may be
explained on the basis of the crystal structure of the metal. As Hall,
Barnett and Merrill (55) have shown, the metallic radius of ytterbium,
in its body-centered cubic modification which is stable at high pres-
sures, is 1.75 2. Since the dicarbide is a body-centered type structure,
its metallic radius would be expected to agree more closely with this
form of the metal, rather than with the closestapacked form of ytter-

bium which exists normally.

C. Knudsen Effusion ExperimentsInvolving Target Collection

 

1. General
Mass spectrometric results, which will be discussed later, show
that europium constituted at least 99% of the vapor in equilibrium with

europium dicarbide. Thus equation 2-15
P = w/Sot (mm/11¢ (2-15)

defines the vapor pressure when M is taken as 152.00. This equation, or
its modified form, equation 2-16, was used to calculate the vapor pres-

sures reported in this section.

56

Table VII. Radii of the lanthanons in the dicarbide phase (2)

 

 

 

rmetallica C - C rcalcC
Sm 1.802 1.285b .1.880
Eu 1.984d 1.285 2.038
Gd 1.802 1.285 1.852
Tb 1.782 1.293 1.820
Yb 1.940 (fcc) 1.287 1.768

1.751 (bcc)e

 

aMetallic radius calculated from the lattice constants for the metal
bAverage C-C distance given by Atoji(21)

CMetallic radius calculated from the lattice constants of the dicarbides
dCalculated from data of Spedding, Hanak and Daane (54)

eData from ref. (55)

57

 

2. .Preliminagy Experiment

A preliminary effusion experiment was undertaken to determine if
the rate of vaporization of europium dicarbide could be measured. A
portion of sample l-35P was heated four times successively.. All of the
material effusing from the cell was collected and analyzed chemically.
The results of the four preliminary effusion runs are shown in Table VIII.

The crucible and contents were not weighed between heatings since
this would have involved exposure to the air, resulting in sample decomr
position. The average time the crucible was exposed to the air while
the collection tubes were being changed was estimated to be twenty
seconds. Since the vacuum was broken by the admission of helium to the
system, the crucible contained helium and the brief exposure to the air
should have resulted in negligible sample decomposition.

The data in Table VIII show considerable scatter. However, since
these were only preliminary data, the scatter may be attributed to
random error and we may conclude that the vaporization process is occur-
ring at a constant rate even when about one half of the sample is removed
from the cell byvaporization. A non—constant effusion rate would
indicate that equilibrium was not being maintained in the effusion cell.
Since the use of the Knudsen method requires maintenance of equilibrium,
a non-equilibrium process cannot be treated by this method.

Another important observation, not shown in the table, was that
the effusing material covered the inverted test tube from a level below
the bottom of the crucible to the top of the tube. This indicated that
some europium Species was passing directly through the walls of the cruci-
ble in addition to effusing through the orifice. TSuch cell leakage

would produce high values for the calculated pressure together with

58

Table VIII. Effusion data for sample l-35P

W

 

Heating Te erature Time Free Eu Effusion Pressure
Number mp Graphite .Collected Rate
OK min. mg. mg. mg./min. atm.x104
l 1565 8 0.00 37.07 4.63 3.52
2 1637 6 7.00 59.89 9.98 7.75
3 1637 7 0.00 57.59 8.23 6.39
4 1642 10 0.00 95.90 9.59 7.53

Orifice diameter: 0.711 mm. at room temperature

 

59

scatter in the data. Therefore, graphite is not a suitable crucible

material for the study of eurOpium dicarbide.

3. Individual Experiments
(a) Experiment E-l'

In order to eliminate the problem of material passing through the
walls of the effusion crucible, the carbon lined molybdenum cell described
in Chapter III, sectioan- , was used in.this and all subsequent effusion
experiments. The exposure temperatures were arbitrarily varied. .After
the initial degassing of the crucible at temperatures between 4000
to 900°, the pressure in the system, continuously monitored with a Veeco
vacuum gauge, remained below 5 x 10""6 torr throughout the remainder of
the experiment.

Chemical analysis of sample 1-44P before the experiment was begun
showed the sunshiometry to be Eu01.89. It was not possible to analyze
the residue since an insufficient quantity remained in the cell. An
x-ray powder diffraction photograph of the residue indicated graphite was
the principal product. I

Duplicate analyses of the material on the target gave-widely differ-
-ing-absorbancy values. The difficulty was investigated in-detail using
standard solutions. A faulty cleaning procedure used on the glassware
caused the erratic results. The original procedure was to clean the
glassware thoroughly in detergent and then rinse well with water. When
the detergent cleaning was followed by treatment with "aqua regia" and
then a thorough water rinse, consistent results were obtained for the
standard solutions. -Apparent1y all of the europium on the glass from

previous analyses was not removed by the detergent solution or perhaps

60

some of the detergent remained on the glass and hindered the formation
of the colored europium complex.

When the analytical method was functioning properly, the solutions
from the targets were reanalyzed with reasonably good results which are
shown in Table IX. During the course of the analysis, new solutions
had to be made and therefore, the absorbancy values for two different
samples of the same concentration may not be the same.

The concentration data from the analysis were used to calculate the
pressures in the Knudsen cell corresponding to each target exposure.

The results are shown in Table X. A plot of ln P vs 104/T is shown in
Figure 3. The line in Figure 3 was calculated by a least squares treatw
ment of the data.

A large amount of scatter is present in the pressures. There are
two probable causes of this scatter. The first, which would be expected
to give a random error, is error in the analysis. The second is bouncing
from the target.

A least squares treatment of the absorbancy values for the standard

europium solutions gave the equation:
-3 «3
AS = (5.538 t 0.008 x 10 )C _ (6.253 t 2.8 x 10 ) (4»3)

where AS is the absorbancy and C is the concentration, in micrograms, of
europium in the sample taken for analysis. Solving this equation for

C gives:

A8 + 6.253 x 10"”3
..C = _3 . (4»4)
5.538 x 10

 

It is evident from equation 4-4 that a change in AS of 6 x 10“3 will

61

 

 

 

Table IX. Analytical data for targets from experiment E-l
Target :Absorbancyay Eu Eu total

No. ug./ml. ug./target

1 .003 .001 1.49 74.5

2 .026 .027 5.91 148

3 .009 .015 3.30 165

4 .034 .026 6.55 327

5 .081 .073 15.03 752

6a* .034 .037 7.54 377

6b .026 .028 6.00 150

7 .041 .055 9.80 245
10 .056 .059 5.75 144
11 .065 .061 6.00 300
12 .044 .048 2.85 142
13a* .051 .044 3.20 160
13b .062 .055 5.00 125
14 .057 .062 5.25 131
15 .043 .037 2.00 100
16 .019 .017 4.38 133
17 .011 .006 2.66 219
18 .011 .007 2.75 138

 

8Values are for duplicate analyses of samples

_,_._

w

*
Targets 6 and 7 and 13 and 14 were used to check for bouncing.

62

Table X. Data for experiment E-l

 

H
__

Target

Temperature

YExposure Time E

 

o ucollected Eu
.No. K min. x 10"6 (gm.) atm.

16 ,1404 120 219 7.53 x 10'5
1 1450 120 74.5 2.60 x 10‘5
2 1321 180 148 3.29 x 10'5
3 1609 90 165 8.09 x 10-5
4 1672 30 327 4.91 x 10"4
5 1578 60 752 5.48 x 10'4

10 1335 180 144 3.21 x 10-5

11 1246 220 300 5.30 x 10"5

12 1486 90 142 6.72 x 10’5

15 1661 30 100 1.50 x 10‘4

17 1503 90 133 6.31 x 10"5

18 1542 90 138 6.61 x 10‘5
6a 1625 30 377
6b 1625 30 150 1.14 x 10-3*
7 1625 30 245

13a 1358 245 160

13b 1358 245 125 7.64 x 10‘5*

14 1358 245 131

A l/T = 7.51 x 10"6

Orifice diameter: 0.80264 mm. at room temperature

0.80664 mm. at exposure temperature

Collimator diameter: 129076 i 0;OOSl cm.

Orifice to collimator distance: 12.858 i 0.004 cm.

 

*Pressure calculated from the sum of europium collected on targets 6a,
6b and 7 and 13a, 13b and 14.

