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Some equilibria in the uranium-plutonium-nitrogen ternary system. An assessment
JOURNAL OF NUCLEAR MATERIALS 47 (1973) 7-16.0
NORTH-HOLLAND PUBLISHING CO., AMSTERDAM
SOME EQUILIBRIA IN THE URANIUM-PLUTONIUM-NITROGEN AN ASSESSMENT
TERNARY SYSTEM.
P.E. POTTER * European Institute for Transuranium Elements,
EURATOM,
Postfach 2266, Karlsruhe, Federal Republic of Germany
Received 2 January 1973
Some assessments of possible equilibria for the ternary system uranium-plutonium-nitrogen have been made and from these equilibria the pressures of the gas phase species, Pu, U and N2 for the system have been calculated. The nature of the vaporization behaviour of alloys of the system is also predicted. Quelques propositions de diagrammes d’e’quilibre possibles pour le systeme ternaire uranium-plutonium-azote sont pre’sentbs. A partir de ces diagrammes possibles sont calculees les pressions des elements Pu, U et N2 sous forme de phase gazeuse. La nature du comportement &la vaporisation des alliages de ce syst&me est ainsi predite. Es werden einige mo;gliche Phasengleichgewichte im tern&en System Uran-Plutonium-Stickstoff angegeben, aus denen die Partialdrucke der in der Gasphase vorliegenden Komponenten Uran, Plutonium und Stickstoff berechnet werden. Ferner wird die Art des Verdampfungsverhaltens von Phasen dieses Systems vorhergesagt.
quinitride region are some tentative results of Lorenzelli [2], which suggest that up to 15 mole % Pu sesquinitride may be soluble in one of the U-sesquinitrides; however, no structures or lattice parameters were given for this phase. Pressure measurements of the gas-phase species in this ternary system have been limited to those over the single-phase solid solution mononitride region. Alexander et al. [3] have measured the Pu pressures using a Knudsen effusion technique over the singlephase mononitride of composition Uo.aPo.2N, and found that up to 2400 K the material remained singlephase. The vaporization behaviour of the binary systems uranium-nitrogen and plutonium-nitrogen has been investigated. U mononitride vaporizes congruently up to a temperature in excess of 1600°C [4] above which uranium is formed. Pu mononitride appears to be stable up to at least 1700°C [5]. The main aim of this paper is to predict the thermal stability of the mononitride phases of the U-Pu-N system and to compare the predicted behaviour with that of the binary U-N and Pu-N systems, and also to examine theoretically
1. Introduction A solid solution of uranium and plutonium mononitride is a possible fast reactor fuel material, and the successful development of the fuel material requires a thorough knowledge of the thermodynamic properties and phase relationships of the ternary uranium-plutonium-nitrogen system. In this paper aspects of both the condensed phase equilibria and the vaporization behaviour with particular reference to the thermal stability of the mononitride are considered. Most of the studies on the ternary system U-Pu-N have been confined to the study of the solid solution between UN and PUN. UN and PuN form a complete range of solid solutions although recent measurements of the lattice parameters by Tennery and Bomar [l] have indicated that there may be a small deviation from Vegard’s law. There are no data available for the equilibria in the two-phase region, U-Pu t U-Pu mononitride, and the only data on the mononitride + ses* On leave of absence from the UKAEA Research Group, Atomic Energy Research Establishment,
Harwell, UK. 7
8
P.E. Potter, Uranium-plutonium-nitrogen 3000
I
/--
_----
ternary system
The two-term equations
2830’
AG”M
=-70398
obtained for * AGf4vN, are
+ 19.30 Teal/mole
AC0f(UN) =-72679+21.37Tcal/mole(above
(300-l
lOOK), 1lOOK).
The two-term equation for AG,q,,N, has been taken directly from the experimental measurements of Pu gas pressure above PUN of Kent and Leary [5] AC0f(PuN) =-70971+19.89Tcal/mole ( 1600 - 2000 K) . For /%U,N, the value used for the free energy of formation was -
AC:=-86238+29.75Tcal/mole(973-1618K) y-UtUN 775O fi -U+UN
obtained from the nitrogen pressure measurements of Bugl and Bauer [8] for the univariant phase field UN + /3-UN1.5of the U-N system. The U-N phase diagram is shown in fig. 1.
L
665O
2. The U-Pu-N phase diagram NITROGEN ATOMIC FRACTION
Fig. 1. The uranium-nitrogen
phase diagram
(after
Benz and
Hutchinson [4]). under what conditions the formation of other phases can occur. The data which have been used in the calculations for the free energies of formation (AC,“) of UN are assessed values. These values have been obtained from the recent specific heat measurements of Oetting and Leitnaker [6] and the enthalpy determinations of O’Hare et al. [7] using fluorine bomb calorimetry. The specific heat (C,) equation obtained was Cp= 11.681+2.6582X
10-3T-9.812X
Cal/mole . K (298- 1700 K) .
104T-2
The phase diagram is considered for three separate regions; the two-phase region, metal + mononitride; the single-phase solid-solution region; and the regions where the sesquinitrides are present. 2.1. The two-phase region U-Pu + U-PMmononitride Some possible equilibria in the two-phase field UL_-x,Pux, (solid or liquid) + W1_-x, Pu,~N) have been calculated. The system cannot be regarded as a pseudobinary system as the concentrations of U and Pu in, the two phases will in general be different. The calculation of this type of equilibria has been described by Rudy [9] and has been applied to plutonium-containing systems by the author [lo]. At equilibrium, the nitrogen potentials (AGwJI) = RT ln p(N, 1) for the two reactions
The values for the heat of formation A%%.15
= - 70.6 + 1 kcal/mole
. * Throughout this paper the symbols used are as follows: ( ) denotes solid state, { } liquid state, ( ) gaseous state, and [ ] dissolved state. R is the gas constant, T the temperature (K), E the interaction parameter regular solution (cal), and In is log,.
