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The solubility of hydrogen in plutonium in the temperature range 475 to 825 degrees centrigrade

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The solubility of hydrogen in plutonium in the temperature range 475 to 825 degrees centrigrade
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Allen, Thomas Howard
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English
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ix, 103 leaves : illustrations (some folded) ; 29 cm

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Subjects / Keywords:
Plutonium -- Analysis ( lcsh )
Hydrogen -- Solubility ( lcsh )
Hydrogen -- Solubility ( fast )
Plutonium -- Analysis ( fast )
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bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

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Includes bibliographical references.
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Submitted in partial fulfillment of the requirements for the degree, Master of Science, Department of Chemistry
Statement of Responsibility:
by Thomas Howard Allen.

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University of Florida
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ocm24526461
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LD1190.L46 1991m .A44 ( lcc )

Full Text
THE SOLUBILITY OF HYDROGEN IN PLUTONIUM
IN THE TEMPERATURE RANGE
475 to 825 DEGREES CENTIGRADE
by
Thomas Howard Allen
B.A., University of Northern Colorado, 1975
B.Mus., University of Northern Colorado, 1975
B.A., University of Colorado at Denver, 1984
A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado in partial fulfillment
of the requirements for the degree of
Master of Science
Department of Chemistry
1991


This thesis for the Master of Science degree by
Thomas Howard Allen
has been approved for the
Department of Chemistry
by
Date


Allen Thomas Howard (M.S., Chemistry)
The Solubility of Hydrogen in Plutonium in the
Temperature Range 475 to 825 Degrees Centigrade
Thesis Directed by Professor Larry G. Anderson
The solubility of hydrogen (H) in plutonium metal
(Pu) was measured in the temperature range of 475 to 825
C for unalloyed Pu (UA) and in the temperature range of
475 to 625 C for Pu containing two-weight-percent
gallium (TWP). For TWP metal, in the temperature range
475 to 600 C, the saturated solution has a maximum
hydrogen to plutonium ratio (H/Pu) of 0.00998 and the
standard enthalpy of formation (AH|^Sj) is (-0.128
0.0123) kcal/mol. The standard entropy of formation
(ASf(S)) is (-0.0915 0.0150) cal/mol K. The phase
boundary of the solid solution in equilibrium with
plutonium dihydride (PuH2) is temperature independent.
In the temperature range 475 to 625 C, UA metal has a
maximum solubility at H/Pu = 0.011 with AH|^Sj = (-0.0209
0.00598) kcal/mol and AS|^Sj = 0. The phase boundary
between the solid solution region and the metal+PuH2 two-
phase region is temperature dependant. The solubility of
hydrogen in UA metal was also measured in the temperature


(-0.104 0.0143)
range 650 to 825 C with AH|^Sj =
kcal/mol and AS|jSj = 0. The phase boundary is
temperature dependent and the maximum hydrogen solubility
has H/Pu = 0.0674 at 825 C. The empirical temperature
(T) pressure (P) relationship for unalloyed metal in
the two-phase region over the 773 to 1098 K range is
ln P(H2, atm) = 14.583 17313.132 [1/T (K)]
and is in poor agreement with literature values. The
most probable cause of the difference is in the
experimental procedures used to measure equilibrium H2
pressures. The enthalpy of formation (AH§) for PuH2 is
(-35.18 0.68) kcal/mole and the entropy of formation
(AS|) is (-33.3 1.03) cal/mole K. These results are in
excellent agreement with the literature values. AH| for
forming PuH2 with TWP metal is (-34.44 1.83) kcal/mole
and AS| = (-33.0 3.0) cal/mole K. AH| for TWP metal is
in poor agreement with the literature values, but AS| is
in excellent agreement. Unexpected features are seen in
the pressure composition isotherms for both the TWP and
UA metals and possible reasons for these features are
presented.
The form and content of this abstract are approved. I
recommend its publication.
Signed
iv


CONTENTS
Figures............................................vii
Tables.............................................J.x
CHAPTER
1. INTRODUCTION........................................1
The Physical & Chemical Properties of Plutonium.3
Focus of the Study..............................12
2. THEORY.............................................16
Introduction....................................16
Adsorption and Dissolution......................17
Determination of Solubility Limit...............22
Thermodynamics..................................26
3. EXPERIMENTAL.......................................29
Method..........................................29
System..........................................33
Materials.......................................37
Data Calculations...............................37
4. RESULTS AND DISCUSSION.............................39
The Solid Phase 475 to 625 C...................39
Two Weight Percent Plutonium.................39
Unalloyed Plutonium..........................45
TWP Inflection Points
51


Geometrical and Electronic
Considerations............................51
Hydrogen Ordering.........................53
Stoichiometric Phases.....................56
Inflection Point Three - Region 4. . . .58
TWP 625 C Isotherm..........................59
Vertical Spacing of Isotherms................59
Hydrogen Solubility in TWP and UA Metals. 60
Slope of Two-Phase Region....................61
The Liquid Phase 650 to 825 C..................61
Thermodynamic Results...........................76
5. CONCLUSIONS........................................92
The Unanswered Questions........................98
REFERENCES............................................99
vi


FIGURES
Figure
1-1. Idealized coefficient of thermal expansion for
unalloyed plutonium..................................7
1-2-A. Plutonium-gallium phase diagram.....................10
1-2-B. Subsection of plutonium-gallium phase diagram to two-
weight-percent Ga...................................11
1-3. Body-centered-cubic unit array......................13
1- 4. Face-centered-cubic unit cell.......................14
2- 1. Potential energy diagram for a noncatalytic
dissociation process................................19
3- 1. Diagram of experimental solubility system...........34
3- 2. Diagram of the solubility reactor.................. 35
4- 1. Idealized isotherm showing all of the features
observed in this study..............................40
4-2. Typical low composition isotherm for two-weight-
percent alloy.......................................41
4-3. Example of the high composition isotherm for two-
weight-percent alloy................................41
4-4. Low composition isotherms for two-weight-percent
alloy. Temperature range 475 to 600 C..............44
4-5. Deconvoluted low composition isotherms for two-
weight-percent alloy. Temperature range 475 to 600
C..................................................46
4-6. Two-weight-percent low composition isotherms with
the addition of the 625 C isotherm.................47
4-7. Typical isotherm for unalloyed metal at low
composition (same temperature as figure 4-2). . . .49
4-8. Typical isotherm for unalloyed metal at high
composition (same temperature as figure 4-3). . . .49


4-9. Unalloyed low composition isotherms.................50
4-10. Unalloyed liquid phase low composition isotherms.
Temperature range 650 to 825 C....................62
4-11. Typical high temperature isotherm...................63
4-12. 750 C Isotherm....................................63
4-13. Family of isotherms for unalloyed liquid phase metal
at low composition with Condit's data (open circles)
superimposed on these data. Temperature range 650 to
825 C......................................................66
4-14. Complete data set of isotherms for unalloyed metal
(exclusive of the 475 C isotherm).................70
4-15. Pressure temperature relationship for unalloyed
plutonium...........................................72
4-16. Free energy of formation versus temperature for
unalloyed plutonium in the solid solution region.
Temperature range 475 to 625 C..............78
4-17. Free energy of formation versus temperature for
unalloyed plutonium in the liquid solution region.
Temperature range 650 to 825 C.....................80
4-18. Free energy of formation versus temperature for two-
weight-percent alloy plutonium in the solid solution
region. Temperature range 475 to 600 C..............81
4-19. Plot of free energy of formation (AG|) versus
temperature (in Kelvin) for the reaction of unalloyed
plutonium with hydrogen to form PuH2>0..............82
4-20. Plot of free energy of formation (AG|) versus
temperature (in Kelvin) for the reaction of two-
weight-percent plutonium with hydrogen to
form PuH2..........................................85
4-21. Unalloyed Plutonium Hydrogen Phase Diagram. . .91
vm


TABLES
1-1. Allotropic forms of unalloyed plutonium and the
temperature ranges at which they exist..............6
1-2. Table of elements and their known reaction with
plutonium............................................9
4-1. Table of H/Pu ratios at inflection points 1 and 2
for unalloyed plutonium.............................71
4-2. Literature values for empirical equation relating
pressure to temperature for unalloyed metal. ... 74
4-3. Comparison of plateau pressures between Mulford and
Sturdy, Allen, and Condit data......................75
4-4. Literature values of enthalpy of formation and
entropy of formation for unalloyed plutonium. . .84
4-5. Comparison of values for AH§ and AS| calculated by
integral and second law methods for the formation of
PuH2 from unalloyed metal...........................87
4- 6. Summary of values for heats and entropies of
formation for the solid solution and PuH2 for both
unalloyed and two-weight-percent metals.............90
5- 1. Comparison of H/Pu values at inflection point 2
between UA and TWP metals in the temperature range
475 to 625 C.......................................93
5-2. Comparison of measured values for enthalpy and
entropy of formation between unalloyed, two-weight-
percent plutonium, and literature values............97
IX


ACKNOWLEDGMENTS
First I would like to thank EG&G Rocky Flats
(formerly Rockwell International) and my manager, Mr. J.
C. Petersell, for allowing me to conduct my thesis
research at work. Secondly, I must also thank Ms. J. A.
Nesheim for her help in the preparation of this thesis.
Also I would like to acknowledge the Chemistry Department
of the University of Colorado at Denver for allowing me
to conduct my thesis research off campus, Dr. L. G.
Anderson for serving as my adviser, and Dr. J. A. Lanning
for serving as Dr. Anderson's replacement.
I would also like to thank the people who gave of
their time to edit this document. They are Mr. G. E.
Bixby and Mr. J. L. Stakebake. Several people helped me
sort out the metallurgy in this paper. They were Mr. A.
L. Rafalski, Dr. C. R. Heiple, and Dr. S. Beitscher.
A very special thank you goes to Mr. D. R. Horrell.
Dave has read this paper almost as many times as I have.
His editing comments and insightful guestions led to many
revisions. Dave also made one other very significant
contribution to this paper, he permitted me use his
computer for endless hours without complaint. I can


truly say that without Dave's cooperation, this thesis
would have never been written.
In my experience, in a project like this, there is
always someone who stands above the rest because of his
unselfishness and his ability. For me this person was
Dr. J. M. Haschke who directed my research activities at
work. It is impossible to list all of the things that
John has done for me or to put into words exactly how I
feel. So, I'll just say that all of your help and
patience have been greatly appreciated. Thanks for
everything Doc.
This work was done under U. S. Department Of Energy
contract number DE-AC04-76DP03533.
xi