63

 

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64

result in an error of roughly one microgram in the calculated concen-
tration. Table IX shows that, on the average, this is the difference in
the absorbancy values for duplicate samples. Thus, the average error in
the measured concentration is approximately ilug, For most of the
measured concentrations, this amounts to a twenty to seventy per cent
error. These data, therefore, are not sufficiently precise to yield
accurate calculated pressures.

Target pairs 6 and 7 and 13 and 14 were exposed simultaneously to
check for bouncing of the effusate from the target, as described in
Chapter III, section G-3. For the pair 6-7, 38% bouncing is indicated;
for pair 13-14, 49% bouncing is indicated. 1Since these targets were
exposed at different temperatures (see Table X) an error that may be a
function of temperature is introduced. These two sets of data are not
sufficient to determine whether bouncingactually varies with temperature
or whether analysis errors are present, but they do indicate that an
error due to less than total adherence to the target is present.

(b) Experiment E-2

This experiment was designed specifically to determine the extent
of bouncing present and its temperature dependence. The same crucible
used in experiment E-l was charged with a portion of sample 2-19P

(stoichiometry EuC The first two targets were "exposed" with the

1.94)'
shutter closed in order to determine the shutter efficiency. The remain-
ing targets were exposed in groups of two, as described in Chapter III,
section G-3. The results of this experiment are shown in Table XI.
Targets l3 and 18 were used to check shutter efficiency. While some

europium may have been present on the target, the quantity was below the

limits of detection of the method (25 micrograms) and the results are

65

Table XI. Data for experiment E-2

 

 

 

 

 

 

 

Target TObserved Exposure Europium Bouncing
No. empegzture time on Target .%
m n. pug.
13“ 850 400 <25 -.-
18a 1198 30 <25 ---
1a 1200 60 213 ---
1b 1200 60 72 46
2 1200 60 85
3a 1117 90 118
3b 1117 90 82 43
4 1117 90 110
Be 1180 60 150
5b 1180 60 42 31
6 1180 60 92
7a 1085 90 100
7b 1085 90 64 54

Orifice diameter: 0.8026 mm. at room temperature
0.8066 mm. at exposure temperature.
Collimator diameter: 1.90756 i 0.0051 cm.

Orifice to collimator distance: 13.125 i 0.004 cm.

 

. *V . 1 ‘ .1

aTargets "exposed" with shutter closed

66

therefore listed as less than twenty-five micrograms. Thus, the shutter
was operating properly and shielding the target from the molecular beam.

The analytical data for the remaining targets indicate that a very
large bouncing effect is present; on the average, 43%. Although great
care was taken in order to make the chemical analysis as accurate as
possible, a difference of one microgram was still evident for duplicate
samples. When a dilution factor of twenty-five is applied, a possible
error of twenty-five micrograms results. If this error is assumed to be
non-randomand in such a direction as to reduce the calculated bouncing,
an average bouncing effect of twenty-six per cent is calculated. Since
there is no valid reason for assuming a non-random error, only fifty-
seven per centuof the effusing molecules whichstrike the collector are
adhering toit.

In order to eliminate or reduce bouncing to an acceptable level of
one to ten per cent, it would have been necessary to redesign the
apparatus to bring the liquid nitrogen into closer proximity to the
targets. Also, in all probability, a number of other variables would
have needed examination. 'These difficulties, combined with the absence
of a precise method for the analysis of europium at low concentrations,
led to the conclusion that further work in this area would not yield
results in proportion to the time Spent. Therefore, the experiments
involving chemical analysis of the collected effusate were terminated
in favor of the use of the mass Spectrometer to determine the decomposition .

pressure of europium dicarbide.

D. Mass Spectrometric Studies of Europium Dicarbide

1. Introduction

67

Since the collection technique and the chemical analysis of the
effusate from the Knudsen cell did not yield reproducible data, the use
of the mass spectrometer for an extensive study of europium dicarbide
seemed mandatory. The mass spectrometer eliminates the difficulties
encountered in chemical analysis. The physical arrangement of the
Knudsen source in the spectrometer is such that very few of the effusing
molecules which bounce from the radiation shielding can enter the ioniz-
ing region of the mass spectrometer. Use of the mass Spectrometer, does,
however, introduce a different source of error since it must be calibrated
with a substance of known vapor pressure in order to obtain partial pres-
sures of europium. This calibration, which involves assumptions that
introduce some error, will be discussed more fully subsequently.

When the mass spectrometer is used for the quantitative determination
of gaseous species, temperature and ion intensity are measured. As a

result of the phase rule, the temperature determines the ion intensity.

2. Conventions for Treatment of Data

 

The experimental data indicated that europium gas was the major
vapor component (99%) above europium dicarbide, thus indicating the

reaction:

EuC Eu + 20 (4~5)

2(8) (g) (S)'

The intensities of Eu151 and Eu153 were determined as a function of

temperature. Equation 2-22,
In k IT = - AHO/RT + ASo/R (2422)

shows that a graph of 1n IT vs 1/T yields the value of AH0 from the

68

slope. The intensity data for the two europium isotopes were treated
separately by the method of least squares to yield two enthalpy values
for each experiment. For the experiment in which silver was used as a
calibrating substance, the value of k in equation 2-22 was determined
and then used to calculate the entropy change for equation 4—5. The
value of k was also used to calculate the pressures corresponding to the
measured ion intensities. These pressures were then used in the third
law method discussed in Chapter II, section B, to determine the enthalpy
of vaporization. In most of the experiments discussed in this section,
large numbers of intensity-temperature measurements were taken. The

data for europium dicarbide are tabulated in Appendix E.

3. Individual Experiments

(a) Experiment MS-l

 

The carbon—lined molybdenum effusion crucible was filled with a
portion of sample 1-44P and situated in the Knudsen source region of the
mass spectrometer. After the Knudsen source region had been degassed
at 9000 for several hours, the cell temperature was increased and inten-
sitydata were collected as a function of temperature. When the instru~
ment was left overnight, the sample was maintained at 8000 by the hot
filament. This procedure resulted in probable contamination of the
sample since the liquid nitrogen source failed, resulting in the release
of a large quantity of water vapor from the cold trap. Since the sam-
ple was exposed to air and to water vapor in the vacuum system the data
obtained from this sample are probably not quantitatively accurate;
however, they are presented as an indication of what might be expected

in further experiments.

69

The data were plotted separately according to the day obtained.
The results are summarized in Table XII. The two europium mass peaks,
151 and 153, were the major species observed in thespectrum, along with
two much smaller peaks identified as europium dicarbide.masses 175 and
177. The intensity of these small peaks was less than one per cent of
that of the europium peaks -- so low that a temperature dependence could
not be measured. No other mass peaks (above background) were observed.
The energy of the ionizing electrons was low enough (15 electron volts)
so that no doubly charged ions would have been expected. None was
observed.

(b) Experiment MS-Z

 

The effusion crucible used previously was charged with a portion of
sample 1-62P. Data were collected over a period of several days. On
the second day, a capacitor in the power supply of the mass spectrometer
failed. After the inStrument was repaired, the operating parameters of
the instrument were readjusted. For this reason, the data are broken
down into two portions, those taken before and those taken after read-
justment, and are listed under the headings MS=2a and MS-2b respectively
in Table XIII.. The data for MS~2a, when plotted as 1n IT vs l/T, fell
on a straight line. All the data for MS~2b, when plotted similarly,
lie on another straight line, even though they were taken on different
days. Therefore, these data were treated as one set.

The enthalpy values for MS-2a are considered unreliable. The
probable causes of unreliability were changes in the instrument prior
to, and caused by, the failure of the capacitor.