or heat term for a
P.E. Potter, Uranium-plutonium-nitrogen
2 [Pulu + (N2) + 2 [PWUN
,
2 FJlpu +(N2)=+2 FJNmN > must be equal and are given by, RTln P(Nz) = 2AG[,,,] -2AG[,) and RTm
_ P(y) = 2AG[,,]
and thus AG[PuN] -”
,
- 2AGI,) -
-[Pu]
=Ac[“N]
- AG[U]
’
where AGIPuN], AG[,,], AC[VN] and AG[,] are the chemical potentials or partial molal-free energies of the individual component phases of the IWO solutions. For ideal solutions, _ AG,ptil = AGofcpuN, + RT ln x2 , AGIUNl = AG&UNl + RT h U-x2)
,
_ =RTlnxl, AG[W _ AG[,] =RTln (l-xl). There is, however, an unsymmetrical deviation from ideality in the uranium-plutonium binary system [ 1 I] between the e-phase and liquid with the more negative deviation being in the solid e-tetragonal phase: there is a minimum in the liquidus curve at - 605°C at a composition of 12- 13 at % uranium. The deviation, however, in terms of energy may be quite small. The effect of deviations from ideality can be assessed by using a regular solution model for the U-Pu alloy. The partial molal free energies of [Pu] and [U] are then given by _ AG[,] =(l-x1)2E+RTln x1 , AGIVI=x12E+RTln(l
The values of x2, for given values of temperature (T K), the interaction parameter (E Cal), and the atom fraction of Pu in the U-Pu alloy (x1) can easily be calculated. For the case when the solutions are ideal, because the U mononitride and Pu mononitride are of similar stability, there is hardly any difference in the concentrations of Pu and U between the two phases. The segregation will increase with increasing temperature; some data for 1300 and 2000 K are shown in fig. 2. The segregation would be more complex when deviations from ideality occur; this is also shown in fig. 2. Experimental measurements are required to determine the magnitude of this segregation. 2.2. The single-phase mononitride region U mononitride exists over a relatively narrow composition range, for example, at 1200°C [ 121 this range is between UNO.sss and UNo.997 (with 300 ppm oxygen present) and for the temperature range 1500-2 100°C [4] the stoichiometry range is between 0.995 and -1.0 (with 200 ppm oxygen present). The variation of stoichiometry for Pu mononitride is not known but is believed to be quite small as the variation of
x2
x2
I
I
E=O 1 XI
XI “2
E-8 Kcals
-x1).
Thus, at equilibrium, AGfqPuN) - “;,“N,
9
ternary system
=RTln
(G)(&)
+ (l-2xJE and for the ideal solution
E=8 KcalS
1300
for the U-Pu alloy, E = 0.
K
2000
K
Fig. 2. The calculated distribution of Pu and U between the two phases UI+, Puxl (condensed) + U1_xl PuXIN).
P.E. Potter, Uranium-plutonium-nitrogen
10
: Single
phase
/ I
>
I
formed with a Pu: (U+Pu) ratio of 0.15. No indication was given of the nature of the crystal lattice, whether it is the P-hexagonal or cw-bee form of the sesquinitride. In this assessment it will be assumed that above -800°C [4], the temperature above which fl-UNr.S is stable, a two-phase field exists, W1_,tPux,N) t W-XBPuXIN r.&, where the sesquinitrrde phase is hexagonal, and x3 has been considered in this assessment with two possible maximum values, a very low value of 0.01, and with the value of 0.15 suggested by Lorenzelli; a corresponding value of x2 of 0.99 (i.e. a small U solubility in Pu mononitride has also been assumed. These values, which are assumed to be independent of the temperature, can be used to calculated the free energy of formation of the hypothetical Pu sesquinitride phase, which can be regarded as stabilized by dissolution in the /3-UN1.5 phase. In this region the nitrogen potentials for the two reactions
b-421
I
i
total pnss”rc minimum
/ 1
1 2 phase
, \
~CUN>+/kUN,,5>
\ \
2 phase -15{U]
t
I
4[UN],,,
I
I
+ (N2)
=
4[UNl~51PuN,.,
and
I -20
ternary system
I
I
must be equal and with the assumption solutions are both ideal then _
:
/
IN21
Fig. 3. (U) and (N2) gas pressures 1500 K.
for the U-UN1.s system
that the solid
at
_ AG[PuN,.5]
lattice parameter observed for this phase, like those for U mononitride is small [ 121. The U-N system is characterised by a very large change in uranium and nitrogen potentials as the single-phase region is traversed; this is illustrated in fig. 3, where the (U) and (N2) pressures for the phase diagram U-UN1.S at 1500 K are shown. It seems reasonable to assume that the mononitride solid solution also exists over a relatively narrow composition range. 2.3. The regions involving the sesquinitrides The nature of the phase diagram in this region is not known. The only studies have been those of Lorenzelli [2] indicating that a sesquinitride phase can be
= AG:,PuN,.,)
+ RT
In x3 ’
where AGIuN,.,I and ACIpu~,.,l are the partial molalfree energies of UNr. 5 and PuNr. 5. Equating the nitrogen potentials for the two reactions, the relationship [AG&JN,
- AG;,PuN,] (l-x3)
=RTln
- [AGhJN,.,,
- AG&‘uN,.,)l
x2
-__ x3
(l-x2)
is obtained. The free energy of formation (AG’$ of hypothetical PuN~.~ calculated from the above relationship with x2 = 0.99 and x3 = 0.0 1 is given by AG&UN,.5,
= -83 694 t 45.70 T cal*mole-’
and with x2 = 0.99 and x3 = 0.15 (Lorenzelli given by
[2]) is
P.E. Potter, Uranium-plutonium-nitrogen
11
ternary system
t
DtCPuN> UI-~~
Pux2N>
+ /3-=UN,.5> (Pu sotumtcd)
Pu
I b) With IS mole % ‘Pu NIn5’ rolubility in UN1.5
Fig. 4. Possible U-Pu-N isothermal sections 15 mole% ‘PuN,.s’ solubility in UN1.s.
A
for the ternary
system
U-Pu-N:
(a) with very small Pu solubility
in UN1.5, (b) with
12
*GLw1s) = -
P. E. Potter, ~runium-p~utoniu~ni~ogen
83 694 + 40.01 T calmole-’
.
There are also other additional phase fields to be considered. For example, the three-phase field p UN1.5 (Pu saturated), (x-UNr., (Pu saturated) and PUN (U saturated) and the two-phase fields cr-UNr,s (with variable Pu concel~tration) and fi-UN1.5 (with variable Pu concentration), and finally PuN+UN2__, . Two possible isothermal sections are shown in fig. 4. The first applies when the Pu solubility in &UNI.S is very low and the second applies to the data of Lorenzelli for Pu soiubility in /MJNr.s.