CHAPTER 1
INTRODUCTION
Metal hydrides have been studied extensively. Much
attention has been focused on the transition metal and
rare earth metal hydrides1. For example, the iron-
hydrogen2 system has been studied extensively because of
the property changes that the metal undergoes due to
hydrogen embrittlement. Palladium3 is used as a
catalyst for organic hydrogenation reactions and because
the metal is easy to handle; its hydrogen absorbing
properties have been thoroughly investigated. More
recently, new materials such as the lanthanum-nickel-
five4 inter-metallics (LaNi5) have been used for H2
storage and supply. The pressure composition -
temperature relationship of LaNi5 can be tailored by the
addition of other metals such as silver, copper, and
iron. With the addition of these other metals, the
formula unit becomes LaNi5_xMx where M = the third metal
in the alloy.
In general, metal hydrides have several uses such as
safe storage for large quantities of H2, supplying
extremely pure H2, the production of pure metals, and as


chemical reducing agents. This study focuses on the
solubility of hydrogen in plutonium (Pu). Although Pu
hydride is not considered to be a reasonable candidate
for some of the above applications (due to its potential
radiological and environmental hazards), this work does
fill a vacancy in the knowledge and understanding of
plutonium chemistry.
Specific interest in the Pu-H system stems from
three areas. First, hydriding is used as a recovery
method for Pu metal and to obtain finely divided metal
powders. The second area of interest is somewhat more
esoteric: the comparison of the H solubility in two
different allotropic forms, delta ($) and epsilon (e)
phases, in the same temperature range. The third area of
interest is in accurately defining the solubility limit
of hydrogen in the metal.
Prior to the initiation of this study only three
other studies of the Pu-H system had been done, one by I.
B. Johns5 and two by Mulford and Sturdy^6'7!. The Johns
work was carried out using unalloyed Pu in the
composition range H/Pu > 2.0 in the temperature range
between 25 and 500 C. The first Mulford and Sturdy
study6, also using unalloyed Pu, investigated the
composition range between H/Pu = 0.1 and 2.0 in the
temperature range between 575 and 800 C. There are a
2


small number of solubility data for the low composition
region, though not enough to accurately determine the
phase boundary for dissolution of hydrogen in the metal.
The second report by Mulford and Sturdy7 covered the
composition range H/Pu > 2.0 in the same temperature
range as their first paper. A Pu-H phase diagram is
presented which combines the results from both references
6 and 7; however, the boundaries indicated for hydrogen
solubility in plutonium differ between the two papers by
approximately a factor of 2 implying that the phase
equilibria and thermodynamic properties are uncertain.
This suggests an error in calculation of the hydrogen
concentration. Concurrent with this experimental work,
an independent study of hydrogen solubility in the liquid
metal was completed by Condit and others.8 The results
of Condit's work are discussed in chapter 4.
The Physical and Chemical Properties of Plutonium
Plutonium was the second transuranic element to be
discovered. It was produced in 1940 by Seaborg,
McMillan, Kennedy and Wahl by bombarding uranium with
deuterons. Naturally occurring Pu has also been found in
uranium ores. The primary use of Pu is in nuclear
weapons although other uses, such as power sources for
spacecraft and fuel for power reactors, have been noted.
3


The isotope used in nuclear weapons is 239Pu while 238Pu
is used in spacecraft power sources.
Plutonium is produced in nuclear reactors by the
reaction of a neutron (n) with 238U fuel rods by the
following sequence:9
238U + n -* 239U + y
239U - 239Np + p -* 239Pu + P
The reactor product is then cooled (not thermally) to
allow the decay of short lived radionuclides. At the end
of the cooling period, the cladding is removed from the
uranium fuel rods and the rods dissolved in acid. The U
and Pu are separated from the solution by solvent
extraction using tributyl phosphate in a kerosene-type
solvent10. After reduction of the Pu+IV to Pu+I11 by
ferro sulfamate, the Pu is removed from the U Pu
organic phase into an aqueous phase. This is followed by
reduction of Pu+I11 to metal.
Plutonium, atomic number 94, is a radioactive
element. The atomic weight is 242 grams/mole*. The
* The atomic weight of Pu is listed as 242 g/mol in
the CRC Handbook of Chemistry and Physics. The atomic
weight is the average weight based on the isotopic
distribution. The isotopic distribution is dependant on
both the neutron energy and time spent in the reactor and
4


metal has a theoretical density of 19.8 g/ml (a phase),
the melting point is 640 C (913 K), and the boiling
point is 3232 C (3503 K). Fifteen isotopes of Pu are
known (molecular weight 232 to 246). The metal exhibits
six allotropic forms (table 1-1) and 5 oxidation states
(+III, +IV, +V, +VI, and +VII) with the +IV state being
the most stable in the solid state. The stability of the
+IV state is due to the lower ionization potential for
the 5f electrons (e). Pu is fissionable (a neutron
source) and small amounts of gamma radiation are emitted,
but the primary mode of decay is by alpha emission.
Unalloyed Pu has a negative coefficient of thermal
expansion prior to melting. Figure l-l11 shows the
idealized thermal expansion of unalloyed Pu on heating.
The phase transitions from <5 -+ S' 6' -* e, and e - liquid
are accompanied by contraction.
The ground state electronic configuration for Pu is
ls22s22p63s23p63d104s24p64d105s25p64f145d106s26p65f67s2 which
would be predicted by the actinide theory. Seaborg12
suggested that actinium and latter elements should form a
series similar to the lanthanide series. This theory was
attractive because of the differences in chemistry
between neptunium and rhenium and between plutonium and
is targeted to yield 239Pu for weapons use. All future
references to Pu and its alloys will assume 239Pu.
5


TABLE 1-1 Allotropic Forms of Unalloyed Plutonium and the Temperature Ranges at Which They Exist.
Phase Symmetry Temperature Range (C) Lattice Constants (A) X-Ray Density
ao b0 c0 P
a mono1 <122 6.183 4.822 10.96 101.79 19.86
p mono 122 207 9.284 10.46 7.859 92.13 17.70
7 ort2 207 315 3.159 5.768 10.16 - 17.40
<5 fee 315 457 4.637 - - - 15.92
5' bet 457 -479 3.34 - - - 16.0
bee 479 640 3.636 - - - 16.51
1Monoclinic
2Orthorhombic


Figure 1-1. Idealized coefficient of thermal expansion for unalloyed
plutonium.
7


osmium. The theory has been supported by the evidence.
As with the lanthanide series, there is also an actinide
contraction which is due to the presence of the 5f
electrons.
Pu reacts with several common gases at elevated
temperatures including 02, NH3, N2, H2, CO, C02 and the
halogens. H2 and 02 react with Pu at room temperature.
The metal also reacts with water and water vapor. Pu
dissolves in several acids including HC1, HBr, HF, dilute
H2S04, HC104, H3P04, and sulfamic acid. HN03, at any
concentration, and concentrated H2S04 do not react with
Pu because of passivation.13
Numerous elements form binary compounds with Pu.
Other elements are miscible or form phases of variable
composition with Pu. Table 1-214 is a partial list of
elements and their expected reaction with Pu. One of the
more studied binary systems is the Pu-Ga system. Figure
1-2A35 shows the Pu-Ga phase diagram and figure 1-2-B
is the Pu-Ga phase diagram up to two-weight-percent Ga.
It is evident from the above discussion that the
chemistry of Pu is rich and complex. This is due in
large measure to the energy spacing of the valance
electrons which leads to varied hybridization.
8


TABLE 1-2
Table of Elements and Their Known Reaction With Plutonium.
Metals Forming Binary Compounds With Pu
Be Mg A1 Sc Mn Fe Co Ni
Cu Zn Ga G Zr Ru Rh Pd
Ag Cd In Sn Sb Hf Re Os
Ir Pt Au Hg T1 Pb Bi
Nonmetals Forming Binary Compounds With Pu
H, B C N,
F, Si P S Cl,
As Se Br, Te
Elements That Are Immiscible In Pu
Li Na K Rb Cs Ca Sr Ba
Transition Metals With Limited or No Miscibility In Pu
V Cr Nb Mo Ta W
Metals That Are Miscible And May Form Phases of Variable Composition With Pu
Ti Y La Ce Pr
Nd Sm Eu Gd Tb
Dy Ho Er Tm Yb
Lu U Np Am
9


Temperature
60
90
100
0 10 20 30 40
50
Atomic Percent Gallium
60 70 80
Figure 1-2-A. Plutonium gallium phase diagram.
10


5
6
7
ATOMIC PERCENT
2 3 4
WEIGHT PERCENT
Figure 1-2-B. Subsection of the plutonium gallium
phase diagram to two-weight-percent Ga. Temperature
range 400 to 700 C.
11


Focus of the Study
The specific interest of this study is in the
solubility of H in the e, 8, and liquid phases of Pu. As
is seen in table 1-1 and figure 1-2-B, the e phase is
present in unalloyed metal in the temperature region
between 475 and 640 C. Epsilon phase metal is body
centered cubic (bcc). Figure 1-316 shows a projection
of a bcc unit array. The unit cell yields 6 tetrahedral
sites or 1.5 octahedral sites per metal atom. These
sites are mutually exclusive because both cannot be
simultaneously occupied by interstitial atoms.
Delta phase metal is face centered cubic (fee).
Figure 1-417 shows a projection of the fee unit cell
with 2 tetrahedral sites and one octahedral site per
metal atom. These sites can be occupied simultaneously
by interstitials.
It has been clearly and repeatedly established that
H, when dissolved in an electropositive metal, prefers
tetrahedral sites1. This being the case, and based on
simple arithmetic, it can be argued that the e phase
metal should dissolve more H than 5 phase metal. The Pu-
li system provides a unique opportunity to test this
hypothesis.
In order to directly compare the solubility of
hydrogen in the 8 and e phases of plutonium at the same
12


