First-principles thermoelasticity of transition metals at high pressure:: Tantalum prototype in the quasiharmonic limit

The thermoelastic properties of tantalum have been investigated over its theoretical high-pressure bcc solid phase (up to 26 000 K at 10 Mbar) using an advanced first-principles approach that accurately accounts for cold, electron-thermal, and ion-thermal contributions in materials where anharmonic effects are small. Specifically, we have combined ab initio full-potential linear-muffin-tin-orbital electronic-structure calculations for the cold and electron-thermal contributions to the elastic moduli with phonon contributions for the ion-thermal part calculated using model generalized pseudopotential theory. For the latter, a summation of terms over the Brillouin zone is performed within the quasiharmonic approximation, where each term is composed of a strain derivative of the phonon frequency at a particular k point. At ambient pressure, the resulting temperature dependence of the Ta elastic moduli is in excellent agreement with ultrasonic measurements. The experimentally observed anomalous behavior of C(44) at low temperatures is shown to originate from the electron-thermal contribution. At higher temperatures, the main contribution to the temperature dependence of the elastic moduli comes from thermal expansion, but inclusion of the electron- and ion-thermal contributions is essential to obtain quantitative agreement with experiment. In addition, the pressure dependence of the moduli at ambient temperature compares well with recent diamond-anvil-cell measurements to 1.05 Mbar. Moreover, the calculated longitudinal and bulk sound velocities in polycrystalline Ta at higher pressure and temperature in the vicinity of shock melting (similar to 3 Mbar) agree well with data obtained from shock experiments. However, at high temperatures along the melt curve above 1 Mbar, the B(') shear modulus becomes negative, indicating the onset of unexpectedly strong anharmonic effects. Finally, the assumed temperature dependence of the Steinberg-Guinan strength model obtained from scaling with the bulk shear modulus is examined at ambient pressure.