3. Vapor~atjo~ behaviour of U-Pu-N alloys As discussed in the introduction, the purpose of these calculations is to predict the nature of the vaporization processes of alloys in the ternary system. However, before considering the behaviour of the ternary system the nature of the behaviour of the binary systems U-N and Vu-N is considered. The pressures of the predominant gas-phase species U gas and N2 above the U-N system are shown in fig. 3 for 1500 K. The contribution from UN gas is very small and even at 2000 K, above single-phase U mononitride, Hoenig [12] calculated a pressure of 10-l’ atm from the data of Gingerich [ 141. The minimum in total pressure corresponds to the congruently evaporating composition, and this evaporation should occur from the singlephase mononitride region up to a temperature of 1643 K, above this temperature U-liquid should be formed for the evaporation in a closed equilibrium system. However, under Lan~uir free evaporation conditions the nitrogen gas will diffuse from the mononitride rather more rapidly than the U-gas, and the formation of metal will occur at a lower temperatures. The relationship between pm,) and pcu) is then given by /IV.,
\0.5
or pm,) = 0. 17pW) , where MN* and Mr_,are the molecular or atomic weights of the vaporizing species. Under these conditions congruent vaporization would occur up to 1495 K, about
ternary system
150 K lower than for the true equilibrium in a closed system. This calculated temperature for the free evaporation case is considerably lower than the experimental values of 1800°C and 17OO’C given by Benz and Bowman [ 151 and later by Benz and Hutchinson [4]. Some recent work of Affortit (161 on the specific heat of UN indicates that metal fo~ation occurred just above 1700°C when filaments of UN were heated in vacua. The discrepancies in the temperatures, that is UN is more stable than predicted, may be due to a slightly lower evaporation coefficient of Nz compared with U. A lowering of the uranium activity by solubility of nitrogen would lower the temperature at which decomposition to uranium liquid and nitrogen gas occurred; ~thou~ the solubility of nitrogen in uranium is low; at 1800 K it is 0.476 at % nitrogen ]171* A similar consideration of the Pu-N system indicates that the congruent vaporizatjon of PUN occurs up to higher temperatures than for UN. Using the value for *G’&,IQ given in sect. 1, congruent vaporization is predicted up to 4142 K in a closed system and up to 3093 K in an open system (Langmuir evaporation). These temperatures are higher than that of 2800 K calculated by Rand [ 181 in a closed system, using an estimated value for AGF(pu~). The mode of vaporization of the alloys in this ternary system can be determined by making an assessment of the possible vapour pressures of the gas-phase species, namely U, Pu and Nz over the possible phase fields of the ternary system. 3.1. The phasefield U1_-x,PuX, (condensed)
+
This two-phase field is firstly considered. Any nitrogen solubihty in the liquid U-Pu alloy has been neglected, a~thou~ the solubility of nitrogen in U expressed as the atom fraction of N is 0.014 at 2000 K, and 0.052 at 2372 K [ 171. The solubility of nitrogen in liquid plutonium and the uranium-plutonium alloys is not known. The (U) and (Pu) pressures can be calculated from the equilibria [U],
=(Ut
3
Pdu
=+m> t
and with the assumption that U and Pu form a regular or ideal solid solution (when E = 0) the pressures are
P.E. Potter, Uranium-plutonium-nitrogen
given by RTlnpwj=RTln(I-xJtx:E-AC!,, Or
RTlnp@)
=RTlnxr
t(l-xr)‘E-
The values used for AC:,,
AG&,rr,.
and AC:,,
are
= 115450-26.13Tcal.g*atom-‘,
AG&u, AG&Pu,
= 80 500 - 23.00T cal.g*atom-’
(19) .
(20)
The nitrogen pressures in this phase field can be obtained from the equilibria represented by the equations [P$
+ 0.5 (Nz) r=
P-NUN 9
[Ul,
+ 0.5 (NJ +
WI,,
.
13
ternary system
The Nz pressures for the binary U-N and Pu-N systems for the metal t mononitride region differ by less than a quarter of an order of magnitude, and thus in the ternary system will not vary significantly. Some data for the pressures of Pu, U and Nz gas, showing the effect of varying the interaction parameter (E) are shown in fig. 5. As mentioned above, nitrogen solubility in the liquid metal phase has been neglected in these considerations, but before any detailed interpretation of(U) and (Pu) pressures in this region are undertaken, the two-component system U-Pu requires some examination; measurements of the (Pu) and (U) pressures would give some indication of any deviation from ideality, particularly in the U-rich region of the system. 3.2. The single-phase mononitride region
For example, RTln~(~Jatm)=2AG&,~~-2RTlnxI+2RTlna~ for an ideal solution, metal phase
or for a regular solution in the
RT In pgu,) = 2AG&,uNj - 2RT In x1 - 2( I-x,)*E +
2RTlnxz.
The pressures of the gas-phase species in the singlephase region can only be estimated from the pressures in the neighbouring phase fields. The estimated pressures can then be compared with the measured values.of Alexander et al. [3]. A linear variation of the component activities across the single-phase region has been assumed.
POOOK
I
n-6
E= 8 Kcal.
G-8
t
Kcal.
E=-8Kcal. 1 .o
I,,,,
0
0.2
PuIoJtPu~ ,Prcssurcs
for
compositions
0.4
0.6
0.8
Pu/(lJtPu) close
to (a)
the
The effect
of deviations
from
idcality
Fig. 5. (Pu), (U) and (Nz) gas pressures for the two-phase region UPu and U-Pu mononitride.
in
P.E. Potter, Uranium~~lut~nium-nitrogen
14
3.3. The region mononitride and sesquinitride
and in practice could be close to unity), and for (U) 3 [UN&,,
Some assessments of the gas-phase pressures involving the sesquinitrides can be attempted in the region expressed as (U1_X2PUX2N)+(U1_X~PUXSN1.S). Firstly,x3 is assumed to be very small, and so the equilibria involving the (N,) and (U) gases can be represented by:
FJNlpUN + 0.25W
2[PW.,l,,,
,
rempemure
ZOOOK
I
2OQOK
Py”
+P,,* O-2
Temperature
5+ (Pu>* 3 [PuNIUN >
when the limit of PuN r.s solub~li~ in UNr.s is
(the activity of (UN,,,) has been assumed to be unity
Temperature
=r 2RJN1.5) + (U) .
In order to calculate the (Pu) gas pressures over this region, a small solubility of PLIin P-UNr,s must be assumed, and an estimate of AG&,uN, $1has already been made. The (Pu) gas phase is given by the equihbrium
for (N4 (UN,.4 =
ternary system
20OOK
Pu/c + p;o-5
/
Pyu+pu-O-Ol
2 phase
Temperature
2200K
Pu/” + pu’O.Tl
5mgk phase
2 phase (ul-x, <“1-x2
‘%I}
+
f’“x2 N’
IF-WI IPU) _
W21
(N2) (U)
IU) 2phoso
?$-$$>
Fig. 6. Pressures Pu/U+Pu = 0.5,
of (Pu), (U) and (Nz) for the U-Pu-N system at constant Pu/U+Pu ratios; (a) 2000 K, WU+PU 2000 K, Pu/U+Pu = 0.2, (d) 2000 K, Pu/U+Pu = 0.01, (e) 2200 K Pu/U+Pu = 0.01.