A large peak corresponding to nitrogen, carbon monoxide, or both was

observed at mass 28. Nitrogen is the major species present in the

70

Table XII. Summary of experiment MS-l

 

I; "

Temperature Enthalpy

 

Day Isotope Range
TObserved °K kca1./mole
1 Eu151 1214 - 1369 37.6 1 2.89a
1 Eu153 1214 - 1369 38.4 i 2.76
2 Eu151 1204 - 1434 40.1 a 1.87
2 Eu153 1204 - 1434 43.7 a 1.23

A 1/T = 8.77 x 10"6

 

aStandard deviation

Table

‘XIII. Summary of experiment MS-2

71

 

 

Temperature

 

Isotope Enthalpy
Number Observed Rgfige kcal./mole
MS-2a 36151 1326 - 1451 61.43 a 3.578
MS-Za Eu153 1326 - 1451 57.02 a 2.48
MS-Zb Eu151 1326 - 1697 50.31 a 1.35
MS-2b Eu153 1326 - 1697 51.68 a 1.71

A l/T = 10.58 x 10'

6

 

aStandard deviation

 

72

residual gas in the vacuum system. Its intensity should increase as the
Knudsen source region is heated.as a result of dggassingwof the radia-
tion shields and vacuum chamber walls. Alcock,‘g£.gl.(56)~have shown
that carbon monoxide is present when uranium dicarbide is heated; there-
fore, it would be expected here also. Since the instrument cannot
distinguish between these two molecules, quantitative estimates of their
relative proportions cannot be made. *

Several times during the course of this experiment, the ion intensity
of Eu151 was observed at constant temperature as a function of time. The
results are shown in Table XIV. Several important observations can be
made from these data. For periodsof up to twenty-seven minutes, the
temperature remained constant within the reading limits of the optical
pyrometer. With the exception of the fifteen minute observation, the
ion currentremained constant with time, indicating a constant rate of
effusion from the Knudsen cell. The fifteen minute observation showed
an upward drift during the first half of the observation period and then
remained constant. This drift may have resulted from a temperature drift,
but the magnitude of the intensity change was greater than would be
expected for the measured temperature change. Finally, when the temperau
ture was returned to 14950 K, after sixteen hours at operating temperau
ture, the ion intensity also returned to the initial value of 0.023 as
indicated by thefirSt and last entries in Table XIV. The constancy of
the effusion rate indicates that equilibrium was maintained in the cell
and that the dicarbide composition was not changing. Eick, Rauh and
Thorn (57) have shown that in the uranium-carbon system, the sample
composition changes during the vaporization process and that, as a result,

the measured vapor pressure decreases with time, since equilibrium is

73

Table XIV. Data on the ion intensity of mass 151 as a function of time

m

 

 

Duration of Initial Final
Observation Ion Intensity Temperature Ion Intensity Temperature
min. nanoamps °K nanoamps 0K
8 0.0236 1469 0.0234 1469
15 0.045 1581 0.053 1585
6 0.083 1589 0.082 1599
6 0.162 1677 0.162 1677

27 0.024 1465 0.023 1463

 

74

nOt established rapidly.

(c) Experiment MS-3

In this experiment, a portion of sample 2-19P was used. The method
and operating conditions were the same as those described previously. I
believe the results obtained in this experiment are all reliable. When
these data were treated by the method of least squares, the enthalpy

values for the disproportionation reaction (4-5) were found to be:

AHO

52.10 i 0.61 kca1./mole ; mass 151
and

AH0 53.92 i 0.61 kcal./mole ; mass 153.

There was insufficient residue to permit chemical analysis. -X-ray
powder diffraction analysis indicated graphite to be the only phase
present in the residue which was not present in the starting material.

In this experiment, small peaks attributable to europium dicarbide
were present, but the intensities could not be determined as a function
of temperature Since they were too low to measure accurately. No other

. . . , a . . . 151
europium containing Species was observed. The ion intenSLty of Eu

was observed at constant temperature as a function of time and was

found to be constant, as before.

(d) Experiment MS—4

 

In this experiment, a silver wire was cleaned by abrasion and heat.
It was then placed in a molybdenum crucible, similar to the one used
previously, but without the carbon liner and with a larger orifice
(1.181 mm. as compared to 0.803 mm.) The crucible was placed in the

mass spectrometer and the intensities of Ag107 and Ag109 were observed

75

as a function of temperature. The ion intensity-temperature data are
listed in Appendix E.

As is indicated in Appendix E, a visible coating appeared on the
window at a cell temperature of 13720 K. The temperature was immediately
reduced to prevent the formation of an extensive deposit. The window
and prism correction measured before the experiment was applied to the
data taken before extensive deposit formation; and the correction
measured after the experiment was applied to the data taken after the
visible deposit formed. Admittedly, this procedure introduces some
error, but since deposit formation occurs more rapidly at high tempera-
tures than at low temperatures, less error would be introduced than if
average values were used.

Prior to this experiment, a shutter was installed between the
Knudsen source and the ionization chamber of the mass spectrometer.
When this shutter was closed during operation, the intensity ofthe
silver peaks fell to zero indicating that the total intensity of the
peaks at masses 107 and 109 resulted from atoms leaving the Knudsen
cell.

The enthalpies of vaporization calculated from these data are:

0

AH 74.23 i 1.13 kcal./mole ; mass 107

411°

74.03 i 0.86 kcal./mole ,; mass 109.

These values are much higher than the accepted value of 64.4 kcal./mole
calculated from the data in Stull and Sinke (58). Mrs. Rebecca Jacobs,
using the same instrument and the same crucible, also experienced diffi-
culty obtaining reliable data for the vaporization of silver. _She also
investigated the vaporization of copper and obtained data in agreement

with reported values.

76

There are some possible explanations for the discrepancy in the
data. A temperature error could have resulted from the formation of a
silver deposit on the window. Every effort was made to measure the
transmittance of the deposit through the same area as was used in the
temperature measurement. However, since this area is small, exact
duplication of the area is difficult. The thickness of the deposit
decreases rapidly outward from the center, and thus, a small shift in
the measuring point would result in a large error in the measured trans-
mittance. A low correction factor based on this transmittance would
result in calculated temperatures lower than the true temperatures. The
high temperature measurements are more affected by transmittancy error
since deposit formation is extensive only at high temperatures. If
temperatures lower than the true temperatures are used for the high
temperature points, the slope of the curve 1n IT vs 1/T is increased,
resulting in a high value for the calculated enthalpy. Another possible
source of error may have resulted from the use of too small a silver
sample. If the volume of silver present were insufficient to cover the

”see” both silver and molyb-

bottom of the crucible, the orifice would
denum. The result would be that the distribution of particles leaving
the effusion cell would no longer follow the cosine law. Since ninety
per cent of the silver in the crucible was vaporized, a changing sample
area would change the distribution of particles effusing from the cell.
Since Mrs. JacObs and the author both experienced, under similar
conditions, trouble in the vaporization of silver,and since she obtained
reliable data for the vaporization of copper, it is assumed that it was

something in the design of the experiments, and not the mass Spectrometer

itself, which was at fault.

77

(e) Experiment MS-5

In this experiment, a portion of sample 2-19P was placed in the
Knudsen cell along with 6.04 mg. of silver wire. After the crucible had
been outgassed, the temperature of the cell was rapidly increased to
13670 K and the intensity of Ag107 was observed as a function of time.
The Ag107 pressure in the Knudsen cell, calculated from the time required
to vaporize all of the silver, was 4.06 x 10“5 atm., as compared to the
accepted value of 3.77 x 10”5 atm. at this temperature. The sensitivity

of the mass Spectrometer was calculated according to equation 2-20:

2 IA At /T
k=i g 3 (4-6)
P
A8

 

and was found to be 2.488 x 102 nanoamps/atm. of Ag107.

After the silver had vaporized, the intensities of the europium
peaks were observed in the usual manner.
The pressures corresponding to the observed intensities were calcu—

lated according to equation 447:

\

= 1 . I O. (I .1 1' "7'6 . no
P 1/r.k ‘GAg/ Eu) . Eu/IAg) /5 )lEu (4 7)

(SAg Eu

The ratio of multiplier sensitivities (SAg/SEu) was taken as unity. The

was estimated from the metal-metal

ratio of the cross section 0 o
( Ag/ Eu)

distances in the crystal as given by Pauling (59). The resulting ratio

W883

' 2
oAg/cEu - (2.878/4.168) — 0.4768. (4w8)

The 1n IT was plotted against l/T, and the enthalpy of vaporization

calculated from the slope was:

78

AH a 49.17 i 0.77 kcal./mole.

Figure 4 shows this plot for Eu151. The scatter about the line in this

graph is typical of the scatter found in the mass spectrometric data
from the other experiments. The entropy was calculated from the intercept

using the constant K from the equations:

P = KIEuTEu (4-9)
and

ln P = 1n IT + 1n K = - AH/RT + AS/R (4-10)
so that

Intercept = AS/R - In K. (4-11)

K was calculated to be 2.9317 x 10“6 for mass 151 and 2.6852 x 10“6 for

mass 153. The resulting value for the entropy for reaction 4-5 is:
AS = 18.43 i 0.57 e.u.

