J. Chem. Thermodynamics 92 (2016) 158–167
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Critical evaluation and thermodynamic optimization of the (U + Bi), (U + Si) and (U + Sn) binary systems Jian Wang a, Kun Wang b,⇑, Chunhua Ma c, Leidong Xie b a
Center for Research in Computational Thermochemistry (CRCT), Department of Chemical Engineering, École Polytechnique, Montréal, Québec H3C 3A7, Canada Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800, PR China c College of Physics and Electronic Engineering, Nanyang Normal University, Nanyang 473061, PR China b
a r t i c l e
i n f o
Article history: Received 10 July 2015 Received in revised form 18 August 2015 Accepted 21 August 2015 Available online 12 September 2015 Keywords: Phase diagram Nuclear materials CALPHAD method (U + Bi) system (U + Si) system (U + Sn) system
a b s t r a c t A complete literature review, critical evaluation and thermodynamic optimization of the phase diagrams and thermodynamic properties in the (U + X) (X: Bi, Si and Sn) binary systems are presented. The CALPHAD method was used for the thermodynamic optimization, the result of which can reproduce all available and reliable experimental phase equilibria and thermodynamic data of the (U + X) (X: Bi, Si and Sn) binary systems using a set of thermodynamic functions. The modified quasi-chemical model in the pair approximation (MQMPA) was used for modelling the liquid solution. The Gibbs energies of all terminal solid solutions and intermetallic compounds were described by the compound energy formalism (CEF) model. All reliable experimental results have been reproduced within measurement error limits. A self-consistent thermodynamic database has been constructed for these (U + X) binary systems; this database can be used as a guide for nuclear materials research. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction The use of uranium in energy production from nuclear fission has given considerable impetus to the investigation of U-based alloys in recent decades. These investigations focus not only on the U-containing compounds used in the fuels, but also on the alloys of U with common elements of structural materials and fission products [1–4]. (U + Bi) and (U + Sn) molten alloys used as mixed fuel have been investigated by many researchers because of their notable advantages such as high specific power, low costs, better neutron economy, etc. [5–8]. Molten Sn is used to dissolve the nitrides and oxides from liquid fuel to extract desired actinide elements and remove the fission products [8,9]. Reliable data of thermodynamic properties and phase transformations of (U + Sn) molten alloys in the extracting process are important for keeping the fuel reactor operating safely. Si, C and Si–C based alloys are candidates for the inert matrix in gas-cooled fast reactor [1,10]. For the design of optimal operation condition of fuel reactor with molten fuel containing (U + Si), a systematic knowledge of the
⇑ Corresponding author. Tel./fax: +86 21 39194119. E-mail addresses:
[email protected] (J. Wang),
[email protected] (K. Wang),
[email protected] (C. Ma),
[email protected] (L. Xie). http://dx.doi.org/10.1016/j.jct.2015.08.029 0021-9614/Ó 2015 Elsevier Ltd. All rights reserved.
phase equilibria and thermodynamic properties of (U + Si) alloys is required. Hence, a better approach is to study the relevant phase diagrams of these (U + X) binary systems that are vital for beginning research and development of nuclear materials. However, on account of stringent experimental conditions, the traditional methods used in much experimental work are impractical. Fortunately, thermodynamic modelling of multi-component systems by the calculation of phase diagrams (CALPHAD approach) has been shown to be a very efficient way to investigate phase equilibria and thermodynamic properties systematically [11,12]. The (U + Bi) and (U + Si) binary systems have been assessed and calculated respectively by Wang et al. [13] and Berche et al. [14]. However, further improvements are necessary for the reproduction of phase diagram and thermodynamic properties. This is because of the gaps and errors in reported experimental values. Details will be discussed in the literature review section. Thermodynamic assessments in metallic nuclear materials systems: (U, Pu)–X (Al, Ga, Co, Fe, Se, Te, Sn, Si, Sb, Bi, Ge, Ag, Cu, Zn, Ni, W, Mn, etc.) [15–17] have been conducted by the present authors using the CALPHAD method in order to develop a thermodynamic database for nuclear materials development. As a part of this database, the present work focuses on comprehensive literature review, critical evaluation and thermodynamic assessments of the (U + Bi), (U + Si) and (U + Sn) binary systems.
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2. Critical literature review
2000
liquid#1+Liquid#2
1200 liquid bcc (U)
800
tetragonal (U) orthorhombic (U)
UBi
400
U3 Bi 4
Temperature,t/ oC
The phase equilibria of the (U + Bi) binary system were first investigated by Abmann and Baldwin [18] using cooling curve analysis and microscopic examination. Two intermetallic compounds UBi and UBi2 were reported in this binary system. Later, Ferro [19] investigated several (U + Bi) binary alloys by X-ray diffraction analysis. A new compound U3Bi4 with cubic Th3P4 (D73) crystal structure was reported. Moreover, the X-ray study by Ferro [19] confirms the existence of compounds UBi and UBi2 with crystal structures of NaCl (B1) and Cu2Sb (C38) types respectively. Ferro [19] also reported that the solid solubilities in terminal phase the U and Bi terminal phases as well as intermetallic compounds are insignificant at low temperature. Teite [20] re-investigated the phase equilibria of the (U + Bi) binary system in the whole composition range using thermal analysis, neutron diffraction and metallography. The existence of compounds UBi, U3Bi4, and UBi2 were confirmed by Teite [20]. U3Bi4 and UBi2 form in peritectic reactions: (liquid + UBi) ? U3Bi4 and (liquid + U3Bi4) ? UBi2 at (1150 and 1010) °C, respectively. The formation temperature of UBi was estimated to lay in the range (1400 to 1450) °C in a syntectic reaction (liquid#1 + liquid#2) ? UBi. It is noted worthy that measurements of the miscibility gap of the liquid phase were faulty in Teite’s work due to the high vapour pressure of Bi above its melting temperature [20]. The solubility of U in Bi-rich liquid solution in the temperature range (515 to 960) °C was determined by Greenwood [21] using a filtration method. Bareis [22] determined the solubility of U in Bi-rich liquid solution at (271 to 700) °C using filtration and flotation methods. The results in the common temperature range from the two authors [21,22] are in good agreement. Gross et al. [23] reported the activity of Bi in the equilibrated phase at 742 °C using effusion method via Bi vapour pressure measurements. The activity of Bi, enthalpies and entropies of formation of UBi, UBi2 and U3Bi4 in the temperature range (725 to 875) °C were investigated by Cosgarea et al. [24]. They used their own vapour pressure measurements of Bi. Due to the unknown molecular weight of the Bi vapour in those experiments, an optical absorption technique was used by Gross et al. [23] and Cosgarea et al. [24] to determine the concentration of each species independently. This may cause large error in the derived thermodynamic properties of the (U + Bi) binary system. This is evidenced by differences in the liquidus curve (see figure 1) reported by Cosgarea et al. [24] in comparison with other investigators [20–22]. Rice et al. [25] investigated the thermodynamic properties of (U + Bi) alloys at (745 to 842) °C using the effusion method [24]. The enthalpies and entropies of formation of UBi, UBi2 and U3Bi4 in the range (745 to 842) °C were derived with the use of Bi vapour pressure measurements. Lebedev et al. [26] studied the thermodynamic properties of (U + Bi) alloys at (496 to 788) °C using electromotive force (emf) measurements. The partial and integral thermodynamic properties (Gibbs energy, enthalpy and entropy of formation) of (U + Bi) alloys at 745 °C were derived by Lebedev et al. [26]. The solubilities of U in liquid Bi at various temperatures were found by Levedev et al. [26] from their emf measurements. Dilute (U + Bi) solutions at (400 to 600) °C were studied by Tien et al. [27] by emf measurements. A thermodynamic optimization of the (U + Bi) binary system was presented by Wang et al. [13]. However, the important experimental values of the liquidus in the Bi-rich region from references [21,22,24,26] were not included in their optimizations. As a result, the calculated phase diagram of the (U + Bi) binary system was erroneous. Hence, a critical review and re-optimization of the
1600
UBi 2
2.1. (U + Bi) binary system
Tietel [20] Greenwood [21] Bareis [22] Cosgarea et al. [24] Lebedev et al. [26] Wang et al. [13]
rhombhedra (Bi)
Bi
20
40
60
80
U
U / at. %
FIGURE 1. The calculated phase diagram of the (U + Bi) binary system with experimental values [20–22,24,26] and calculated result from Wang et al. [13].
