Multiphase improved Steinberg–Guinan model for vanadium

Vanadium has been observed recently to transform from the body-centered cubic (bcc) crystal structure to a rhombohedral structure at high pressure (∼0.69 Mbar) [Y. Ding et al., Phys. Rev. Lett. 98, 085502 (2007)]. Recent theoretical work predicts a transformation to a second rhombohedral phase at 1.2 Mbar before transforming back to the bcc structure at 2.8 Mbar at absolute zero temperature [B. Lee et al., Phys. Rev. B 75, 180101(R) (2007)]. Here we develop an analytic model for the shear modulus in these phases based on ab initio calculations of the single-crystal elastic moduli and a finite element based homogenization technique. The form of the shear modulus is suited to application in strength models such as in the Steinberg–Guinan form and other analogous continuum-level models.