The error in both the enthalpy and entrOpy is the standard deviation
obtained from the least squares treatment.

During the experiment, the intensities of the peaks at masses 151,
28 and 18 were measured as a function of the energy of the ionizing
electrons. The data, plotted as ion intensity versus electron energy,
are shown in Figure 5.

When the straight line portions of the curves were extrapolated to
zero ion intensity, electron volt values of 8.0, 16.0 and 18.6 were

found for masses 151, 18 and 28 reapectively. If the peak at mass 28

79

 

 

 

 

 

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is assumed to be nitrogen, the intercept for this curve should be 15.6
e.v. By applying the difference between the measured appearance poten-
tial and the ionization potential for nitrogen as a correction factor to
the other two values, ionization potentials of 5.0 e.v. and 13.0 e.v.
were obtained for europium and water, respectively. The accepted values
are 5.6 e.v. and 12.8 e.v. The close agreement between accepted and
calculated ionization potentials indicates that europium atoms are
present as a component of the vapor from the Knudsen cell and that the
europium atoms do not result from fragmentation.of some higher molecular
weight species.

In this experiment, an attempt was made to measure the concentration
of gaseous europium dicarbide as a function of temperature. The sphctrum
was scanned with low energy ionizing electrons (10 e.v.) in order to
prevent fragmentation of any unstable dicarbide molecule.

A typical mass spectrum of the europiummeuropium dicarbide peaks
obtained at 14790 K is shown in Figure 6. The intensities of the
dicarbide peaks obtained at this and other temperatures are on the order
of one per cent of the intensity of the europium peaks. The dicarbide
peaks were not present when the ionization energy was raised to the
normal operating value of 18.0 e.v. Thus, gaseous europium dicarbide
is present in the vapor phase above solid europium dicarbide, but the
molecule is quite unstable.

After completion of the experiment, there was insuffiCient residue
to permit chemical analysis. X-ray powder diffraction analysis showed
that graphite was the only material present in the residue which was not

present in the starting material, as was typical of previous experiments.

82

 

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Hal/RE 6‘ 711/5 MAJ: SPEC 7790M 0F
[09 09/4/44 — EUR Op/UM
OICARBIOE.

 

83

4. Treatment of data

 

(a) Calculation of AHF

The data for the enthalpy of vaporization of europium dicarbide
from eXperiments MS-Z, MS-3 and MS-S were combined with the enthalpy of
vaporization of europium (42.066 kca1./mole) reported by Spedding, Hanak
and Daane (54). The resulting enthalpies of formation, assuming ACp is

zero, are for equation 4-12:

Eu(s) + 1.87 C(s) hiEucl.87(s) (4-12)
AH398 = -8.93 i 2.18 kca1./mole ; MS-2
Anggs = -11.04 a 0.86 kca1./mole ; MS-3
AH398 = -7.10 i 0.77 kca1./mole ; MS-S.

(b) Calculation of the Free Energy Functions
It was shown that the vaporization of europium dicarbide proceeds

according to the reaction:

EuC 2 Eu (4-5)

1.87 '(g) + 1.87 C

(S)'

The second law value of the enthalpy of vaporization obtained from a
plot of 1n IT vs l/T can be checked by means of a third law calculation

based on the equation:

0

A 298

= -T [A(G; - H /T)] ~ RT In P. (4‘13)

‘0
H298
The necessary free energy functions were taken from published reports

or estimated as follows:

1) Eugs & )

Taken from Stull and Sinke (58).

 

84

2) Ca(s)

Taken from Stull and Sinke (58).

3) Graphite

Taken from Stull and Sinke (58).

4) Eungs)

No data were available for this compound; therefore, the free energy
functions were estimated as a function of temperature from the data on
calcium carbide given by Kelly (60) and Kelly and King (61). The calcu-

lations were based on the hypothetical reaction:

CaCZ<s> + Eu(s) EuC2(S) + Ca(s). (4-14)
The free energy function for europium dicarbide then becomes:
fefEUCZ = fefCaC2 — fefca + fefEu. (4-15)

The estimated values of the free energy function for europium
dicarbide were combined with the free energy functions for europium gas
and graphite to give the change in the free energy function for reaction
4~5. The results are shown in Table XV and Figure 7. The enthalpy of
the vaporization reaction was then calculated using these data and the
pressure data from experiment MS-S. The results shown in Table XVI lead

to the average value:

0

= 1 -. i . ' . . .
H298 5 .72 0 80 kcal /mole

A

This value, combined with the enthalpy of vaporization for europium,

 

85

Table XV. Free energy functions for EuC

 

 

 

2

T 7 ~fef l-"feffi -fef 7‘ :Afef

o EuC2(s) Eu Graphite(s)

K cal./deg.-mole ca1./deg.-mole ca1./deg.—mole ca1./deg.-mole
1100 27.01 47.96 3.31 20.70
1200 28.21 48.29 3.60 20.47
1300 29.34 48.59 3.86 20.18
1400 30.18 48.87 4.11 20.15
1500 31.42 49.15 4.37 19.71
1600 32.37 49.41 4.61 19.51

 

 

86

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87

Table XVI. Third law values of the enthalpy of vaporization for EuC2

 

 

Temperature From mass 151 From mass 153
0K AH298 AH398
kcal. mole kcal./mole
1263 51.875 52.336
1263 51.975 51.705
1298 51.677 51.627
1298 51.299 50.128
1339 51.253 51.568
1339 51.731 50.043
1372 51.061 51.177
1372 51.061 51,177
1401 51.004 51.071
1401 50.834 50.946
1464 50.764 50.933
1464 50.764 50.805
1335 51.242 51.772
1335 51.242 51.227
1139 51.668 51.861
1214 51.697 51.648
1214 51.727 51.648
1280 51.965 51.573
1280 51.920 51.598
1350 51.000 51.051
1350 51.000 51.081
1412 50.822 50.638
1412 50.673 50.638
1479 50.992 50.858
1479 ‘ 50.868 50.932
1537 ‘ . 50.978 50.755
1537 50.846 50.886
1190 50.905 51.063
1190 51.239 51.397
1356 51.510 51.408
1356 51.403 51.408
1457 51.215 51.308
1457 51.053 51.308
1518 51.062 50.932
1518 51.002 50.932
1554 51.052 51.194
1554 51.281 51.237
1568 50.989 51.187
1568 51.029 51.187
1587 51.257 51.275
1587 51.082 51.193
1520 51.248 51.272
1520 51.443 51.272
1356 51.894 51.915
1356 51.852 52.049

Mean of all values: 51.22 kcal./mole; Standard deviation: 0.80 kcal./mole

 

 

88

yields a value of -9.16 i 0.80 kcal./mole for the enthalpy of formation
of europium dicarbide.

The pressure data from experiment E-l were used to calculate enthal-
pies of vaporization. The results are given in Table XVII. These data
show considerable scatter as would be expected from the scatter in the
pressure data used in the calculations. Comparison of these enthalpies
with those calculated from experiment MSwS shows these data to be, in
general, higher than the latter. This is expected, since the "bouncing”,
found in experiments E-l and E-2, would cause the caflculated pressure to
be low.

Even though these data show considerable scatter, the average value
(56.29 kcal./mole) is close to the average value calculated from the
data from experiment MS-S (51.22 kcal./mole). This closeness indicates
that the pressures calculated from the mass spectrometric data are true
pressures and thus, that the enthalpy of vaporization obtained from these
data is correct.

In summary, the second law method yields the following heats of

vaporization for europium dicarbide:

51.00 i 2.18 kcal./mole ; MS-Z
53.11 i 0.86 kcal./mole ; MS-3
49.17 i 0.77 kcal./mole ; MS-S.

The average value is 51.09 i l.42./mole. The third law calculation
of the enthalpy of vaporization yields a value of 51.22 i 0.80 kcal./mole,
in excellent agreement with the second law value. The enthalpy of

formation calculated for europium dicarbide from the second law is

Table XVII.