(U + Bi) binary system are imperative for the purpose of improvement of the overall ((U, Pu) + X) system.
2.2. (U + Si) binary system The phase equilibria of the (U + Si) binary system were first investigated by Cullity [28] using thermal analysis, microscopy and X-ray analysis. Four terminal solid solutions, with very small solid solubilities, and six intermetallic compounds were reported. These latter were e, U5Si3, USi, U2Si3, USi2, and USi3. The e compound forms at 930 °C in a peritectic reaction: (bcc (U) + U5Si3) ? e. Kaufmann [29] and Kaufmann et al. [30] reinvestigated the phase equilibria of the (U + Si) binary system in the whole composition range using thermal analysis, X-ray analysis, and microscopy. Six intermetallic compounds (e, U5Si3, USi, U2Si3, USi2 and USi3) were confirmed by Kaufmann and Kaufmann et al. [29,30]. Therein, U5Si3 and USi2 melt congruently at (1665 and 1700) °C respectively [29,30]. Later, these six compounds were re-examined by Zachariasen [31] using X-ray analysis. Some compounds were differently identified by Zachariasen [31], who designated ‘‘e” to be ‘‘U3Si”, and ‘‘U5Si3” to be ‘‘U3Si2. Moreover, ‘‘U2Si3” is a polymorphic form of ‘‘USi2”. Brown and Norreys [32,33] studied some (U + Si) binary alloys at compositions around 33.3 at.% Si using X-ray analysis and metallography. The highest stable temperature of USi2 was confirmed as 450 °C by Brown and Norreys [33]. Furthermore, a new intermetallic compound USi1.88, with very high melting temperature, was observed by Brown and Norreys [33]. In order to resolve these contradictions, Vaugoyeau et al. [34] re-investigated the phase equilibria of the (U + Si) binary system in the composition region (34.5 to 55.6) at. % U using high and low temperature X-ray analysis. The existence of compounds USi, U3Si5, U3Si2 and USi1.88 was confirmed. U3Si5 melts congruently at (1770 ± 10) °C. USi forms in a peritectic reaction, (liquid + U3Si5) ? USi at (1580 ± 10) °C, according to the measurements of Vaugoyeau et al. [34]. This is consistent with the result of 1575 °C reported by Kaufmann et al. [30]. The temperature of eutectic reaction: liquid ? (USi + U3Si2) was reported as (1540 ± 10) °C by Vaugoyeau et al. [34], which is about 20 °C lower than that reported by Kaufmann et al. [30]. Finally, the melting temperature of USi1.88, reported by Brown and Norreys [33], was also measured by Vaugoyeau et al. [34]. USi1.88 melts in a peritectic reaction: (liquid + U3Si5) ? USi1.88 at (1710 ± 10) °C. The solid solubilities of Si in U terminal phases bcc (U), Tetragonal (U) and Orthorhombic (U) were reviewed by Katz and Rabinowitch [35] and Shunk [36]. Dwight [37] reported that U3Si undergoes an
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allotropic phase transformation at 770 °C. Remschnig et al. [38] studied several (U + Si) binary alloys annealed at temperatures from (1000 to 1400) °C using X-ray analysis. The existence and crystal structure of U3Si, U3Si2 (U3Si2-type), USi (FeB-type), U3Si5 (defect AlB2-type), USi1.88 (defect ThSi2-type) and USi3 (Cu3Autype) were confirmed. The fully ordered stoichiometric compound USi2, has the ThSi2-type and/or the AlB2-type reported earlier by Brown and Norreys [32,33]. It could not be found by Remschnig et al. [38]. Noël et al. [39] reported a new (U + Si) binary compound with composition U5Si4. Recently, four key samples of compositions (3.97, 8.69, 46.32 and 74.68) at.% Si were prepared and investigated by Berche et al. [14] using DTA measurements and SEM/ EDS analysis. The eutectic temperature of the reaction liquid ? (U3Si2 + bcc (U)) was reported as (994 ± 3) °C by Berche et al. [14], according to their DTA measurements of the U66.03Si3.97 alloy composition. This is about (9 ± 3) °C higher than the value reported by Kaufmann et al. [30]. Berche et al. [14] found (988 ± 3) °C for the same eutectic reaction from DTA measurements of U91.31Si8.69 alloy composition. Thus, there is at least 6 °C difference in the results of the two investigations [14]. The temperature of the eutectic reaction liquid ? (U3Si2 + USi) was reported as (1547 ± 5) °C by Berche et al. [14]. This is in reasonable agreement with the value of (1540 ± 10) °C found by Vaugoyeau et al. [34]. The existence of U5Si4, reported by Noël et al. [39], was also confirmed by Berche et al. [14]. The temperature of the peritectic reaction (liquid + U3Si2) ? U5Si4, and temperature of the eutectic reaction liquid ? (USi + U5Si4) were reported as (1567 ± 5) °C and (1547 ± 5) °C, respectively. The enthalpies of formation of USi3, USi2, USi and U3Si2 were measured by Gross et al. [40] using direct calorimetry with pure elements and uncombined elements obtained from reaction with tellurium. The enthalpies of formation of USi3, USi2, USi and U3Si2 were reported as (33.05, 43.51, 40.17, and 33.89) kJ mol-atom1 from the pure elements. The enthalpies of formation of USi3, USi2, and USi were measured as (32.22, 42.69, and 43.52) kJ mol-atom1 by Gross et al. [40] using elements obtained from reaction with tellurium. Alcock and Grieveson [41] employed Kundsen cell effusion to measure the silicon vapour pressure for the two-phase region of the (U + Si) system in the temperature range (1402 to 1567) °C. The enthalpies of formation of USi3 USi2, USi and U3Si2 were derived by Alcock and Grieveson [41]. The results reported by Gross et al. [40] and Alcock and Grieveson [41] are in good agreement. O’Hare et al. [42] reported the enthalpy of formation of U3Si as (26.05 ± 4.8) kJ molatom1 using fluorine bomb calorimetry. Recently, the heat capacities of compounds U3Si and U3Si5 were investigated by White et al. [43,44]. There are no experimental data reported for the thermodynamic properties of the liquid phase. The thermodynamic optimization of the (U + Si) binary system was carried out by Berche et al. [14]. However, further careful thermodynamic modelling of the (U + Si) binary system is still required, due to the omission of phases USi2 [32,33] and U4Si5 [14] in the previous calculated phase diagram by Berche et al. [14]. The same is true for the recently reported heat capacity data of White et al. [43,44].
