Comprehensive nuclear materials 2 03 thermodynamic and thermophysical properties of the actinide nitrides

Comprehensive nuclear materials 2 03 thermodynamic and thermophysical properties of the actinide nitrides Comprehensive nuclear materials 2 03 thermodynamic and thermophysical properties of the actinide nitrides Comprehensive nuclear materials 2 03 thermodynamic and thermophysical properties of the actinide nitrides Comprehensive nuclear materials 2 03 thermodynamic and thermophysical properties of the actinide nitrides

2.03 Thermodynamic and Thermophysical Properties of the Actinide Nitrides M Uno University of Fukui, Fukui, Japan T Nishi and M Takano Japan Atomic Energy Agency, Tokai-mura, Ibaraki, Japan ß 2012 Elsevier Ltd All rights reserved 2.03.1 Introduction 61 2.03.2 2.03.2.1 2.03.2.2 2.03.2.3 2.03.2.4 2.03.2.5 2.03.3 2.03.3.1 2.03.3.2 2.03.3.3 2.03.3.4 2.03.3.4.1 2.03.3.4.2 2.03.3.4.3 2.03.3.4.4 2.03.3.5 2.03.4 2.03.4.1 2.03.4.2 2.03.4.3 2.03.4.4 2.03.5 References Phase Diagrams and Crystal Structure Uranium Nitrides Plutonium Nitride Thorium Nitride Neptunium, Americium, and Curium Nitrides Nitride Solid Solutions and Mixtures Thermal Properties Melting or Decomposition Vaporization Behavior Heat Capacity Gibbs Free Energy of Formation Uranium mononitride Plutonium mononitride Uranium and plutonium mononitride Neptunium mononitride and americium mononitride Thermal Conductivity Mechanical Properties Mechanical Properties of UN Thermal Expansion of UN Mechanical Properties of PuN Mechanical Properties of Other MA or MA-Containing Fuels Summary 62 62 63 63 64 65 67 67 68 71 72 73 74 75 75 76 79 79 81 81 82 83 83 Abbreviations ADS An CTE fcc HD LTE TD MA MD XRD Accelerator-driven system Actinide Coefficients of linear thermal expansion Face-centered cubic (diamond point) Hardness Linear thermal expansion Theoretical density Minor actinide Molecular dynamics X-ray diffraction 2.03.1 Introduction Uranium nitride UN not only has the same isotropic crystal structure as uranium dioxide UO2 but also has a higher melting point, higher metal atom density, and higher thermal conductivity, compared to UO2 UN thus has advantages as a nuclear fuel compared to UO2, is well studied, and many of its material properties have been known for a long time However, UN has some disadvantages as a nuclear fuel because of its low chemical stability and the problem of 14C 61 62 Thermodynamic and Thermophysical Properties of the Actinide Nitrides Plutonium nitride and thorium nitride have been also well studied, mainly with regard to their suitability as nuclear fuels Other actinide nitrides with higher atomic number are also important as potential nuclear fuels but the data on these fuels are insufficient because they are difficult to obtain and handle In this section, the physicochemical properties of the actinide nitrides, mainly uranium nitrides and plutonium nitride, are discussed First of all, phase stability and crystal structures of the nitrides are described Then, their thermal, thermodynamic, and mechanical properties which are relevant to their suitability as nuclear fuels, are discussed Characteristics of their preparation and irradiation as nuclear fuels are described in Chapter 3.02, Nitride Fuel 2.03.2 Phase Diagrams and Crystal Structure 2.03.2.1 Uranium Nitrides References for specific data are given separately for each section below, but readers are also referred to a classic, outstanding book1 which summarizes, from the viewpoint of suitability as nuclear fuels, the various properties of not only the nitrides but also the other compounds The binary phase diagram shown in Figure 12 is taken from data published in 1960,3–7 and is still valid The phase stability of U–N systems PN2 >> 105 Pa Liquid 3000 2850Њ has been summarized by Chevalier et al.8 There are two uranium nitrides, UN and U2N3; the former has an NaCl-type cubic structure, and the latter has an M2O3-type cubic structure at low temperature (a-U2N3) and hexagonal structure at higher temperature (b-U2N3), as shown in Figure The lattice parameter of UN is reported to be about 4.890 A˚ at room temperature9–11; this, however, can vary, depending on the presence of carbon impurities.10 The lattice parameter of a-U2N3 is 10.688–10.70 A˚,9,11 but U2N3 becomes a solid solution, with N2, at a higher nitrogen pressure (126 atm); and its lattice parameter decreases with an increase in nitrogen content The lattice parameters of b-U2N3 are reported to be a ¼ 3.69 and c ¼ 5.83 A˚9 or a ¼ 3.70 and c ¼ 5.80 A˚.10 Although the phase diagram, where nitrogen pressure is greater than 105 Pa (Figure 1), shows that UN melts at 3123 K and that UN and U2N3 have a wide range of nonstoichiometry, at lower nitrogen pressure; UN decomposes such that UN and U2N3 have little nonstoichiometry, as shown in Figure 312,13; here the b-U2N3 in the previous graph is denoted as UN2 The N/U ratio of UN below a nitrogen pressure of atm is reported to be nearly 1.00 at temperatures between 1773 and 2373 K.14 U2N3 actually decomposes to UN and UN decomposes to U and nitrogen at nitrogen pressure below 2.5 atm As the decomposition of UN must influence the properties of the fuel pellets, and the decomposition of U2N3 is the last stage in the formation of UN through carbothermic reduction, the equilibrium nitrogen pressure of UN and U2N3 is very important from the viewpoint of their use as nuclear 2500 T (ЊC) UN UN + Liq ~1950Њ 2000 UN a-U2N3 + Liq UN + a-U2N3 ~1450Њ 1500 a-U2N3 ss a-U2N3 ss + b-U2N3 ss 1130Њ g-U + UN ~970Њ 775Њ b-U + UN 665Њ a-U + UN 500 UN + b-U2N3 Wt% b-U2N3 ss 1000 (a) b-U2N3 ss + liq (b) U N 10 12 N Figure U–N phase diagram at nitrogen pressure larger than 105 Pa Data from Levinskii, Yu V Atom Energ 1974, 37(1), 216–219; Sov Atom Energ (Engl Transl.) 1974, 37(1), 929–932 (c) Figure Crystal structures of (a) UN, (b) a-U2N3, and (c) b-U2N3 Thermodynamic and Thermophysical Properties of the Actinide Nitrides Atom ratio 0.2 0.4 0.6 1400 0.8 1200 1000 800 1.6 1.2 3000 105 Pa Liquid 63 T (ЊC) 2.5 ϫ 105 Pa U2N3 2600 log PN2 (Pa) UN + N2 T (ЊC) 2200 UN1–x + Liq 1800 U + N2 1400 1127Њ 1000 UN+ U2N3 UN2 + N2 UN + UN2 105 Pa g-U + UN 775Њ 668Њ b-U + UN a-U + UN 600 10 20 30 40 50 60 70 10 104/ T (K–1) (a) At.% Figure U–N phase diagram at nitrogen pressure smaller than atm Data from Storms, E K Special Report to the Phase Equilibria Program; American Ceramic Society: Westerville, OH, 1989; Muromura, T.; Tagawa, H J Nucl Mater 1979, 79, 264 2.03.2.2 2.03.2.3 Thorium Nitride Though thorium is a fertile material, recent research on thorium and its compounds as nuclear fuel is scanty The Th–Th3N4 phase diagram, reported in 196618, is shown in Figure There are two solid compounds in this system, ThN and Th3N4; the former is an NaCl-type cubic structure with 2250 2000 1750 T (ЊC) UN Plutonium Nitride In the Pu–N system, as shown in Figure 5,15 there is only one structure for the mononitride, PuN: an NaCl-type face-centered cubic (fcc) structure with a ¼ 4.904 A˚ PuN is a line compound with little nonstoichiometry, and is reported not to congruently melt up to 25 bar nitrogen pressure.16 However, there is a study on the safety assessment of fuels on the basis of vaporization behavior in which the melting temperature of Pu–N is given as 2993 K under a nitrogen pressure of 1.7  104 Pa.17 2500 log PN2 (Pa) fuel The reported decomposition curves are shown in Figure 4.3 It is seen from these graphs, for example, that UN decomposes at 3073 K and U2N3 decomposes 1620 K at nitrogen pressure of atm More detailed decomposition behavior of UN as well as other actinide nitrides will be discussed in Section 2.03.3.1 2750 U + N2 (b) 3.5 104/T (K–1) 4.5 Figure (a) Decomposition curve of U2N3 (b) Decomposition curve of UN Reproduced from Bugl, J.; Bauer, A A J Am Ceram Soc 1964, 47(9), 425–429, with permission from Springer The dotted line is referred from P Gross, C Hayman and H Clayton, ‘‘Heats of Formation of Uranium Silicides and Nitrides’’; In Thermodynamics of Nuclear Materials- Proceedings of Symposium on Thermodynamics of Nuclear Materials, Vienna, May 1962, International Atomic Energy Agency a ¼ 5.169 A˚,18 and the latter is a rhombohedron with a ¼ 9.398 A˚ and a ¼ 23.78 19 The congruent melting point is 2820  C at nitrogen pressure of 64 Thermodynamic and Thermophysical Properties of the Actinide Nitrides 3000 Weight percent nitrogen MP(ssL) 3830 ЊC Dashed lines schematic 2500 L PuN Temperature (ЊC) 2000 1500 1000 -640 ЊC MP 640 ЊC TP 483 ЊC 500 TP 483 ЊC TP 320 ЊC TP 215 ЊC TP 125 ЊC a -483 ЊC -320ЊC -483 ЊC -215 ЊC -125ЊC aa g b a 0 Pu 10 15 20 25 30 35 40 45 50 55 Atomic percent nitrogen Figure Phase diagram of Pu–N Reproduced from Wriedt, H A Bull Alloys Phase Diagrams 1989, 10, 593, with permission from American Chemical Society 3000 2820 Њ ± 30 Њ 2500 Congruent sublimation compositions Thermal arrests Liquidus Melting points Solidus, established micrographically Solvus, established metallographically N solubility in Th (Gerds and Mallett)115 atm Hypo- and hyper-ThN appear above 1350  C Th3N4 decomposes to ThN in vacuum above 1400  C with the formation of a small amount of oxide.20 As ThN oxidizes more easily than UN it is important to consider the temperature and nitrogen and oxygen pressures during the preparation of ThN by thermal decomposition of Th3N4.21 Temperature (ЊC) ThN + Th (liq.) 2.03.2.4 Neptunium, Americium, and Curium Nitrides 2000 1800 Њ ± 25 Њ 1754 ±15 ThN + bccTh 1605 Њ ± 20 Њ 1500 1350 Th3N4 + ThN ThN + fccTh 1000 Th 0.2 0.4 0.6 0.8 N2: Th ratio 1.0 ThN 1.2 1.4 Th3N4 1.6 Figure Phase diagram of Th–N system Reproduced from Benz, R.; Hoffman, C G.; Rupert, G N J Am Chem Soc 1967, 89, 191–197, with permission from Elsevier These nitrides are also usually prepared by carbothermic reduction of the oxides.22–24 As it is very difficult to prepare bulk samples due to their high radioactivity, there have been no systematic