Third law values of the enthalpy of vaporization for EuC

calculated from experiment E-l

89

2

 

 

Temperature AH§98
0K kcal. mole
1404 54. 61
1450 59.15
1321 53.69
1609 61.49
1672 57.71
1578 54.39
1335 54.26
1246 49.67
1486 57.34
1661 61.28
1503 58.51
1542 59.75
1625 53.10
1358 52.79

mean

56.29

 

 

90

-9.02 i 1.42 kcal./mole and is in excellent agreement with the third law
value of -9.16 i 0.80 kcal./mole.

Chupka and co-workers (22) found the heat of formation of lanthanum
dicarbide to be ~44 kcal./mole; Jackson and co-workers (24) found the
heat of formation of gadolinium to be -26 kcal./mole. The heat of forma-
tion of calcium carbide is listed (62) as -15 kcal./mole. Comparison of
these numbers with the heat of formation of europium dicarbide, ~9.09
kca1./mole, supports the conclusion that europium dicarbide is more like
the alkaline earth dicarbides than the other lanthanon dicarbides.

The pressure of eurOpium gas in equilibrium with europium dicarbide

may be described by the equation:
1ne P(atm) = - 23709 i 715/T + 9.270 t 0.886.

Thw slope of this line is the average value of the slope for experiments

MSqu, MS~3 and MS-S. The intercept is from the data from experiment MS-S.

5. Analysis of Errors

 

An examination of the errors involved in the determination of the
experimental quantities should allow one to ascertain whether or not the
scatter in the data plotted in Figure 4 can be ascribed to random errors
in the measurements or whether other factors were involved. This evalu
uation can be made best by examining the error in one of the representa—
tive datum. The point selected is the one occurring at T = 10700 with
intensity 0.031 nanoamps°

The observed scatter results from two sources. One is the error in
measurement of the ion intensity; the other is the error in measurement

of the temperature. The measured intensity was 0.031 i 0.003; the

91

temperature 10700 i 5.00. The standard deviation of the term 1n IT,

as calculated from the computer program for the least squares treatment
of the data, is 1n IT = 3.7657.i 0.112 or IT = 40.68 i 1.12. The contri-
bution from the error in temperature measurement is as follows: For an
error, AT, in the temperature, the correSponding displacement is A l/T
which equals A T/Tz. From the estimated error in the temperature, the
uncertainty in the reciprocal of the temperature is 7.37 i 0.03 x 10-4.

Examination of Figure 4 shows that most of the points fall within
the expected deviation. We can thus conclude that there are no random
errors unaccounted for in these experimental data.

The determination of the pressure from the mass spectrometer with
silver causes no additional error in the determination of the slope of
the resulting line since a constant factor is applied to all of the
data. However, an error in this constant will affect the intercept of
the In P vs 1/T graph and thus, the entropy calculated from this inter-
cept.

According to Chupka and Inghram (25), the ratio of the ionization

cross section in equation 4~7:
P =[(l/rik)(GAg/0Eu) (1/TAg)] IEUTEU (4-7,

may be in error by as much as a factor of two. If this is the case,
this error will be, by far, the largest error in any of the above terms.
The excellent agreement between the second and third law values for the
enthalpy of vaporization indicates that pressures calculated from the
above equation are very close to the true pressures, and that this ratio
is substantially correct. However, if we assume that this error is

large, we can calculate the maximum expected error in the entropy,

92

neglecting the error in the other quantities since they are small. The

+2.932 -6
-1.466 x 10

for the data for mass 151. The intercept and the error in it from the

bracketed term in equation 4-7 was calculated to be 2.932

In IT vs 1/T graph of data of experiment MB-S are 21.90 i 0.19. Combin-

ation of this intercept and its error, with K and its estimated error,

0

= :1:
298 18.20 175 e.u. When

results in an entropy and error of AS
this value is combined with the data for mass 153, the resulting average

entropy and its error are: A3298 = 18.43 i 1.75 e.u.

E. Suggestions for Further Research

As has already been indicated, the europium dicarbide samples
used in this study always contained small quantities of another europiumr
carbon phase. Additional studies are necessary to prepare pure europium
dicarbide and to determine the composition of this minor phase. A
complete phase study of this system should be instructive. One method
for accomplishing this goal would be to prepare samples of various
europium to carbon ratios, in a system that could be quenched rapidly
to freeze in any metastable phase that might be present at high tempera«
tures.

If a pure sample of europium dicarbide could be prepared, its heat
capacity should be determined as a function of temperature in order to
obtain accurate values for the free energy function. Most of the
thermodynamic functions reported for europium are estimates. A deter-
mination of these quantities should be made.

Europium dicarbide should be examined by Knudsen techniques involv-
ing collection and subsequent analysis of the effusate in order to deter~

mine more accurately the decomposition pressure. One method for

 

 

93

accomplishing this would be to redesign the apparatus used in this
study in order to cool more effectively the targets used to collect the
effusate.

Finally, the europium-oxygen-carbon system should be studied to
determine the effect of small quantities of oxygen on the stability of

the solid phase.

 

 

 

10.
ll.

12.

13.

14.

15.
16.
17.
18.

19.

20.

21.

22.

LITERATURE CITED

0. Pattersson, Bericht., 28, 2419 (1895).

H. Mbissan, Comp. Rend., 122, 148 (1896).

3213.,,l§1, 595 (1900).

H. Mbissan and A. Etard, Comp. Rend., 122, 573 (1896).
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M. A. Damiens, Ann. Chim., 19, 137 (1918).

M. van Stackelberg, Z. E1ectrochem.,.31, 542 (1931).

M. von Stackelberg, Z. Phys, Chem., Abt. 22, 437 (1930).

L. K. Frevel, H. W. Rinn and H. C. Anderson, Anal. Chem., 18, 83
(1946).

M. J. Villelume, Comp. Rend., 232, 235 (1951).
F. Gaume-Mahn, Bull. Soc. Chim. France, 1956, 1862.

M. Atoji, K. Gschneidner, Jr., A. H. Daane, R. E. Rundel and
F. H. Spedding, J. Am. Chem. Soc., 89, 1804 (1958).

F. H. Spedding, K. Gschneidner, Jr., and A. H. Daane, AMIE Trans.,
215, 192 (1959). ,

F. H. Spedding, K. Gschneidner, Jr., and A. H. Daane, J. Am. Chem.
Soc., 89, 4499 (1958).

R. C. Vickery, R. Sedlacek and A. Ruben, J. Chem. Soc., 1222) 498:
IR;Q., 503.

Ihi§., 505.

N. N. Greenwood and A. J. Osborn, J. Chem. Soc., 1261, 1775.

G. V. Samsonov, T. Ya. Kosolapova, M. D. Lyutoga and G. N. Makarenko,
Analit. Khim., 1963, 8.

E. A. Dancy, L. H. Everett and C. L. MtCabe, AMIE Trans., 224, 1095
(1962).

M. Atoji, J. Chem. Phys., _3_§_, 1950 (1961).

W. A. Chupka, J. Berkowitz and M. G. Inghram, J. Phys. Chem., 62
611 (1958).

94

 

 

23.

24.

25.
26.
27.
28.
29.

30.

31.

32.

33.

34.
35.
36.
37.

38.

39.

40.

41.

42.

43.

95

G. F. Wakefield, Dissertation Abstr., 22, 3433 (1962).

D. D. Jackson, G. W. Barton, 0. H. Krikorian and R. S. Newbury,
University of California Radiation Laboratory, UCRL — 6701
(1962). r

W. A. Chupka and M. G. Inghram, J. Chem. Phys., 21, 371 (1953).

ibid., 1313 (1953).

W. A. Chupka and M. G. Inghram, J. Phys. Chem., 52, 100 (1955).

R. E. Honig, J. Chem. Phys., 22, 126 (1954).

R. J. Thorn and G. H. Winslow, J. Chem. Phys.,,gg, 186 (1957).

D. White, A. Sommer, P. N. Walsh and H. W. Goldstein, in Advances
in Mass Spectrometry, vol. 2, Pergamon Press, New York, 1962.

 

H. W. Goldstein, P. N. Walsh and D. White, J. Phys. Chem., 65, 1400
(1961).
.1,-
D. White, P. N. Walsh, H. W. Goldstein and D. F. Dever, ibid.,
1404 (1961).

M. G. Inghram and J. Drowart, Mass Spectrometry Applied to High
Temperature Chemistry, Proceedings of an International
Sympesium on High Temperature Technology, MCGraw-Hill, 1960,
pp. 219 - 240.