(c)
= 0.8, (b) 2OOOK
P.E. Potter, Uranium-plutonium-nitrogen
Free Evaporation Temperature 2000K
ternary system
Table 1 A comparison of the calculated and experimental data for the (Pu) pressures and total pressures above the congruently vaporizing Uo.sPuu.2 mononitride.
Px+p”=o*2
Temperature (K)
1400 1600 1800 2000 2200 2400
2 phase
I
/+-x2
I
15
(Pu) pressure (log P(Pu))
Total pressure
(atm)
(atm)
(log Ptotal)
Experimental [ 31
calculated
Experimental [ 31
calculated
-
-
-
-
9.70 7.80 6.39 5.11 4.24 3.51
10.0 8.05 6.60 4.86 4.30 3.40
9.64 7.76 6.22 4.86 4.17 3.44
9.70 7.75 6.20 4.80 4.00 3.10
/
P”x,N>\
I
I
Fig. 7. The free evaporation behaviour for the U-Pu-N system at 2000 K with Pu/U+Pu = 0.2.
x3 = 0.01, the only variable in the calculation providingx3 Q 0.01 will be x2 for a given temperature. However, when the maximum value of x3 is 0.15, the equilibrium within the two-phase region W1_,2Pu,2N) + W1_-x, PuXs Nr.& must be considered, in order to obtain the relationship between x3 and x2 at a given temperature. 3.4. The mode of vaporization of the ternary system U-Pu-N The importance of this assessment is that it enables a prediction of the effect of plutonium additions on the stability of the mononitride phase, although normally it would not be expected that the temperatures in the centre of a nitride fast reactor fuel element would exceed a temperature greater than ca. 1500°C. The calculations of the pressures of the gas-phase species in the bivariant phase fields enable some predictions to be made as to the nature of the composition changes in the system during evaporation in a closed system and also in an open system. The pressures along a line of constant Pu: U ratio are firstly considered for a closed system. The pressures are shown in fig. 6.for a nominal Pu/U+Pu ratio of 0.8, 0.5, 0.2 and 0.01 for 2000 and 2200K. There
is a minimum in the total pressure even when the Pu/UtPu ratio is 0.01 at 2000 K; at 2200 K the minimum is no longer present. The minimum in total pressure means that as alloys of the system evaporate in a closed system at these temperatures, alloys in the twophase region (metal and mononitride) will lose predominantly Pu into the gas-phase and become singlephase, whilst those in the two-phase region (mononitride + sesquinitride) will lose nitrogen and also become single-phase. As the total plutonium concentration decreases, the total pressure at the minimum decreases and the alloy will remain single-phase until sufficient quantities of Pu and N2 have been removed into the gas phase, and then the alloy will change composition with the formation of the metalphase: the Pu concentration of both phases will be very low. It should be remembered that in a free evaporation experiment the heavier gas-phase species, namely (U) and (Pu) gas, will be removed more slowly than (N,) gas, and so the composition of apparent congruent vaporization changes towards higher metal compositions in the solid alloy. The weight loss is now proportional to Pi ,,I@ where Mi is the molecular weight of the vaporizing species (i) whose equilibrium pressure is Pi eq,. this effect is shown in fig. 7 for 2000 K and shows that the position of the minimum is slightly changed. Finally, it is now possible to make a comparison between the measurements of Alexander et al. [3] and the present calculations. Measurements of Pu
16
P.E. Potter, Uranium-plutonium-nitrogenternary system
pressure were made by the Knudsen effusion method between 1400 and 2400 K over U&‘LI~.~N. The comparison of the measured and calculated pressures is shown in table 1, and there is good agreement between the two sets of values.
4. Conclusions This assessment has shown that uranium-plutonium mononitride will vaporize from the single-phase region up to a temperature which increases with increase in plutonium concentration.
References [I] V.J. Tennery and ES. Bomar, J. Am. Ceram. Sot. 54 (1971) 247. [2] R. Lorenzelli, CEA Report R-3536 (1968). [3] CA. Alexander, J.S. Ogden and W.M. Pardue, Plutonium 1970 and other Actinides, ed. W.N. Miner, Nucl. Metallurgy 17 (The Metallurgical Society of the American Institute of Mining, Metallurgical and Petroleum Engineers Inc., New York) pt. I, p. 95. [4] R. Benz and W.B. Hutchinson, J. Nucl, Mater. 36 (19701 135. [S] R.A. Kent and J.A. Leary, High Temp. Sci. 1 (1969) 176.
[6] F.L. Oetting and J.M. Leitmaker, J. Chem. Thermodynamics 4 (19721 199. [7] P.A.G. O’Hare, J.L. Settle, H.M. Feder and W.N. Hubbard, Thermodynamics of Nuclear Materials 1967, IAEA, Vienna (1968) p. 285. [S] J. Bugl and A.A. Bauer, Compounds of Interest in Nuclear Reactor Technology, Ed. J.T. Waber, P. Chiotti, W.N. Miner (Edwards Bros. Inc. Ann. Arbor, Mich., 1964) p. 215. [ 91 R. Rudy, The~odyn~ics of Nuclear Materials, IAEA, Vienna (1962) p. 244. [lo] P.E. Potter, UKAEA Report AERE-R-625 1 (1969). [ 111 F.H. Ellinger, R.O. Elliott and E.M. Cramer, J. Nucl. Mater. 3 (1959) 241. [12] C.L. Hoenig, J. Amer. Ceram. Sot. 54 (1971) 391. 1131 K.E. Spear and J.M. Leitmaker, USAEC report ORNLTM-2106 (1968). [ 141 K.A. Gingerich, J. Chem. Phys. 47 (1967) 2192. [ 151 R. Benz and M.G. Bowman, J. Am. Chem. Sot. 88 (1966) 264. [ 161 C. Affortit, J. Nucl. Mater. 34 (1970) 105. [ 171 J. Bugl and A.A. Bauer, J. Am. Ceram. Sot. 47 (19641 425. [18] M.H. Rand, Atomic Energy Review 4, Special Edition I, (IAEA, Vienna, 1966). [ 191 R.J. Ackermann and R.J. Thorn, IAEA technical panel on the thermodynamics of uranium and plutonium carbides, Vienna (September 1968). [20] R.J. Ackermann, R.L. Faircloth and M.H. Rand, J. Phys. Chem. 70 (1966) 3698.
