DOI QR코드

DOI QR Code

The mechanical and thermodynamic properties of α-Na3(U0.84(2),Na0.16(2))O4: A combined first-principles calculations and quasi-harmonic Debye model study

  • Chen, Haichuan (Key Laboratory of Fluid and Power Machinery, Ministry of Education)
  • Received : 2020.05.25
  • Accepted : 2020.07.21
  • Published : 2021.02.25

Abstract

The mechanical properties of α-Na3(U0.84(2),Na0.16(2))O4 have been researched using the first-principles calculations combined with the quasi-harmonic Debye model. The obtained lattice parameters agree well with the published experimental data. The results of elastic constants indicate that α-Na3(U0.84(2),Na0.16(2))O4 is mechanically stable. The polycrystalline moduli are predicted. The results show that the α-Na3(U0.84(2),Na0.16(2))O4 exhibits brittleness and possesses obvious elastic anisotropy. The hardness shows that it can be considered a "soft material". Furthermore, the Debye temperature θD and the minimum thermal conductivity kmin are also discussed, respectively. Finally, the thermal expansion coefficient α, isobaric heat capacity CP and isochoric heat capacity CV are evaluated through the quasi-harmonic Debye model.

Keywords

References

  1. K. Aoto, P. Dufour, H.Y. Yang, J.P. Glatz, Y. Kim, Y. Ashurko, R. Hill, N. Uto, A summary of sodium-cooled fast reactor development, Prog. Nucl. Energy 77 (2014) 247-265. https://doi.org/10.1016/j.pnucene.2014.05.008
  2. H. Ohshima, S. Kubo, Sodium-cooled fast reactor, in: Igor L. Pioro (Ed.), Handbook of Generation IV Nuclear Reactors, Woodhead Publishing, Elsevier, Duxford, UK, 2016, pp. 98-118.
  3. G.L. Hofman, J.H. Bottcher, J.A. Buzzell, G.M. Schwartzenberger, Thermal conductivity and thermal expansion of hot-pressed trisodium uranate (Na3UO4), J. Nucl. Mater. 139 (1986) 151-155. https://doi.org/10.1016/0022-3115(86)90032-2
  4. M.G. Adamson, M.A. Mignanelli, P.E. Potter, M.H. Rand, On the oxygen thresholds for the reactions of liquid sodium with urania and urania-plutonia solid solutions, J. Nucl. Mater. 97 (1981) 203-212. https://doi.org/10.1016/0022-3115(81)90434-7
  5. M.A. Mignanelli, P.E. Potter, An investigation of the reaction between sodium and hyperstoichiometric urania, J. Nucl. Mater. 114 (1983) 168-180. https://doi.org/10.1016/0022-3115(83)90254-4
  6. M.A. Mignanelli, P.E. Potter, The reactions of sodium with urania, plutonia and their solid solutions, J. Nucl. Mater. 130 (1985) 289-297. https://doi.org/10.1016/0022-3115(85)90318-6
  7. R. Scholder, H. Glaser, uber Lithium- und Natriumuranate(V) und uber strukturelle Beziehungen zwischen den Verbindungstypen Li7AO6 und Li8AO6, Z. Anorg. Allg. Chem. 327 (1964) 15-27. https://doi.org/10.1002/zaac.19643270104
  8. J.P. Marcon, O. Pesme, M. France, Rev. Int. Hautes Temp. Refract. 9 (1972) 193-196.
  9. S.F. Bartram, R.E. Fryxell, Preparation and crystal structure of NaUO3 and Na11U5O16, J. Inorg. Nucl. Chem. 32 (1970) 3701-3706. https://doi.org/10.1016/0022-1902(70)80187-7
  10. R. Lorenzelli, T. Athanassiadis, R. Pascard, Chemical reactions between sodium and (U,Pu)O2 mixed oxides, J. Nucl. Mater. 130 (1985) 298-315. https://doi.org/10.1016/0022-3115(85)90319-8