Figure 1-3. Body-centered-cubic unit array. Open
circles are metal atoms, solid circle is tetrahedral
site, and solid diamond is octahedral site.
13


Figure 1-4. Face-centered-cubic unit cell. Large open
circles are metal atoms. Solid circles are tetrahedral
sites and solid diamonds are octahedral sites.
I
!
14
i


temperatures, the stability range of one of the phases
must be altered. As shown by figure 1-2-B, the S phase
is stable up to 600 C when two-weight-percent Ga is
alloyed with the plutonium. Since the e phase is formed
by unalloyed Pu over the temperature range 479 640 C,
the relative solubilities of hydrogen in the two phases
can be determined from equilibrium H2 pressure
measurements in the 479 600 C range.
The value of equilibrium measurements extends far
beyond this objective. The solubility limit of hydrogen
in solid and liquid plutonium can be more accurately
defined and the thermodynamic properties of the Pu-H
system can be more adequately determined than is possible
from earlier studies.
15


CHAPTER 2
THEORY
Introduction
The dissolution of hydrogen (H) in a metal is a
multi-step process that includes: 1) adsorption of H2 on
the metal surface, 2) dissociation of the H2 molecule,
and 3) movement of hydrogen atoms into the bulk metal.
Once in the metal, hydrogen occupies interstitial sites
or defects in the metal, e.g., at grain boundaries. The
amount of hydrogen dissolved depends on the size,
geometries (tetrahedral or octahedral, etc.),
concentration of interstitial vacancies, the defect
concentration, and the chemical environment provided by
the metal. Within the metal, hydrogen can move or exists
as H, H+, or H depending on the specific chemical
environment.
The following sections will more fully expand the
concepts of dissolution, the determination of the
solubility limit, and the calculation of thermodynamic
guantities based on the experimental data.


Adsorption and Dissolution
Adsorption can occur as described by two mechanistic
models. The first mechanism involves a loosely bound,
high energy state in which the molecule is held on the
metal surface through Van der Waals forces. In this
state the molecule can be easily removed from the metal
with vacuum and moderate heating. The second mechanism
of adsorption involves a strong gas to metal chemical
interaction, called chemisorption. Chemisorption is a
chemically bound state in which the adsorbed molecule
shares, donates, or accepts electrons from the metal
surface. The gas can remain on the surface as a
chemisorbed species or continue to the next step,
dissociation.
The second step in the dissolution process is the
dissociation of the gas molecule. For this step to
occur, one of the following two conditions must exist at
the metal surface: 1. the surface must be catalytic or,
2. the adsorbed molecule must have sufficient kinetic
energy to dissociate. If the metal surface is catalytic
and the adsorbate is H2, the energies and symmetries of
occupied free orbitals of the metal overlap with the
antibonding orbitals of the H2 molecule and dissociation
follows. The activation energy of this process is very
low.
17


Figure 2-1 shows a potential energy diagram (PED)
for a non-catalytic dissociation process. Curve 1 is the
PED for the chemisorption of H2 and curve 2 is the PED
for the metal-H atom bond. In this case, in order for
dissociation to occur, the hydrogen molecule must have
sufficient total energy to traverse, right to left, along
curve 1 until it intersects with curve 2. At the
intersection of curve 1 and curve 2, the molecule can
follow curve 2, dissociate, and the atom react with the
metal surface. If the molecule does not have sufficient
energy to overcome EA (EA is the intersection of curve 1
and curve 2), then it is adsorbed at point Qc.
Dissociation must precede dissolution.
, *1 Q , ,
According to Speiser the chemisorption bond
between hydrogen and Pu is covalent. This is supported
by recent theoretical calculations by Eriksson et al.19,
using the film linear muffin-tin orbital method. By
analogy with Pu02, Eriksson assumed the surface form to
be PuH2. The results show that the density of states is
dominated by the 6d orbitals for Pu and the Is orbital
for hydrogen. Little charge transfer between Pu and
hydrogen is observed (this is also observed in the bulk
hydride). This suggest that the H-Pu bond is covalent
and is a hybridization of the His and the Pu6d orbital.
The total energy is minimized when the H atom is 0.03A
18


Potential Energy
Distance From Surface ------>
Figure 2-1. Potential energy diagram for a noncatalytic dissociation
process. Curve 1 is the potential energy diagram for chemisorption
of H2. Curve 2 is the potential energy diagram for the formation of
a metal-hydrogen bond. The intersection of the two curves is the
activation energy for bond formation.
19


from the surface plane. In addition, the His energy
states are about 6 eV below the Fermi level, while the Pu
6d states are at or above the Fermi level.
Titanium (Ti) forms a cubic dihydride similar to
that of Pu. In looking at the Ti-H system, Switendick20
has shown that since the His orbitals lie below the Fermi
level, the energy of the system is lowered when the
hydrogen orbitals are filled.
Haschke et al.21 suggest that hydrogen in bulk PuH2
is hydridic (H) and that Pu is in the +III oxidation
state, with one electron from the metal donated to each
of the H atoms and the third electron going to the
conduction band. Recent XPS work by Larson and Motyl22
on clean metal surfaces shows the Pu metal to be in the
+III oxidation state even when exposed to hydrogen
pressures as low 1 X 10-5 torr. The findings of Haschke
and Switendick and the experimental evidence of Larson do
not agree with the theory of Speiser and Eriksson, but no
explanation is offered. This area requires additional
investigation.
In the following discussions, it will be assumed
that the hydrogen is H. With this condition existing at
the surface, movement of hydrogen into the bulk metal
should be quite facile, as there would be no energy
barrier between the electronic state of the hydrogen at
20


the metal surface and the electronic state of the
hydrogen in the bulk metal. On the other hand, should
the dissociated hydrogen at the surface be bound in other
chemical states (e.g., covalent bonds), then some
activation energy should be present relating to the
conversion of the hydrogen surface state to the H needed
in the bulk metal state.
The spatial orientation for the approach of the
hydrogen molecule is critical to the type of surface
interaction. There are two ways in which hydrogen can
approach the metal surface: with the bond axis parallel
to or perpendicular to the metal surface. The bulk of
the electron density in hydrogen is between the two H
atoms. Therefore, if H2 approaches the metal surface in
a parallel manner, then, based on coulombic arguments,
one would expect a Van der Waals type of interaction. In
a perpendicular attack, the H2 presents an area of low e
density to the metal. Since Pu is electro-positive, the
donation of an e to hydrogen is more likely with
hydrogen in the perpendicular orientation. The higher
the probability of chemisorption, the higher the
probability of dissociation and dissolution. Hoffmann23
presents a case for H2 attacking nickel perpendicularly.
Although no information was found on the parallel
attack of hydrogen, it can be argued that this type of
21


attack would lead to a Van der Waals type of interaction.
This is because the bulk of the electron density of
hydrogen is between the two H atoms and the electron
density of Pu at the surface is very diffuse. Electron-
electron interactions would prevent interaction in the
more positive regions of the hydrogen molecule.
Determination of Solubility Limit
The Gibbs' phase rule (equation 2-1) leads to a
method for determining the solubility limit.
Specifically,
F = C P + 2 (2-1)
where, F is the number of degrees of freedom (variables),
specifically, "...the number of variables to which values
must be assigned, in order to specify completely the
state of the system"24; C is the number of components in
the system, specifically ,"... a chemical species whose
concentration in a phase can be varied independently of
the other species' concentrations"25; and P is the
number of phases in the system. A phase is considered to
be any homogeneous part of the system.
There are three degrees of freedom in the Pu-H
system: pressure (P), temperature (T), and composition
(C) of the solid (liquid) phase26. At the start of a
Pu+H2 equilibrium experiment, the temperature is set to a
22


specified value and there is no hydrogen in the metal.
When a small amount of H2 is added to a constant volume
system, some of the hydrogen dissolves in the Pu metal
(the dissolution process can be followed by the drop in
H2 pressure) and at equilibrium, the pressure is P-^ If
the above process is repeated at a higher starting
pressure than Pl7 equilibrium is established at a new
pressure P2, where Px < P2. During this process the
composition has changed from C-^ to C2. By adding a third
charge of gas, it is observed that the process will
repeat itself. Therefore, at each pressure, Px, P2, ...,
Pn, along an isotherm in a single-phase region, it is
clear that either the P or the C must be defined in order
to completely specify the state. This is characteristic
of the Pu-H solid solution region. Therefore, there are
two degrees of freedom in this region.
The same result can be seen by using equation 2-1.
There are 2 components, hydrogen and plutonium (C = 2).
There are 2 phases, gas and solid (P = 2). Inserting
these values for C and P into equation 1, we see that F =
2, the expected result. Therefore, a plot of pressure vs
composition yields a curve with a positive slope, which
is characteristic of a solid solution region.
At sufficiently high H2 pressures, plutonium forms a
compound with H2, plutonium dihydride (PuH2). If enough
23


H2 is added to form PuH2, at equilibrium, the pressure is
now P3, the dihydride decomposition pressure at the
specified temperature. The system has crossed the
solubility limit and a phase change has occurred. The
system has now entered the two-phase region. The two-
phase region is plutonium metal saturated with H (phase
1) in equilibrium with PuH2 (phase 2).
If additional hydrogen is added to the system, the
resultant equilibrium pressure (P4) will be equal to P3.
On the pressure vs composition plot, this region is seen
as a flat line (slope = 0). Since P3 = P4; and if the
process is repeated, P3 = P4 = P5; it is seen that in the
two phase region, only the temperature need be specified
to completely define the state of the system. That is,
the pressure and composition are a function only of
temperature. Therefore, there is only one degree of
freedom in this region.
This is also seen from the phase rule. The number
of components C = 2 (number of species (S) = 3, number
of relations (R) =1, C = S R)27, and the number of
phases = 3. Applying equation 2-1, the degrees of
freedom = 1. The intersection of the region where F=1
and the region where F=2 is the solubility limit of the
solid solution.
24