studies on their phase stability However, it has been established that there is only mono nitride in these systems from the fact that no nitrogen absorption occurred upon cooling in nitrogen atmospheres during carbothermic reduction These mono nitrides have an NaCl-type face-centered cubic structure, and their lattice parameter ranges from 0.4899 to 0.5041 A˚, as shown in Table 1.24 The similarity in the crystal structure of these three nitrides, as well as uranium and plutonium nitrides, is advantageous as nuclear Thermodynamic and Thermophysical Properties of the Actinide Nitrides Lattice parameter of some actinide nitrides Mononitride Lattice parameter a (nm) NpN−PuN |aPuN À a| (nm) |aAmN À a| (nm) UN NpN PuN AmN CmN YN ZrN TiN 0.4888 0.4899 0.4905 0.4991 0.5041 0.4891 0.4576 0.4242 0.4905 Lattice parameter difference 0.0017 0.0006 – 0.0086 0.0136 0.0014 0.0329 0.0663 0.0103 0.0092 0.0086 – 0.0050 0.0100 0.0415 0.0749 Source: Minato, K.; et al J Nucl Mater 2003, 320, 18–24, with permission from Elsevier fuels, especially as accelerator-driven system (ADS) targets of nitride solid solutions that contain a large amount of minor actinides (MAs) Experimental research on their vaporization behavior has revealed that the congruent melting temperature of NpN was 2830  C.25 There are scarcely any data on the phase stability and other properties of pure CmN Some data on Cm and U or Pu solid solutions have been reported, and these will be discussed in the next section 2.03.2.5 Nitride Solid Solutions and Mixtures As (U,Pu)N were some of the most promising candidates for the first breeder reactors, they are the best studied nitride solid solution fuels UN and PuN form a continuous solid solution, and the lattice parameter increases with an increase in the plutonium content, and is accompanied by a large deviation from Vegard’s law, as shown in Figure 7,26 suggesting the nonideality of the solution A diagram of the calculated U–Pu–N ternary phase at 1000  C, shown in Figure 8,1 suggests that there is a relatively narrow range of possible (U,Pu)N compositions, as is the case with U–N and Pu–N binary systems It is suggested that the sesquinitride solid solution (U,Pu)N1.5 exists in a system in which PuN may constitute up to 15 mol%27, although this is not depicted in Figure As uranium monocarbide and plutonium monocarbide, as well as other actinide carbides, have an NaCl-type fcc structure, actinide nitrides and actinide carbides form solid solutions Some research performed on actinide nitride carbides, for example, U–N–C, Pu–N–C,28–30 have investigated the suitability of these carbonitride fuels and the impurities in nitride fuels after carbothermic reduction Phase Lattice parameter (nm) Table 65 0.4900 0.4895 UN−PuN UN−NpN 0.4890 UN UN NpN Vegard’s law 0.2 0.4 0.6 Composition 0.8 PuN NpN PuN Figure Lattice parameter of some actinide nitride solid solution Reproduced from Minato, K.; et al J Nucl Mater 2003, 320, 18–24 stability graphs of U and/or Pu–N–C, both with and without oxygen, also have been constructed in order to make pure nitride fuels.31,32 The irradiation behavior of (U and/or Pu)–N–C fuels also has been reported,33 but the details of this data are out of the scope of this chapter As MAs are usually burnt with uranium and plutonium for transmutation, and as Am originally exists in Pu, (MA,U)N or (MA,Pu)N have also been well studied As mentioned above, the vaporization behavior of (Pu,Am)N has been studied34, and abnormal vaporization of Pu and Am was observed The lattice parameters of (U,Np)N and (Np,Pu)N increase with increase in Np and Pu content, and with a small deviation from ideality, as shown in Figure 7.24 Although scarcely any data for pure CmN has been obtained, X-ray diffraction data for (Cm0.4Pu0.6)N has been reported, as shown in Figure 9.24 Inert matrix fuels, where MA as well as uranium and plutonium are embedded in a matrix, are also being considered for use in ADS for transmutation Recent research in MAs has focused on using various nitride solid solutions and nitride mixtures as inert matrix fuels For ADS targets, matrices have been designed and selected so as to avoid the formation of hot spots and to increase the thermal stability, especially in the case of Americium nitride Considering their chemical stability and thermal conductivity, ZrN, YN, TiN, and AlN were chosen as candidates for the matrix.16,35 ZrN has an NaCl-type 66 Thermodynamic and Thermophysical Properties of the Actinide Nitrides α-U2N3 + (U, Pu)N + N2 N U-Pu-N 1000 ЊC α + β + (U,Pu)N atm β + (U,Pu)N UN PuN α-U2N3 + (U,Pu)N Liquid Solid U Pu Figure U–Pu–N ternary phase diagram at 1000  C Reproduced from Matzke, H J Science of Advanced LMFBR Fuels; North Holland: Amsterdam, 1986, with permission from Elsevier 5000 0.56 111 PuO2 0.54 CmO2 Intensity Lattice parameter (nm) 4000 200 30 mol% Am 3000 2000 0.52 10 mol% Am 1000 CmN 30 0.50 PuN 0.48 PuN PuO2 0.2 0.4 0.6 Composition 0.8 CmN CmO2 Figure Lattice parameter of (Pu,Cm)N and (Pu,Cm)O2 Reproduced from Minato, K.; et al J Nucl Mater 2003, 320, 18–24, with permission from Elsevier fcc structure with a ¼ 4.580 A˚ and has nearly the same thermal conductivity as UN, has a high melting point, good chemical stability in air, and a tolerable dissolution rate in nitric acid Recently, abundant data have been made available for ZrN-based inert matrix fuels It is planned that (Pu,Zr)N, with about 20–25% Pu, will be used to burn Pu in a closed fuel cycle.36 The lattice parameter of (Pu,Zr)N decreases with an AmN(111) 32 ZrN(111) AmN(200) 34 36 2q (deg) ZrN(200) 38 40 Figure 10 X-ray diffraction patterns for Am–ZrN Reproduced from Minato, K.; et al J Nucl Mater 2003, 320, 18–24 increase in the Zr content, and is between that of PuN and ZrN, in accordance with Vegard’s law.24 It has also been estimated, using a model, that (Pu, Zr)N with 20–40 mol% PuN, does not melt till up to 2773 K; this is based on experimental thermodynamic data which show that U0.9Zr0.8N does not melt till up to 3073 K.37 In the case of (Am,Zr)N, it is reported that two solid solutions are obtained when Am content is over 30%24, as shown in Figure 10 The Am content of the two phases have been estimated, from the lattice parameter, to be 14.5 and 43.1 mol% A thermodynamic modeling of a uranium-free inert Thermodynamic and Thermophysical Properties of the Actinide Nitrides T (K) 3200 102 3000 101 PuN UN 100 10–1 Congruent melting ThN 10–2 Melting or Decomposition In this section, the melting points and decomposition temperatures of actinide mononitrides are discussed in conjunction with the nitrogen pressures because this behavior depends on the nitrogen partial pressure of the system The vapor pressure of a metal gas over the solid nitride is discussed in the next section as ‘vaporization behavior.’ The liquid mononitride MN (liq.) can be observed when congruent melting occurs under a pressurized nitrogen atmosphere; otherwise the solid mononitride MN (s) decomposes into nitrogen gas and liquid metal that is saturated with nitrogen, according to the following reaction, MNsị ẳ 1=2N2 ỵ Mliq; sat: with Nị ẵ1 Olson and Mulford have determined the decomposition temperatures of ThN,41 UN,6 NpN,25 and PuN42 by the optical observation of the nitride granules when they were heated under controlled nitrogen pressures Figure 11 shows the relationship between the nitrogen pressure p (atm) in logarithmic scale and the reciprocal decomposition temperature 1/T (KÀ1) The solid curves show the following equations: ThN : log patmị ẳ 8:086 33224=T ỵ 0:958 1017 T 2689 T Kị 3063ị ẵ2 UN : log patmị ẳ 8:193 29540=T ỵ 5:57 1018 T 2773 T Kị 3123ị ẵ3 NpN : log patmị ẳ 8:193 29540=T þ 7:87  10À18 T ð2483 T ðKÞ 3103Þ 2600 UN (Hayes) 2.03.3 Thermal Properties 2.03.3.1 2800 NpN Nitrogen pressure (atm) matrix fuel, for example, (Am0.20Np0.04Pu0.26Zr0.60), has also been accomplished.38 In contrast to ZrN, TiN does not dissolve MA nitrides even though TiN also has an NaCl-type fcc structure This is explained by the differences in lattice parameter, which was estimated by Benedict.39 A mixture of PuN and TiN was obtained by several heat treatments above 1673 K, and the product, in which one phase was formed, did not contain the other phase.40 TiN, as well as ZrN, have nonstoichiometry It is also reported that a TiN ỵ PuN mixture may be hypostoichiometric although (Pu,Zr)N is hyperstoichiometric 67 ½4Š 10–3 3.2 3.4 3.6 3.8 10 000/ T (K–1) Figure 11 Decomposition pressures of ThN, UN, NpN, and PuN as a function of reciprocal temperature above 2500 K reported by Olson and Mulford.6,25,41,42 PuN : log patmị ẳ 8:193 29540=T ỵ 11:28 1018 T 2563 T Kị 3043ị ẵ5 The temperature at which the vertical rise in nitrogen pressure is observed for ThN, UN, and NpN corresponds to the congruent melting point, and is 3063 Æ 30 K for ThN (p ! 0.7 atm), 3123 Æ 30 K for UN (p ! 2.5 atm), and 3103 Ỉ 30 K for NpN (p ! 