It should be noted that the samples prepared by Treick et al. [45] showed definite water contamination of U-containing phases, which may affect their observed results. Rundle and Wilson [46] reported the compound USn3, with Cu3Au (L12)-type of crystal structure from their X-ray analysis. Later, the phase equilibria of the (U + Sn) binary system in the whole composition range were studied by Frost and Maskrey [47] using thermal analysis and microscopy. U3Sn5 and U5Sn4, reported by Treick et al. [45], were confirmed by Frost and Maskrey [47]. The melting temperature of USn3 was reported as 1350 °C in a peritectic reaction (U3Sn5 + liquid) ? USn3. This agrees with the value reported by Treick et al. [45]. Sari et al. [48] investigated the phase equilibria of the (U + Sn) binary system with metallographic examination, EPMA, DSC, hardness testing, and X-ray analysis. Three new compounds U3Sn7, USn2, and USn were identified by Sari et al. [48]. The melting point of USn3 was reported as 1350 °C by Sari et al. [48], which is in good agreement with the data of Treick et al. [45] and Frost and Maskrey [47]. It also should to be noted that samples were contaminated in the Sari et al. [48] work. This arose from use of the graphite crucible for melting the sample. According to the phase diagram of the (U + C) binary system, about 1 at.% C can be dissolved into liquid U at 1100 °C, and this value increases to about 10 at.% C around 1592 °C. Recently, Palenzona and Manfrinetti [49] re-investigated the phase equilibria of the (U + Sn) binary system, in the composition region of (0 to 75) at.% Sn, using differential thermal analysis, metallography, X-ray analysis, and SEM. The existence of five previously reported compounds U5Sn4, USi, USn2, U3Sn7, and USn3 was confirmed by Palenzona and Manfrinetti [49]. A nearly totally new phase diagram of the (U + Sn) binary system was suggested by Palenzona and Manfrinetti [49]. For example, the melting temperature of USn3 was reported as 1340 °C by Palenzona and Manfrinetti [49] in a peritectic reaction (U3Sn7 + liquid) ? USn3. This is 10 °C lower than previously reported [45,47,48]. The congruent melting temperature of U5Sn4 was reported as 1390 °C by Palenzona and Manfrinetti [49], which is 110 °C lower than that reported by Treick et al. [45]. Alcock and Grieveson [41] measured the vapour pressure of Sn over several two-phase equilibrated composition regions in the temperature range (1402 to 1567) °C using Kundsen cell effusion. The enthalpies of formation of U3Sn5 and U3Sn2 at 25 °C were derived as (27.2 and 26.8) kJ mol-atom1 respectively from their vapour pressure measurements [41]. The enthalpy of formation of USn3 was also reported as 24 kJ mol-atom1 by Alcock and Grieveson [41] using solution calorimetery. Johnson and Feder [50] reported the enthalpy of formation of USn3 as 36.5 kJ molatom1 using emf measurements. Kadochnikove et al. [51] reported the enthalpy of formation of USn3 as 42.9 kJ molatom1, in the temperature range (540 to 844) °C, based on their emf measurements results. Colient et al. [52] measured the enthalpy of formation of USn3 by solution calorimetry, and a value of 35.3 kJ mol-atom1 at 25 °C was reported. Pattanaik et al. [53] studied the Gibbs energies of formation of USn3, U3Sn7, USn2 and USn using emf measurements with high temperature molten salt galvanic cells. The enthalpies and entropies of formation of those compounds were derived from their emf measurements [53]. There are no experimental data reported on the thermodynamic properties of the liquid phase.
2.3. (U + Sn) binary system 3. Thermodynamic modelling Treick et al. [45] studied the phase equilibria of the (U + Sn) binary system using metallography, X-ray analysis and thermal analysis. Three intermetallic compounds (U5Sn4, U3Sn5 and USn3) were reported. U5Sn4 forms congruently at 1500 °C, and U3Sn5 and USn3 form peritectically at (1380 and 1350) °C, respectively.