After all the Pu metal is converted to PuH2, the
system enters another solid solution region. In this
region H2 dissolves in PuH2. As with the metal solid
solution region, there are 2 degrees of freedom and the
same arguments hold.
The solubility limit can also be determined by using
Sievert's law18. The reaction for the dissolution of H2
in a metal is
^^2|tui ^(in solution)
The equilibrium constant (K) for this reaction is
g _ (in solution)
(H2>* ~ (Ph2),/4
where [H]^in solution) is the concentration of hydrogen in
solution, (H2(gaS))Js is the quantity of hydrogen gas, NH
is the atom fraction of hydrogen in solution, and (P^)*5
is the square root of the hydrogen pressure, therefore,
N = K*P* (2-2)
Equation 2-2 is Sievert's law, which states that the
solubility of a diatomic gas in a metal is proportional
to the square root of the gas pressure. Therefore, on a
plot of concentration vs P^, the inflection point
(change in slope) is the solubility limit and the slope
of the line is the equilibrium constant.
25


Thermodynamics
At equilibrium the chemical potential (/x) of the
hydrogen gas is equal to the chemical potential of the
hydrogen dissolved in the metal.
= ^ (2
Since /x is defined as (5G/6n)T p (the change in free
energy (G) with respect to a change in quantity (n) at
constant temperature (T) and pressure (P)) and at
equilibrium there is no net change in quantity ( constant);
Therefore,
(equilibrium)
= G.
(2-4)
and
G ^ (H) P (2-5)
G = G + R*T*lnP (2-6)
After rearrangement equation 2-6 becomes
AG = R *T *InP (2-7)
The total AG for the process from H/Pu = 0 to H/Pu >
0, can be obtained by Gibbs-Duhem28 integration. The
Gibbs-Duhem equation can be written as
Y, njd^ = o (2-8)
26


or in this case,
E niG
1 = 0.
(2-9)
Equations 2-8 and 9 state that at constant temperature
and pressure, in a closed system, the total free energy
is constant. Therefore, in a two component system, a
change in the free energy of one component yields a
corresponding, but opposite change in the other
component. That is, the free energies of the two
components cannot change independently29. Therefore,
the Gibbs-Duhem equation can be written as follows
where dG is a constant.
In these experiments, the quantity of Pu does not
change; therefore, nPu does not change and dnPu = 0.
Equation 2-10 becomes
The total free energy to a specific composition can be
calculated by integrating equation 2-11 over the
composition range of interest.
The entropy (AS) and the enthalpy (AH) for the
reaction can be calculated from the Gibbs equation
dG = GHdnH + GPudnPu
(2-10)
dG = GHdiiH
(2-11)
(2-12)
27


AG = AH TAS
(2-13)
by plotting AG vs temperature. The plot should yield a
straight line with AH equal to the y-axis intercept and
(-AS) equal to the slope of the line.
28


CHAPTER 3
EXPERIMENTAL
Method
The experimental technique chosen to measure the
hydrogen (H) solubility in Pu metal was a pressure -
volume temperature (PVT) method. The experiments were
performed isothermically, i.e., by varying gas pressure
at a constant temperature. The experiments were
performed in three groups: 1. unalloyed (UA) coupons,
at 25 degree increments in the temperature range 475 to
625 C, 2. two-weight-percent (TWP) coupons also in 25
degree increments in the above temperature range, and 3.
UA coupons at 50 degree increments in the temperature
range 650 to 825 C. The general experimental method is
described below. However, due to the high reactivity of
molten Pu, special handling procedures were required at
temperatures above the melting point of Pu. These
special procedures will also be described below.
Using the PVT method, a 1 to 6 gram Pu coupon is
first cleaned with a motorized stainless steel wire brush
to remove all surface oxide. The coupon is considered
clean when the metal surface has a shiny metallic luster.


The coupon is then weighed on a standard analytical
balance to the nearest 0.1 mg and placed immediately in
the reactor and the reactor sealed. The reactor is then
connected to the pressure vacuum system and evacuated
to a pressure of about 140 millitorr (mtorr). The
reactor and system are then flushed at least 3 times with
100 torr of high-purity helium. The system and reactor
are then pumped overnight to achieve an ultimate pressure
< 10 mtorr.
Once the system is at a pressure < 10 mtorr, it is
leak checked. The leak check is accomplished by first
valving out the vacuum pump. A mass spectrum of the
residual gas is then taken using a quadrupole residual
gas analyzer (RGA). The RGA is then valved out of the
system and the system allowed to sit for at least one
hour. During this time the pressure is monitored using a
capacitance manometer calibrated for 1 torr full scale.
The pressure is monitored as a qualitative indicator of
the leak check. At the end of 1 hour, another mass
spectrum is taken. The system is considered to be leak
tight if the nitrogen 14 peak (14N) is the same height as
the 14N peak in the first spectrum and is less than the
height of the mass 15 peak. It is normal in this
situation for the water peak (18H20) C02, and CO to rise
as these species are out-gassed from the surface of the
30


reactor. If leaks are found, they are repaired before
the test continues.
After the system has passed the leak check, a small
amount of H2 (approximately 0.1 to 0.5 torr) is added to
the gas reservoir, the initial H2 pressure recorded and
the reservoir valved off. During this operation, the
reactor is valved out of the system so that no H2 can
come in contact with the Pu coupon. The manifold is
evacuated and the reactor is then opened to the vacuum
pump and heated to the test temperature using a
resistance furnace controlled by a PID temperature
controller. During the heat-up, the reactor and coupon
are both under dynamic vacuum.
Once the specified test temperature has been
achieved, the vacuum pump is valved out of the system and
the H2 contained in the reservoir is released into the
reactor and allowed to react with the Pu coupon. The
progression of the reaction is followed using both a
strip chart recorder and a digital data acquisition
system. The reaction is considered complete when the H2
pressure is steady. At this point: 1. the final system
pressure, the reactor temperature, and the room
temperature are recorded, and 2. the reactor is valved
out of the system and another charge of H2 is added to
the gas reservoir. Each additional charge of H2 is at a
31


higher pressure than the previous charge. The above
process is continued until pressure in the system exceeds
760 torr or the experiment is terminated.
When working below 640 C, the Pu coupon is in
contact with the quartz reactor walls. Above 640 C, the
molten Pu will react with the quartz reactor; therefore,
a protective liner is used. The liner is a 304 stainless
steel cup coated with erbium oxide (Er203) which is
resistant to attack by molten Pu. However, the coating
must be out-gassed prior to use in an experiment because
some of the out-gassing constituents (H2, H20, C02, and
CO) from the coating will react with the Pu coupon.
The coating is prepared by a bake-out procedure
under dynamic vacuum at the experimental temperature.
Periodically during the bake-out, the system is flushed
with high-purity He. After completion of this step, the
cup is again baked-out at the test temperature with 5 to
10 g of Pu to reduce the oxide coating to a slightly
substoichiometric oxide (Er203_5) At the completion of
this process, the cup is ready for use. During loading
and unloading of the Pu coupon, exposure of the coating
to air is minimized.
32


System
Figure 3-1 is a diagram of the system. The parts of
the system opened to the reactor during the test are the
1 liter stainless steel gas reservoir; three MKS Baratron
capacitance manometers in the pressure ranges 0 to 1
torr, 0 to 100 torr, and 0 to 1000 torr; and the
interconnecting manifolds. The RGA is connected to the
manifold through a high pressure (HP) valve and valved in
or out of the system as needed. The volume of the system
has been calibrated with a standard volume traceable to
the National Institute Of Standards And Technology
through the Rocky Flats Standards Laboratory.
The manifolds are made of \ inch outer-diameter
(o.d.) HP 304 stainless steel tubing and Autoclave
Engineering \ inch HP fittings and regulating valves.
The reactor (figure 3-2) is a quartz-Kovar tube that is 6
inches long, % inches in diameter, and sealed at one end.
The Kovar end is welded to a 2% inch Varian vacuum
flange. The mating vacuum flange contains a \ inch HP
nipple for connection to the vacuum system and a HIP
high pressure thermocouple pass-through. A 1/16 inch
o.d. type K chromel-alumel thermocouple is used to
measure the reactor temperature.
Surrounding the quartz tube is a 304 stainless steel
outer tube with a % inch HP nipple welded in the side.
33


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e m
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IE
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A A A
13
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am of experimental solubility system.
ASH
2. 1000 torr MKS Bartron pressure transducer
3. 1 torr MKS Bartron pressure transducer
4. Granville-Phillips thermocouple gauge tub<
5. 50 torr bourdon tube pressure gauge
6. 1000 PSI bourdon tube pressure gauge
7. 100 PSI pressure gauge
8. V' Autoclave Engineers high pressure regu!
9. 9/16" Autoclave Engineers high pressure r<
10. h" high pressure tubing
11. 9/16" high pressure.tubing
12. 10 micron Autoclave Engineers particle fi!
13. 600 PSI Autoclave Engineers rupture disk <
14. To glovebox exhaust
£
3
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X
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REACTOR
KoVar \ \
Quartz Liner \ \
Outer wall! 304 Stainless Steel \ ^
\ ThermoeoupIe Passthrough
304 Stainless Steel
HighpreSSue Tube
To P/V Sy Stem
MATING
FLANGE
Figure 3-2. Diagram of the solubility reactor.
35


The outer tube is welded to the vacuum flange and
protects the quartz tube from mechanical damage and
provides containment for the hydrogen gas in an inert
atmosphere should the quartz tube break during an
experiment. Prior to the beginning of each test, after
the reactor has reached the test temperature, the volume
between the quartz tube and the outer tube is evacuated
and back-filled with He to a pressure 640 torr.
The RGA is a Balzers QMG 112 quadrupole mass
spectrometer with a mass range of 1 to 200 atomic mass
units (amu) and a Faraday cup detector. The RGA is
differentially pumped with a Balzers TSH 040 50
liter/minute turbo-molecular pump. The RGA is used, as
described above, for leak testing both before and after a
gas charge, periodically during the test, and for
verifying the purity of the H2. The test gas is
introduced into the analyzing chamber via a Balzers EVN
010 needle valve. The pressure in the analyzing chamber
is maintained in the 106 torr range during analysis.
The PID process controller is a Micricon Multi-loop
Controller with two independent PID loops. The two
independent loops can be linked to allow furnace control
from the internal thermocouple. This feature of the
controller was used on the isotherms at or below 625 C.
36