 

 

Chem. Abstr., 52, 2304 (1961).

M. Knudsen, Ann. Physik., 28, 75 (1909).

I21§., 999 (1909).

1219':.22: 179 (1909).

J. Bockris, J. L. White and J. D. Mackenzie, Physiocochemical

Mbasurements at High Temperatures, Buttefworth Scientific
Publications, London, 1959.

 

 

K. D. Carlson, Argonne National Laboratory Report, ANL - 6156 (1960).

J. G. Edwards, Ph.D. Thesis, Oklahoma State University, Stillwater,
Oklahoma (1964).

R. D. Freeman and J. G. Edwards, Technical Documentary Report,
ASD ~ TDR - 63 - 754 (1963).

G. L. Galloway and H. A. Eick, J. Inorg. Nucl. Chem., in press.

L. H. Spinar and J. L. Margrave, Spectrochem. Acta, 12, 244 (1958).

 

 

 

44.

45.

46.
47.
48.
49.

50.

51.

52.

53.

54.

55.

56.

57.

58.

59.

60.

61

62.

63.

96

L. Winterbottom and J. P. Hirth, J. Chem. Phys., 31, 784 (1962).

G. Inghram, W. A. Chupka and R. F. Porter, J. Chem. Phys., 23,
2159 (1955).

W. Otvgs and D. P. Stevenson, J. Am. Chem. Soc., 18, 546 (1956).
C. Wiley, Science, 124, 817 (1956).

C. Wiley and I. H. McLaren, Rev. Sci. Instr., 26, 1150 (1955).

. W. Rinehart, Anal. Chem., 26, 1820 (1954).

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

 

A. Kent, Ph.D. Thesis, Michigan State University, East Lansing,
Michigan (1963).

P. Palenik and J. C. Warf, Inorg. Chem., 1, 345 (1962).

V. Svec, J. Capellen and F. E. Saalfeld, J. Inorg. Nucl. Chem.,
36, 721 (1964).

. H. Spedding, J. J. Hanak and A. H. Daane, AMIE Trans., 212, 379

(1958).
T. Hall, J. D. Barnett and L. Marrill, Science, 139, 111 (1963).
B. Alcock, H. A. Eick, E. G. Rauh and R. J. Thorn, A Comparison

of the Calculated and Observed Vaporization Behavior of the
Uranium Dicarbide Phase, Nuclear Metallurgy, vol. X, 1964.

 

A. Eick, E. G. Rauh and R. J. Thorn, Vaporization Studies of
the Uranium Dicarbide Phase, Thermodynamics of Nuclear
Materials, IAEA, Vienna, 1962.

 

R. Stull and G. C. Sinke, Thermodynamic Properties of the
Elements, American Chemical Society, Washington, D. C., 1956.

 

Pauling, The Nature of the Chemical Bond, Cornell University
Press, Ithica, New York, 1960.

 

. K. Kelley, Contributions to the Data on Theoretical Metallurgy,

 

x11, U. 3. Bureau of Hines Bulletin 584, (1960).

K. Kelley and E. G. King, Contributions to the Data on Theoreti-
cal Metallurgy, XIV, U. 8. Bureau of Mines Bulletin 592 (1961).

 

 

D. Rossini, D. D. Wagman, W. H. Evans, 8. Levine and I. Jaffe,
Circular of the National Bureau of Standards,500, 1952.

G. Rauh, R. C. Sadler and R. J. Thorn, Argonne National Laborau
tory Report, ANL - 6536 (1962).

 

..___

APPENDICES

97

 

 

 

 

Table AI

APPENDIX A

. Correction for Leeds and Northrup Pyrometer Serial No. 1619073

 

T

Low Range

 

High Range
TOCScale TOCNBS TOCScale TOCNBS

800 796 1100 1092
850 845 1200 1189
900 893 1300 1289
950 943 1400 1391
1000 994 1500 1494
1050 1045 1600 1598
1100 1097 1700 1702
1150 1149

1200 1201

1225 1226

 

98

 

 

APPENDIX B
THE MASS SPECTROMETER KNUDSEN SOURCE

The high temperature Knudsen source constructed by the author for
these studies was patterned after a model lent to Dr. H. A. Eick by
Mr. E. G. Rauh of the Argonne National Laboratory. The details of this
source have been reported by Rauh, Sadler and Thorn (63). The physical
arrangement of this source is shown in Figure B~l.

The sourde used in this study was modified by replacing the helical
filament with one of a hair pin design, as recommended by Mr. Rauh.

The source is shown standing on a lucite base which serves to sup--
port it when it is out of the mass spectrometer. The assembly is support-
ed in the mass spectrometer by a stainless steel plate (A) through which
pass six electrical connections and one movable rod (B) which is used to
tilt the assembly for .alignment with the mass Spectrometer slit. Above
this plate, a stainless steel ring (C) is supported on three 2.54 mm,
(0.100") diameter tungsten legs, one of which is attached to the movable
rod (B). .This ring serves both as support for the assembly and for elec-
trical isolation in conjunction with the three boron nitride plated (D).
Immediately above the boron nitride plates are four tantalum radiation
shields (E) spun from 0.5 mm. (0.020") sheet. The crucible is supported
on three 2.54 mm. (0.100")-tungsten legs which are pointed to reduce the
contact area, and consequently, the heat transfer down these 1egs..

The filament (F) around the crucible (G) is made by bending 0.037
mm. (0.015") diameter tungsten wire in the form of a continued hair pin.
It is supported on nine 2.54 mm. (0.100") diameter tungsten rods, two

of which serve as electrical conductors. The filament and crucible are

99

 

 

 

100

 

‘Figure B-l . The Mass Spectrometer Knudsen Source Aafiéfifiiya

 

101

surrounded by a molybdenum radiation shield (H) which in turn supports
two tantalum radiation shields (J).

In the initial construction, the three plates (D) were machined
from Lava - Grade A. (American Lava Corporation, Chattanooga, Tennessee).
This material, a hydrous aluminum silicate, is easily machined. When
fired, it expands slightly and becomes very hard. Lava was found unsuit-
able since it apparently absorbs large quantities of gas when exposed
to air. This absorbed gas is then released over a long period of time
as the Lava is heated in vacuum, producing an objectionably high back-
ground pressure in the mass spectrometer. New plates, machined from

boron nitride, eliminated this problem.

 

 

 

 

 

 

APPENDIX C
THE ELECTRON BOMBARDMENT POWER SUPPLY

The plans for the power supply were furnished by Mr. E. G. Rauh of
Argonne National Laboratory. The schematic diagrams for the power supply
are shown in Figures C-1 and C—2. These diagrams were followed exactly
with the exception of the shield bias supply which was omitted entirely
since it was not needed for the intended applications.

The basic operation of the power supply is as follows: The filament
supply (Figure Cm2), a low voltage high current transformer, supplies
current to heat the filament in the Knudsen source to temperatures at
which thermbnic emission of electrons occurs. In manual control opera-
tion, the ”set power” circuit supplies a selected potential to the input
of the operational amplifier, which in turn supplies current to the
Vectrol thyratron grid controls in the D. C. power circuit (Figure C-l).
The grid controls in turn apply a potential to the grids of the thyratron
tubes. The phase of this signal is varied with respect to the phase of
the plate voltage, thereby causing the tubes to conduct for a certain
fraction of a cycle. This fraction depends on the relative phase angles
of the grid and plate voltages. The direct current output from the
thyratrons is filtered and applied between the filament and crucible of
the Knudsen source; the crucible being positive with respect to the
filament. The electrons resu1ting from the thermionic emission of the
filament are accelerated by this potential and gain kinetic energy
which they release to the crucible upon impact, thereby heating the

crucible.

102

 

 

 

 

 

 
 

103

 

 

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3‘\3\\ .32.»! 6.3.1.3... 939 >n~x\\.}k \m.
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1.11.?{56 i‘V

 

 

 

 

 

 

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Electron Bombardment Power Supply - Power Circuit

Figure C-l.

 

 

 

 

104

 

 

 

 

 

 

 

 

90
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Electron Bombardment Power Supply - Control Circuit

Figure C-2.

105

When operated manually, the potential between the filament and
crucible is held constant. As the crucible heats, radiation from the
crucible supplies additional heat to the filament, resultingin greater
thermflxflc emission of electrons. These electrons are accelerated and
heat the crucible to a higher temperature. Thus a cycle sets in; the
crucible temperature increases rapidly and excessive current flows in
the power supply. This condition is termed ”run-away”.

