Lattice Dynamics of BCC Titanium and Its Nonlinear Response to High Temperature Deformations in Ab Initio Molecular Dynamics

Using the ab initio molecular dynamics method, the dynamics of the bcc titanium lattice and its response to high temperature deformations are studied. The results of calculation of phonon spectra with use of the harmonic Hamiltonian and the Hamiltonian containing third-order force constants are compared. It is shown that the lattice dynamics of bcc titanium cannot be correctly described without taking into account the anharmonic terms. Stress–strain curves are calculated for specified deformation scheme η 1 = η 11 = η, η 6 = 2η 12 = η. Analytical expressions of the dependence of the nonzero components of the stress tensor on the strain magnitude are given for this deformation scheme, which take into account the elastic constants up to the fourth order inclusive. All second-order elastic constants, three third-order elastic constants, and four fourth-order elastic constants of bcc titanium are calculated.