At temperatures of 650 C and above, the furnace was
controlled from the outside thermocouple.
Materials
The Pu metal was from the Rocky Flats foundry and,
with the exception of the Ga content in the TWP metal,
contained ppm impurity levels of Al, Fe, Ni, and Si.
Chemical analysis of the TWP metal showed the average Ga
content to be 1.802 weight percent.
The helium gas was high-purity and the supplier's
analysis was accepted. The typical helium gas analysis
was N2 = 0.1 ppm, CH4 = 0.9 ppm, and H20 = 1.2 ppm. The
hydrogen gas was also high-purity and again the
manufacture's analysis was accepted without further
testing. Typical analysis of a H2 cylinder was 02 and N2
< 2 ppm; CO, C02, Ar, and H20 < 1 ppm; and CH4 < 0.5 ppm.
Data Calculations
The quantity of H2 dissolved in each charge is
calculated from pressure change data using the ideal gas
equation of state;
PV = nRT (3-1)
Where P = pressure in atmospheres (ATM), V = volume in
liters (L), n = number of moles (mol), R = the ideal gas
constant (0.0821 L*ATM / mol*K), and T = temperature in
37


Kelvin (K). The composition, expressed as the molar
ratio of H/Pu, was then calculated. The loge (In) of the
equilibrium pressure is then plotted versus composition.
The free energy (AG), is calculated from the equilibrium
pressure at the test temperature using equation 2-7 and
also plotted as a function of composition. The
thermodynamic parameters free energy, enthalpy, and
entropy, are then calculated as explained in chapter 2.
38


CHAPTER 4
RESULTS AND DISCUSSION
The Solid Phase 475 to 625 C
The primary objective of this study was to measure
the solubility of H in Pu at compositions below H/Pu =
0.1. However, some of the isotherms were carried out to
the high composition region, H/Pu ) 0.1. Figure 4-1 is
an idealized isotherm showing all of the features
observed in this study. It is presented as a guide to
the following discussion.
Two Weight Percent Plutonium
Figure 4-2 is a typical TWP low composition isotherm
for temperatures < 600 C. Regions 1 & 2 together make
up the solid solution region. This region is
characterized by increasing pressure with increasing
composition (2 degrees of freedom). At the termination
of this region, inflection point 2, the metal is
saturated with hydrogen. Region 3 is the two-phase
region (one degree of freedom). This represents the
region consisting of a mixture of plutonium dihydride
(PuH2) and hydrogen saturated Pu metal. This region is


X
a
s Noioay
ui _J
Q O
m W
QC Z
a o o
> H H
Z J u
h o ui
Q (S K

h N0103*
Z
o
H
(3
UJ

X
0
C9
Ui
X
ui
to
c
X
a.
1
o
3
3 N0I33M
H
3
J
.............. O
to
T N0I33M q §
H H
_J u
O UI
is ac
3
CL
X
X
z
o
H
I
M
w
o
0.
z
o
o
3anss3dd ui
Figure 4-1. Idealized isotherm showing all of the
features observed in this study.
40


COMPOSITION (H/Pu)
Figure 4-2. Upper plate is a typical low composition
isotherm for two-weight-percent alloy. Figure 4-3.
Lower plate is an example of the high composition
isotherm for two-weight-percent alloy.
41


characterized by constant pressure with changing
composition. Region 1 is unexpected and its significance
will be discussed below.
Figure 4-3 is an example of the high composition
region for TWP metal. Theory states that the slope of
the pressure-composition curve between IP2 and IP3 should
be 0; however, a statistically significant slope is
observed on all isotherms. Region 4 is also unexpected
and suggests that filling of octahedral sites in the
substoichiometric dihydride begins before all of the
tetrahedral sites in the fee metal lattice are occupied.
The temperature dependence of region 4 is not known,
since only one isotherm was taken to the higher H/Pu
values.
Region 5, is the second solid solution region. In
region 5, hydrogen is being dissolved in the dihydride
phase by continuing to occupy octahedral sites. At
sufficiently high hydrogen pressures PuH3 is formed.
Two forms of trihydride are known, cubic and
hexagonal30. The cubic trihydride is formed at moderate
temperatures and high H2 pressures. In this phase
hydrogen fills all tetrahedral and octahedral sites in
the fee metal lattice. When sufficient thermal energy
and H2 pressure is provided, the cubic trihydride
transforms into the hexagonal trihydride. The two forms
42


of trihydride have different properties, with the cubic
form burning spontaneously in air, while the hexagonal
form is stable in air.
Figure 4-4 shows the experimental data for the TWP
isotherms at temperatures < 600 C in regions 1, 2, and
three. Linear regression analysis of inflection points 1
and 2 versus temperature, shows that neither has a
statistically significant temperature dependence.
The isotherms in region 1 (figure 4-4) are closely
spaced and in fact the 575 and 600 C isotherms cross in
this region. Based on theory, the isotherms cannot cross
and should be vertically spaced similarly to the
corresponding segments in the two-phase region. In
region 2, the vertical spacing of the isotherms expands
somewhat so that it is closer to the spacing in the two-
phase region. The reason for the change in vertical
spacing is unknown. The most probable reason for line
crossing is error in the PVT measurements.
To deconvolute the lines in region 1, each line was
given a common slope, which is the average of all the
slopes in the region. The X value was chosen as the
average of inflection point one for the 6 isotherms. The
Y value was then calculated from a plot of In P vs
temperature. The Y axis intercept was then calculated
from the eguation for a straight line using the average
43


In PRESSURE (Bar)
COMPOSITION (H/Pu)
Figure 4-4. Low composition isotherms for two-weight-
percent alloy. Temperature range 475 to 600 C.
44


slope and the X and Y coordinates determined above.
Similar calculations were also performed on the lines in
region two. Figure 4-5 shows the results with the
inflection points and the Y-axis intercepts corrected for
the observed temperature relationships and the
theoretical constraints.
Figure 4-6 shows the addition of the 625 C
isotherm. As is seen, inflection point 2 moved
significantly to the right and inflection point 1 was
lost. The line defining the solid solution region
undercuts the 550, 575, and 600 C isotherms. The
predicted plateau pressure, based on a plot of plateau
pressures vs 1/T for temperatures between 475 and 600
C, shows the measured pressure (7.7 torr) to be
significantly less than the calculated pressure (12.6
torr). These results are inconsistent with anticipated
behavior.
Unalloyed Plutonium
Figure 4-7 shows a typical low composition isotherm
for unalloyed plutonium. In a comparison with figure 4-
2, it is observed that the UA metal has a lower hydrogen
solubility and that inflection point one is missing. A
comparison of the plateau pressures in the two-phase
region shows that the UA plateau pressure at each
temperature is lower by about one loge unit when compared
45


In PRESSURE (Bar)
CD
*T
I
in
co
i
i
co
i
03
i
o
Ti
i
mmivn ri 1111 m i [ i 11111 n 11111111 m 111 h 11 n 111 rri | ri nri umiTq
CM
"ri
i
600
l m 111 h I m 111111 Luiil-iiu Lt 11 Ji i.ul 11 ii 11111 l.i 11 lLluiI
hi Mi an
*0.01 0.00 0.01 0.02 0.03 0.04 0.05 0.06
COMPOSITION (H/Pu)
Figure 4-5. Deconvoluted low composition isotherms for
two-weight-percent alloy. Temperature range 475 to 600
C.
46


In PRESSURE (Bar)
COMPOSITION (H/Pu)
Figure 4-6. Two-weight-percent low composition isotherms
with the addition of the 625 C isotherm.
47


to the TWP plateau pressure. Figure 4-8 is a typical UA
metal high composition isotherm. Inflection point 3 is
not observed in UA metal, i.e., region 4 is missing.
Figure 4-9 shows the UA family of isotherms.
Comparison of figure 4-9 to figures 4-5 and 4-6 shows
that in general, the solubility of hydrogen is lower in
UA than in TWP and the plateau pressures over the two-
phase region are lower in UA metal than in TWP metal.
Exceptions to this generality are for the 475 and 625 C
isotherms in which the plateau pressures for TWP and UA
are comparable. In the 475 C isotherms, the
solubilities are also similar but in the 625 C isotherm
the limiting solubility (inflection point 2) differs
significantly. Inflection point 1 is absent from all UA
isotherms. As in the TWP isotherms, the lines in the
solid solution region are closely spaced and there is
significant crossing. The vertical spacing between the
475 and 500 C isotherms in the two-phase region is much
less than would be expected based on the higher
temperature isotherms. The pressure composition curves
in the two-phase region have statistically significant
slopes and the UA metal phase boundary (inflection point
2) is temperature dependant.
Five areas of interest come out of these results:
1. the unexpected inflection points (1 and 3) in the TWP
48


COMPOSITION (H/Pu)
Figure 4-7. Upper plate is a typical isotherm for
unalloyed metal at low composition (same temperature as
figure 4-2). Figure 4-8. Lower plate is a typical
isotherm for unalloyed metal at high composition (same
temperature as figure 4-3) .
49


In PRESSURE (Bar)
Figure 4-9. Unalloyed low composition isotherms.
Temperature range 475 to 625 C.
50


solid solution and two-phase regions, 2. the marked
increase in the TWP hydrogen solubility and the lower
plateau pressure at 625 C, 3. the closely spaced
isotherms in the solid solution region of both UA and
TWP, 4. the overall higher hydrogen solubility in TWP,
and 5. the slope of the pressure-composition curve in the
two-phase region. Each of these areas will be discussed
in the following sections.
TWP Inflection Points
There are three possible explanations for inflection
point 1 observed in the TWP solid solution region: 1.
geometrical and electronic considerations, 2. ordering
of hydrogen in the Pu metal lattice, or 3. the existence
of numerous stoichiometric phases across regions one and
two. The presence of inflection point 1 for TWP metal
and its absence for unalloyed metal suggest that its
existence is related to the presence of gallium.
Geometrical and Electronic Considerations. Hydrogen
solubility is determined by three factors: 1. the
geometry of the interstitial site, 2. the size of the
interstitial site, and 3. the electronic (or chemical)
environment (the difference in electronegativity between
H and Pu). The geometry of the interstitial site is
determined by the spacial relationship of the metal atoms
51