10 atm) The congruent melting for PuN was not achieved in the nitrogen pressure range up to 24.5 atm The presence of an oxide phase, as an impurity, seems to lower the melting point and decomposition temperature In the case of ThN mentioned above, the melting point and decomposition temperature of a specimen containing 0.6 wt% oxygen fell by $130 K from those of the oxygen-free specimens ($0.04 wt% oxygen) A similar experiment conducted by Eron’yan et al.43 with ZrN, a transition metal nitride that has the same crystal structure, has revealed a decrease in the melting point by 200–300 K when the oxygen content increased from 0.15 to 0.5–1.0 wt% Some data sets on the equilibrium nitrogen pressure, in eqn [1] for UN and uranium carbonitride 68 Thermodynamic and Thermophysical Properties of the Actinide Nitrides T (K) 2200 2000 UN (Hayes) UC1–xNx (Ikeda) 1: x = 2: x = 0.69 3: x = 0.48 4: x = 0.3 UC1–xNx (Prins) 5: x = 6: x = 0.79 7: x = 0.5 8: x = 0.36 9: x = 0.2 10–4 Nitrogen pressure (atm) 10–5 1800 10–6 16 14 T (K) 3200 3000 3600 3400 Timofeeva Brundiers TPRC Smirnov Houska Hayes Takano Aldred Benedict Kruger 10 AmN 1273 K PuN NpN 293 K 10–7 2800 12 CTE (10–6 K–1) 2400 10–3 UN TiN ZrN HfN 10–8 4.2 4.4 4.6 4.8 5.2 5.4 5.6 10 000/ T (K–1) log patmị ẳ 1:8216 ỵ 1:882 103 T 23543:4=T 3170Þ 3.2 3.4 3.6 3.8 Figure 13 Coefficients of linear thermal expansion at 293 (open symbols) and 1273 K (closed symbols) for some transition metal nitrides and actinide nitrides plotted against reciprocal decomposition temperature under atm of nitrogen For references see Table U(C,N), as measured by the Knudsen-cell and massspectroscopic technique at lower temperatures, are available and are shown in Figure 12 The dotted curve represents the correlation for UN developed by Hayes et al.46 using eight data sets available in literature.4–6,44,45,47–49 The nitrogen pressure is given as: T ðKÞ 2.8 10 000/T (K–1) Figure 12 Decomposition pressures of U(C,N) as a function of reciprocal temperature below 2400 K Solid lines by Ikeda et al.44 and broken lines by Prins et al.45 Dotted line for UN reviewed by Hayes et al.46 ð1400 2.6 ½6Š The N2 pressure for decomposition of UC1ÀxNx, as measured by Ikeda et al.44 and Prins et al.45, decreases with a decrease in x, together with a lowering in the activity of UN in UC1ÀxNx The nitrogen pressure over UC0.5N0.5, at a certain temperature in the graph, is approximately one-fifth of that of UN When considering a nitride or carbide as nuclear fuel for fast reactors, it should be noted that the decomposition pressure of nitrogen can be lowered and that the reactivity of carbide with moisture can be moderated by employing the carbonitride instead of the nitride or carbide No experimental data on the melting behavior of transplutonium nitrides such as AmN and CmN have been reported Takano et al.22 have examined the relationship between the decomposition temperature and the instantaneous coefficients of linear thermal expansion (CTE) and used it to predict the decomposition temperature of AmN Figure 13 shows the CTE at 293 and 1273 K plotted against reciprocal decomposition temperature under atm of nitrogen for some transition metal nitrides (TiN, ZrN, HfN) and actinide nitrides (UN, NpN, PuN) The data used for this is summarized in Table 26,22,25,41–43,50–59 with references Except for the large CTE value for PuN at 293 K, a reasonable linear relationship is shown by the agreement of the broken lines From the CTE values for AmN, determined by the high-temperature X-ray diffraction technique, the decomposition temperature of AmN under atm of nitrogen was roughly predicted to be 2700 K, which is much lower than that of PuN 2.03.3.2 Vaporization Behavior In this section, the vapor pressure of a metal gas over a solid actinide nitride is summarized Thermodynamic and Thermophysical Properties of the Actinide Nitrides 69 Table Summary of melting point, decomposition temperature and linear thermal expansion coefficient (CTE) for some transition metal nitrides and actinide nitrides Nitride Congruent melting point (m.p.) (K) Decomposition temperaturea (K) References CTE (10À6 KÀ1) 293 K TiN 3550 3180 50 ZrN 3970 3520 43 HfN NAb 3620 50 ThN UN 3063 3123 (3063)c 3050 41 NpN 3103 2960 25 PuN NA 2860 42 AmN NA ($2700?) 22 References Method or comment 52 51 53 51 54 55 XRD, TiN0.95 TPRC XRD, ZrN0.99 TPRC XRD XRD 56 51 22 57 22 58 59 22 XRD TPRC XRD XRD XRD XRD Dilatometer XRD 1273 K 7.0 6.3 6.5 5.7 5.7 10.1 10.4 7.9 8.9 – 8.0 – 10.3 11.1 9.9 – 12.2 – 11.6 13.0 – – 7.5 7.4 7.9 7.6 10.0 10.3 – 9.4 a Under atm of nitrogen Not available Congruent melting under atm of nitrogen b c : N2(g), Hayes et al.46 : U(g), Hayes et al.46 : U(g), Suzuki et al.61 : U(g), Alexander et al.62 log p (Pa) The major vapor species observed over UN are nitrogen gas, N2(g), and mono-atomic uranium gas, U(g) UN(g) can also be detected in addition to U(g) and N2(g),60 but its pressure is three orders of magnitude lower than that of U(g); therefore, the contribution of UN(g) can be ignored in practice Some data on the pressures of N2(g) and U(g) over solid UN(s) are shown in Figure 14 Hayes et al.46 have derived equations for the pressures of N2(g) and U(g), which were developed by fitting the data from eight experimental investigations According to that paper, the reported data on N2(g) agree with each other, but that of U(g) over UN(s) vary somewhat The U(g) pressure obtained by Suzuki et al.61 is a little higher than that predicted from the equation developed by Hayes et al., but is in agreement with values given by Alexander et al.62 It is well known that the evaporation of UN is accompanied by the precipitation of a liquid phase, where UN(s) ¼ U(1) þ 1/2N2(g) and U(1) ¼ U(g) The reported vapor pressure of U(g) over UN(s) is close to or a little lower than that over metal U.63 It is suggested that the dissolution of nitrogen and/or impurity metal from crucibles into the liquid phase could affect the observed partial pressure Some scattering of the previously reported data on U(g) over UN(s) may be also caused by a reaction of the liquid phase in UN with the crucible material From this viewpoint, it appears that the partial pressure of U(g) -2 -4 -6 -8 104/T (K-1) Figure 14 Partial pressure of N2(g) and U(g) over UN (s) as a function of temperature Adapted from Hayes, S L.; Thomas, J K.; Peddicord, K L J Nucl Mater 1990, 171, 300–318; Suzuki, Y.; Maeda, A.; Arai, Y.; Ohmichi, T J Nucl Mater 1992, 188, 239–243; Alexander, C A.; Ogden, J S.; Pardue, W H J Nucl Mater 1969, 31, 13–24 over UN(s) should be a little higher than that proposed by Hayes et al The vapor species over PuN are nitrogen gas N2(g) and mono-atomic plutonium gas Pu(g) PuN(g) is not detected because PuN is more unstable than UN.64 The N2 pressure over PuN has been reported by Alexander et al.,65 Olson and Mulford,42 70 Thermodynamic and Thermophysical Properties of the Actinide Nitrides : Suzuki et al.61 : Kent and Leary68 : Sheth and Leibowitz et al.69 log p (Pa) –1 –2 –3 –4 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 104/T (K–1) Figure 15 Partial pressure of Pu(g) over PuN(s) as a function of temperature Data from Suzuki, Y.; Maeda, A.; Arai, Y.; Ohmichi, T J Nucl Mater 1992, 188, 239–243; Kent, R A.; Leary, J A High Temp Sci 1966, 1, 176–183; Sheth, A.; Leibowitz, L ANL-AFP-2, Argonne National Laboratory; Chemical Engineering Division: Argonne, WI, 1975 : (U0.80Pu0.20)N : (U0.65Pu0.35)N log p (Pa) –1 Pu : (U0.40Pu0.60)N : (U0.20Pu0.80)N : PuN –2 –3 U : UN : (U0.80Pu0.20)N : (U0.65Pu0.35)N –4 5.0 5.5 6.0 6.5 7.0 104/T (K–1) Figure 16 Partial pressure of U(g) and Pu(g) over UN(s), PuN(s) and mixed nitride as function of temperature Reproduced from Suzuki, Y.; Maeda, A.; Arai, Y.; Ohmichi, T J Nucl Mater 1992, 188, 239–243 Table Pardue et al.,66 and Campbell and Leary.67 These data seem to agree with each other The vapor pressure of Pu(g) over PuN(s), as a function of temperature, is shown in Figure 15 The values reported in the different studies almost completely agree with each other.61,68,69 According to Alexander et al.,65 the ratio Pu(g)/ N2(g) is 5.8 throughout the investigated temperature range of 1400–2400 K, which suggests that PuN evaporates congruently; that is, PuN(s) ¼ Pu(g) þ 1/2N2(g) However, Suzuki et al have reported that Pu(g) over PuN(s), at temperatures lower than 1600 K, is a little higher than the values extrapolated from the high-temperature data, and that it approaches that over Pu metal with further decrease in temperature There is some possibility that a liquid phase forms at the surface of the sample during the cooling stages of the mass-spectrometric measurements, because PuN has a nonstoichiometric composition range at elevated temperatures, while it is a line compound at low temperatures The vapor pressure of U(g) and Pu(g) over UN(s), (U,Pu)N(s), and PuN(s) are shown in Figure 16 Table gives the vapor pressures of U(g) and Pu(g) which are represented in Figure 16 in the form of logarithmic temperature coefficients It is noteworthy that the vapor pressure of Pu(g) over mixed nitride was observed to increase with an increase in the PuN content Nakajima et al.70 have measured the vapor pressure of Np(g) over NpN(s) in the temperature range of 1690–2030 K by using the Knudsen-cell effusion mass spectrometry This data is plotted in Figure 17 as a function of temperature The partial pressure of Np (g) can be expressed using the following equation: log p NpgịPaị ẳ 10:26 22 200=T ẵ7 The vapor pressures of Np(g) over NpN(s) obtained by Nakajima et al are similar to those of Np(g) over Partial pressure of U and Pu over UN, PuN, and (U,Pu)N Compound Vapor species Vapor pressure log p (Pa) Temperature range (K) UN (U0.80Pu0.20)N U U Pu U Pu Pu Pu Pu 10.65–25 600T1 (T,K) 10.90–26 400T1 (T,K) 9.86–20 500T1 (T,K) 11.03–26 900T1 (T,K) 9.59–19 600T1 (T,K) 11.14–22 000T1 (T,K) 10.76–21 100T1 (T,K) 11.74–22 500T1 (T,K) 753–2 028 793–1 913 653–1 933 813–1 833 593–1 833 553–1 773 553–1 733 558–1 738 (U0.65Pu0.35)N (U0.40Pu0.60)N (U0.20Pu0.80)N PuN Source: Suzuki, Y.; Maeda, A.; Arai, Y.; Ohmichi, T J Nucl Mater 1992, 188, 239–243 Thermodynamic and Thermophysical Properties of the Actinide Nitrides 71 Am(g) over AmN log p (Pa) Np(g) over NpN –1 Pu(g) over PuN –2 –3 U(g) over UN –4 Heat capacity (J mol–1 K–1) 70 60 : Alexander et al.65 : Oetting75 50 Np(g) over Np(l) 500 –5 5.0 5.5 104/T (K–1) 6.0 Figure 17 Temperature dependence of partial pressure of Np(g) over Np(1), Np(g) over NpN(s) and Am(g) over AmN(s) together with those of U(g) and Pu(g) over UN(s) and PuN(s) as a function of temperature Adapted from Suzuki, Y.; Maeda, A.; Arai, Y.; Ohmichi, T J Nucl Mater 1992, 188, 239–243; Nakajima, K.; Arai, Y.; Suzuki, Y J Nucl Mater 1997, 247, 33–36; Ackermann, R J.; Rauh, E G J Chem Thermodyn 1975, 7, 211–218; Takano, M.; Itoh, A.; Akabori, M.; Minato, K.; Numata, M In Proceedings of GLOBAL 2003, Study