In the present work, the thermodynamic optimization of the (U + X) (X = Bi, Si and Sn) binary systems has been carried out by means of the FactSage thermodynamic software [54]. The phases of the (U + X) binary systems considered are listed in table 1, with
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J. Wang et al. / J. Chem. Thermodynamics 92 (2016) 158–167 TABLE 1 Phase crystal structure and thermodynamic model used in the present work. Phase
Strukturbericht
Prototype
Liquid bcc (U)
A2
W
Tetragonal (U) Orthorhombic (U) bct (Sn) Diamond (Si)
Ab A20 A5 A4
Tetra (U) Ortho (U) Sn Diam (C)
Rhombohedric (Bi) UBi2 U3Bi4
A7 C38 D73
Rhomb (Bi) Cu2Sb Th3P4
UBi
B1
NaCl
Space group
Im3m P42 =mnm Cmcm I41 =amd Fd3m C2=m P4=nmm I43d Fm3m I4=mcm
aU3Si bU3Si
L12
AuCu3
U3Si2 U5Si4 USi U3Si5 U9Si17 (USi1.88) USi2 USi3
D5a
U3Si2
B27 C32 Cc C32 L12
FeB AlB2 ThSi2 AlB2 AuCu3
U3Sn7 USn2 USn U5Sn4
oC20 oC12 oP24 hP18
Ce3Sn7 ZrGa2 ThIn Ti5Ga4
Pm3m P4=mbm Pnma P6=mmm I41 =amd P6=mmm Pm3m Cmmm Cmmm Pbcm P63 =mcm
MQMPA CEF CEF CEF CEF CEF CEF ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST
Z i ni Z A nA þ Z B nB
ði ¼ A or BÞ:
The thermodynamic properties of the liquid phase were modelled using the Modified Quasichemical Model in the Pair Approximation (MQMPA) developed by Pelton et al. [56,57], which has been applied successfully in previous works [58–62]. A detailed description of the MQMPA and its associated notation are given in references [56,57]. The same notation is used in the present work, and a brief description of MQMPA is given as follows: For the binary (A–B) system, the quasichemical pair exchange reaction can be considered as:
Dg AB ;
ð1Þ
where the i–j pair represents a first-nearest-neighbour pair of atoms. The Gibbs energy change for the formation of one mole of (A–B) pairs according to Reaction (1) is DgAB/2. Let nA and nB be the number of moles of A and B, nAA, nBB, and nAB be the number of moles of A–A, B–B, and A–B pairs. ZA and ZB are the coordination numbers of A and B. Then the Gibbs energy of the solution is given by:
G ¼ ðnA GoA þ nB GoB Þ T DSconfig þ ðnAB =2ÞDg AB ;
ð2Þ
where GoA and GoB are the molar Gibbs energies of the pure component A and B, and DSconfig is the configurational entropy of mixing given by randomly distributing the A–A, B–B, and A–B pairs in the one-dimensional Ising approximation. The expression for DSconfig is:
¼ RðnA ln X A þ nB ln X B Þ X AA Y 2A
þ nBB ln
X BB Y 2B
þ nAB ln
! X AB ; 2Y A Y B
ð5Þ
ð6Þ
Z B nB ¼ 2nBB þ nAB :
ð7Þ
It may be noted that there is no exact expression for the configurational entropy in three dimensions. Although equation (3) is only an approximate expression in three dimensions, it is exact one-dimensionally (when Z = 2) [57]. As explained in [57], one is forced by the approximate nature of equation (3) to use non-exact values for the coordination numbers in order to yield good fits between the experimental data and calculated ones. The mathematical approximation of the one-dimensional Ising model of equation (3) can be partially compensated by selecting values of ZA and ZB which are smaller than the experimental values [63]. As is known, the MQMPA model is sensitive to the ratio of coordination numbers, but less sensitive to their absolute values. From a practical standpoint for the development of large thermodynamic databases, values of ZA and ZB of the order of 6 have been found necessary for the solutions with a small or medium degree of ordering (i.e. alloy solutions) [57]. DgAB is the model parameter to reproduce the Gibbs energy of the liquid phase of the A–B binary system, which is expanded as a polynomial in terms of the pair fractions, as follows:
X X oj i g io g AB ðX BB Þ j ; AB ðX AA Þ þ iP1
ðA AÞpair þ ðB BÞpair ¼ 2ðA BÞpair ;
ð4Þ
Z A nA ¼ 2nAA þ nAB ;
Dg AB ¼ Dg oAB þ
3.1. Liquid phase
R nAA ln
Yi ¼
ði; j ¼ A or BÞ;
Moreover, the following elemental balance equations can be written:
the models used to describe their thermodynamic properties. The thermodynamic parameters of the pure elements are the recommended SGTE values [55].
DS
nij nAA þ nBB þ nAB
Modela
a MQM: Modified Quasichemical Model with pair approximation; CEF: compound energy formalism; ST: stoichiometric compound.
config
X ij ¼
ð3Þ
where XAA, XBB, and XAB are the mole fractions of the A–A, B–B, and A–B pairs respectively; YA and YB are the coordination-equivalent fractions of A and B:
ð8Þ
jP1
oj where Dg oAA ; g io AB and g AB are the adjustable model parameters which can be functions of temperature. The equilibrium state of the system is obtained by minimizing the total Gibbs energy at constant elemental composition, temperature and pressure. The equilibrium pair distribution is calculated by setting:
@G @nAB
¼ 0:
ð9Þ
nA ; nB
This gives the ‘‘equilibrium constant” for the ‘‘quasichemical pair reaction” of equation (1):
X 2AB Dg ¼ 4 exp AB : X AA X BB RT
ð10Þ
Moreover, the model permits Z A and Z B to vary with composition as follows [57]:
1 1 2nAA 1 nAB þ A ; ¼ A Z A Z AA 2nAA þ nAB Z AB 2nAA þ nAB
ð11Þ
1 1 2nBB 1 nAB þ B ; ¼ B Z B Z BB 2nBB þ nAB Z AB 2nBB þ nAB
ð12Þ
A A where Z AA and Z AB are the values of Z A when all nearest neighbours of an atom A are As, and when all nearest neighbours of an atom A
are Bs respectively. Z BBB and Z BAB are defined similarly. The composition of maximum short-range ordering (SRO) is determined by the A =Z BAB . ratio of the coordination numbers Z AB
3.2. Solid solutions The compound energy formalism (CEF) was introduced by Hillert [64] to describe the Gibbs energy of solid phases with
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TABLE 2 Calculated invariant reactions in the (U + Bi) binary system in comparison with experimental values. Reaction
Reaction type
Temperature, t/°C
Composition, at.% U
Liquid M (UBi2 + Rhomb (Bi))
Eutectic
Ortho (U) M (Tetra (U) + UBi)
Eutectiod
Tetra (U) M (bcc (U) + UBi)
Eutectiod
(Liquid + U3Bi4) M UBi2
Peritectic
(Liquid + UBi) M UBi2
Peritectic
Liquid M (UBi + bcc (U))
Eutectic
(Liquid#1 + liquid#2) M UBi
Syntectic
270 271 668 669 776 776 1010 1010 1150 1151 1130 1133 1400–1450 1440
0 0 0 0 0 0 21.4 21.7 27.3 28.8 99.9 100 98.8 98.9
References
33.3 33.3 0 0 0 0 42.9 42.9 50 50 50 50 49.6 49.6
100 100 50 50 50 50 33.3 33.3 42.9 42.9 100 100 50 50
[20] This [20] This [20] This [20] This [20] This [20] This [20] This
work work work work work work work
3.3. Stoichiometric phases The molar Gibbs energies of pure elements and stoichiometric phases can be described by:
Present work t =25 oC t =800 oC Wang et al. [13] t =25 oC t =800 oC
-10 -20
GoT ¼ HoT TSoT ; HoT ¼ D298:15K Hof þ
-40
Cosgare et al. [24] t =25 oC t =745 to 842 oC Rice et al. [25] t =25 oC t =745 to 842 oC Lebedev et al. [26] t =25 oC t =500 to 830 o C Tien et al. [27] t =25 oC t =400 to 600 oC
-70
20
U 3 Bi 4
-60
UBi
-50
Bi
ð13Þ Z
-30
UBi 2
Enthalpy of formation , ∆Hf / kJ·mol-atom-1
0
40
60
80
Z SoT ¼ 298:15 K Sof þ
T
CpdT;
ð14Þ
ðCp=TÞdT;
ð15Þ
298:15 K T
298:15 K
where D298:15 K Hof is the molar enthalpy of formation of a given spe-
U
U / at. %
FIGURE 2. The calculated enthalpies of formation of intermediate compounds in the (U + Bi) binary system with experimental values [24–27] and calculated result from Wang et al. [13].