(the packing of metal atoms, bcc, fee, etc.) and the size
of the site is a function of the distance between the
metal atoms. Ellinger et al.31 have shown that the
average Pu lattice parameter decreases with increasing Ga
content. This suggests that an attractive force is
operating, and this conclusion is supported by the
difference in electronegativity between Ga (1.81)32 and
Pu (1.28)32. These values imply that the electrons
shared between Ga and Pu spend more time around Ga than
Pu.
A comparison of the atomic radii of Pu (1.62 A)33
and Ga (1.81 A)32 shows that Ga is moderately larger than
Pu. It can be argued that the tetrahedral sites
surrounding Ga would be moderately larger when compared
to the tetrahedral sites surrounding Pu. The hydrogen in
Pu is in the form of H, therefore, this large atom would
tend to move to the larger sites. In the large sites
surrounding Ga, electron transfer to hydrogen is less
energetic because of the smaller difference in
electronegativity between hydrogen (2.20)32 and Ga
(1.81). Therefore the slope of the line on the In P vs
composition curve is quite steep.
When the large sites are filled, hydrogen must go
into the smaller sites. The difference in
electronegativity between hydrogen and Pu is larger than
52


between Ga and hydrogen; therefore, the electron transfer
to hydrogen is more energetic. The result is a decrease
in the slope in region 2 and the accommodation of
hydrogen in the smaller site. The point at which this
begins to occur is inflection point one.
This is seen in the In pressure vs composition
curves. At inflection point 1, the slope of the line
decreases indicating a larger free energy and suggests
that the size of the site has a smaller effect than the
chemical environment.
Two additional possibilities may be placed under
this heading. The first is the expansion of the Pu
lattice as hydrogen is added. Anisotropic lattice
expansion has been noted in the rare earth hydrides36.
The second is simply filling of octahedral sites.
Hydrogen Ordering. Inflection point 1 may also be
caused by ordering of the hydrogen atoms within the Pu
lattice. Numerous researchers have noted hydrogen
pairing and hydrogen-pair chains in rare earth
hydridest35-40]. in general, ordering is observed at room
temperatures and below and, when compared to Pu, at much
higher hydrogen concentrations (H/Metal 0.03 to 0.18).
In the H-Pu system, the solid solution region is at a
much lower hydrogen concentration (H/Pu 0.01) and at
higher temperatures. Ordering is anticipated based on
53


the fact that the hydride ions seek to minimize their
coulombic interactions, but the data do not support
pairing under these test conditions.
Hydrogen pairs were first proposed for rare earth
hydride solutions after neutron diffraction studies were
performed at low temperatures. These studies were
prompted by the discovery of a low temperature
resistivity anomaly34 in the rare earth hydrides. On
the basis of data from neutron scattering experiments,
Blaschko et al.35 proposed the existence of chains of
hydrogen pairs in these hydrides. The hydrogen atoms are
located on next nearest neighbor tetrahedral sites with a
metal atom in between the two hydrogen atoms. The chains
are 3 to 4 pairs long36 and the pairs are staggered
along the c axis of the hep cell37. The hydrogen-pair
chains have been shown to interact with each other. A
theoretical basis38'39 has also been established
showing the existence of hydrogen pairs.
The ordering is both temperature and concentration
dependent. Blaschko et al.37 show that the diffraction
features associated with pairing decrease in intensity
with increasing temperature. At 300 K, about 30% of the
hydrogen is paired and dissociation occurs by breaking of
the hydrogen chain before the pairs dissociate. The
pair mechanism is not changed by the hydrogen
54


concentration, but, pair formation becomes diffusion
controlled.
Anderson et al.40 have also studied the temperature
and concentration dependence of pair formation.
Anderson's data lead to different conclusions. At high
hydrogen concentrations, Anderson shows a significant
temperature dependence on the diffraction features
associated with hydrogen pairing. At 240 K, only minimal
evidence for pairing is observed. Anderson also shows
that no pairing is observed at concentrations as high as
H/M = 0.06.
Both Anderson and Blaschko agree that the driving
force behind pair formation is a lowering of the metal
lattice distortion. However, Anderson believes that at
low concentrations an occupied isolated tetrahedral site
is more stable, which leads to a significant
concentration dependence.
The basic fact that allows the formation of H-pairs
is the existence of a low temperature ( 300 K) hydrogen
solid solution region in the rare earths. The reason
given for the extended solid solution region is the lack
of sufficient thermal energy to transform from the metal
hep lattice to the hydride cubic lattice. This situation
is not observed in Pu, possibly due to the large enthalpy
of formation for PuH2.
55


Although the rare earth hydrides are, in most cases,
comparable to Pu hydride, the analogy seems invalid in
this case. If the driving force for pair formation is
relief of metal lattice strain, it can be argued that
there is sufficient thermal energy to allow metal
rearrangement to relieve distortion at 475 C and above.
Furthermore, at the highest hydrogen solubility in Pu,
the concentration of hydrogen is only 1/3 of that at
which the rare earths show decreased or no indication of
pair formation. A conservative interpretation of the
data shows that a temperature change of 130 K (170 to 300
K) yields a significant decrease in pairing. Therefore
doubling that temperature (to 648 K) should further
reduce pairing. It is therefore doubtful that inflection
point 1 is due to this type of hydrogen ordering.
Stoichiometric Phases. The existence of solid
solutions (phases with variable compositions) has been
questioned. Anderson41 has suggested that continuous
changes in the free energy composition curve, as
observed in figure 4-4, may result from the presence of a
series of closely spaced line phases. A line phase is a
compound "of ordered structure and definite composition."
The focus, to this point has been on the most simple unit
cell and the stoichiometry that it represents. However,
there is the possibility of a "super structure" in which
56


the structure for a given composition is defined by an
enlarged unit cell that frequently has lower symmetry
than the simple cell.
There are two possibilities for explaining the line
structure in the In P versus composition plots. The
first deals with the temperature dependence of the line
phase. In free energy composition temperature
(G,C,T) space, the line phase is a surface and will be
seen (in 2 dimensions, G and C space) as an extremely
narrow parabola. As the temperature is increased, the
surface begins to expand in G and C space finally ending
in a broad surface representing non-stoichiometry.
Simply stated, above a certain temperature, the most
stable form is the non-stoichiometric form while below
that temperature the stoichiometric form is most stable.
The second possibility for explaining the solid
solution is the formation of numerous stoichiometric
phases. In this case, the line phases appear on the free
energy plot as a continuous change, because data were not
taken at a frequency high enough to show the actual
phases. The phases may coexist with each other.
Eyring42 has shown the existence of closely spaced
phases in the praseodymium-oxygen and terbium-oxygen
systems. Each of the Prn02n_2 and Tbn02n_2 oxides (where n
= 7 to 12) are line phases. The various phases can be
57


shown to be derivations of the same basic crystal
structure. Simply by taking out (putting in) oxygen, the
new phase and its structure are formed. The key factor
is that several phases can coexist because they are all
easily derived from and related to the starting crystal
structure and have similar free energies. It should be
noted that this situation can also have the above
temperature dependence superimposed on it.
Inflection Point Three Region 4. Since the
majority of the metal is consumed at the start of
inflection point 3, the effect of the metal phase on the
system should be minimal. With the exception of the Ga
content, the hydride product of both UA and TWP metals
should be the same, that is, cubic hydride. However, the
UA isotherms do not show inflection point three. This
now focuses attention on the Ga and how the Ga is
accommodated in the hydride.
There is no information in the literature on how Ga
is accommodated in Pu hydride. It is known, however,
that Ga does not react with hydrogen on an elemental
basis to form a hydride.43 No metallographic or
chemical distribution data were obtained on the TWP
hydride during the course of these experiments. However,
using similar arguments as in the above section, the Ga
in the hydride may make filling of the octahedral sites
58


energetically favorable.
TWP 625 C Isotherm
The isotherm for TWP alloy at 625 C shows a marked
increase in hydrogen solubility and an unexpectedly low
plateau pressure. An examination of the Pu-Ga phase
diagram (figure 1-2-B) shows that the 625 C isotherm
lies in the 6+e region. The transition from a single
phase region to a mixed phase region causes a change in
the defect structure of the metal. Defects can also hold
H. Since the metal defects are also an energetically
favorable holding site for hydrogen, additional hydrogen
can be accommodated above that dissolved in the
interstitial lattice sites. The result is an increase in
the observed H/Pu ratio and a lowering of the plateau
pressure.
Vertical Spacing Of Isotherms
It was noted that in the solid solution regions of
both TWP and UA metals, the vertical spacing of the
isotherms changed when going from the solid solution
region to the two-phase region. Such behavior seems to
be a unique feature of the Pu-H system as no model
hydride system was found to be similar. Although no
explanation can be offered at this point, the results
imply that unlike the hydriding reaction in the two-phase
59


region, the dissolution process has a low temperature
dependence.
Hydrogen Solubility in TWP and UA Metals
One of the original hypotheses of this work was that
UA metal should dissolve more hydrogen than TWP metal.
This hypothesis was based on the fact that in the
temperature range, 500 to 600 C, UA metal is in the e
phase. The e phase, as stated earlier, is body-centered-
cubic (bcc) and the interstitial sites are tetrahedral (6
tetrahedral sites per metal atom) or octahedral ( 1.5
sites per atom). In the same temperature range TWP is in
the S phase and has 2 tetrahedral sites and one
octahedral site per metal atom. Since H prefers
tetrahedral sites, with more tetrahedral sites, UA metal
should dissolve more hydrogen.
The data in figures 4-4 and 4-9 show that TWP metal
has the higher hydrogen solubility. The occurrence of a
Ga-H2 reaction has already been ruled out, but another
possible explanation is H-H repulsive interactions,
provided that hydrogen in Pu is hydridic (H). The fee
unit cell in two-weight-percent Ga (5 phase) has a
lattice parameter of 4.59 A. In bcc e phase metal the
unit cell has a lattice parameter of 3.64 A. Lundin et
al.44 has shown a correlation between tetrahedral hole
size and the stability of hydrides: the larger the hole
60


the more stable the hydride. An estimate of the hole
radius for S and e phases, based on a regular
tetrahedron, is 0.66 and 0.64 A respectively. In the
solid solution region, TWP has the more negative AG|
which is consistent with this argument.
Slope of Two Phase Region
As stated above, the plateau should be flat in the
two-phase region. However, in both TWP and UA metals,
the plateau has a statistically significant slope. In
general, the slopes are larger for TWP metal (average
value = 0.674) than for UA metal (average value = 0.329).
The Ga in the metal, here considered as a contaminant,
may contribute to the higher slope. Although there is no
Ga added to the UA metal, there are a known amount of
contaminants in the metal (see chapter 3 for chemical
analysis of the metal). Other metals such as palladium
also show a larger plateau slope with increasing
contaminant concentration.45
The Liquid Phase 650 to 825 C
Figure 4-10 shows the family of isotherms between
650 and 825 C. These isotherms were measured for UA
metal only. In the liquid solution region (region 1),
all of the isotherms (figure 4-11), with the exception of
the 750 C isotherm (figure 4-12), have a low composition
61


in
Figure 4-10. Unalloyed liquid phase low composition
isotherms. Temperature range 650 to 825 C.
62