on the Stability of AmN and (Am,Zr)N, New Orleans, LA, Nov 16–20, 2003; p 2285, CD-ROM liquid Np metal found by Ackermann and Rauh71; these all are shown in Figure 17 Therefore, the decomposition mechanism is considered to be the following reaction: NpN(s) ẳ Np(1) ỵ 1/2N2(g), Np(1) ẳ Np(g) Takano et al.72 have estimated the vapor pressure of Am(g) over AmN by using values of the Gibbs free energy of formation available in literature.34 The evaporation of AmN obeys the following reaction: AmN(s) ẳ Am(g) ỵ 1/2N2(g) The estimated vapor pressure of Am over AmN, expressed as a function of temperature, is log p AmgịPaị ẳ 12:913 20197=T 1623 < T Kị < 1733ị ẵ8 The calculated vapor pressures of Am over AmN are plotted in Figure 17 as a function of temperature The vapor pressure of Am over AmN is higher than those of other actinide vapor species over their respective nitrides 2.03.3.3 Heat Capacity Data on the heat capacities of actinide nitrides are very limited due to the experimental difficulties In this section, the heat capacities of uranium nitride 1000 1500 Temperature (K) 2000 Figure 18 Heat capacities of PuN Data from Alexander, C A.; Clark, R B.; Kruger, O L.; Robins, J L Plutonium and Other Actinides 1975; North-Holland: Amsterdam, 1976; pp 277; Oetting, F L J Chem Thermodyn 1978, 10, 941–948 UN, plutonium nitride PuN, neptunium nitride NpN, and americium nitride AmN are summarized Hayes et al.46 recommended an equation for the heat capacity of UN based on a comparison of nine data sets; these seem to agree with each other at low temperatures but their data are limited, and to some extent scattered, at elevated temperatures The previously reported values for the heat capacity of UN exhibit an almost linear increase with temperature, except those reported by Conway and Flagella.73 They report that Cp–T curves exhibit a strong upward trend at temperatures over 1500 K This behavior is analogous to that of the actinide carbides, as pointed out by Blank.74 The assessment by Hayes et al uses the results of Conway and Flagella Thus, the heat capacity data reported by Hayes et al can be considered reliable The heat capacity of UN, expressed by Hayes et al., is as follows: Cp ð Jmol1 K1 ị ẳ  2 exp Ty y 51:14 ỵ 9:491 10 T T exp y À T   11 2:642 10 18081 ỵ exp T2 T 298 < T Kị < 2628ị ẵ9 where y is the empirically determined Einstein temperature of UN, 365.7 K The heat capacities of PuN are shown in Figure 18 Information on the heat capacity of PuN is very scarce and is limited to the low temperatures Moreover, the two data sets on PuN given by Alexander 72 Thermodynamic and Thermophysical Properties of the Actinide Nitrides 80 : UN (Hayes et al.46) : PuN (Oetting75) : (U0.8Pu0.2)N (Alexander et al.65) 100 Heat capacity (J mol–1 K–1) Heat capacity (J mol–1 K–1) 120 : (U0.45Pu0.55)N (Kandan et al.78) 80 60 40 500 1000 1500 2000 Temperature (K) 2500 3000 Figure 19 Heat capacities of UN, PuN, and (U,Pu)N Data from Hayes, S L.; Thomas, J K.; Peddicord, K L J Nucl Mater 1990, 171, 300–318; Oetting, F L J Chem Thermodyn 1978, 10, 941–948; Alexander, C A.; Ogden, J S.; Pardue, W M Thermophysical properties of (UPu)N In Plutonium 1970 and Other Actinides PT.1; 1970, 17, 95–103; Kandan, R.; Babu, R.; Nagarajan, K.; Vasudeva Rao, P R Thermochim Acta 2007, 460, 41–43 et al.65 and Oetting75 are not consistent Matsui and Ohse76 have critically reviewed the heat capacity data of PuN and have argued that the Oetting correlation is more reliable Therefore, the heat capacity data, as reported by Oetting, is given here The heat capacity function of PuN given by Oetting is À1 À1 À2 Cp ð J mol K ị ẳ 1:542 10 T ỵ 45:00 298 < T ðKÞ < 1562Þ 60 40 : UN (Hayes et al.46) : NpN (Nishi et al.79) : PuN (Oetting75) : AmN (Nishi et al.79) 20 400 600 800 Temperature (K) 1000 Figure 20 Heat capacities of UN, NpN, PuN, and AmN Adapted from Hayes, S L.; Thomas, J K.; Peddicord, K L J Nucl Mater 1990, 171, 300–318; Oetting, F L J Chem Thermodyn 1978, 10, 941–948; Nishi, T.; Itoh, A.; Takano, M.; et al J Nucl Mater 2008, 377, 467–469 of NpN and AmN were prepared by the carbothermic reduction of their respective oxides The enthalpy increments were measured using a twin-type drop calorimeter in a glove box The heat capacities were determined by derivatives of the enthalpy increments The measured heat capacity of NpN is expressed by Cp J mol1 Kị ẳ 1:872 102 T ỵ 42:75 334 < T Kị < 1562ị ẵ11 The measured heat capacity of AmN is expressed by ½10Š The heat capacities of UN, PuN, and (U,Pu)N are shown in Figure 19 If the heat capacities of solid solutions can be estimated from those of its raw materials with the same structure on the basis of the additive law, it can be expected that the values for the (U,Pu)N solid solutions are an intermediate between those of UN and PuN However, the heat capacities of (U,Pu)N, as reported by Alexander et al.77 and Kandan et al.,78 are smaller than those of UN, by Hayes et al., and PuN, by Oetting In addition, the temperature dependencies of the heat capacities of PuN and its solid solutions are almost linear, although it has been suggested that they can shift toward larger values at elevated temperatures, as does UN It is considered that these discrepancies are probably due to the lack of experimental data Thus, it is necessary to obtain the accurate heat capacity of PuN and (U,Pu)N Recently, the heat capacities of NpN and AmN were determined by drop calorimetry.79 The samples Cp J mol1 Kị ẳ 1:563 102 T ỵ 42:44 354 < T Kị < 1071ị ẵ12 These are shown in Figure 20, together with those of UN,46 NpN,79 and PuN.75 Although there are no distinct differences, the heat capacity of AmN was slightly lower than those of UN, NpN, and PuN The heat capacities of (Np,Am)N and (Pu,Am)N solid solutions were also obtained The heat capacities decreased slightly with an increase in Am content This tendency was attributed to the heat capacity of AmN being slightly smaller than those of NpN and PuN.80 2.03.3.4 Gibbs Free Energy of Formation Some data on the Gibbs free energy of formation for actinide nitrides exist In this section, the Gibbs free energy of formation of uranium nitride, UN, plutonium nitride, PuN, uranium and plutonium mixed nitride, (U,Pu)N, neptunium nitride, NpN, and americium nitride, AmN are summarized Thermodynamic and Thermophysical Properties of the Actinide Nitrides Table 73 The standard thermodynamic functions of UN T (K) Cp (J molÀ1 KÀ1) HÀH298 (J molÀ1) S (J molÀ1 KÀ1) À(GÀH298)/T (J molÀ1 KÀ1) DfG (J molÀ1) 298 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400 2500 2600 2628 47.95 48.04 51.49 53.64 55.27 56.63 57.84 58.98 60.06 61.12 62.18 63.28 64.47 65.81 67.38 69.27 71.59 74.40 77.81 81.86 86.62 92.11 98.35 105.33 113.04 115.32 96 5089 10 352 15 801 21 397 27 121 32 963 38 915 44 975 51 140 57 413 63 799 70 312 76 969 83 798 90 837 98 132 105 738 113 716 122 133 131 063 140 580 150 757 161 669 164 866 62.68 63.00 77.34 89.08 99.01 107.63 115.27 122.15 128.42 134.19 139.56 144.57 149.28 153.74 157.98 162.01 165.87 169.58 173.14 176.58 179.90 183.12 186.24 189.28 192.23 193.04 62.68 62.68 64.62 68.37 72.67 77.06 81.37 85.53 89.51 93.31 96.94 100.41 103.71 106.87 109.87 112.72 115.41 117.93 120.28 122.43 124.39 126.14 127.67 128.98 130.05 130.31 À270 978 À270 812 À262 582 À254 530 À246 614 À238 788 À231 011 À223 235 À215 267 À206 948 À198 457 À190 019 À181 626 À172 640 À163 550 À154 384 À145 111 À135 687 À126 062 À116 178 À105 969 À95 367 À84 302 À72 701 À60 489 À56 954 The values of DfG for UN were calculated from the values of DH298 and thermal functions for uranium and nitrogen Source: Hayes, S L.; Thomas, J K.; Peddicord, K L J Nucl Mater 1990, 171, 300–318; Matsui, T.; Ohse, R W High Temp High Press 1987, 19, 1–17; Cordfunke, E H P.; Konings, R J M.; Potter, P E.; Prins, G.; Rand, M H Thermochemical Data for Reactor Materials and Fission Products; Elsevier: Amsterdam, 1990; p 667; Chase, M W.; Curnutt, J L.; Prophet, H JANAF Thermochemical Tables; Dow Chemical Co.: Midland, MA, 1965 2.03.3.4.1 Uranium mononitride The Gibbs free energy (G) for UN has been reported by Hayes et al.46 On the basis of the equations for Cp and HÀH298, they have determined other thermal functions of UN(s) in the temperature range of 298–2628 K They have then calculated the values of the thermal functions from their equations for heat capacity, setting S298 to be 62.68 J molÀ1 KÀ1; these are given in Table The values of Gibbs free energy of formation DfG for UN were thus calculated from the values of DH29876 and thermal functions of uranium81 and nitrogen.82 The values of entropy S, free energy function À(GÀH298)/T, and Gibbs free energy of formation DfG of UN(s) are also given in Table The values of DfG at various temperatures were fitted to a polynomial function of temperature using the least-squares method The DfG of UN was thus expressed as the following equation: Df GJmol1 ị ẳ 2:941 105 ỵ 80:98T 0:04640T ỵ 3:085 10À6 T À 1:710  106 =T ð298 < T Kị< 2628ị ẵ13 Matsui and Ohse76 have also reported DfG values for UN The temperature dependences of DfG for UN are shown in Figure 21 The UN DfG values of these two studies agree well with each other below 1800 K, but there seems to be some discrepancy between them at higher temperatures It should be noted that the values of DfG for UN contain some uncertainty due to the inaccuracy of the data on the HÀH298 values The values of DfG, as estimated by Matsui and Ohse have a large range of error because the calculation was performed by extrapolating the values of HÀH298 Thus, the data for the DfG of UN, as reported by Hayes et al., are considered to be the reference standard at the present 74 Thermodynamic and Thermophysical Properties of the Actinide Nitrides 2.03.3.4.2 Plutonium mononitride Gibbs free energy of formation (kJ mol–1) The most reliable standard thermodynamic function data for PuN are those reported by Matsui and