To prevent ”run-away”, a Hall Multiplier (Siemens Type MB26~EI-38/MU),
shown in Figure C-2, is placed in the direct current circuit in such a
manner that a voltage which is proportional to the D. C. potential between
the filament and crucible is impressed across the coil of the multiplier.
A current which is proportional to the bombarding electron current is
also passed through the Hall probe. The Hall Multiplier operates in
such a manner that the output of the Hall probe is proportional to the
product of the voltage across the multiplier coil and the current through
the probe.

The output of the Hall probe is added algebraically to the output
of the ”set power” circuit. This difference-signal is then amplified by
the operational amplifier, now operating at a higher gain since the
difference signal is small. The operation from this point is the same
as in manual control.

Additional circuits-are shewn in-Figures Cfll‘and 092, these are
power supplies which supply the necessary operating voltage and currents
to the electronic components and safety circuits which prevent damage
to the power supply and personnel. The design of these circuits is

standard and need not be discussed here.

is.»

APPENDIX D
COMPUTER PROGRAM FOR LEAST SQUARES DATA FITTING

This program was written to perform least squares fitting of data
to a straight line of the form y = ax + b. The program also calculates
the standard deviation of the calculated slope and intercept, as well as
the expected standard deviation for an individual 1 value. The equations
were taken from Youden (50).

Two input parameters, N and g, are used in the program. E is the
number of 5:1 pairs in the data set and is necessary in the calculations.
2 is an arbitrary parameter. A value of zero for g causes the program,
using statements 29 and 30, to compute the reciprocal of x. This is
used, for example, when treating In P vs l/T data. A value of A greater
than zero causes the program to skip statements 29 and 30.

Statements 45, 46 and 47 are optional and may be deleted from the
program if desired. Their function is to convert the input value of y
to 1n 1.

After the slope, intercept, and standard deviations are calculated,
a set of values for y are calculated from the slope and intercept and the
input values of x. These ”1 calc” values are compared to the input X
values and if the difference is more than three times the standard devia-
tion, the y value is rejected and the computations repeated. Dr. George
Sturgeon modified the program so that the maximum difference of & calc - ll
is tested first. This procedure is necessary since a point rejected when
it is just outside the limit of acceptance, might fall within this limit
when a point with a larger difference is subsequently rejected.

The complete program follows:

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107

PROGRAM LSTSQRS

DIMENSION X(50),Y(50),YCALC(50),DEV(50),T(50),Z(50)
10 READ11,N,J
11 FORMAT(212)

IF(N)12,16,12
12 READ13,(X(I),Y(I),I=1,N)
13 FORMAT (2FlO.5)
45 DO471=1,N
46 Z(I)=Y(I)
47 Y(I)=LOFG(Y(I))
29 IE(J)3O,3O,14
30 D031I=1,N
31 X(I)=l.0/X(I)
14 SUMX=0
SUMY=0
SUMKY=0
SUMX2=O
SUMY2=0
D050I=1,N
SUMX=SUME+X(I)
SUMY=SUMY+Y(I)
SUMEY=SUMXY+X(I)*Y(I)
SUMX2=SUMK2+X(I)**2
50 SUMY2=SUMY2+Y(I)**2
FN=N
A=(FN*SUMEY-SUMX*SUMY)/(EN*SUMx2-SUMX**2)
B:(SUMY*SUMx2-SUMEY*SUMX)/(FN*SUMX2-SUMX**2)
PRINT60,A,B
FORMAT(1HO,2X,6HSLOPE=,E12.6,5X,lOHINTERCEPT=,E12.6)
FRACT=((SUMXY—SUME*SUMY/FN)**2)/(SUME2-SUMN**2/FN)
E=SUMY2-(SUMY**2/FN)-FRACT
SZ=E/(FN~2.0)
S=SQRTF(SZ)
SA2=sz/(SUMN2-(SUME**2/FN))
SA=SQRTF(SA2)
ssz=sz*SUME2/(FN*SUME2-SUMX**2)
SB=SQRTF(SB2)
PRINT70,S,SA,SB
70 FORMAT(1HO,2X,22HSTD DEV OF A SINGLE Y=,E14.8,/,

117HSTD DEV OF SLOPE=,E14.8,/,
221HSTD DEV OF INTERCEPT=,E14.8)

DO80l=1,N
80 YCALC(I)=A*X(I)+B
DO90l=l,N
T(I)=ABSF(Y(I)-YCALC(I))
CONTINUE
VMAX = T(1)
DO 89 I= 1,N
TEST = VMAX — T(I)
IF (TEST) 82,89,89
82 VMAX = T(I)

JAM = I
89 CONTINUE

4

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107

PROGRAM LSTSQRS
DIMENSION X(SO),Y(50),YCALC(50),DEV(50),T(50),Z(50)
10 READ11,N,J
11 FORMAT(212)
IF(N)12,16,12
12 READl3,(X(I),Y(I),I=l,N)
13 FORMAT (2F10.5)
45 D0471=1,N
46 Z(I)=Y(I)
47 Y(I)=LOFG(Y(I))
29 IF(J)30,30,14
30 DO31I=1,N
31 X(I)=1.0/X(I)
14 SUME=O
SUMY=O
SUMNY=O
SUMx2=O
SUMY2=O
DOSOI=1,N
SUMX=SUMR+X(I)
SUMY=SUMY+Y(I)
SUMEY=SUMNY+X(I)*Y(I)
SUMX2=SUME2+X(I)**2
SUMY2=SUMY2+Y(I)**2
FN=N
A=(FN*SUMXY—SUMX*SUMY)/(FN*SUMX2-SUMX**2)
B:(SUMT*SUMm2—SUMEY*SUMX)/(FN*SUMx2—SUMX**2)
PRINT60,A,B
6O FORMAT(1H0,2X,6HSLOPE=,E12.6,5X,lOHINTERCEPT=,E12.6)
FRACT=((SUMXY-SUMx*SUMY/FN)**2)/(SUMX2-SUMN**2/FN)
E=SUMY2-(SUMY**2/FN)-FRACT
SZ=E/(FNn2.0)
S=SQRTF(SZ)
SA2=sz/(SUMX2—(SUMR**2/FN))
SA=SQRTF(SA2)
SB2=SZ*SUMX2/(FN*SUMX2-SUMX**2)
SB=SQRTF(SBZ)
PRINT70,S,SA,SB
7o FORMAT(lHO,2X,22HSTD DEV OF A SINGLE Y=,E14.8,/,
117HSTD DEV OF SLOPE=,E14.8,/,
221HSTD DEV 0F INTERCEPT=,E14.8)
D080l=1,N
8O YCALC(I)=A*X(I)+B
DO9OI=1,N
T(I)=ABSF(Y(I)-YCALC(I))
CONTINUE
VMAx = T(l)
D0 89 I: 1,N
TEST = VMAx — T(I)
IF (TEST) 82,89,89
82 VMAX = T(I)
JAM = I
89 CONTINUE

 

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DEV=T(JAM)-3.0*S i
IF(DEV) 115,100,100

100 PRINT 200, Y(JAM)

200 F0RMAT(1H0,2X,IAHREJECTED POINT,5S,E14.8)

D0 110 I = JAM,N

X(I) = X(I+l)

Z(I)=Z(I+1)

Y(I) = Y(I + 1)

N = N - 1

GO TO 14

115 PRINT 120(Z(I),Y(I),YCALC(I),T(I),I=1,N)

120 FORMAT(1HO,2X,4HYIN=,16x,2HY=,16x,6EYCALc=,16x,2HT=,///,
1(2x,4(E14.8,2x)))
GO TO 10

16 STOP
END
END

11

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Table E-l.