cies from pure elements (D298:15 K Hof of element stable at T = 298.15 K and 101.3 kPa is assumed as 0 J mol1; reference state), D298:15 K Sof is the molar entropy at T = 298.15 K and Cp is the molar heat capacity. The heat capacities of compounds in the (U + Bi) and (U + Sn) binary systems, where not reported experimentally, were evaluated using the Neumann–Kopp rule [65]. 4. Results and discussion 4.1. (U + Bi) binary system
0 UBi 2
-10
The calculated phase diagram of the (U + Bi) binary system is shown in figure 1, with experimental data [20–22,24,26] and the calculated results of Wang et al. [13]. Three intermetallic compounds UBi2, U3Bi4 and UBi were considered in the present
Wang et al. [13] UBi
-5
U 3 Bi 4
Entropy of formation, ∆Sf / J·K-1·mol-atom-1
5
Present work
-15 Cosgare et al. [24] t =745 to 842 oC Rice et al. [25] t =745 to 842 oC Lebedev et al. [26] t =500 to 830 o C Tien et al. [27] t =400 to 600 oC
-20 -25 -30
1 Cosgarea et al. [24], t =816 oC Cosgarea et al. [24], t =745 oC Gross et al. [23], t =742 oC
t=742 oC
0.8
aBi
Bi
20
40
60
80
U
U / at. %
activity
-35 0.6
0.4
FIGURE 3. The calculated entropies of formation of intermediate compounds in the (U + Bi) binary system with literature data [24–27] and calculated result from Wang et al. [13].
sub-lattices. Ideal mixing of species on each sub-lattice is assumed. In the present work, all the solid solutions in the (U + X) (X = Bi, Si and Sn) system were modelled with the CEF based on their crystal structure. The Gibbs energy expressions are based on each sublattice model, and the details were described in Hillert’s work [64].
t =816 oC
0.2
Bi
20
40
60
80
U
U / at. %
FIGURE 4. The calculated activity of Bi in the (U + Bi) liquid phase at (816 and 742) °C in comparison with experimental values [23,24].
J. Wang et al. / J. Chem. Thermodynamics 92 (2016) 158–167
163
TABLE 3 Optimized model parameters of the MQMPA for the liquid phase in the (U + Bi), (U + Si) and (U + Sn) binary systems. Coordination numbers
a
a
Gibbs energies of pair exchange reactions, g/J G/J
i
j
Z iij
U
Bi
6
6
Dg Bi;U =J ¼ 4184:5 4:60T=K ð73303:7 þ 7:32T=KÞX BiBi þ 119285:8X 2BiBi 63513:1X 3BiBi þ 11296:8X UU
U
Si
5.4
4.6
Dg Si;U =J ¼ 60668 þ 14:54T=K þ 12468:3X SiSi 119285:8X 2SiSi ð4351:4 9:71T=KÞX UU þ 1029:3X 2UU
U
Sn
4.5
5.5
Dg Sn;U =J ¼ 27300:6 3:14T=K þ 35145:6X SnSn 32007:6X 2SnSn þ 6276:0X UU þ 8368X 2UU
For all pure elements (U, Bi, Si and Sn),
Z ijj
Z ijj
¼ 6.
TABLE 4 Optimized parameters of solid solutions and compounds in the (U + Bi), (U + Si), and (U + Sn) binary systems. Phase, model and thermodynamic parameters, G/J and Cp/J K1 mol1 Orthorhombic_U phase, format (Bi, Si, Sn, U) rho orth bct orth orth orth diamo Gorth þ 4:2; Bi =J ¼ GBi þ 4184:5; GSn =J ¼ GSn þ 41:8; GU =J ¼ GU ; GSi =J ¼ GSi
L0Si;U =J ¼ 58583:0; L0Sn;U =J ¼ 202948:3 Tetragonal_U phase, format (Bi, Si, Sn, U) rho tetr bct tetr orth diamo þ 3166:1 þ 3:18T=K; Gtetr þ 4:2; Gtetr Bi =J ¼ GBi þ 2092:3; GSn =J ¼ GSn þ 41:8; GU =J ¼ GU Si =J ¼ GSi
L0Si;U =J ¼ 60675:3; L0Sn;U =J ¼ 203785:2 bcc_A2 phase, format (Bi, Si, Sn, U) diamo o rhmo o bct Gbcc þ 2092:0; Gbcc þ 47000:0 þ 22:5T=K; Gbcc Bi =J ¼ GBi Si =J ¼ GSi Sn =J ¼ GSn þ 41:8; ortho Gbcc þ 9514:9 þ 9:57T=K; L0Si;U =J ¼ 79505:5 þ 8:37T=K; U =J ¼ GU
L0Sn;U =J ¼ 200856:0 2:51T=K diamond_Si phase, format (Si, U) =J ¼ Gorth þ 3186:9 þ 3:18T=K; Gdiamo =J ¼ Gdiamo ; L0Si;U =J ¼ 96232:0 Gdiamo U U Si Si bct_Sn phase, format (Sn, U) orth bct þ 4:2; Gbct Gbct U =J ¼ GU Sn ¼ Gsn
U3 Bi4 Phase; format ðUÞ3 ðBiÞ4 : G=J ¼ 4Gorth þ 3Grho U Bi 320059:0 þ 40:71T=K þ 2Grho UBi2 Phase; formatðUÞðBiÞ2 : G=J ¼ Gorth U Bi 111806:0 þ 5:97T=K þ Grho UBi Phase; formatðUÞðBiÞ : G=J ¼ Gorth U Bi 87899:6 þ 8:13T=K U5 Sn4 Phase; format ðUÞ5 ðSnÞ4 : G=J ¼ 5Gorth þ 4Gbct U Sn 836376:0 þ 274:12T=K þ 7Gbct U3 Sn7 Phase; format ðUÞ3 ðSnÞ7 : G=J ¼ 3Gorth U Sn 488457:5 þ 92:30T=K þ 3Gbct USn3 Phase; formatðUÞðSnÞ3 : G=J ¼ Gorth U Sn 160260:0 þ 20:70T=K þ Gbct USn2 Phase; formatðUÞðSnÞ2 : G=J ¼ Gorth U Sn 164040:0 þ 35:90T=K þ 2Gbct USn Phase; formatðUÞðSnÞ : G=J ¼ Gorth U Sn 166581:0 þ 51:11T=K RT