  11. P.A.G. O'Hare, W.A. Shinn, F.C. Mrazek, A.E. Martin, Thermodynamic investigation of trisodium uranium(V) oxide (Na3UO4) I. Preparation and enthalpy of formation, J. Chem. Thermodyn. 4 (1972) 401-409. https://doi.org/10.1016/0021-9614(72)90023-7
  12. D.R. Fredrickson, P.A.G. O'Hare, Enthalpy increments for α- and β-Na2UO4 and Cs2UO4 by drop calorimetry the enthalpy of the α to β transition in Na2UO4, J. Chem. Thermodyn. 8 (1976) 353-360. https://doi.org/10.1016/0021-9614(76)90075-6
  13. G.L. Hofman, J.H. Bottcher, J.A. Buzzell, G.M. Schwartzenberger, Thermal conductivity and thermal expansion of hot-pressed trisodium uranate (Na3UO4), J. Nucl. Mater. 139 (1986) 151-155. https://doi.org/10.1016/0022-3115(86)90032-2
  14. H.C. Chen, W.Y. Tian, First-principles investigation of the physical properties of cubic and orthorhombic phase Na3UO4, Physica B 524 (2017) 144-148. https://doi.org/10.1016/j.physb.2017.08.052
  15. A.L. Smith, P.E. Raison, L. Martel, D. Prieur, T. Charpentier, G. Wallez, E. Suard, A.C. Scheinost, C. Hennig, P. Martin, K.O. Kvashnina, A.K. Cheetham, R.J.M. Konings, A new look at the structural properties of trisodium uranate Na3UO4, Inorg. Chem. 54 (7) (2015) 3552-3561. https://doi.org/10.1021/acs.inorgchem.5b00136
  16. M.-C. Illy, A.L. Smith, G. Wallez, P.E. Raison, R. Caciuffo, R.J.M. Konings, Thermal expansion of the nuclear fuel-sodium reaction product Na3(U0.84(2),Na0.16(2))O4 - structural mechanism and comparison with related sodium-metal ternary oxides, J. Nucl. Mater. 490 (2017) 101-107. https://doi.org/10.1016/j.jnucmat.2017.03.045
  17. J.P. Perdew, A. Ruzsinszky, G.I. Csonka, O.A. Vydrov, G.E. Scuseria, L.A. Constantin, X.L. Zhou, K. Burke, Restoring the density-gradient expansion for exchange in solids and surfaces, Phys. Rev. Lett. 100 (2008) 136406. https://doi.org/10.1103/PhysRevLett.100.136406
  18. B. Sadigh, A. Kutepov, A. Landa, P. Soderlind, Assessing relativistic effects and electron correlation in the actinide metals Th to Pu, Appl. Sci. 9 (2019) 5020. https://doi.org/10.3390/app9235020
  19. J.P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77 (1996) 3865-3868. https://doi.org/10.1103/PhysRevLett.77.3865
  20. C.G. Broyden, The convergence of a class of double-rank minimization algorithms 2. The new algorithm, J. Inst. Maths. Appl. 6 (1970) 222-231. https://doi.org/10.1093/imamat/6.3.222
  21. R. Fletcher, A new approach to variable metric algorithms, Comput. J. 13 (1970) 317-322. https://doi.org/10.1093/comjnl/13.3.317
  22. D. Goldfarb, A family of variable-metric methods derived by variational means, Math. Comput. 24 (1970) 23-26. https://doi.org/10.1090/S0025-5718-1970-0258249-6
  23. D.F. Shanno, Conditioning of quasi-Newton methods for function minimization, Math. Comput. 24 (1970) 647-656. https://doi.org/10.1090/S0025-5718-1970-0274029-X
  24. R.A. Cowley, Acoustic phonon instabilities and structural phase transitions, Phys. Rev. B 13 (1976) 4877-4885. https://doi.org/10.1103/PhysRevB.13.4877
  25. M. Bom, K. Huang, Dynamical Theory of Crystal Lattices, Clarendon, Oxford, 1954.
  26. R. Hill, The elastic behaviour of a crystalline aggregate, Proc. Phys. Soc. 65 (1952) 349-354. https://doi.org/10.1088/0370-1298/65/5/307