NORTH-HOLLAND PUBLISHING CO., AMSTERDAM
SOME EQUILIBRIA IN THE URANIUM-PLUTONIUM-NITROGEN AN ASSESSMENT
TERNARY SYSTEM.
P.E. POTTER * European Institute for Transuranium Elements,
EURATOM,
Postfach 2266, Karlsruhe, Federal Republic of Germany
Received 2 January 1973
Some assessments of possible equilibria for the ternary system uranium-plutonium-nitrogen have been made and from these equilibria the pressures of the gas phase species, Pu, U and N2 for the system have been calculated. The nature of the vaporization behaviour of alloys of the system is also predicted. Quelques propositions de diagrammes d’e’quilibre possibles pour le systeme ternaire uranium-plutonium-azote sont pre’sentbs. A partir de ces diagrammes possibles sont calculees les pressions des elements Pu, U et N2 sous forme de phase gazeuse. La nature du comportement &la vaporisation des alliages de ce syst&me est ainsi predite. Es werden einige mo;gliche Phasengleichgewichte im tern&en System Uran-Plutonium-Stickstoff angegeben, aus denen die Partialdrucke der in der Gasphase vorliegenden Komponenten Uran, Plutonium und Stickstoff berechnet werden. Ferner wird die Art des Verdampfungsverhaltens von Phasen dieses Systems vorhergesagt.
quinitride region are some tentative results of Lorenzelli [2], which suggest that up to 15 mole % Pu sesquinitride may be soluble in one of the U-sesquinitrides; however, no structures or lattice parameters were given for this phase. Pressure measurements of the gas-phase species in this ternary system have been limited to those over the single-phase solid solution mononitride region. Alexander et al. [3] have measured the Pu pressures using a Knudsen effusion technique over the singlephase mononitride of composition Uo.aPo.2N, and found that up to 2400 K the material remained singlephase. The vaporization behaviour of the binary systems uranium-nitrogen and plutonium-nitrogen has been investigated. U mononitride vaporizes congruently up to a temperature in excess of 1600°C [4] above which uranium is formed. Pu mononitride appears to be stable up to at least 1700°C [5]. The main aim of this paper is to predict the thermal stability of the mononitride phases of the U-Pu-N system and to compare the predicted behaviour with that of the binary U-N and Pu-N systems, and also to examine theoretically
1. Introduction A solid solution of uranium and plutonium mononitride is a possible fast reactor fuel material, and the successful development of the fuel material requires a thorough knowledge of the thermodynamic properties and phase relationships of the ternary uranium-plutonium-nitrogen system. In this paper aspects of both the condensed phase equilibria and the vaporization behaviour with particular reference to the thermal stability of the mononitride are considered. Most of the studies on the ternary system U-Pu-N have been confined to the study of the solid solution between UN and PUN. UN and PuN form a complete range of solid solutions although recent measurements of the lattice parameters by Tennery and Bomar [l] have indicated that there may be a small deviation from Vegard’s law. There are no data available for the equilibria in the two-phase region, U-Pu t U-Pu mononitride, and the only data on the mononitride + ses* On leave of absence from the UKAEA Research Group, Atomic Energy Research Establishment,
Harwell, UK. 7
8
P.E. Potter, Uranium-plutonium-nitrogen 3000
I
/--
_----
ternary system
The two-term equations
2830’
AG”M
=-70398
obtained for * AGf4vN, are
+ 19.30 Teal/mole
AC0f(UN) =-72679+21.37Tcal/mole(above
(300-l
lOOK), 1lOOK).
The two-term equation for AG,q,,N, has been taken directly from the experimental measurements of Pu gas pressure above PUN of Kent and Leary [5] AC0f(PuN) =-70971+19.89Tcal/mole ( 1600 - 2000 K) . For /%U,N, the value used for the free energy of formation was -
AC:=-86238+29.75Tcal/mole(973-1618K) y-UtUN 775O fi -U+UN
obtained from the nitrogen pressure measurements of Bugl and Bauer [8] for the univariant phase field UN + /3-UN1.5of the U-N system. The U-N phase diagram is shown in fig. 1.
L
665O
2. The U-Pu-N phase diagram NITROGEN ATOMIC FRACTION
Fig. 1. The uranium-nitrogen
phase diagram
(after
Benz and
Hutchinson [4]). under what conditions the formation of other phases can occur. The data which have been used in the calculations for the free energies of formation (AC,“) of UN are assessed values. These values have been obtained from the recent specific heat measurements of Oetting and Leitnaker [6] and the enthalpy determinations of O’Hare et al. [7] using fluorine bomb calorimetry. The specific heat (C,) equation obtained was Cp= 11.681+2.6582X
10-3T-9.812X
Cal/mole . K (298- 1700 K) .
104T-2
The phase diagram is considered for three separate regions; the two-phase region, metal + mononitride; the single-phase solid-solution region; and the regions where the sesquinitrides are present. 2.1. The two-phase region U-Pu + U-PMmononitride Some possible equilibria in the two-phase field UL_-x,Pux, (solid or liquid) + W1_-x, Pu,~N) have been calculated. The system cannot be regarded as a pseudobinary system as the concentrations of U and Pu in, the two phases will in general be different. The calculation of this type of equilibria has been described by Rudy [9] and has been applied to plutonium-containing systems by the author [lo]. At equilibrium, the nitrogen potentials (AGwJI) = RT ln p(N, 1) for the two reactions
The values for the heat of formation A%%.15
= - 70.6 + 1 kcal/mole
. * Throughout this paper the symbols used are as follows: ( ) denotes solid state, { } liquid state, ( ) gaseous state, and [ ] dissolved state. R is the gas constant, T the temperature (K), E the interaction parameter regular solution (cal), and In is log,.