Figure 4-11. Upper plate is a typical high temperature
isotherm showing low composition inflection point and a
solubility wall. Figure 4-12. Lower plate is the 750 C
isotherm which shows no low composition inflection point.
63


inflection point (IP1) In a manner consistent with the
lower temperature UA isotherms, there is significant
crossing of the lines in regions 1 and two. The 825 C
isotherm undercut both the 700 and 750 C isotherms and
the 750 C isotherm undercut the 700 C isotherm. At the
measured solubility limit (IP2), there is a discontinuity
in the pressure. The pressure goes up, without change in
composition, until it reaches the dihydride decomposition
(plateau) pressure for that temperature. This behavior
is also observed in the 625 C and to some extent the 600
C isotherm (figure 4-9). At that point, the system
moves into the two-phase region. The two-phase region,
at these temperatures, is solid PuH2** and liquid metal
saturated with hydrogen.
The 650, 700, and 750 C plateaus all have slopes of
similar value to the lower temperature plateaus. The
slope of the 825 C plateau is larger and there is an
unexpected increase in the hydrogen solubility based on
the earlier data. Both of these observations are
probably due to iron (Fe) contamination of the Pu melt.
The Fe is present because the Er203 coating on the
**The melting point (MP) of PuH2 has not been
measured due to the extremely high H2 pressures required
to keep it from decomposing. However, the MP is expected
to be in the same range as TiO^ and the iso-structural
compound CaF2 whose melting points are 1550 and 1360 C
respectively.
64


stainless steel containment vessel failed during the
experiment. Plutonium readily forms a low melting Pu-Fe
alloy, Pu6Fe46. The Er203 coating on the 750 C
isotherm also failed, but the only change observed was
the loss of the low composition inflection point (IP1).
The difference in the two runs may be the amount of Fe
that reacted. There were no diagnostic tests run to
determine the amount of Fe in either melt and there was
no indication in the PVT data taken during the experiment
that any change had occurred.
Condit et al.47 has also studied the solubility of
H in Pu in this same temperature range, but by a
different technique. Condit introduced a known quantity
of H2 into a gas tight chamber containing a measured mass
of Pu. The H2 reacted with the Pu at room temperature
and then the temperature of the system was varied. The
equilibrium pressure was measured as a function of
temperature and the composition of the solubility limit
was calculated from PVT measurements for the temperatures
at which the pressure dependence changed. Figure 4-13
shows Condit's data superimposed on the current data.
The two data sets are in fair agreement and Condit's data
confirm the shape of the phase boundary. It should be
noted that at the same temperatures, in all cases, Condit
has measured a higher plateau pressure. The H/Pu ratios
65


LO
(JB0) 3UnSS3dd UI
Figure 4-13. Family of isotherms for unalloyed liquid
phase metal at low composition with Condit's data (open
circles) superimposed on these data. Temperature range
650 to 825 C.
66


at inflection point 2 (and 2A) vary from excellent
agreement at 650 and 825 C to fair agreement at 700 C
and off by a factor of 2 at 750 C.
It was proposed above that the increased hydrogen
solubility at 825 C is due to Fe contamination of the
Pu. However, Condit's data suggest that Fe has no effect
on the solubility of hydrogen, but changes only the slope
of the plateau in region 3.
Three areas of interest come out of these data: 1.
super-saturation of the gas phase near the solubility
limit, 2. the crossing of isotherms in the liquid
solution region, and 3. appearance of an inflection
point in the liquid solution region.
As was stated earlier, it is clear that isotherms in
the solid and liquid solution regions are closely spaced
and that the crossing is due to errors in the PVT
measurements. Undercutting of the isotherms in the
higher temperature ranges is also promoted by their
unusual shape. That is, since the lower temperature
isotherm reaches its solubility limit at a lower pressure
than the dihydride decomposition pressure, the only way
for the phase boundary to maintain its shape is by
undercutting the previous isotherms.
The shape of the 650 to 825 C isotherms suggests
inhomogeneity in the molten phase. Wittenberg48 has
67


suggested that "liquid like clusters" exist in the bcc
solid phase at temperatures around 600 C which creates
an inhomogeneous system. A similar isotherm shape was
also observed in the 600 and 625 C runs, which supports
this hypothesis. If this hypothesis is accepted, then,
both the supersaturation and the inflection point can be
explained.
The explanation is as follows. Hydrogen first
dissolves in the residual e phase metal. This is
supported by the fact that there is a correlation between
IP1 in the liquid phase and IP2 in the solid phase. Once
the solid phase is saturated, hydrogen then dissolves in
the liquid phase. The point at which the solid is
saturated and the liquid begins to dissolve hydrogen is
the observed inflection point. Because the metal
contracts on melting (which implies an attractive force
and ordering in the liquid phase), the hydrogen
solubility is limited. When both the solid and molten
metal phases are saturated with hydrogen, no more
hydrogen can dissolve, but the hydrogen pressure has not
reached the dihydride decomposition pressure. Therefore,
the composition cannot change, but the pressure must go
up until the plateau pressure is reached. When the
plateau pressure is reached, the system moves into the
two-phase region.
68


The isotherms for the unalloyed solid and liquid
form a consistent data set (exclusive of the 475 C
isotherm). Figure 4-14 is a graphical representation of
the data and table 4-1 is a table of the solubility
limits. It is evident that the phase boundary is
temperature dependant. A plot of ln(H/Pu) vs 1/T yields
the following equation,
In = (3.31 0.57)
Pu
(6968.66 500.)
T
The functionality of the phase boundary is therefore
-iL = Be
Pu
where B = 27.2 and A = 6968.66. Based on the above
results, H/Pu at 300 K is (2.22 X 10-9 1.23). Assuming
a 5 gram Pu sample, 2.3 X 10-11 moles of H2 are dissolved
in the metal at room temperature. The same analysis was
done for Condit's data and the results show that at 300 K
the calculated H/Pu ratio is (4.38 X 10-12 1.16).
Assuming a 5 gram metal sample, 4.58 X 10-14 moles of H2
are dissolved in the metal.
The pressure temperature relationship (figure 4-
15) in the saturated metal + hydride two-phase region of
the unalloyed system is defined by the following
equation,
69


(JB0) 3UnSS3Hd UI
Figure 4-14. Complete data set of isotherms for
unalloyed metal (exclusive of the 475 C isotherm).
70
COMPOSITION (H/Pu)


TABLE 4-1 Table of H/Pu Ratios at Inflection Points 1 and 2 for Unalloyed Plutonium.
TEMPERATURE H/Pu RATIO at H/Pu RATIO at
DEGREES INFLECTION POINT INFLECTION POINT
C ONE TWO
475 0.00267
500 0.00327
525 0.00402
550 0.00746
575 0.00718
600 0.0107
625 0.00819
650 0.00265 0.0156
700 0.00505 0.0178
750 0.0254
825 0.0162 0.0674
71


In PRESSURE (Atm)
Figure 4-15. Pressure temperature relationship for
unalloyed plutonium.
72


(4-1)
, A,
In P = A. +
1 T
where P is the pressure at the phase boundary in
atmospheres, T is the temperature in kelvin, A1 = (14.583
0.355), and A2 = (-17313.132 315). Table 4-249
lists the results of other researchers. As is seen in
table 4-3, when compared to the present results, the
pressures defined by the results of Mulford and Sturdy6
are generally higher at a given temperature. The In P vs
1/T curves cross near 535 C and the situation is
reversed at low temperatures. Comparison of equilibrium
pressures for this work with those in table 4-3 from the
work of Condit shows that the present values are
substantially lower.
A common factor between the work by Mulford and
Sturdy6 and that by Condit8 is in the experimental
method. In both studies (and in that by Johns5), the
plutonium was hydrided at room temperature, and then
pressure measurements were made as the temperature of the
closed system was increased. The differences in the data
suggests that the plateau pressure may be sensitive to
the temperature at which the hydride is formed or to the
heating procedure. Differences in plateau pressure are
commonly associated with the so-called hysteresis effects
in which the plateau observed during hydride formation
73


TABLE 4-2 Literature Values for Empirical Equation Relating Pressure to Temperature for Unalloyed Metal.
RESEARCHER A1 a2
I. B. Johns (673 to 773)*** 18.10 -19894
Mulford and Sturdy (727 to 1073) 16.42 -18800
Haschke and Stakebake (600 to 769) 16.25 -19150
Current results for comparison (773 to 1098) 14.58 -17313
***Numbers in parentheses are the temperature range
of the work in Kelvin.
74


