Elastic moduli of tungsten to 15 Mbar, phase transition at 6.5 Mbar, and rheology to 6 Mbar

The elastic constants of the bcc and fcc structures of W at 0 K versus reduced volume and pressure were obtained from first-principles, all-electron, density-functional calculations to V/V₀=0.40 (P=15.3Mbar). The dhcp and the fcc phase were calculated to be more stable than the bcc phase above 6.5 Mbar. The energy versus $c/a$ along Bain's path was calculated for different fractional volumes. The single-crystal constants of the bcc structure were used to calculate the shear modulus G of the polycrystalline bcc aggregate versus pressure. These results were used with the Chua and Ruoff pressure scaling relation to show that at 6 Mbar, the yield strength has increased by a factor of 4.5. The pressure dependence of the yield strength is compared with recent measurements.