or heat term for a
P.E. Potter, Uranium-plutonium-nitrogen
2 [Pulu + (N2) + 2 [PWUN
,
2 FJlpu +(N2)=+2 FJNmN > must be equal and are given by, RTln P(Nz) = 2AG[,,,] -2AG[,) and RTm
_ P(y) = 2AG[,,]
and thus AG[PuN] -”
,
- 2AGI,) -
-[Pu]
=Ac[“N]
- AG[U]
’
where AGIPuN], AG[,,], AC[VN] and AG[,] are the chemical potentials or partial molal-free energies of the individual component phases of the IWO solutions. For ideal solutions, _ AG,ptil = AGofcpuN, + RT ln x2 , AGIUNl = AG&UNl + RT h U-x2)
,
_ =RTlnxl, AG[W _ AG[,] =RTln (l-xl). There is, however, an unsymmetrical deviation from ideality in the uranium-plutonium binary system [ 1 I] between the e-phase and liquid with the more negative deviation being in the solid e-tetragonal phase: there is a minimum in the liquidus curve at - 605°C at a composition of 12- 13 at % uranium. The deviation, however, in terms of energy may be quite small. The effect of deviations from ideality can be assessed by using a regular solution model for the U-Pu alloy. The partial molal free energies of [Pu] and [U] are then given by _ AG[,] =(l-x1)2E+RTln x1 , AGIVI=x12E+RTln(l
The values of x2, for given values of temperature (T K), the interaction parameter (E Cal), and the atom fraction of Pu in the U-Pu alloy (x1) can easily be calculated. For the case when the solutions are ideal, because the U mononitride and Pu mononitride are of similar stability, there is hardly any difference in the concentrations of Pu and U between the two phases. The segregation will increase with increasing temperature; some data for 1300 and 2000 K are shown in fig. 2. The segregation would be more complex when deviations from ideality occur; this is also shown in fig. 2. Experimental measurements are required to determine the magnitude of this segregation. 2.2. The single-phase mononitride region U mononitride exists over a relatively narrow composition range, for example, at 1200°C [ 121 this range is between UNO.sss and UNo.997 (with 300 ppm oxygen present) and for the temperature range 1500-2 100°C [4] the stoichiometry range is between 0.995 and -1.0 (with 200 ppm oxygen present). The variation of stoichiometry for Pu mononitride is not known but is believed to be quite small as the variation of
x2
x2
I
I
E=O 1 XI
XI “2
E-8 Kcals
-x1).
Thus, at equilibrium, AGfqPuN) - “;,“N,
9
ternary system
=RTln
(G)(&)
+ (l-2xJE and for the ideal solution
E=8 KcalS
1300
for the U-Pu alloy, E = 0.
K
2000
K
Fig. 2. The calculated distribution of Pu and U between the two phases UI+, Puxl (condensed) + U1_xl PuXIN).
P.E. Potter, Uranium-plutonium-nitrogen
10
: Single
phase
/ I
>
I
formed with a Pu: (U+Pu) ratio of 0.15. No indication was given of the nature of the crystal lattice, whether it is the P-hexagonal or cw-bee form of the sesquinitride. In this assessment it will be assumed that above -800°C [4], the temperature above which fl-UNr.S is stable, a two-phase field exists, W1_,tPux,N) t W-XBPuXIN r.&, where the sesquinitrrde phase is hexagonal, and x3 has been considered in this assessment with two possible maximum values, a very low value of 0.01, and with the value of 0.15 suggested by Lorenzelli; a corresponding value of x2 of 0.99 (i.e. a small U solubility in Pu mononitride has also been assumed. These values, which are assumed to be independent of the temperature, can be used to calculated the free energy of formation of the hypothetical Pu sesquinitride phase, which can be regarded as stabilized by dissolution in the /3-UN1.5 phase. In this region the nitrogen potentials for the two reactions
b-421
I
i
total pnss”rc minimum
/ 1
1 2 phase
, \
~CUN>+/kUN,,5>
\ \
2 phase -15{U]
t
I
4[UN],,,
I
I
+ (N2)
=
4[UNl~51PuN,.,
and
I -20
ternary system
I
I
must be equal and with the assumption solutions are both ideal then _
:
/
IN21
Fig. 3. (U) and (N2) gas pressures 1500 K.
for the U-UN1.s system
that the solid
at
_ AG[PuN,.5]
lattice parameter observed for this phase, like those for U mononitride is small [ 121. The U-N system is characterised by a very large change in uranium and nitrogen potentials as the single-phase region is traversed; this is illustrated in fig. 3, where the (U) and (N2) pressures for the phase diagram U-UN1.S at 1500 K are shown. It seems reasonable to assume that the mononitride solid solution also exists over a relatively narrow composition range. 2.3. The regions involving the sesquinitrides The nature of the phase diagram in this region is not known. The only studies have been those of Lorenzelli [2] indicating that a sesquinitride phase can be
= AG:,PuN,.,)
+ RT
In x3 ’
where AGIuN,.,I and ACIpu~,.,l are the partial molalfree energies of UNr. 5 and PuNr. 5. Equating the nitrogen potentials for the two reactions, the relationship [AG&JN,
- AG;,PuN,] (l-x3)
=RTln
- [AGhJN,.,,
- AG&‘uN,.,)l
x2
-__ x3
(l-x2)
is obtained. The free energy of formation (AG’$ of hypothetical PuN~.~ calculated from the above relationship with x2 = 0.99 and x3 = 0.0 1 is given by AG&UN,.5,
= -83 694 t 45.70 T cal*mole-’
and with x2 = 0.99 and x3 = 0.15 (Lorenzelli given by
[2]) is
P.E. Potter, Uranium-plutonium-nitrogen
11
ternary system
D
Pux2N>
+ /3-=UN,.5> (Pu sotumtcd)
Pu
I b) With IS mole % ‘Pu NIn5’ rolubility in UN1.5
Fig. 4. Possible U-Pu-N isothermal sections 15 mole% ‘PuN,.s’ solubility in UN1.s.
A
for the ternary
system
U-Pu-N:
(a) with very small Pu solubility
in UN1.5, (b) with
12
*GLw1s) = -
P. E. Potter, ~runium-p~utoniu~ni~ogen
83 694 + 40.01 T calmole-’
.
There are also other additional phase fields to be considered. For example, the three-phase field p UN1.5 (Pu saturated), (x-UNr., (Pu saturated) and PUN (U saturated) and the two-phase fields cr-UNr,s (with variable Pu concel~tration) and fi-UN1.5 (with variable Pu concentration), and finally PuN+UN2__, . Two possible isothermal sections are shown in fig. 4. The first applies when the Pu solubility in &UNI.S is very low and the second applies to the data of Lorenzelli for Pu soiubility in /MJNr.s.