TABLE 4-3 Comparison of Plateau Pressures Between Mulford and Sturdy, Allen, and Condit data.
TEMPERATURE PRESSURE PRESSURE PRESSURE
Degrees C Atmospheres Atmospheres Atmospheres
(Mulford & Sturdy) (Allen) (Condit)
475 0.000310
500 0.000366 0.000371
525 0.000791
550 0.00161 0.00164
575 0.00293
600 0.00610 0.00576
625 0.0106
650 0.0196 0.0153 0.0292
700 0.0551 0.0432 0.0740
750 0.141 0.107 0.188
800 0.335 0.267 0.449
(825 C)
75


(progressive addition of hydrogen along an isotherm) is
higher than that encountered during hydride decomposition
(progressive removal of hydrogen along the isotherm).3
The higher formation pressure is apparently necessary to
compensate for strain energy expended in expanding the
metal lattice during hydriding. In the procedure used by
Mulford and Sturdy and by Condit, hydride decomposed as
the temperature increased. Although a lower pressure is
expected than for the formation procedure used in this
study, the reverse pressure relationship is observed.
However, the heating method simultaneously induces large
changes in temperature, pressure, and composition of the
system within a few hours. In contrast, the isothermal
formation procedure used in the present study induces
small changes in pressure and composition over a period
of weeks. The isothermal method promotes annealing and
attainment of a minimum-energy configuration in the
system; the non-isothermal method tends to produce a non-
equilibrium system with a high hydrogen pressure.
Thermodynamic Results
The reaction for the dissolution of H in Pu metal
can be represented by the following eguation,
PU + H2 (gaS) PUH2(S)'
76


where subscript S indicates H in solution. AS| for the
reaction can be estimated using equation 4-2,
A£>f(298) = Spuj^ SMetal SPuh2 (4-2)
and correcting the calculated value to the median
temperature of 836 K. At 298 K, S§2 = 31.21150, Sftetal =
13.1851, and S§uH2 = 14.351, cal/mol K. The entropy
values for the metal and the dihydride are approximately
equal, opposite in sign, and therefore, contribute little
to the overall entropy. Therefore, AS|^2g8j is (-31.211)
cal/mol K. Assuming ACg for the formation of dihydride
is independent of temperature, the calculated entropy
value is (-32.15) cal/mol K at the median temperature of
836 K.
Figure 4-16 shows a linear regression analysis of
AGf(S, vs T for the solid solution region of UA metal in
the temperature range 500 to 625 C integrated between
H/Pu = 0 and 0.0028. The slope of the line is somewhat
positive and it can be seen that the positive slope is
due to the points at 575 and 600 C. Statistical
analysis of the data shows that the first order
coefficient is not significant, which suggests that the
entropy of formation for the solid solution is 0,
therefore, AG|^Sj = AH|^Sj. Based on the above analysis,
AGf(S) = AH|(S) = (-0.0209 0.00578) kcal/mol at the
median temperature of 836 K.
77


in
in
Figure 4-16. Free energy of formation versus temperature
for unalloyed plutonium in the solid solution region.
Temperature range 475 to 625 C.
78


Comparison of the calculated entropy value with the
measured value shows that the two are in poor agreement.
ASf(S, ~ 0 suggests that AG|(S)^ in this region, is
independent of temperature and that the order in the
solid phase is approximately the same as in the gas
phase. The disorder is possibly due to the high mobility
of H in plutonium.
Figure 4-17 shows a linear regression analysis of
AGf(S) vs T for H dissolution in UA metal in the
temperature range 650 to 825 C integrated between H/Pu =
0 and 0.0082. As in the solid phase, statistical
analysis of the data shows the first order coefficient to
be insignificant. Since the Y intercept from this
analysis is positive and the reaction is obviously
spontaneous, the average value of AG|^Sj is used.
Therefore, AG|^Sj = AH|^Sj = (-0.104 0.0143) kcal/mol.
Figure 4-18 shows a linear regression analysis of
AGf^) vs T for H dissolution in the TWP alloy. The
calculated value for AH|^Sj is (-0.128 0.0122) kcal/mol
and the value for AS|jSj is (-0.0915 0.0150) cal/mol K
at the median temperature of 811 K integrated between
H/Pu = 0 and 0.0088. These data are consistent with
anticipated results for the solid solution region.
Figure 4-19 shows a linear regression analysis of
AG| vs T for UA metal in the temperature range 525 to 750
79


in
o
Figure 4-17. Free energy of formation versus temperature
for unalloyed plutonium in the liquid solution region.
Temperature range 650 to 825 C.
80


05
CO
Figure 4-18. Free energy of formation versus temperature
for two-weight-percent alloy plutonium in the solid
solution region. Temperature range 475 to 600 C.
81


FREE ENERGY OF FORMATION (kcal/mol)
Figure 4-19. Plot of free energy of formation (AG§)
versus temperature (in Kelvin) for the reaction of
unalloyed plutonium with hydrogen to form PuH2>0.
82


C for the dihydride. The data include only isotherms
for which measurements were made in region five.
Analysis of the data shows that AH§ for UA metal is (-
35.18 0.68) kcal/mol and AS| for UA metal is (-30.19
0.749) cal/mol at the median temperature of 911 K. As
seen in table 4-452, the AH| value is approximately 3
kcal/mol more positive than those of other workers.
Figure 4-20 shows a linear regression analysis of
AG| vs T for TWP metal in the temperature range 475 to
600 C. The analysis assumes the terminal point to be
H/Pu= 1.69****. AH| is (-34.44 1.83) kcal/mol and
AS| is (-33.0 3.) cal/mol K. The entropy value is in
excellent agreement with the values shown in table 4-4.
However, the calculated enthalpy value is significantly
lower than the values in table 4-4. The lower enthalpy
value would be expected since the TWP plateaus are at
higher pressures than those for UA metal.
In addition to the above integral method for the
calculation of AH| and AS|, these thermodynamic
properties can be calculated from second law principles.
Equation 4-3,
****The terminal point was chosen as 1.69 because the
shape of the isotherm would not allow for extrapolation
beyond that point and the temperature dependence of
region 4 is not known.
83


TABLE 4-4
Literature Values of Enthalpy of Formation and Entropy of Formation for Unalloyed Plutonium.
RESEARCHER AHf (Kcal/Mole) -ASf (cal/Mole K)
I. B. Johns -39.5 2.3 35.9 2.8
Mulford and Sturdy -37.12 1.2 32.6 1.
Haschke and Stakebake -38.1 1.7 32.3 1.7
J. w. Ward median temp 550 K -37.2 2.6 33.1 2.6
Below are current results for comparison.
TWP -34.4 1.83 33.0 3.
UA -35.2 0.68 30.2 0.75
84


FREE ENERGY (kcals/mole)
o
Figure 4-20. Plot of free energy of formation (AG|)
versus temperature (in Kelvin) for the reaction of two-
weight-percent plutonium with hydrogen to form PuH2.
85


(4-3)
can be derived from equations 2-7 and 2-13, where R =
1.987 cal/mol K, T = temperature in Kelvin, and P =
pressure in atmospheres. As can be seen from the above
equation, a plot of In P vs 1/T yields a straight line
where AS§/R is the Y intercept and AH|/R is the slope of
the line. This is exactly the form of equation 4-1.
Substitution of the values for Ax and A2 from equation 4-
1 into equation 4-3 yields the following results: AS| =
(-28.976 0.705) cal/mol K and AH| = (-34.40 0.626)
kcal/mol at the median temperature of 911 K for UA metal.
This analysis assumes that the substoichiometric two-
phase region is entered into immediately and does not
take into account the contribution to the total free
energy from the solid solution region.
Comparison of the thermodynamic values to H/Pu = 2.0
calculated by both second law and integral methods
provides internal verification of the data. If the
values of the two methods agree, then the possibility of
systematic errors can be ruled out. It is clear from
table 4-5 that the values for AH| and AG| from the two
methods are, within experimental error, in excellent
agreement. These data show that the contribution to the
86


TABLE 4-5 Comparison of Values for AH| and AS§ Calculated by Integral and Second Law Methods for the Formation of PuH2 From Unalloyed Metal.
Integral Second Law
AHf (kcal/mol) -35.18 0.68 -34.40 0.626
ASf (cal/mol K) -30.19 0.749 -28.976 0.705
87


total free energy from the solid solution region is
minimal.
The question remains as to the 3 kcal/mol difference
in the AH| values between these data and the data of
Haschke49 (table 4-4). The Haschke value was calculated
using integral methods based on the data of Mulford and
Sturdy6. The terminal composition of the solid solution
region was taken as H/Pu = 0.01. The isotherms were
extrapolated to H/Pu = 0 and their temperature dependence
was assumed to be similar to the two-phase region. The
AH|(S) was calculated to be (-2.1 0.21) kcal/mol.
The Haschke value and this value are in poor
agreement. Two reasons are seen for this. One is the
limits of integration; Haschke estimated the solubility
limit to be at H/Pu = 0.01. These data were calculated
based on a solubility limit of H/Pu = 0.0027. The second
reason is the temperature dependence of the isotherms in
the solid solution region. These data show there to be
no temperature dependence and Haschke assumed the
temperature dependence to be similar to that in the two-
phase region.
The integral method for calculation of AH| takes
into account the contribution of AH|^Sj. If the region
corresponding to AH|^Sj is overestimated then AH| will be
more negative. It is clear from these data that the
88


average H solubility in UA metal (H/Pu = 0.006) is much
less than H/Pu = 0.01 and that the temperature dependence
of AG§ is, at best, minimal. Therefore, when Haschke's
data are corrected for the above factors, the values of
AH| calculated from the integral, second law, and
Haschke's data are in excellent agreement (tables 4-5 and
4-6) .
Figure 4-21 shows the Pu-H phase diagram derived
from data for UA metal. The phases are labeled on the
diagram. The general shape of the diagram is similar to
that for the rare earth hydrides. The miscibility gap
closes at the top of the diagram but the shape and
temperature of closure is not known. However, there will
clearly be some equilibrium condition between the
dihydride on the right and hydrogen saturated liquid on
the left. Although the general shape of the
substoichiometric dihydride dihydride phase boundary is
confirmed by the data, some question is raised by the
out-lying points at low temperature. There is no
explanation for these points at this time. These
boundary compositions are derived from data with a large
potential for cumulative error and should be used with
appropriate caution.
89