U9 Si17 Phase; format ðUÞ9 ðSiÞ17 : G=J ¼ 1093083:4 þ 816:17T=K þ
0
C p dT
R T Cp 0
T
dT T=K
C p ¼ 624:7 þ 0:1277T=K 705827:70ðT=KÞ2 0:000056957376ðT=KÞ2 519:9ðT=KÞ1 ; 298:15K 6 T < 678K ¼ 706:0 þ 0:0396T=K 706723:98ðT=KÞ2 0:000006860376ðT=KÞ2 15300ðT=KÞ1 ; 678K 6 T < 1983K ¼ 749:8; 1938K 6 T 6 3600K R RT T C U5 Si4 Phase; format ðUÞ5 ðSiÞ4 : G=J ¼ 346188:0 þ 329:64T=K þ 0 C p dT 0 Tp dT T=K C p ¼ 225:9 þ 0:00278T=K 1799017ðT=KÞ2 þ 0:000133ðT=KÞ2 ; 298:15K 6 T < 955K ¼ 334:6 þ 0:0153T=K 1413336ðT=KÞ2 þ 0:0000000853ðT=KÞ2 ; 955K 6 T < 1840K ¼ 362:5; 1840K 6 T 6 3600K Phase, model and thermodynamic parameters, G/J, or G/(J K1) U3 Si5 Phase; format ðUÞ3 ðSiÞ5 : G=J ¼ 342048:6 þ 262:47T=K þ
RT 0
C p dT
R T Cp 0 T dT T=K
C p ¼ 193:0 þ 0:04T=K þ 280:1ðT=KÞ2 0:000019ðT=KÞ2 173:3ðT=KÞ1 ; 298:15 K 6 T < 678 K ¼ 220:1 þ 0:01T=K 18:66ðT=KÞ2 0:000002301ðT=KÞ2 5100ðT=KÞ1 ; 678 K 6 T < 2043 K ¼ 229:8; 2043 K 6 T 6 3600 K R RT T C U3 Si2 Phase; format ðUÞ3 ðSiÞ2 : G=J ¼ 177979:0 þ 193:92T=K þ 0 C p dT 0 Tp dT T=K C p ¼ 126:4 þ 0:000142T=K 938076:6ðT=KÞ2 þ 0:000079711ðT=KÞ2 ; 298:15 K 6 T < 955 K ¼ 191:6 þ 0:00765T=K 706668ðT=KÞ2 þ 0:000000042624ðT=KÞ2 ; 955 K 6 T < 1938 K ¼ 206:98; 1938 K 6 T 6 3600 K R RT T C U3 Si Phase; format ðUÞ3 ðSiÞ : Ga =J ¼ 102200 þ 164:35T=K þ 0 C p dT 0 Tp dT T=K C ap ¼ 105:1 þ 0:0188T=K 584742ðT=KÞ2 þ 0:000017090212ðT=KÞ2 ; 298:15 K 6 T < 1073 K ¼ 134:176; 1073 K 6 T 6 3000 K
DHa!b ¼ 20400; T ¼ 1043 K
USi3 Phase; formatðUÞðSiÞ3 : G=J ¼ 136294:8 þ 105:04T=K þ
RT 0
C p dT
R T Cp T dT T=K 0
C p ¼ 95:4 þ 0:00897T=K 1137138:2ðT=KÞ2 þ 0:0000266202ðT=KÞ2 ; 298:15 K 6 T < 955 K ¼ 117:2 þ 0:0115T=K 1060002ðT=KÞ2 þ 0:000063936ðT=KÞ2 ; 955 K 6 T < 1783 K ¼ 137:846; 1783 K 6 T 6 3000 K R RT T C USi2 Phase; format ðUÞðSiÞ2 : G=J ¼ 125220:3 þ 89:06T=K þ 0 C p dT 0 Tp dT T=K Cp ¼ 71:9 þ 0:0146T=K 117684:6ðT=KÞ2 0:00000632623ðT=KÞ2 57:77ðT=KÞ1 ; 298:15 K 6 T < 723 K ¼ 78:825; 723 K 6 T 6 3000 K R RT T C USi Phase; formatðUÞðSiÞ : G=J ¼ 83701:5 þ 67:91T=K þ 0 C p dT 0 Tp dT T=K C p ¼ 49:74 þ 0:00132ðT=KÞ 430470:2ðT=KÞ2 þ 0:0000265776ðT=KÞ2 ; 298:15 K 6 T < 955 K ¼ 71:49 þ 0:00383ðT=KÞ 353334ðT=KÞ2 þ 0:000000021312ðT=KÞ2 ; 955 K 6 T < 1848 K ¼ 78:4538; 1848 K 6 T 6 3600 K
J. Wang et al. / J. Chem. Thermodynamics 92 (2016) 158–167
4.2. (U + Si) binary system According to the reported discussed above, nine intermetallic compounds USi3 U3Si2, U5Si4, USi, USi1.88 (U9Si17), aU3Si, bU3Si, USi2, and U3Si5 were taken into account in the thermodynamic optimization. As mentioned in section 2.2, a further experimental work is required to verify the existence of USi2 and U5Si4. The optimised heat capacities of intermetallic compounds in the present work are shown in figure 5, with the reported experimental data of White et al. [43,44]. The heat capacities of aU3Si, bU3Si, and U3Si5 were optimised on the base of the reported experimental values from White et al. [43,44]. Heat capacities of the remaining compounds USi3, U3Si2, U5Si4, USi, U9Si17 (USi1.88) and USi2 were determined using the Neumann–Kopp rule [64] guided by the known heat capacity data of aU3Si, bU3Si, and U3Si5. The calculated standard enthalpies of formation of solid compounds (with reference to orthorhombic _U and diamond_Si) are shown in figure 6, with experimental values from references [40–42] and calculated results from reference [14]. Due to the experimental data lacking
45 White et al., [43], U3 Si 5 White et al., [44], U3 Si
Heat capacity, Cp / J·K-1· mol-atom-1
40
U3 Si 2
U5 Si 4
USi
35 β U3 Si USi3
αU3 Si
30
U9 Si 17 U3 Si 5 USi2
25
20
15 0
200
400
600
800
1000
1200
1400
1600
1800
2000
Temparature, t / oC
FIGURE 5. The calculated heat capacities of (U + Si) intermetallic compounds with experimental values [43,44].