3. Vapor~atjo~ behaviour of U-Pu-N alloys As discussed in the introduction, the purpose of these calculations is to predict the nature of the vaporization processes of alloys in the ternary system. However, before considering the behaviour of the ternary system the nature of the behaviour of the binary systems U-N and Vu-N is considered. The pressures of the predominant gas-phase species U gas and N2 above the U-N system are shown in fig. 3 for 1500 K. The contribution from UN gas is very small and even at 2000 K, above single-phase U mononitride, Hoenig [12] calculated a pressure of 10-l’ atm from the data of Gingerich [ 141. The minimum in total pressure corresponds to the congruently evaporating composition, and this evaporation should occur from the singlephase mononitride region up to a temperature of 1643 K, above this temperature U-liquid should be formed for the evaporation in a closed equilibrium system. However, under Lan~uir free evaporation conditions the nitrogen gas will diffuse from the mononitride rather more rapidly than the U-gas, and the formation of metal will occur at a lower temperatures. The relationship between pm,) and pcu) is then given by /IV.,
\0.5
or pm,) = 0. 17pW) , where MN* and Mr_,are the molecular or atomic weights of the vaporizing species. Under these conditions congruent vaporization would occur up to 1495 K, about
ternary system
150 K lower than for the true equilibrium in a closed system. This calculated temperature for the free evaporation case is considerably lower than the experimental values of 1800°C and 17OO’C given by Benz and Bowman [ 151 and later by Benz and Hutchinson [4]. Some recent work of Affortit (161 on the specific heat of UN indicates that metal fo~ation occurred just above 1700°C when filaments of UN were heated in vacua. The discrepancies in the temperatures, that is UN is more stable than predicted, may be due to a slightly lower evaporation coefficient of Nz compared with U. A lowering of the uranium activity by solubility of nitrogen would lower the temperature at which decomposition to uranium liquid and nitrogen gas occurred; ~thou~ the solubility of nitrogen in uranium is low; at 1800 K it is 0.476 at % nitrogen ]171* A similar consideration of the Pu-N system indicates that the congruent vaporizatjon of PUN occurs up to higher temperatures than for UN. Using the value for *G’&,IQ given in sect. 1, congruent vaporization is predicted up to 4142 K in a closed system and up to 3093 K in an open system (Langmuir evaporation). These temperatures are higher than that of 2800 K calculated by Rand [ 181 in a closed system, using an estimated value for AGF(pu~). The mode of vaporization of the alloys in this ternary system can be determined by making an assessment of the possible vapour pressures of the gas-phase species, namely U, Pu and Nz over the possible phase fields of the ternary system. 3.1. The phasefield U1_-x,PuX, (condensed)
+
This two-phase field is firstly considered. Any nitrogen solubihty in the liquid U-Pu alloy has been neglected, a~thou~ the solubility of nitrogen in U expressed as the atom fraction of N is 0.014 at 2000 K, and 0.052 at 2372 K [ 171. The solubility of nitrogen in liquid plutonium and the uranium-plutonium alloys is not known. The (U) and (Pu) pressures can be calculated from the equilibria [U],
=(Ut
3
Pdu
=+m> t
and with the assumption that U and Pu form a regular or ideal solid solution (when E = 0) the pressures are
P.E. Potter, Uranium-plutonium-nitrogen
given by RTlnpwj=RTln(I-xJtx:E-AC!,, Or
RTlnp@)
=RTlnxr
t(l-xr)‘E-
The values used for AC:,,
AG&,rr,.
and AC:,,
are
= 115450-26.13Tcal.g*atom-‘,
AG&u, AG&Pu,
= 80 500 - 23.00T cal.g*atom-’
(19) .
(20)
The nitrogen pressures in this phase field can be obtained from the equilibria represented by the equations [P$
+ 0.5 (Nz) r=
P-NUN 9
[Ul,
+ 0.5 (NJ +
WI,,
.
13
ternary system
The Nz pressures for the binary U-N and Pu-N systems for the metal t mononitride region differ by less than a quarter of an order of magnitude, and thus in the ternary system will not vary significantly. Some data for the pressures of Pu, U and Nz gas, showing the effect of varying the interaction parameter (E) are shown in fig. 5. As mentioned above, nitrogen solubility in the liquid metal phase has been neglected in these considerations, but before any detailed interpretation of(U) and (Pu) pressures in this region are undertaken, the two-component system U-Pu requires some examination; measurements of the (Pu) and (U) pressures would give some indication of any deviation from ideality, particularly in the U-rich region of the system. 3.2. The single-phase mononitride region
For example, RTln~(~Jatm)=2AG&,~~-2RTlnxI+2RTlna~ for an ideal solution, metal phase
or for a regular solution in the
RT In pgu,) = 2AG&,uNj - 2RT In x1 - 2( I-x,)*E +
2RTlnxz.
The pressures of the gas-phase species in the singlephase region can only be estimated from the pressures in the neighbouring phase fields. The estimated pressures can then be compared with the measured values.of Alexander et al. [3]. A linear variation of the component activities across the single-phase region has been assumed.
POOOK
I
n-6
E= 8 Kcal.
G-8
t
Kcal.
E=-8Kcal. 1 .o
I,,,,
0
0.2
PuIoJtPu~ ,Prcssurcs
for
compositions
0.4
0.6
0.8
Pu/(lJtPu) close
to (a)
the
The effect
of deviations
from
idcality
Fig. 5. (Pu), (U) and (Nz) gas pressures for the two-phase region UPu and U-Pu mononitride.
in
P.E. Potter, Uranium~~lut~nium-nitrogen
14
3.3. The region mononitride and sesquinitride
and in practice could be close to unity), and for (U) 3 [UN&,,
Some assessments of the gas-phase pressures involving the sesquinitrides can be attempted in the region expressed as (U1_X2PUX2N)+(U1_X~PUXSN1.S). Firstly,x3 is assumed to be very small, and so the equilibria involving the (N,) and (U) gases can be represented by:
FJNlpUN + 0.25W
2[PW.,l,,,
,
rempemure
ZOOOK
I
2OQOK
Py”
+P,,* O-2
Temperature
5+ (Pu>* 3 [PuNIUN >
when the limit of PuN r.s solub~li~ in UNr.s is
(the activity of (UN,,,) has been assumed to be unity
Temperature
=r 2RJN1.5) + (U) .
In order to calculate the (Pu) gas pressures over this region, a small solubility of PLIin P-UNr,s must be assumed, and an estimate of AG&,uN, $1has already been made. The (Pu) gas phase is given by the equihbrium
for (N4 (UN,.4 =
ternary system
20OOK
Pu/c + p;o-5
/
Pyu+pu-O-Ol
2 phase
Temperature
2200K
Pu/” + pu’O.Tl
5mgk phase
2 phase (ul-x, <“1-x2
‘%I}
+
f’“x2 N’
IF-WI IPU) _
W21
(N2) (U)
IU) 2phoso
?$-$$>
Fig. 6. Pressures Pu/U+Pu = 0.5,
of (Pu), (U) and (Nz) for the U-Pu-N system at constant Pu/U+Pu ratios; (a) 2000 K, WU+PU 2000 K, Pu/U+Pu = 0.2, (d) 2000 K, Pu/U+Pu = 0.01, (e) 2200 K Pu/U+Pu = 0.01.
