Thermal equation of state of tantalum

We have investigated the thermal equation of state of bcc tantalum from first principles using the full-potential linearized augmented plane wave (LAPW) and mixed-basis pseudopotential methods for pressures up to 300 GPa and temperatures up to 10 000 K. The equation of state at zero temperature was computed using LAPW. For finite temperatures, mixed basis pseudopotential computations were performed for 54 atom supercells. The vibrational contributions were obtained by computing the partition function using the particle in a cell model, and the finite-temperature electronic-free energy was obtained from the LAPW band structures. We discuss the behavior of thermal equation of state parameters such as the Gr\"uneisen parameter γ, the thermal expansivity α, and the Anderson-Gr\"uneisen parameter δT as functions of pressure and temperature. The calculated Hugoniot shows excellent agreement with shock-wave experiments. An electronic topological transition was found at approximately 200 GPa.