  27. H.C. Chen, J.C. Wei, Y.Q. Chen, W.Y. Tian, Theoretical investigation of the mechanical and thermodynamic properties of titanium pernitride under high temperature and high pressure, J. Alloys Compd. 726 (2017) 1179-1185. https://doi.org/10.1016/j.jallcom.2017.08.107
  28. J.P. Watt, Hashin-Shtrikman bounds on the effective elastic moduli of polycrystals with monoclinic symmetry, J. Appl. Phys. 51 (1980) 1520. https://doi.org/10.1063/1.327803
  29. S.F. Pugh, XCII. Relations between the elastic moduli and the plastic properties of polycrystalline pure metals, Phil. Mag. 45 (1954) 823-843. https://doi.org/10.1080/14786440808520496
  30. G.N. Greaves, A.L. Greer1, R.S. Lakes, T. Rouxel, Poisson's ratio and modern materials, Nat. Mater. 10 (2011) 823-837. https://doi.org/10.1038/nmat3134
  31. D.G. Pettifor, Theoretical predictions of structure and related properties of intermetallics, Mater. Sci. Technol. 8 (1992) 345, 329. https://doi.org/10.1179/mst.1992.8.4.345
  32. X.Q. Chen, H.Y. Niu, D.Z. Li, Y.Y. Li, Modeling hardness of polycrystalline materials and bulk metallic glasses, Intermetallics 19 (2011) 1275-1281. https://doi.org/10.1016/j.intermet.2011.03.026
  33. H. Ozisik, E. Deligoz, K. Colakoglu, E. Ateser, The first principles studies of the MgB7 compound: Hard material, Intermetallics 39 (2013) 84-88. https://doi.org/10.1016/j.intermet.2013.03.016
  34. J.F. Nye, Physical Properties of Crystals, Oxford University Press Inc., New York, 1985, p. 145.
  35. L. Anderson, A simplified method for calculating the Debye temperature from elastic constants, J. Phys. Chem. Solid. 24 (1963) 909-917. https://doi.org/10.1016/0022-3697(63)90067-2
  36. D.G. Cahill, S.K. Watson, R.O. Pohl, Lower limit to the thermal conductivity of disordered crystals, Phys. Rev. B 46 (1992) 6131. https://doi.org/10.1103/PhysRevB.46.6131
  37. D.R. Clarke, Materials selection guidelines for low thermal conductivity thermal barrier coatings, Surf. Coating. Technol. 163-164 (2003) 67-74. https://doi.org/10.1016/S0257-8972(02)00593-5
  38. D.R. Clarke, C.G. Levi, Materials design for the next generation thermal barrier coatings, Annu. Rev. Mater. Res. 33 (2003) 383-417. https://doi.org/10.1146/annurev.matsci.33.011403.113718
  39. J.P. Long, C.Z. Shu, L.J. Yang, M. Yang, Predicting crystal structures and physical properties of novel superhard p-BN under pressure via first-principles investigation, J. Alloys Compd. 644 (2015) 638-644. https://doi.org/10.1016/j.jallcom.2015.04.229
  40. W.Y. Tian, J.H. Cai, H.C. Chen, Theoretical study the electronic, elastic properties and thermodynamics properties of ternary phosphide SrPt6P2, J. Phys. Chem. Solid. 106 (2017) 10-15. https://doi.org/10.1016/j.jpcs.2017.03.002
  41. M.A. Blanco, E. Francisco, V. Luana, GIBBS: isothermal-isobaric thermodynamics of solids from energy curves using a quasi-harmonic Debye model, Comput. Phys. Commun. 158 (2004) 57-72. https://doi.org/10.1016/j.comphy.2003.12.001

Cited by

  1. Theoretical prediction of anisotropic in elasticity, density of states and thermodynamic properties of Ti-X (X = Fe, Co, Zn) vol.94, pp.12, 2021, https://doi.org/10.1140/epjb/s10051-021-00240-6