PHYSICAL REVIEW B 84, 014116 (2011) Elastic constants, phonon density of states, and thermal properties of UO 2 M. Sanati, 1,2,* R. C. Albers, 2 T. Lookman, 2 and A. Saxena 2 1 Physics Department, Texas Tech University, Lubbock, Texas 79409-1051, USA 2 Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 89404, USA (Received 18 August 2010; revised manuscript received 26 April 2011; published 29 July 2011) The elastic properties and phonon density of states of UO 2 have been studied by first-principles spin-polarized electronic-structure calculations in both the local density approximation (LDA) and the generalized-gradient approximation (GGA) for the experimentally determined antiferromagnetic spin configuration. Calculations have also been done both with and without Hubbard corrections (LDA + U and GGA + U ). The elastic properties and phonon density of states are in very good agreement with experimental measurements when the Hubbard correction is included. The elastic constants and low-frequency (acoustic mode) phonons are in reasonably good agreement with experiment for all the different calculations. However, when Hubbard corrections are not included, the high-frequency phonons are pushed to lower frequencies and the optical phonons are significantly underestimated. The melting temperature is approximated by using an empirical equation, which uses elastic constants as input parameters, and is in good agreement with experiment. The first-principles calculations are also used to obtain the specific heat and entropy within the harmonic approximation at finite temperatures. It is shown that harmonic approximation is valid up to room temperature. The Debye temperature is estimated using two different methods. The predicted values are in excellent agreement with experimental results. It is shown that inclusion of the spin-orbit interaction does not significantly alter either the elastic or thermal properties. DOI: 10.1103/PhysRevB.84.014116 PACS number(s): 63.20.dk, 62.20.de I. INTRODUCTION Oxide fuels have received much experimental and the- oretical attention because of their unique properties, such as high stability, melting temperature, fusion point, and the capacity to retain fission products. 1 For example, UO 2 is a commonly used fuel in pressurized heavy-water nuclear reactors. Understanding the physical, mechanical, and thermal properties of the fuel materials is primarily of interest in ensuring integrity of the core under operating conditions. Developing reliable theoretical modeling of such properties is a significant help, especially for the fuels without adequate experimental data such as PuO 2 . The elastic constants contain quite a bit of information about the stability and mechanical properties of solids. They are, for example, directly related to the bulk, shear, and Young’s moduli. Also, the Debye temperature can be approximated by using the average speed of sound waves, which can be calculated from the elastic constants. 2 This is the easiest method for estimating this quantity, since it can be obtained either by experimental measurement or theoretical calculation. In addition, thermodynamic data such as the specific heat can also be used to determine the Debye temperature. Based on experimental measurements of the elastic con- stants, Fritz 3 reported a Debye temperature of 385 K for the UO 2 system, while with a similar approach Marlowe and Kaznoff 4 found 875 K. Jones et al. 5 reported a Debye temperature of 160 K obtained from low-temperature interpo- lation of their specific heat measurement. Dolling et al. 6 have used the phonon density of states obtained from their neutron diffraction data in order to obtain the vibrational specific heat and to calculate the Debye temperature over a temperature interval between 0 and 500 K, with a zero-temperature value of 395 K. The enormous range of estimated or measured Debye temperatures strongly suggests that independent and reliable modeling would be extremely useful for resolving this controversy. First-principles band-structure calculations can provide valuable insight into physical, elastic, and thermal properties of materials. However, 5f -electron systems often have electronic correlation effects that cause the failure of conventional band- structure approaches such as the local density approximation (LDA) and generalized gradient approximation (GGA) to accurately predict many aspects of these materials. For example, such approaches predict a fluorite (Fm 3m) metallic ferromagnetic ground state for UO 2 , while the observed ground state is an antiferromagnetic insulator with a band gap of about 2.0 eV. 7 Several corrections to band theory that involve adding a Hubbard term to the Hamiltonian such as the DFT + U method 8,9 and dynamical mean-field theory (DMFT), 11 and also some other first-principles approaches such as the GW quasiparticle method 12 and hybrid density-functional theory, 13 do correctly predict the actual ground state for many materials, including UO 2 (note that GW approximations have not yet been performed on UO 2 ). However, the picture is muddied somewhat by the fact that some simple band-structure calculations on UO 2 , such as for the lattice parameters and bulk modulus, appear less sensitive to the correlations effects and are in good agreement with experiment. Since the elastic parameters are directly related to the low-frequency or acoustic phonons, it is not clear whether first-principles calculations with or without corrections would give a similar phonon density of states at all frequencies. The study of phonon spectra and lattice vibrations are of particular interest since many physical properties of crystals, including their specific heat, entropy, thermal expansion, thermal conductivity, phase transformations, melting, sound velocity, optical properties, and interaction with radiations such as x-ray and neutrons, are all related to the vibrations of the atoms in a solid. Therefore, it is essential to have a 014116-1 1098-0121/2011/84(1)/014116(7) ©2011 American Physical Society