Equation of state for tungsten obtained by direct solving the partition function

Utilization of metal tungsten (W) as the structural material or pressure scale requires accurate knowledge of the equation of state (EOS), which is far beyond the available experimental measurements. In the present work, a direct integral approach (DIA) with ultrahigh efficiency was applied to calculate the EOS of W up to 500 GPa and 3000 K with ab initio calculations. Compared with previous static compression experiments up to 150 GPa under room temperature and 35 GPa at high temperatures up to 1673 K, all the deviations of the calculated pressure are within or comparable to the uncertainty of experiments. Predictions for higher-temperature and simultaneously higher-pressure EOS up to 300 GPa and 3000 K differ slightly from the comprehensive analysis by Litasov et al. [J. Appl. Phys. 113, 133505 (2013)] via fitting available experimental data with the empirical equation. These results indicate that the EOS of crystal W obtained from DIA should be convincible, and DIA without any empirical or artificial parameters may find its wide applications for predicting thermodynamic properties of condensed matter in the future.