National Research Nuclear University “MEPhI” (Moscow Engineering Physics Institute), Moscow, Russia:

S. A. Gubin, Professor, Head of a Chair No. 4 “Chemical Physics”
I. V. Maklashova, Senior Lecturer of a Chair No. 4 “Chemical Physics”, e-mail: ivmaklashova@mephi.ru

During the power plant exploitation, UO₂-containing fuel pellets are subjected to high temperatures and pressure, irradiation and mechanical stress. Uranium dioxide can be appeared at high pressures and temperatures in the case of accidents, such as compression in shock wave or high-speed collision. In such conditions, an intensive defect formation of crystal structure is formed. Therefore it is necessary to predict the phase states and thermophysical parameters of uranium dioxide in a wide range of pressure and temperature changes, including extreme conditions, taking into account the defect and deviations from stoichiometric composition of UO_2+x. Equations of state (EOS) in the Mie-Grunaisen form for solid and liquid UO₂ are obtained taking into account the formation of crystal structure defects, deviations from stoichiometry and thermal excitation energy of electrons. It is shown that amount of defects is increased with increasing of temperature and pressure. Thermophysical and thermodynamic properties of UO₂ phases are calculated in a wide range of pressures and temperatures. Accounting for defect formation and electronic excitation can correctly describe the experimentally obtained accelerated growth of thermal expansion coefficient and specific heat of solid UO₂ up to the melting point. Correct account of defect formation is required for reliable scaling of temperature and pressure of melting or polymorphic transformation of UO₂ under compression in shock waves. In this case, the crystal structure and energy of compressed uranium dioxide are changed in the shock wave. Otherwise it is impossible to distinguish the polymorphic transformation from accumulation of defects in material crystalline structure. The resulting EOSs allow to estimate the parameters of the shock wave compression and melting of uranium dioxide in the wide range of pressures and temperatures.

1. Termodinamicheskie svoystva individualnykh veshchestv : spravochnoe izdanie (Thermodynamic properties of individual substances : reference book). Under the editorship of V. P. Glushko. Third eddition. Moscow : Nauka, 1982. Vol. 4, Book. 1, 2.
2. Razrabotka, proizvodstvo i ekspluatatsiya teplovydelyayushchikh elementov energeticheskikh reaktorov (Development, production and exploitation of fuel units of energetic reactors). In two volumes. Volume 1. Under the editorship of F. G. Reshetnikov. Moscow : Energoizdat, 1995. 62 p.
3. Ronchi C., Iosilevskiy I., Yakub E. Equation of State of Uranium Dioxide. Berlin : Springer, 2004. 366 p.
4. MATPRO - A Library of Materials Properties for Light-Water-Reactor Accident Analysis. Edited by D. T. Hargman. Idaho : Idaho National Engineering Laboratory, Lockheed Idaho Technologies Company, 1995. 667 p.
5. Fink J. K., Chasanov M. G., Leibowitz L. Thermophysical properties of uranium dioxide. Journal of Nuclear Materials. 1981. Vol. 102. pp. 17–25.
6. Molodets A. M., Fortov V. E. Fazovye perekhody dioksida urana pri vysokikh davleniyakh i temperaturakh (Phase transforms of uranium dioxide with high pressures and temperatures). Pisma v Zhurnal eksperimentalnoy i teoreticheskoy fiziki = Letters to Journal of Experimental and Theoretical Physics. 2002. Vol. 80, Iss. 3. pp. 196–199.
7. Idiri M., Le Bihan T., Heathman S., Rebizant J. Behavior of actinide dioxides under pressure: UO₂ and ThO₂. Physical Review B. 2004. Vol. 70. pp. 014113-1–104107-8.
8. Manara D., Ronchi C., Sheindlin M., Lewis M., Brykin M. Melting of stoichiometric and hyperstoichiometric uranium dioxide. Journal of Nuclear Materials. 2005. Vol. 342. pp. 148–163.
9. Boyarchenkov A. S., Potashnikov S. I., Nekrasov K. A., Kupryazhkin A. Ya. Molecular dynamics simulation of UO₂ nanocrystals melting under isolated and periodic boundary conditions. Journal of Nuclear Materials. 2012. Vol. 427. pp. 311–322.
10. Arima T., Idemitsu K., Inagaki Y., Tsujita Y., Kinoshita M., Yakub E. Evaluation of melting point of UO₂ by molecular dynamics simulation. Journal of Nuclear Materials. 2009. Vol. 389. pp. 149–154.
11. Malygin V. B., Naboychenko K. V., Shapovalov A. S., Bibilashvili Yu. K. Rekomendatsii dlya rascheta kharakteristik termicheskoy polzuchesti dioksida urana pri analize rabotosposobnosti tvelov (Recommendations for calculation of characteristics of thermal creep of uranium dioxide during analysis of fuel rod work capacity). Atomnaya energiya = Atomic Energy. 2009. Vol. 107, No. 6. pp. 317–320.
12. Crocombette J. P., Jollet F., Thien Nga L., Petit T. Plane-wave pseudopotential study of point defects in uranium dioxide. Physical Review B. Vol. 64. pp. 104107-1–104107-12.
13. Molodets A. M. Obobshchennaya funktsiya Gryunayzena dlya kondensirovannykh sred (Generalized Grunaisen function for condensed mediums). Fizika goreniya i vzryva = Combustion, Explosion, and Shock Waves. 1995. Vol. 31, No. 5. pp. 132–133.
14. Fizicheskie velichiny : spravochnik (Physical quantities : reference book). Under the editorship of I. S. Grigorev, E. Z. Meylikhov. Moscow : Energoizdat, 1991. 1232 p.
15. Pujol M. C., Idiri M., Havela L., Heathman S., Spino J. Bulk and Young’s modulus of doped UO₂ by synchrotron diffraction under high pressure and Knoop indentation. Journal of Nuclear Materials. 2004. Vol. 324. pp. 189–197.
16. Hua Y. Geng, Hong X. Song, Q. Wu. Theoretical assessment on the possibility of constraining point-defect energetic by pseudo phase transition pressures. Physical Review B. 2013. Vol. 87, Iss. 17. pp. 174107.
17. Ignatova O. N., Kaganova I. I., Malyshev A. N., Podurets A. M. et al. Vliyanie udarno-volnovogo nagruzheniya na vnutrennyuyu mikrostrukturu i mekhanicheskie svoystva melkozernistoy medi (Influence of shock-wave load on internal microstructure and mechanical properties of fine-grain copper). Fizika goreniya i vzryva = Combustion, Explosion, and Shock Waves. 2010. Vol. 46, No. 6. 119 p.
18. Kormer S. B. Opticheskie issledovaniya svoystv udarno szhatykh kondensirovannykh dielektrikov (Optimal testing of properties of shocked condensed dielectrics). Uspekhi fizicheskikh nauk = Advances in Physical Sciences. 1968. Vol. 94, Iss. 4. pp. 641–687.
19. Kotelnikov R. B. et al. Vysokotemperaturnoe yadernoe toplivo (Hightemperature nuclear fuel). Moscow : Atomizdat, 1978.
20. Sushil Kumar Kapil. Evaluation of the thermodynamic critical constants for uranium di-oxide. Journal of Nuclear Materials. 1976. Vol. 60, Iss. 2. pp. 158–166.
21. Martin D. G. The thermal expansion of solid UO₂ and (U, Pu) mixed oxides — a review and recommendations. Journal of Nuclear Materials. 1988. Vol. 152, Iss. 2/3. pp. 94–101.
22. LASL Shock Hugoniot Data. Edited by S. P. Marsh. Berkeley : University California Press, 1980.