Ohse.76 Matsui et al have calculated the thermal functions of PuN(s) using the recommended –100 equations for Cp and the HÀH298 values of Oetting75, and setting S298 to be 64.81 J molÀ1 KÀ1; these are summarized in Table The values of Cp and HÀH298 higher than 1600 K are extrapolations of the data reported by Oetting.75 The values of DfG for PuN were calculated with DH298 set at À299 200 J molÀ1(83) and the thermal functions for plutonium84 and nitrogen.82 The values of entropy S, the free energy function À(GÀH298)/T, and Gibbs free energy of formation DfG of PuN(s) are also given in Table The DfG of PuN is expressed with the following equation: Df GJmol1 ị ẳ 3:384 105 ỵ 152:0T À 0:03146T –200 À 5:998  10À6 T þ 6:844  106 =T : Hayes et al.46 : Matsui and Ohse76 –300 500 1000 1500 2000 2500 Temperature (K) Figure 21 Temperature dependences of the Gibbs free energy of formation, DfG for UN(s) Data from Hayes, S L.; Thomas, J K.; Peddicord, K L J Nucl Mater 1990, 171, 300–318; Matsui, T.; Ohse, R W High Temp High Press 1987, 19, 1–17 Table ð298 < T ðKÞ< 3000ị 3000 ẵ14 The temperature dependencies of the DfG for PuN are shown in Figure 22 The values of DfG are close to those derived from the precise vapor pressure measurements by Kent and Leary,68 with a difference of around kJ molÀ1 at 1000 K and kJ molÀ1 at 2000 K The standard thermodynamic functions of PuN T (K) Cp (J molÀ1 KÀ1) HÀH298 (J molÀ1) S (J molÀ1 KÀ1) À(GÀH298)/T (J molÀ1 KÀ1) DfG (J molÀ1) 298 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400 2500 3000 49.60 49.63 51.17 52.71 54.26 55.80 57.34 58.88 60.42 61.97 63.51 65.05 66.59 68.13 69.68 71.22 72.76 74.30 75.84 77.38 78.93 80.47 82.01 83.55 91.26 92 5132 10 326 15 674 21 177 26 834 32 645 38 610 44 729 51 003 57 430 64 012 70 749 77 639 84 685 91 884 99 237 106 744 114 405 122 221 130 191 138 314 146 593 190 296 64.81 65.12 79.61 91.19 100.94 109.42 116.97 123.81 130.09 135.92 141.38 146.53 151.40 156.05 160.50 164.76 168.88 172.85 176.70 180.44 184.08 187.62 191.08 194.46 210.37 64.81 64.81 66.78 70.54 74.81 79.16 83.43 87.54 91.48 95.26 98.88 102.35 105.68 108.88 111.97 114.95 117.83 120.63 123.33 125.96 128.52 131.02 133.45 135.82 146.94 À273 247 À273 073 À264 338 À254 777 À245 152 À235 469 À225 714 À215 918 À205 913 À195 883 À185 888 À175 923 À166 005 À156 135 À146 323 À136 571 À126 892 À117 270 À107 730 À98 274 À88 895 À79 594 À70 388 À61 269 À17 Source: Matsui, T.; Ohse, R W High Temp High Press 1987, 19, 1–17 Thermodynamic and Thermophysical Properties of the Actinide Nitrides 2.03.3.4.3 Uranium and plutonium mononitride Gibbs free energy of formation (kJ mol–1) The standard thermodynamic function data for (U0.8Pu0.2)N were determined using an ideal-solution model Matsui et al have estimated the entropy at 298 K (S298) for (U0.8Pu0.2)N to be 67.07 J molÀ1 KÀ1 –100 75 from S298 values for UN (62.43 J molÀ1 KÀ1) and PuN (64.81 J molÀ1 KÀ1) coupled with an entropy of mixing term, assuming an ideal solution The values of the thermal functions for (U0.8Pu0.2)N have been calculated by Matsui et al and are summarized in Table The enthalpy of formation for (U0.8Pu0.2)N was estimated to be À296.5 kJ molÀ1, on the basis of an ideal-solution model with DH298(UN) ¼ À295.8 kJ molÀ1 and DH298(PuN) ¼ À299.2 kJ molÀ1 The values of entropy S, free energy function À(GÀH298)/T, and Gibbs free energy of formation DfG of (U0.8Pu0.2)N(s) are also given in Table The equation of DG for (U0.8Pu0.2)N is given as Df Gð J molÀ1 Þ ẳ 2:909 105 ỵ 67:56T ỵ 0:007980T 200 À 1:098  10À6 T À 7:455  105 =T : Matsui and Ohse76 : Kent and Leary68 –300 500 1000 1500 2000 2500 3000 Temperature (K) Figure 22 Temperature dependences of the Gibbs free energy of formation, DfG for PuN(s) Data from Matsui, T.; Ohse, R W High Temp High Press 1987, 19, 1–17; Kent, R A.; Leary, J A High Temp Sci 1969, 1, 176–183 Table ½15Š ð298 < T ðKÞ < 3000Þ 2.03.3.4.4 Neptunium mononitride and americium mononitride Nakajima et al.70 have estimated the values of DfG for NpN(s) Figure 23 shows the temperature dependence of DfG, together with DfG for UN(s), as given The standard thermodynamic functions of (U0.8Pu0.2)N T (K) Cp (J molÀ1 KÀ1) HÀH298 (J molÀ1) S (J molÀ1 KÀ1) À(GÀH298)/T (J molÀ1 KÀ1) DfG (J molÀ1) 298 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400 2500 3000 48.18 48.26 51.46 53.57 55.24 56.71 58.07 59.37 60.63 61.87 63.12 64.35 65.57 66.79 68.01 69.22 70.43 71.64 72.85 74.05 75.26 76.46 77.66 78.87 84.87 96 5172 10 354 15 796 21 395 27 134 33 007 39 007 45 184 51 433 57 806 64 302 70 921 77 661 84 522 91 505 98 608 105 832 113 177 120 643 128 228 135 935 143 761 184 696 67.07 67.39 83.85 93.47 103.39 112.02 119.68 126.60 132.92 138.91 144.35 149.45 154.26 158.83 163.18 167.34 171.33 175.17 178.87 182.45 185.93 189.30 192.58 195.77 210.68 67.07 67.07 70.92 72.77 77.07 81.45 85.76 89.92 93.91 97.83 101.49 104.98 108.33 111.55 114.64 117.62 120.49 123.27 125.96 128.56 131.09 133.55 135.94 138.27 149.12 À272 623 À272 463 À264 527 À256 576 À248 723 À240 926 À233 156 À225 395 À217 422 À209 381 À201 030 À192 746 À184 520 À175 853 À167 164 À158 499 À149 859 À141 237 À132 654 À124 114 À115 614 À107 156 À98 723 À90 365 À45 975 Source: Matsui, T.; Ohse, R W High Temp High Press 1987, 19, 1–17 Thermodynamic and Thermophysical Properties of the Actinide Nitrides 30 –90 –100 : UN (Hayes et al.46) : PuN (Matsui and Ohse76) : NpN (Nakajima et al.70) 25 –110 –120 –130 –140 –150 1600 1700 1800 1900 Temperature (K) 2000 2100 Figure 23 Temperature dependences of the Gibbs free energy of formation, DfG for NpN(s) compared with those for UN(s) and PuN(s) Data from Hayes, S L.; Thomas, J K.; Peddicord, K L J Nucl Mater 1990, 171, 300–318; Matsui, T.; Ohse, R W High Temp High Press 1987, 19, 1–17; Nakajima, K.; Arai, Y.; Suzuki, Y J Nucl Mater 1997, 247, 33–36 Thermal conductivity (Wm–1 K–1) Gibbs free energy of formation (kJ mol–1) 76 UN (Arai et al.86) 20 NpN (Nishi et al.87) NpN (Arai et al.88) 15 PuN (Arai et al.86) 10 by Hayes et al.46 and the DfG for PuN(s), as given by Matsui and Ohse.76 The line for NpN(s) is that of the following equation and was determined by a leastsquares treatment of the data: Df G J mol1 ị ẳ 295 900 ỵ 89:88T 1690 < T Kị < 2030ị ½16Š Nakajima et al have evaluated these results in the temperature range of 1690–2030 K using the data of N2(g) pressure over NpN(s) ỵ Np(1) derived upon extrapolation of the experimental data given by Olson et al Then, Nakajima et al.85 have also carried out a mass-spectrometric study on NpN(s) co-loaded with PuN(s) in order to control the N2(g) pressure by the congruent vaporization of PuN(s) The DfG value calculated for NpN(s) almost completely agrees with that obtained from eqn [16] Ogawa et al.34 have estimated the Gibbs free energy of formation for AmN from the partial pressure of Am(g) over (Pu,Am)N Their values of DG for AmN(s) are given by the following equation: DG J mol1 ị ẳ 297659 ỵ 92:054T 298 < T Kị < 1600ị 2.03.3.5 ẵ17 Thermal Conductivity In order to determine the thermal conductivity, it is necessary to obtain the thermal diffusivity Thermal diffusivity is determined by the laser flash method AmN (Nishi et al.87) 500 1000 Temperature (K) 1500 Figure 24 Thermal conductivities of actinide mononitrides Data from Arai, Y.; Suzuki, Y.; Iwai, T.; Ohmichi, T J Nucl Mater 1992, 195, 37–43; Nishi, T.; Takano, M.; Itoh, A.; Akabori, M.; Arai, Y.; Minato, K In Proceedings of the Tenth OECD/NEA International Information Exchange Meeting on Actinide and Fission Product Partitioning and Transmutation, Thermal Conductivities of Neptunium and Americium Mononitrides, Mito, Japan, Oct 6–10, 2008; 2010, CD-ROM; Arai, Y.; Okamoto, Y.; Suzuki, Y J Nucl Mater 1994, 211, 248–250 The temperature dependence of the thermal conductivities of actinide mononitrides is shown in Figure 24 The thermal conductivity of UN was assessed by Arai et al.,86 that of NpN was assessed by Nishi et al.87 and Arai et al.,88 that of PuN was assessed by Arai et al.86 and that of AmN was assessed by Nishi et al.87 These are plotted here The thermal conductivities of the actinide mononitrides increased with an increase in temperature over the temperature range investigated The increase in thermal conductivities of the actinide mononitrides is probably due to the increase in the electronic component Figure 24 clearly shows that the thermal conductivity of the actinide mononitrides decreases with increase in the atomic number of actinide elements Although phonons and electrons both may contribute to the thermal conductivity of actinide mononitrides, the electronic contribution is probably predominant at higher temperatures The electrical resistivity of actinide mononitrides increases with an increase in the Thermodynamic and Thermophysical Properties of the Actinide Nitrides atomic number, so the tendency of the thermal conductivity to decrease with an increase in the atomic number would indicate a reduction in electronic contribution.89 The thermal conductivity values of NpN, as reported by Nishi and by Arai, agree well with each other below 1100 K, but there is some discrepancy between the two data sets at higher temperatures It should be noted that the thermal conductivity values of NpN have some uncertainty due to the inaccuracy of the heat capacity data Nishi has determined thermal conductivity values using experimental heat capacity values However, the thermal conductivity of NpN has a large range of error because the heat capacity of NpN at temperatures higher than 1067 K were calculated by simply extrapolating eqn [11] As a result, the data sets of Arai et al are taken here as the reference standard for the thermal conductivities of UN, NpN, and PuN The thermal conductivities of UN, NpN, and PuN corrected to 100% TD (theoretical density) are given by UN : l ¼ À17:75 þ 0:08808T À 6:161  10À5 T þ 1:447 108 T ẵ18 680 < T Kị < 1600ị NpN : l ẳ 7:89 ỵ 0:0127T 4:32 106 