(c)
= 0.8, (b) 2OOOK
P.E. Potter, Uranium-plutonium-nitrogen
Free Evaporation Temperature 2000K
ternary system
Table 1 A comparison of the calculated and experimental data for the (Pu) pressures and total pressures above the congruently vaporizing Uo.sPuu.2 mononitride.
Px+p”=o*2
Temperature (K)
1400 1600 1800 2000 2200 2400
2 phase
I
/+-x2
I
15
(Pu) pressure (log P(Pu))
Total pressure
(atm)
(atm)
(log Ptotal)
Experimental [ 31
calculated
Experimental [ 31
calculated
-
-
-
-
9.70 7.80 6.39 5.11 4.24 3.51
10.0 8.05 6.60 4.86 4.30 3.40
9.64 7.76 6.22 4.86 4.17 3.44
9.70 7.75 6.20 4.80 4.00 3.10
/
P”x,N>\
I
I
Fig. 7. The free evaporation behaviour for the U-Pu-N system at 2000 K with Pu/U+Pu = 0.2.
x3 = 0.01, the only variable in the calculation providingx3 Q 0.01 will be x2 for a given temperature. However, when the maximum value of x3 is 0.15, the equilibrium within the two-phase region W1_,2Pu,2N) + W1_-x, PuXs Nr.& must be considered, in order to obtain the relationship between x3 and x2 at a given temperature. 3.4. The mode of vaporization of the ternary system U-Pu-N The importance of this assessment is that it enables a prediction of the effect of plutonium additions on the stability of the mononitride phase, although normally it would not be expected that the temperatures in the centre of a nitride fast reactor fuel element would exceed a temperature greater than ca. 1500°C. The calculations of the pressures of the gas-phase species in the bivariant phase fields enable some predictions to be made as to the nature of the composition changes in the system during evaporation in a closed system and also in an open system. The pressures along a line of constant Pu: U ratio are firstly considered for a closed system. The pressures are shown in fig. 6.for a nominal Pu/U+Pu ratio of 0.8, 0.5, 0.2 and 0.01 for 2000 and 2200K. There
is a minimum in the total pressure even when the Pu/UtPu ratio is 0.01 at 2000 K; at 2200 K the minimum is no longer present. The minimum in total pressure means that as alloys of the system evaporate in a closed system at these temperatures, alloys in the twophase region (metal and mononitride) will lose predominantly Pu into the gas-phase and become singlephase, whilst those in the two-phase region (mononitride + sesquinitride) will lose nitrogen and also become single-phase. As the total plutonium concentration decreases, the total pressure at the minimum decreases and the alloy will remain single-phase until sufficient quantities of Pu and N2 have been removed into the gas phase, and then the alloy will change composition with the formation of the metalphase: the Pu concentration of both phases will be very low. It should be remembered that in a free evaporation experiment the heavier gas-phase species, namely (U) and (Pu) gas, will be removed more slowly than (N,) gas, and so the composition of apparent congruent vaporization changes towards higher metal compositions in the solid alloy. The weight loss is now proportional to Pi ,,I@ where Mi is the molecular weight of the vaporizing species (i) whose equilibrium pressure is Pi eq,. this effect is shown in fig. 7 for 2000 K and shows that the position of the minimum is slightly changed. Finally, it is now possible to make a comparison between the measurements of Alexander et al. [3] and the present calculations. Measurements of Pu
16
P.E. Potter, Uranium-plutonium-nitrogenternary system
pressure were made by the Knudsen effusion method between 1400 and 2400 K over U&‘LI~.~N. The comparison of the measured and calculated pressures is shown in table 1, and there is good agreement between the two sets of values.
4. Conclusions This assessment has shown that uranium-plutonium mononitride will vaporize from the single-phase region up to a temperature which increases with increase in plutonium concentration.
References [I] V.J. Tennery and ES. Bomar, J. Am. Ceram. Sot. 54 (1971) 247. [2] R. Lorenzelli, CEA Report R-3536 (1968). [3] CA. Alexander, J.S. Ogden and W.M. Pardue, Plutonium 1970 and other Actinides, ed. W.N. Miner, Nucl. Metallurgy 17 (The Metallurgical Society of the American Institute of Mining, Metallurgical and Petroleum Engineers Inc., New York) pt. I, p. 95. [4] R. Benz and W.B. Hutchinson, J. Nucl, Mater. 36 (19701 135. [S] R.A. Kent and J.A. Leary, High Temp. Sci. 1 (1969) 176.
[6] F.L. Oetting and J.M. Leitmaker, J. Chem. Thermodynamics 4 (19721 199. [7] P.A.G. O’Hare, J.L. Settle, H.M. Feder and W.N. Hubbard, Thermodynamics of Nuclear Materials 1967, IAEA, Vienna (1968) p. 285. [S] J. Bugl and A.A. Bauer, Compounds of Interest in Nuclear Reactor Technology, Ed. J.T. Waber, P. Chiotti, W.N. Miner (Edwards Bros. Inc. Ann. Arbor, Mich., 1964) p. 215. [ 91 R. Rudy, The~odyn~ics of Nuclear Materials, IAEA, Vienna (1962) p. 244. [lo] P.E. Potter, UKAEA Report AERE-R-625 1 (1969). [ 111 F.H. Ellinger, R.O. Elliott and E.M. Cramer, J. Nucl. Mater. 3 (1959) 241. [12] C.L. Hoenig, J. Amer. Ceram. Sot. 54 (1971) 391. 1131 K.E. Spear and J.M. Leitmaker, USAEC report ORNLTM-2106 (1968). [ 141 K.A. Gingerich, J. Chem. Phys. 47 (1967) 2192. [ 151 R. Benz and M.G. Bowman, J. Am. Chem. Sot. 88 (1966) 264. [ 161 C. Affortit, J. Nucl. Mater. 34 (1970) 105. [ 171 J. Bugl and A.A. Bauer, J. Am. Ceram. Sot. 47 (19641 425. [18] M.H. Rand, Atomic Energy Review 4, Special Edition I, (IAEA, Vienna, 1966). [ 191 R.J. Ackermann and R.J. Thorn, IAEA technical panel on the thermodynamics of uranium and plutonium carbides, Vienna (September 1968). [20] R.J. Ackermann, R.L. Faircloth and M.H. Rand, J. Phys. Chem. 70 (1966) 3698.