0
U 3 Si U 3 Si 2
U 5 Si 4
-30
USi
-20
U 5 Si 3
-10
U 9 Si 17 (USi 1.88 )
Gross et al. [40], direct calorimetry, t =25 oC Gross et al. [40], Tellurium reaction, t =25 o C Alcock et al. [41], vapor pressure, t =25 o C O’ Hare et al. [42], fluorine bomb claorimetry, t =25 o C
USi 3
-40
-50
Berche et al. [14] Present work
USi 2
Enthalpy of formation , ∆Hf / kJ·mol-atom-1
optimization. The present calculated peritectic temperatures of reactions (liquid + UBi) M U3Bi4 and (liquid + U3Bi4) M UBi2 are (1150 and 1010) °C, respectively. These are in good agreement with the experimental data reported by Teite [20]. The present calculated temperature of syntectic reaction (liquid#1 + liquid#2) M UBi is 1440 °C, which is in the temperature range (1400 to 1450) °C estimated by Teite [20]. All the calculated invariants of (U + Bi) binary system are listed in table 2. The present calculated results are in good agreement with the experimental data [20–22,26], except the one reported by Cosgarea et al. [24]. As shown in figure 1, the experimental results reported by Cosgarea et al. [24] deviate widely with the results reported by other investigators [20–22,26]. Therefore, less weight was given to either phase equilibria or thermodynamic data from Cosgarea et al. [24] in the present optimization work. Since there are no experimental data reported on solid solubilities of all terminal solid phases rhombohedric (Bi), orthorhombic (U), tetragonal (U) and bcc (U), these terminal solid phases were treated as ideally mixing solutions, without interaction parameters in the present optimizations. As shown in figure 1, the present calculated phase diagram shows sensible improvement over the previous optimization of Wang et al. [13]. The calculated enthalpies of formation of solid phases at 25 °C (with reference to orthorhombic _U and rhombohedric _Bi) and 800 °C (with reference to bcc_U and liquid_Bi) are shown in figure 2 compared to experimental values [24–27] and the calculated results from Wang et al. [13]. The calculated entropies of formation of solid phases at 800 °C (with reference to bcc_U and liquid_Bi) are shown in figure 3 with the experimental data from references [24–27] and the calculated results of Wang et al. [13]. As shown in figure 2, the present calculated enthalpies of formation of compounds are in good agreement with experimental values. However as shown in figure 3, the reported experimental entropies of formation of compounds show large derivations. The values reported by Rice et al. [25] and Lebedev et al. [26], which are in reasonable agreement with each other, were used as preferred input for the present optimization. The calculated activity of Bi in the liquid phase at 816 °C is shown in figure 4 compared to the experimental data reported by Gross et al. [23] and Cosgarea et al. [24]. In figure 4, there is inconsistency in the results from two different groups of investigators [23,24]. Further experimental work is needed to clarify. The figures and table 2 show our calculated results are in good agreement with all reliable experimental values. A complete set of thermodynamic parameters describing the Gibbs energy of each phase in the (U + Bi) binary system used in the present work are listed in tables 3 and 4.
Si
20
40
60
U
80
U / at. %
FIGURE 6. The calculated enthalpies of formation of (U + Si) intermetallic compounds with experimental values [40–42].
-4.5 -5.5 Partial pressure, log(PSi / atm)
164
-6.5
Pure Si 52 at. % U 26 at. % U
-7.5 37 at. % U
-8.5 -9.5 -10.5
5.2
48 at. % U
Alcock and Grieveson [41] Pure Si 26 at. % U 32 at. % U 33 at. % U 37 at. % U 38 at. % U 48 at. % U 52 at. % U 58 at. % U
5.4
58 at. % U
5.6
5.8
6.0
6.2
6.4
Temperature, 10 4·T/K
FIGURE 7. The calculated partial pressure of Si over (U + Si) binary alloys in different compositions in comparison with the experimental values [41].
of enthalpy of mixing of liquid (U + Si) phase, the coordination number of liquid (U + Si) was estimated based on the experimental data of solids as shown in table 3. It is because that the short range ordering pair of (U + Si) usual forms around the composition with most negative enthalpy of formation of solids (xSi = (50 to 60) at.
165
J. Wang et al. / J. Chem. Thermodynamics 92 (2016) 158–167
% in the (U + Si) binary system). The present calculated partial pressures of Si over a serial of alloys are shown in figure 7, with the experimental values reported by Alcock and Grieveson [41]. The calculated phase diagram of the (U + Si) binary system is shown in figure 8, with the experimental data from references [14,30,34–37] and the calculated results of Berche et al. [14]. All the reported compounds, including the compounds USi2 and U5Si4 omitted in Berche’s work [14], were considered in the present work. All the thermodynamic parameters of the (U + Si) binary system are listed in tables 3 and 4. All calculated invariant reactions of the (U + Si) binary system in the present work are summarized in table 5. As shown in the figures and table 5, a reasonable
2000
1600
Kaumann et al. [30] Vaugoyeau et al. [34] Katz and Rabinowitch [35] Shunk et al. [36] Dwight [37]
1400
Berche et al. [14] Thermal analysis Calculated
liquid
U 3 Si 2
600
USi
800
bcc (U)
βU 3 Si U 5 Si 4
1000
U 9 Si 17 (USi 1.88 ) U 5 Si 3
1200
USi 3
Temperature, t/ o C
1800
tetragonal (U)
4.3. (U + Sn) binary system Due to sample contamination problem evident in early investigators [45,48] (discussed above), the experimental results reported by Palenzona and Manfrinetti [49] were used only as the principle input in the present thermodynamic optimizations. The reported experimental data from Treick et al. [45] and Sari et al. [48] were disregarded. All the reported intermetallic compounds, except U3Sn5 (which was not observed by Palenzona and Manfrinetti [49]), were considered in the present optimization. The calculated phase diagram of the (U + Sn) binary system is shown in figure 9 with the experimental data from Treick et al. [45] and Palenzona and Manfrinetti [49]. The calculated standard enthalpies of formation of compounds (with reference to orthorhombic _U and bct_Sn) and 521 °C (with reference to orthorhombic _U and liquid_Sn) are shown in figure 10 compared to experimental data [41,50–53]. It is same as discussed in (U + Si) binary system, due to the experimental data lacking of enthalpy of mixing of liquid (U + Sn) phase, the coordination number of liquid (U + Sn) was estimated based on the experimental values for solids as shown in table 3. It is because that the composition with most negative enthalpy of formation of solids is located in the range (40 to 50) at.% Sn in the (U + Sn)
USi 2
200 Si
orthorhombic (U)
αU3 Si
diamond (Si)
400
agreement has been achieved between the experimental data and calculated results.
20
40
60
1600
U
80
Palenzona and manfrinetti [49] Treick et al. [45]
U / at. %
1400
FIGURE 8. The calculated phase diagram of the (U + Si) binary system with the experimental values [14,30,34–37] and calculated result from Berche et al. [14].