T 740 < T Kị< 1600ị ẵ19 PuN : l ẳ 8:18 ỵ 0:0522T 9:44 107 T 680 < T Kị< 1600ị ẵ20 The thermal conductivity of AmN, corrected to 100% TD, has been reported only by Nishi et al.87 The thermal conductivities of Am, corrected to 100% TD, in the temperature range from 473 to 1473 K can be expressed by l ¼ 8:99 ỵ 0:00147T 2:54 108 T 30 a 20 b c d UN 15 a : (U0.80Pu0.20)N PuN b : (U0.65Pu0.35)N c : (U0.40Pu0.60)N d : (U0.20Pu0.80)N Thermal conductivity (Wm–1 K–1) Thermal conductivity (Wm–1 K–1) 25 ½21Š The thermal conductivities of (U,Pu)N solid solutions have been reported by Arai et al.,86 Ganguly et al.,90 Alexander et al.,77 and Keller.91 The data of Arai et al for the (U,Pu)N solid solutions agrees with the data of the other investigations The data reported by Arai et al are plotted in Figure 25 The temperature dependence of thermal conductivity for (U,Pu)N solid solutions is similar to the other mononitrides; but thermal conductivity decreases rapidly with the addition of PuN This means that a simple averaging method cannot be applied for the evaluation of the thermal conductivity of the solid solutions of actinide mononitrides The thermal conductivities of (U,Np)N and (Np,Pu)N solid solutions have been reported by Arai et al.89 and those of (Np,Am)N and (Pu,Am)N solid solutions have been reported by Nishi et al.80 Data on (U,Np)N and (Np,Pu)N solid solutions are plotted in Figure 26 and the data on (Np,Am)N and (Pu,Am)N solid solutions are plotted in Figure 27 The behavior of (U,Np)N, (Np,Pu)N, (Np,Am)N, and (Pu,Am)N solid solutions was found to be similar to that of (U,Pu)N The composition dependence of the thermal conductivities for (U,Pu)N, (U,Np)N, (Np,Pu)N, (Np,Am) N, and (Pu,Am)N solid solutions at 773 and 1073 K are shown in Figure 28 It can be seen from these graphs that the thermal conductivities of (U,Pu)N and 30 10 77 25 a b 20 15 10 800 1000 1200 1400 1600 Temperature (K) Figure 25 Thermal conductivity of (U,Pu)N solid solutions Reproduced from Arai, Y.; Suzuki, Y.; Iwai, T.; Ohmichi, T J Nucl Mater 1992, 195, 37–43 d e NpN PuN a : (U0.75Np0.25)N b : (U0.50Np0.50)N c : (U0.25Np0.75)N 600 c UN 600 800 1000 d : (Np0.67Pu0.33)N e : (Np0.33Pu0.67)N 1200 1400 1600 Temperature (K) Figure 26 Thermal conductivity of (U,Np)N and (Np,Pu)N solid solutions Reproduced from Arai, Y.; Nakajima, K.; Suzuki, Y J Alloys Compd 1998, 271–273, 602–605 78 Thermodynamic and Thermophysical Properties of the Actinide Nitrides 20 (Np,Am)N 15 NpN a 10 AmN b c a : (Np0.75Am0.25)N b : (Np0.50Am0.50)N c : (Np0.25Am0.75)N Thermal conductivity (Wm–1K–1) Thermal conductivity (Wm–1 K–1) 20 (Pu,Am)N 15 10 500 1000 Temperature (K) a AmN b PuN a : (Pu0.75Am0.25)N b : (Pu0.50Am0.50)N 500 1000 Temperature (K) Figure 27 Thermal conductivities of (Np,Am)N and (Pu,Am)N solid solutions Reproduced from Nishi, T.; Takano, M.; Itoh, A.; et al IOP Conf Ser Mater Sci Eng 2010, 9, 012017 25 At 773 K 20 15 10 : (U,Pu)N : (U,Np)N : (Np,Pu)N : (Np,Am)N : (Pu,Am)N 0.4 0.6 0.8 1.0 0.0 0.2 Compositions of solid solutions UN NpN PuN NpN PuN AmN Thermal conductivity (Wm–1 K–1) Thermal conductivity (Wm–1 K–1) 25 At 1073 K 20 15 10 : (U,Pu)N : (U,Np)N : (Np,Pu)N : (Np,Am)N : (Pu,Am)N 0.4 0.6 0.8 1.0 0.0 0.2 Compositions of solid solutions UN NpN PuN NpN PuN AmN Figure 28 Composition dependence of the thermal conductivities of (U,Pu)N, (U,Np)N, (Np,Pu)N, (Np,Am)N, and (Pu,Am)N solid solutions at 773 and 1073 K Reproduced from Nishi, T.; Takano, M.; Itoh, A.; et al IOP Conf Ser Mater Sci Eng 2010, 9, 012017 (Np,Pu)N decrease with an increase in the Pu content; that of (U,Np)N decreases with an increase in Np content, and those of (Np,Am)N and (Pu,Am)N decrease with an increase in Am content It has been proposed that the thermal conductivities of the actinide mononitrides decrease with an increase in the atomic number of the actinide element because the electrical resistivities of the actinide mononitrides have a tendency to increase with an increase in the atomic number.89 Thus, the decrease in thermal conductivity with an increase in Pu or Np or Am content may correspond to the lowering of the electronic contribution These data suggest that the thermal conductivities of the binary actinide nitride solid solutions are lower than those derived from the arithmetic mean of their constituent nitrides In addition, the thermal conductivities of (Np0.33Pu0.67)N, (Np0.25Am0.75)N, and (Pu0.50Am0.50)N, at 773 and 1073 K, were smaller than those of PuN or AmN, especially at lower temperature Although the mechanism for this degradation in the thermal conductivity of the solid solutions has not yet been clarified, it might be caused by phonon scattering between Np and Pu, and Np or Pu and Am atoms, as this tendency was prominent at the lower temperature Porosity correction is necessary to estimate the thermal conductivity with 100% TD (lTD) for the present handbook from the measured values (l), with lTD being needed to compare the thermal conductivity of the actinide mononitrides Arai et al have Thermodynamic and Thermophysical Properties of the Actinide Nitrides made this correction using the Maxwell–Eucken equation: lTD ẳ ỵ bPị l Pị ½22Š where P is porosity and the constant b is related to the characteristics of pores in the matrix Unity is a popular value of b, and is used in the case where samples are fabricated by a conventional powdermetallurgical route However, it should be noted that b might be about when samples have large and closed pores, especially when they are prepared by using pore formers, as pointed out by Arai et al.86 On the other hand, Nishi et al.80,87,92 have made a porosity correction using the Schulz equation: l ẳ lTD PịX given the above interaction The swelling behavior is also important and is described in another chapter Thermal expansion is discussed in this chapter 2.03.4.1 2.03.4 Mechanical Properties During irradiation in reactors, the fuel pellets are deformed by various processes, including densification, thermal expansion, swelling by fission products, and creep This deformation may eventually lead to an interaction with the cladding, which has resulted in reactor failure The elastic and plastic properties of fuel pellets, as well as creep rate, are very important, Mechanical Properties of UN The mechanical properties of UN have been summarized by Hayes et al.94 A summary of the different measurements of creep rate is plotted in Figure 29 As the creep rate depends on many parameters such as stress level, stoichiometry, density, and impurity, as well as temperature, there is no systematic trend at each specific temperature High temperature, steady state creep is generally expressed by the following equation,94 ½23Š They have proposed a parameter X ¼ 1.5 for closed pores that are spherical in shape Among a variety of porosity correction formulas, eqn [23] was in the best agreement with the results of finite element computations in a wide range of porosities up to 0.3, as reported by Bakker et al.93 79 e_ ¼ Ad Àm sn expfÀQ =RT g ½24Š where e_ is creep rate, A is a constant, d is grain size, s is stress, m is the grain size exponent, n is the stress exponent, Q is the activation energy, R is the gas constant, and T is the temperature n and m are involved in the creep mechanism, and the value of n is especially important in determining the mechanism that controls the creep Hayes et al have tried to estimate the n values using several creep data sets reported in individual studies, and they have found that almost all n values were in the range of 4.0–5.9, suggesting a dislocation climb mechanism in UN Assuming a dislocation climb mechanism, where creep rate does not depend on grain size, with an average n value of 4.5, and an m value of zero, the following correlation94 is suggested; e_ ¼ 2:054  10À3 s4:5 expfÀ39369:5=T g ½25Š 10–3 Creep rate (s–1) 10–4 Fassler et al.102 Vandervoort et al.103 Uchida and Ichikawa104 10–5 10–6 10–7 10–8 1300 1400 1500 1600 1700 1800 1900 2000 2100 Temperature (K) Figure 29 Experimental data for steady sate creep rate of UN Reproduced from Hayes, S L.; Thomas, J K.; Peddicord, K L J Nucl Mater 1990, 171, 271–288, with permission from Elsevier 80 Thermodynamic and Thermophysical Properties of the Actinide Nitrides 3.0E + This work Honda and Kikuchi105 Padel and deNovian96 Whaley et al.107 Young’s modulus (MPa) 2.5E + 2.0E + Padel and deNovian96 Honda and Kikuchi105 Guinan and Cline106 Whaley et al.107 Speidel and Keller 108 Taylor and McMurtry109 Samsonov and Vinitskii110 Hall111 1.5E + 1.0E + 5.0E + 0.00 0.05 0.10 0.15 Porosity 0.20 0.25 0.30 Figure 30 Measured Young’s modulus and fitting curves for UN Reproduced from Hayes, S L.; Thomas, J K.; Peddicord, K L J Nucl Mater 1990, 171, 271–288, with permission from Elsevier This equation is valid only for the creep of theoretically dense UN in the temperature range of 1770– 2083 K and under stress ranging from 20 to 34 MPa It has been reported that if the density of UN is below the TD, the creep rate can be obtained by multiplying it with the following factor,95 f pị ẳ 0:987 expf8:65pg pị27:6 ½26Š where p is the porosity Various measurements of Young’s modulus at room temperature are summarized in Figure 30 Young’s modulus depends not only on temperature but also on porosity The variation in Young’s modulus, as a function of porosity, has been measured by two different methods, velocity measurement and frequency measurement; but no clear difference between the results of these two methods has been found A power law relation was fitted to these experimental data at room temperature and was combined with the linear temperature dependence data reported by Padel and deNovion96 and the following correlation was obtained94: E ¼ 0:258D 3:002 À5 ½1 À 2:375  10 T Š ½27Š where E is the Young’s modulus and D is the ratio of density with TD in percent This equation is valid where the ratio of TD is from 75% to 100% and