APPENDIX E

COMPILATION OF MASS SPECTROMETRIC DATA

Data for experiments MS-Z and MS-3

 

 

 

o 4 a Intensity Intensit
T C 10 IT mass 151 mass 153y
(Observed) (True)
nanoamps nanoamps
MS-2a
975 7.948 0.0047 0.0047
1040 7.539 0.0064 0.0086
1040 7.539 0.0080 0.0086
1060 7.471 0.0086 0.0104
1060 7.471 0.0092 0.0102
1060 7.421 0.0112 0.0128
1075 7.334 0.0152 0.0140
1130 7.030 0.0316 0.0316
1130 7.030 0.0304 0.0352
1157 6.981 0.0480 0.0480
MS-2b

1040 7.539 0.0034 0.0026
1040 7.539 0.0036 0.0029
1065 7.392 0.0038 0.0062
1153 6.910 0.0128 0.0148
1153 6.910 0.0138 0.0148
1145 6.951 0.0132 0.0140
1170 6.824 0.0236 0.0232
1170 6.824 0.0220 0.0220
1184 6.808 0.0236 -~—b
1220 6.644 0.0340 0.0390
1220 6.642 0.0335 -~-
1176 6.846 0.0210 0.0250
1176 6.846 0.0230 0.0200
1214 6.737 0.0340 0.0340
1214 6.737 0.0350 ---
1249 6.512 0.0465 0.0465
1249 6.512 0.0465 0.0485
1296 6.312 0.0640 0.0640
1297 6.308 0.0530 «~-
1259 6.469 0.0400 0.0500
1310 6.254 0.0800 0.0800
1310 6.254 0.0820 =--
1339 6.137 0.1180 0.1000
1384 5.963 0.1600 0.1600
1384 5.863 0.1620 —--
1403 5.892 0.1600 0.1800

109

110

Table E-l. (continued)

 

1117 7.099 0.0150 0.0190
1043 7.522 0.0039 0.0034
1138 6.987 0.0130 0.0156
1170 6.824 0.0250 0.0250
1170 6.824 0.0240 ---
1168 6.834 0.0230 ---
1217 6.655 0.0350 0.0400
1237 6.565 0.0450 0.0500
1255 6.486 0.0500 0.0550
MS-3

883 8.606 0.0016 0.0020
881 8.621 0.0011 0.0014
917 8.358 0.0034 0.0026
917 8.358 0.0037 0.0045
964 8.033 0.0048 0.0073
970 7.993 0.0055 ---
970 7.993 0.0050 -—-
970 7.993 0.0055 ---
887 8.526 0.0019 0.0017
887 8.576 0.0021 0.0021
926 8.295 0.0046 0.0036
928 8.281 0.0041 0.0046
927 8.287 0.0045 0.0030
970 7.993 0.0075 0.0085
972 7.980 0.0116 -~-,
1018 7.685 0.0208 0.0208
1018 7.685 0.0200 0.0220
1103 7.187 0.0790 0.0790
1102 7.193 0.0750 0.0800
1069 7.380 0.0450 0.0420
1067 7.392 0.0450 0.0450
927 8.289 0.0046 0.0046
929 8.274 0.0038 0.0060
1026 7.636 0.0220 0.0240
1026 7.636 0.0232 -11
977 7.946 0.0041 0.0060
977 7.946 0.0050 0.0050
1026 7.636 0.0212 0.0260
1108 7.161 0.0860 0.0860
1064 7.409 0.0490 0.0490
1064 7.409 0.0530 —~-
1170 6.836 0.1800 0.1800
1170 6.836 0.0800 0.1800
1210 6.699 0.2400 0.2800
1212 6.690 0.2400 -~-
1257 6.489 0.3750 0.4000
1297 6.320 0.5000 0.5200
1298 6.316 0.5000 -——
1275 6.412 0.4000 0.4000

 

aA l/T = 10.58 x 10'6 for MS—2; A 1/T = 9.39 x 10‘6 for MS-3

b , , .
A blank in this column indicates that the IntenSIty of mass 15l was
measured as a function of time at the corresponding temperature.

 

 

 

 

 

 

 

111

Table E-2. Data for experiment MS-4-Ag.

 

 

 

 

o 4 a Intensity Intensity
(Obgegved) :gréz) mass 107 mass 109
nanoamps nanoamps
983 7.889 0.0240 0.0244
983 7.889 0.0248 0.0248
960 8.041 0.0144 0.0122
960 8.041 0.0112 0.0104
953 8.086 0.0122 0.0102
1021 7.648 0.0440 0.0360
1021 7.648 0.0430 ——-b
965 8.008 0.0192 0.0168
965 8.008 0.0192 0.0172
983 7.889 0.0268 0.0228
983 7.889 0.0252 0.0252
1023 7.638 0.0600 0.0640
1023 7.638 0.0600 0.0560
1001 7.773 0.0430 0.0400
1001 7.773 0.0420 0.0410
1050 7.473 0.1300 0.1160
1050 7.473 0.1260 0.1200
1030 7.592 0.0800 0.0800
1030 7.592 0.0900 0.0780
1074 7.332 0.1700 0.1640
1074 7.332 0.1700 0.1640
1050 7.473 0.1200 0.1160
1050 7.473 0.1200 0.1100
1075C 7.290 0.2480 0.2200
1075 7.290 0.2600 0.2280
973 7.917 0.0260 0.0240
973 7.917 0.0272 0.0240
944 8.114 0.0112 0.0104
944 8.114 0.0090 0.0106
903 8.404 0.0048 0.0036
903 8.404 0.0038 0.0043
a A l/T 3.957 x 10"6 before the experiment

A 1/T = 6.627 x 10' after the experiment
b Intensity not measured

C Visible coating appeared on the window

 

 

 

 

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Table E-3. Data for experiment ME-S
ToC 104/Ta Intensity Pressure Intensity Pressure
(Observed) (True) mass 151 mass 1515 mass 153 mass 1535
nanoamps atm. x 10 nanoamps atm. x 10
982 7.915 0.0077 2.852 0.0070 2.375
982 7.915 0.0074 2.741 0.0090 3.053
1015 7.705 0.0140 5.327 0.0150 5.228
1015 7.705 0.0156 5.937 0.0150 5.228
1054 7.468 0.0268 10.52 0.0260 9.347
1054 7.468 0.0224 8.792 0.0260 9.347
1085 7.289 0.0430 17.29 0.0450 16.58
1085 7.289 0.0430 17.29 0.0450 16.58
1112 7.139 0.0610 25.05 0.0650 24.45
1112 7.139 0.0630 25.87 0.0680 25.58
1171 6.832 0.1300 55.79 0.1340 52.66
1171 6.832 0.1300 55.79 0.1400 55.02
1050 7.492 0.0240 9.393 0.0228 8.174
1050 7.492 0.0240 9.393 0.0280 10.57
860 8.781 0.0012 0.4008 0.0012 0.3671
934 8.239 0.0048 1.708 0.0044 1.434
934 8.239 0.0039 1.388 0.0044 1.434
998 7.812 0.0110 4.128 0.0120 4.124
998 7.812 0.0108 4.055 0.0104 4.111
1064 7.410 0.0336 13.29 0.0360 13.04
1064 7.410 0.0332 13.13 0.0356 12.90
1123 7.080 0.0740 30.64 0.0860 32.63
1123 7.080 0.0780 32.31 0.0860 32.63
1185 6.763 0.1400 60.69 0.1600 63.53
1185 6.763 0.1460 63.30 0.1560 61.95
1252 6.512 0.2600 117.1 0.2880 118.8
1252 6.512 0.2560 115.2 0.2 60 113.8
911 8.402 0.0038 1.326 0.0038 1.214
911 8.402 0.0033 1.151 0.0033 1.055
1070 7.375 0.0300 11.93 0.0340 12.38
1070 7.375 0.0312 12.40 0.0340 12.38
1165 6.862 0.1040 44.44 0.1100 43.04
1165 6.862 0.1100 47.00 0.1100 43.04
1235 6.587 0.2000 89.01 0.2280 92.93
1235 6.587 0.2040 90.79 0.2280 92.93
1270 6.434 0.2800 127.6 0.2920 121.9
1270 6.434 0.2600 118.5 0.2880 120.2
1283 6.379 0.3200 147.1 0.3280 138.1
1283 6.379 0.3160 145.2 0.3280 138.1
1302 6.300 0.3500 162.9 0.3800 162.0
1302 6.300 . 0.3700 172.2 0.3900 166.2
1237 6.578 0.1920 85.58 0.2080 84.91
1237 6.578 0.1800 80.21 0.2080 84.91
1070 7.375 0.0260 10.33 0.0278 10.12
1070 7.375 0.0264 10.44 0.0268 9.758

 

a A 1/T = 9.33 x 10”

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DIFMISTRY UDRARY

 

 

 

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