[14] This work [14] This work [34] [30] This work [33] This work Dwight This work [34] This work [34] [30] This work [34] This work [30] This work [30] This work [30] This work [30] This work
19.1 17.8 98.6 99.4
75 75 97.7 98.7
[34] This work [30] This work
53.7
50 50 60 60
25 25
34.7 34.7
50
37.5 37.5
34.7 34.7 75 75
U5Sn4
USn
USn3
U3Sn7 USn2
orthorhombic (U)
400 200
bct (Sn)
Sn
20
40
60
80
U
U / at. %
FIGURE 9. The calculated phase diagram of the (U + Sn) binary system with experimental values [45,49].
0 -10 -20 -30 -40 -50 -60 -70 -80 -90
T= 25 oC
t = 25 oC Colinet et al. [52] Kadochnikov et al. [51] Johnson and Feder [50] Alcock and Grieveson [41]
T=521 oC
t =521 o C Colinet et al. [52] Kadochnikov et al. [51] Johnson and Feder [50] Pattanaik et al. [53]
-100 USn
37.5 28.5 37.5 92.1 98.4 88.5 98.2 75 98.2 75 98.6 10.7 1.4 9.7 1.1 100 75 99.4 75
55.6 55.6 55.6 55.6 37.5 37.5 37.5 33.3 33.3 75 75 50 50 60 60 60 34.7 34.7 60 60 60 60 75 75 100 99.5
53
tetragonal (U)
-110 -120 Sn
20
U5Sn 4
1547 ± 5 1553 Peritectic 1567 ± 5 1562 Congruently 1770 ± 10 melting 1700 1773 (USi3 + USi1.88) Eutectiod 450 M USi2 450 aU3Si M bU3Si Allotropic 770 770 (Liquid + U3Si5) Peritectic 1580 ± 10 M USi 1576 Liquid M U3Si2 Congruently 1540 ± 10 melting 1665 1664 (Liquid + U3Si5) Peritectic 1710 ± 10 M USi1.88 1715 Liquid M (bcc Eutectic 985 (U) + U3Si2) 985 bU3Si M (bcc (U) Eutectiod 930 + U3Si2) 929 Liquid M (diamo Eutectic 1315 (Si) + USi3) 1317 Eutectiod 665 (Tetra (U) 665 + aU3Si) M ortho (U) (Liquid + USi1.88) Peritectic 1510 ± 10 M USi3 1511 (bcc (U) + aU3Si) Eutectiod 795 M tetra (U) 794
600
USn 2
Eutectic
bcc (U)
800
USn 3
Liquid M (USi + U5Si4) (Liquid + U3Si2) M U5Si4 Liquid M U3Si5
Temperature, Composition, at.% References t/°C U
1000
U3Sn 7
Reaction type
Enthalpy of formation , ∆Hf / kJ·mol-atom-1
Reaction
Temperature, t/ o C
TABLE 5 Calculated invariant reactions in the (U + Si) binary system in comparison with experimental data.
liquid
1200
40
60
80
U
U / at. %
FIGURE 10. Calculated enthalpies of formation of (U + Sn) binary compounds at (25 and 521) °C with the experimental values [41,50–53].
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Pattanaik et al. [53]
-5 -10 -15
-25 -30
USn 2
USn 3
-20
U3Sn 7
-35
Sn
USn
-40 20
U5Sn 4
Entropy of formation, ∆Sf / J·K-1·mol-atom-1
0
40
60
80
U
U / at. %
The reported experimental results of the liquidus in the Bi-rich region of the (U + Bi) binary system were evaluated and used in the present thermodynamic optimization. The allotropic transformation of U3Si, and compounds USi2 and U5Si4 in the (U + Si) binary system were evaluated and taken into account in the present thermodynamic optimization. The heat capacities of all intermetallic compounds in the (U + Si) binary system were optimised following the recent experimental results of White et al. [43,44]. Further experimental work is still needed to confirm the existence of USi2 and U5Si4. Five intermetallic compounds USn3, U3Sn7, USn2, USn, and U5Sn4 established by Palenzona and Manfrinetti [49] were included in the present thermodynamic optimization. A self-consistent thermodynamic database of the (U + X) (X = Bi, Si and Sn) binary systems was constructed which will aid in the development of U-based nuclear materials for industrial applications.
FIGURE 11. Calculated entropies of formation of (U + Sn) binary compounds at 521 with the experimental values [53].
Acknowledgement TABLE 6 Calculated invariant reactions in the (U + Sn) binary system in comparison with experimental data. Reaction
Reaction type Temperature, Composition, t/°C at.% U
Liquid M (bcc (U) + U5Sn4) (bcc (U) + U5Sn4) M tetra (U) (Tetra (U) + U5Sn4) M ortho (U) (Liquid + U5Sn4) M USn Liquid M U5Sn4
Eutectic Eutectiod Eutectiod Peritectic Congruently melting Peritectic
(Liquid + USn) M USn2 (Liquid + USn2) Peritectic M U3Sn7 (Liquid + U3Sn7) Peritectic M USn3 Liquid M Eutectic (USn3 + bct (Sn))
1130 1129 776 665 668 1385 1382 1390 1393 1360 1360 1350 1350 1340 1340 232 232
This work was supported by the ‘‘Thorium Molten Salt Reactor” (TMSR), the ‘‘Strategic Priority Research Program” of the Chinese Academy of Sciences (XDA02020300).
References
88 0.97 1.6 55.6 0.47 55.6 55.6 0.29 55.6 55.6 50 55.6
55.6 [49] 55.6 This work [49] 0.46 This work [49] 0.32 This work 50 [49] 50 This work 55.6 [49] 55.6 This work [49] 74.4 50 33.3 This work [49] 77.9 33.3 30 This work [49] 80.4 30 25 This work [49] 0 25 0 This work
binary system as shown in figure 10. Calculated entropies of formation of compounds at 521 °C (with reference to orthorhombic _U and liquid_Sn) are shown in figure 11, with experimental data from Pattanaik et al. [53]. All calculated invariant reactions of (U + Sn) binary system in the present work are summarized in table 6. As shown in the figures and table 6, a reasonable agreement is seen between the experimental and present calculated results. A complete set of thermodynamic parameters describing the Gibbs energy of each phase in the (U + Sn) binary system are listed in tables 3 and 4.
5. Conclusions A critical literature review and evaluation of phase equilibria of the (U + X) (X = Bi, Si and Sn) binary systems have been presented in the present work. A thermodynamic assessment of the (U + Bi), (U + Si) and (U + Sn) binary systems have been carried out by the CALPHAD method in the present work. The Gibbs energy of the liquid phase was optimised with the modified quasi-chemical model in pair approximation (MQMPA) and the terminal solid solutions and intermetallic compounds were described with the sub-lattice model.
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JCT 15-487