the temperature ranges from 298 to 1473 K As this equation fits well with all the experimental data obtained from samples with uncontrolled pore shape and orientation, porosity distribution, average grain size, grain shape, orientation, and impurities, as shown in Figure 30, the dependence of Young’s modulus on these parameters is small The following correlation94 of the shear modulus with density and temperature was obtained by a method similar to that used for determining the Young’s modulus: G ẳ 1:44 102 D3:446 ẵ1 2:375  10À5 T Š ½28Š where G is the shear modulus This relation is valid under the same density and temperature conditions as the Young’s modulus As the data for the bulk modulus could not be measured directly and was calculated from measurements of Young’s and shear modulus in the various studies, the degree of data scatter is larger here, compared to the other properties The following correlation94 with density and temperature was obtained in a method similar to that used for Young’s modulus and shear modulus: K ¼ 1:33  10À3 D4:074 ½1 À 2:375  10À5 T Š ½29Š where K is the bulk modulus Poisson’s ratio for UN was assumed to be independent of temperature Similar to the bulk modulus, Poisson’s ratio can be estimated from measurements of Young’s modulus and shear modulus, and small errors in measurements of Young’s and shear Thermodynamic and Thermophysical Properties of the Actinide Nitrides 81 Lattice parameter (Å) 5.05 5.00 Benz et al.112 Kempter and Elliott113 This work Kempter and Elliott113 4.95 4.90 4.85 200 700 1200 1700 Temperature (K) 2200 2700 Figure 31 Variation of lattice parameter of UN with temperature Reproduced from Hayes, S L.; Thomas, J K.; Peddicord, K L J Nucl Mater 1990, 171, 262–270, with permission from Elsevier modulus have resulted in the large scatter of these calculations Under the assumption that Poisson’s ratio is independent of temperature, the following correlation94 with porosity is obtained: n ¼ 1:26  10À3 D1:174 ½30Š where n is Poisson’s ratio and D is the density ranging 70–100% The hardness values, which are easily obtained experimentally, decreased with porosity and temperature The hardness decrease with porosity linearly and decrease with temperature exponentially In the porosity range of 0–0.26 and the temperature range of 298–1673 K, the following correlation94 is valid: HD ẳ 951:8f1 2:1pgexpf1:882 103 T g ẵ31 where HD is the diamond point hardness 2.03.4.2 Thermal Expansion of UN The thermal expansion of UN has also been estimated by Hayes et al.56, as shown in Figure 31 As thermal expansion, measured by the dilatometer method, is affected by sample density and has a large degree of uncertainty, thermal expansion was calculated from the temperature dependence of the lattice parameter The lattice parameter also is influenced by impurities, but the variation due to impurities is much less than the variation with temperature The temperature dependence of lattice parameter56 is given by: a ẳ 4:879 ỵ 3:254 105 T ỵ 6:889 109 T ẵ32 where a is the lattice parameter in Angstroms The linear thermal expansion coefficient56 is given by: a ẳ 7:096 106 ỵ 1:409  10À9 T ½33Š where a is the mean linear thermal expansion coefficient and T is temperature 2.03.4.3 Mechanical Properties of PuN There are very few studies on the mechanical properties of pure PuN Matzke1 has reported the elastic moduli of (U0.8Pu0.2)N at room temperature, the porosity dependence of its Young’s modulus, its Poisson ratio, and the temperature dependence of its elastic moduli The Young’s modulus of (U0.8Pu0.2)N is about 5% higher than that of pure UN According to Matzke, the room temperature hardness of pure PuN is 3.3 GPa, about half that of UN Thermal expansion of PuN has been recently reexamined by Takano et al.22 The temperature dependence of the lattice parameter of PuN aT (nm) can be expressed as aT ẳ 0:48913 ỵ 4:501 106 T ỵ 6:817 1010 T 4:939 10À14 ½34Š The linear thermal expansion of PuN is higher than that of UN, as shown in Figure 32.22 The recent progress in material chemistry calculation techniques has enabled the prediction of those properties of the actinide compounds which have not been experimentally measured Figure 33 shows the temperature dependence of the linear 82 Thermodynamic and Thermophysical Properties of the Actinide Nitrides 1.4 1.4 UN Takano et al.22 NpN PuN AmN 1.2 1.2 1.0 LTE (%) LTE (%) (Pu0.59Am0.41)N (Np0.21Pu0.52Am0.22Cm0.05)N (Pu0.21Am0.18Zr0.61)N ZrN 1.0 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0.0 200 400 600 800 1000 1200 1400 1600 T (K) Figure 32 Temperature dependence of linear thermal expansion of PuN Reproduced from Takano, M.; Akabori, M.; Arai, Y.; Minato, K J Nucl Mater 2008, 376, 114–118, with permission from Elsevier 18 0.0 200 400 600 800 1000 1200 1400 1600 T (K) Figure 34 Temperature dependence of linear thermal expansion of minor actinide containing nitride fuels Reproduced from Takano, M.; Akabori, M.; Arai, Y.; Minato, K J Nucl Mater 2009, 389, 89–92, with permission from Elsevier by doping with Pu This calculation study also reported the compressibility and other thermal and thermodynamic properties of PuN 16 Linear thermal expansion coefficient, alin, (10–6 K–1) (Np0.55Am0.45)N 14 2.03.4.4 Mechanical Properties of Other MA or MA-Containing Fuels 12 10 500 1000 1500 2000 2500 3000 3500 Temperature, T (K) UN (MD) Kurosaki et al.97 PuN (MD) Kurosaki et al.99 (U0.8Pu0.2)N (MD) Figure 33 Temperature dependence of calculated linear thermal expansion of PuN Reproduced from Kurosaki, K.; Yano, K.; Yamada, K.; Uno, M.; Yamanaka, S J Alloys Compd 2001, 319, 253–257, with permission from Elsevier thermal expansion of PuN which was calculated by a molecular dynamic method.97 It is seen that the calculation predicts a high thermal expansion of PuN and an increase in the thermal expansion of (U,Pu)N Recent studies on MA-containing fuels have measured the thermal expansion of various Np–Pu– Am–Cm–N compounds (shown in Figure 3498), as well as those of NpN and AmN (Figure 32) As shown in Figure 32, the thermal expansion of AmN is the same as that of PuN; however, the thermal expansion of NpN is smaller than PuN and AmN, but is the same as that of UN The thermal expansion of Np–Pu–Am–Cm–N fuels decreases with a decrease in Np content, as shown in Figure 34 The thermal expansion of ZrN inert matrix fuels also decreases due to the low thermal expansion of ZrN Molecular dynamics (MD) calculations have also predicted the thermal expansion of some MA nitrides; these are shown in Figure 35.99 The lack of data on MA nitrides, especially the nitrides of pure transuranium elements, is due to the difficulty in obtaining and treating bulk samples There have been some attempts to calculate the Thermodynamic and Thermophysical Properties of the Actinide Nitrides Linear thermal expansion coefficient , a lin (10–6 K–1) 20.0 20.0 20.0 MD result MD result Ref [56] Ref [108] Ref [114] 17.5 17.5 15.0 20.0 MD result Ref [57] MD result Ref [65] 17.5 17.5 15.0 15.0 15.0 12.5 12.5 12.5 12.5 10.0 10.0 10.0 10.0 7.5 7.5 7.5 7.5 ThN UN 5.0 5.0 1000 2000 3000 Temperature T (K) NpN 5.0 1000 2000 3000 Temperature T (K) 83 PuN 5.0 1000 2000 3000 Temperature T (K) 1000 2000 3000 Temperature T (K) Figure 35 Temperature dependence of calculated linear thermal expansion of minor actinide nitrides Reproduced from Kurosaki, K.; Adachi, J.; Uno, M.; Yamanaka, S J Nucl Mater 2005, 344, 45–49, with permission from Elsevier mechanical properties of these actinide nitride samples One such attempt combined the calculations for longitudinal velocity and porosity.100 In the method employed, a newly proposed correlation between Poisson’s ratio and the ultrasonic longitudinal velocity was utilized, and the elastic properties of uranium nitride as well as uranium dioxide were estimated from the porosity and longitudinal velocity derived from ultrasonic sound velocity measurements; these had been previously used to determine mechanical properties of actinide materials Another method estimated fracture toughness from the Young’s modulus, hardness, the diagonal length and the length of micro cracks Except for Young’s modulus, all the other properties were obtained by an indentation method.101 In this study, not only was the fracture toughness reported, but its load dependence, in the case of UN, was also reported these are difficult to obtain and handle and are scarce Some properties of the inert matrix fuels such as (An,Zr)N solid solution and AnN and TiN mixture have been obtained through recent studies on the targets for transmutation in an ADS Recent progress in experimental procedures and estimation methods, which are supported by developments in model calculation, have also been discussed The progress made in experimental techniques and calculation science has brought about growth in the understanding of the behavior of these nitrides However, we need to accumulate more data, especially in the thermal and mechanical properties around 1673 K, in-reactor temperature, and the variation of those with burnup, in order to accurately predict the in-reactor behavior of these fuels (see Chapter 3.02, Nitride Fuel) 2.03.5 Summary References In this chapter, various properties of actinide nitrides have been discussed As nitride fuels have some advantages over the oxide fuels, thermal and thermodynamic properties of UN, PuN and their solid solutions have been thoroughly studied On the other hand, some properties (especially physical) need bulk samples for measurements, especially the transuranium elements such as NpN, AmN, and CmN; Matzke, H J Science of Advanced LMFBR Fuels; North Holland: Amsterdam, 1986 Levinskii, Yu V Atom Energ 1974, 37(1), 216–219; Sov Atom Energ (Engl Transl.) 1974, 37(1), 929–932 Bugl, J.; Bauer, A A J Am Ceram Soc 1964, 47(9), 425–429 Inouye, H.; Leitnaker, J M J Am Ceram Soc 1968, 51(1), 6–9 Gingerich, K A J Chem Phys 1969, 51(10), 4433–4439 84 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 Thermodynamic and Thermophysical Properties of the Actinide Nitrides Olson, W M.; Mulford, R N R J Phys Chem 1963, 67(4), 952–954 Tagawa, H J Nucl Mater 1971, 41(3), 313–319 Chevalier, P Y.; Fischer, E.; Cheynet, B J Nucl Mater 2000, 280, 136–150 Hansen, M.; Anderko, K Constitution of Binary Alloys; McGraw-Hill: New York, 1958 Elliott, R P Constitution of Binary Alloys, First Supplement; McGraw-Hill: New York, 1965 Shunk, F A Constitution of Binary Alloys, Second Supplement; McGraw-Hill: New York, 1969 Storms, E K Special Report to the Phase Equilibria Program; American Ceramic Society: Westerville, OH, 1989 Muromura, T.; Tagawa, H J Nucl Mater 1979, 79, 264 Benz, R.; Bowman, M G J Am Chem Soc 1966, 88(2), 264 Wriedt, H A Bull Alloys Phase Diagrams 1989, 10, 593 Kleykamp, H J Nucl Mater 1999, 275, 1–11 Joseph, M.; Sivakumar, N.; Manoravi, P Annu Nucl Energ 2004, 31, 1163–1175 Benz, R.; Hoffman, C G.; Rupert, G N J Am Chem Soc 1967, 89, 191–197 Benz, R.; Zachariasen, W H Acta Crystallogr 1969, 21, 838 Uno, M.; Katsura, M.; Miyake, M J Alloys Compd 1986, 121, 615–619 Uno, M.; Katsura, M.; Miyake, M Inorg Chim Acta 1987, 140, 123–126 Takano, M.; Akabori, M.; Arai, Y.; Minato, K J Nucl Mater 2008, 376, 114–118 Takano, M.; et al Synthesis of americium mononitride by carbothermic reduction method In: Proceedings Global ’99, Jackson Hole, WY, Aug 29–Sept 3, 1999; CD-ROM, 1999 Minato, K.; et al J Nucl Mater 2003, 320, 18–24 Olson, W M.; Mulford, R N R J Phys Chem 1966, 70, 2932–2934 Suzuki, Y.; Arai, Y J Alloys Compd 1998, 271–273, 577–582 Potter, P E J Nucl Mater 1973, 47, Williams, J.; Sambell, R A J Less Common Met 1959, 1, 217–226 Katsura, M.; Naoumidis, A.; Nickel, H J Nucl Mater 1970, 36, 169–179 Bradbury, M H.; Matzke, H J Nucl Mater 1980, 91, 13–22 Ogawa, T.; Shirasu, Y.; Minato, K.; Serizawa, H J Nucl Mater 1997, 247, 151–157 Sood, D.; Argarwal, R.; Venugopal, V J Nucl Mater 1997, 247, 293–300 Walker, C T Nucl Technol 1978, 39, 289–296 Ogawa, T.; Ohmichi, T.; Maeda, A.; Arai, Y.; Suzuki, Y J Alloys Compd 1995, 224, 55–59 Itoh, A.; Akaboti, M.; Takano, M.; Ogawa, T.; Numata, M.; Itonaga, F J Nucl Sci Technol 2002, (Suppl 3), 737–740 Ciriello, A.; et al J Alloys Compd 2009, 473, 265–271 Thetford, R.; Mignaneli, M J Nucl Mater 2003, 320, 44–53 Jolkkonen, M.; Streit, M.; Wallenium, J J Nucl Sci Technol 2004, 41, 457–465 Benedict, U The solubility of solid fission products in carbides and nitrides of uranium and plutonium, part II: Solubility rules based on lattice parameter differences, EUR 5766EN; 1977 Arai, Y.; Nakajima, K J Nucl Mater 2000, 281, 244–247 Olson, W M.; Mulford, R N R J Phys Chem 1965, 69, 1223–1226 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 Olson, W M.; Mulford, R N R J Phys Chem 1964, 68, 1048–1051 Eron’yan, M A.; Avarbe, R G.; et al Izv Akad Nauk Sssr Neorg Mater 1976, 12, 247–249 Ikeda, Y.; Tamaki, M.; Matsumoto, G J Nucl Mater 1976, 59, 103–111 Prins, G.; Cordfunke, E H P.; Depaus, R J Nucl Mater 1980, 89, 221–228 Hayes, S L.; Thomas, J K.; Peddicor, K L J Nucl Mater 1990, 171, 300–318 Alexander, C A.; Ogden, J S.; et al Trans Am Nucl Soc 1969, 12, 581 Vozzella, P A.; DeCrescente, M A Thermodynamic Properties of Utanium Mononitride, Pratt and Whitney Aircraft Co., PWAC-479; 1965 Bugle, J.; Bauer, A A J Am Ceram Soc 1964, 47, 425–429 Eron’yan, M A.; Avarbe, R G.; et al Teplofizika Vysokikh Temp 1976, 14, 398–399 Touloukian, Y S et al., Eds Thermophysical Properties of Matter; IFI/Plenum: New York, 1977; Vol 13 Houska, C R J Phys Chem Solids 1964, 25, 359–366 Smirnov, V S.; Kosukhin, V V.; et al Izv Akad Nauk Sssr Neorg Mater 1991, 27, 2565–2569 Timofeeva, I I.; Shvedova, L K.; et al Izv Akad Nauk Sssr Neorg Mater 1972, 8, 1169–1170 Brundiers, G D Herstellung, Aufbau und Eigenschaften von Hafnium-verbindungen im System Hf-C-N-O, KFK 2161; 1975 Hayes, S L.; Thomas, J K.; Peddicord, K L J Nucl Mater 1990, 171, 262–270 Aldred, A T.; Dunlap, B D.; Harvey, A R.; Lander, D J G H.; Muller, M H Phys Rev B 1974, 9, 3766–3779 Benedict, U.; Dufour, C.; et al J Nucl Mater 1978, 73, 208–212 Kruger, O L.; Moser, S B USAEC Report ANL-7155: 105; 1965 Venugopal, V.; Kulkarni, S G.; Subbanna, C S.; Sood, D D J Nucl Mater 1992, 186, 259–268 Suzuki, Y.; Maeda, A.; Arai, Y.; Ohmichi, T J Nucl Mater 1992, 188, 239–243 Alexander, C A.; Ogden, J S.; Pardue, W H J Nucl Mater 1969, 31, 13–24 Ackermann, R J.; Rauh, E G J Phys Chem 1969, 73, 769–778 Green, D W.; Reedy, G T J Chem Phys 1978, 69, 552–555 Alexander, C A.; Clark, R B.; Kruger, O L.; Robins, J L Plutonium and Other Actinide 1975; North-Holland: Amsterdam, 1976; p 277 Pardue, W M.; Storhok, V W.; Smith, R A Plutonium 1965; Chapman and Hall: London, 1967; p 721 Campbell, G M.; Leary, J A J Phys Chem 1966, 70, 2703–2707 Kent, R A.; Leary, J A High Temp Sci 1969, 1, 176–183 Sheth, A.; Leibowitz, L ANL-AFP-2, Argonne National Laboratory; Chemical Engineering Division: Argonne, WI, 1975 Nakajima, K.; Arai, Y.; Suzuki, Y J Nucl Mater 1997, 247, 33–36 Ackermann, R J.; Rauh, E G J Chem Thermodyn 1975, 7, 211–218 Takano, M.; Itoh, A.; Akabori, M.; Minato, K.; Numata, M In Proceedings of GLOBAL 2003, Study on the Stability of AmN and (Am,Zr)N, New Orleans, LA, Nov 16–20, 2003; p 2285, CD-ROM Thermodynamic and Thermophysical Properties of the Actinide Nitrides 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 Conway, J B.; Flagella, P N GEMP-1012; 1969 Blank, H In Materials Science and Technology; Nuclear Materials; VCH: Weinheim, 1994; Vol 10A, p 203 Oetting, F L J Chem Thermodyn 1978, 10, 941–948 Matsui, T.; Ohse, R W High Temp High Press 1987, 19, 1–17 Alexander, C A.; Ogden, J S.; Pardue, W M Thermophysical properties of (UPu)N In Plutonium 1970 and Other Actinides PT.1; 1970, 17, 95–103 Kandan, R.; Babu, R.; Nagarajan, K.; Vasudeva Rao, P R Thermochim Acta 2007, 460, 41–43 Nishi, T.; Itoh, A.; Takano, M.; et al J Nucl Mater 2008, 377, 467–469 Nishi, T.; Takano, M.; Itoh, A.; et al IOP Conf Ser Mater Sci Eng 2010, 9, 012017 Cordfunke, E H P.; Konings, R J M.; Potter, P E.; Prins, G.; Rand, M H Thermochemical Data for Reactor Materials and Fission Products; Elsevier: Amsterdam, 1990; p 667 Chase, M W.; Curnutt, J L.; Prophet, H JANAF Thermochemical Tables; Dow Chemical Co.: Midland, MA, 1965 Johnson, G K.; VanDeventer, E H.; Kruger, O L.; Hubbard, W H J Chem Thermodyn 1969, 1, 89–98 Oetting, F L.; Rand, M H.; Ackermann, R J The Chemical Thermodynamics of Actinide Elements and Compounds, Part 1: The Actinide Elements; IAEA: Vienna, 1976; p 87 Nakajima, K.; Arai, Y.; Suzuki, Y J Nucl Mater 1999, 275, 332–335 Arai, Y.; Suzuki, Y.; Iwai, T.; Ohmichi, T J Nucl Mater 1992, 195, 37–43 Nishi, T.; Takano, M.; Itoh, A.; Akabori, M.; Arai, Y.; Minato, K In Proceedings of the Tenth OECD/NEA International Information Exchange Meeting on Actinide and Fission Product Partitioning and Transmutation, Thermal Conductivities of Neptunium and Americium Mononitrides, Mito, Japan, Oct 6–10, 2008; 2010, CD-ROM Arai, Y.; Okamoto, Y.; Suzuki, Y J Nucl Mater 1994, 211, 248–250 Arai, Y.; Nakajima, K.; Suzuki, Y J Alloys Compd 1998, 271–273, 602–605 Ganguly, C.; Hegde, P V.; Sengupta, A K J Nucl Mater 1991, 178, 234–241 Keller, D L BMI-1845; 1968 Nishi, T.; Takano, M.; Itoh, A.; Akabori, M.; Minato, K.; Kizaki, M J Nucl Mater 2006, 355, 114–118 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 85 Bakker, K.; Kwast, H.; Cordfunke, E H P J Nucl Mater 1995, 223, 135–142 Hayes, S L.; Thomas, J K.; Peddicord, K L J Nucl Mater 1990, 171, 271–288 Hayes, S L.; Thomas, J K.; Peddicord, K L Development of creep rate porosity correction factor; Advanced Nuclear Fuel Laboratory; Department of Nuclear Engineering, Texas A&M University, ANFL-10-O; 1989 Padel, A.; deNovion, Ch J Nucl Mater 1969, 33, 40–51 Kurosaki, K.; Yano, K.; Yamada, K.; Uno, M.; Yamanaka, S J Alloys Compd 2001, 319, 253–257 Takano, M.; Akabori, M.; Arai, Y.; Minato, K J Nucl Mater 2009, 389, 89–92 Kurosaki, K.; Adachi, J.; Uno, M.; Yamanaka, S J Nucl Mater 2005, 344, 45–49 Phani, K K.; Sanyal, D.; Sengupta, A K J Nucl Mater 2007, 366, 129–136 Adachi, J.; et al J Nucl Mater 2009, 384, 6–11 Fassler, M H.; Hugel, F J.; Decrescente, M A Compressive Creep of UC and UN, PWAC-482, Pratt and Whitney Aircraft Co., 1965 Vandervoort, R R.; Barmore, W L.; Cline, C F Trans Met Soc AIME 1968, 242, 1466 Uchida, M.; Ichikawa, M J Nucl Mater 1973, 49, 91 Honda, T.; Kikuchi, T J Nucl Sci Technol 1968, 6, 59 Guinan, M.; Cline, C F J Nucl Mater 1971, 43, 205 Whaley, H L.; Potter, R A.; Fulkerson, W Ultrasonic Velocity Measurements in UN, ORNL-4370, Oak Ridge National Laboratory, 1968 Speidel, E O.; Keller, D L Fabrication and Properties of Hot-Pressed Uranium Mononitride, BMI-1633, Battelle Memorial Institute, 1963 Taylor, K M.; McMurtry, C H Synthesis and Fabrication of Refractory Uranium Compounds, ORO-400, Carborundum Co., 1961 Samsnov, G V.; Vinitskii, I M Handbook of Refractory Compounds; IFI/Plenum DATA Co.: New York, 1980; p 303 Hall, A R J Nucl Mater 1970, 37 Benz, R.; Balog, G.; Baca, B H High Temp Sci 1970, 15, 221 Kempter, C P.; Elliot, R O J Chem Phys 1959, 30, 1524 Aronson, S.; Cisney, E.; Guingerich, K A J Am Ceram Soc 1967, 50(5), 248 Gerds, A F.; Mallet, M W J Electrochem Soc 1954, 101, 175  ... 89. 92 93.91 97.83 101.49 104.98 108.33 111.55 114.64 117. 62 120 .49 123 .27 125 .96 128 .56 131.09 133.55 135.94 138 .27 149. 12 27 2 623 27 2 463 26 4 527 25 6 576 24 8 723 24 0 926 23 3 156 22 5 395... 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 Thermodynamic and Thermophysical Properties of the Actinide Nitrides Olson, W M.; Mulford, R N R J Phys Chem 1963, 67(4), 9 52 954... 183. 12 186 .24 189 .28 1 92. 23 193.04 62. 68 62. 68 64. 62 68.37 72. 67 77.06 81.37 85.53 89.51 93.31 96.94 100.41 103. 71 106.87 109.87 1 12. 72 115.41 117.93 120 .28 122 .43 124 .39 126 .14 127 .67 128 .98