Lattice dynamics, third-order elastic constants, and thermal expansion of titanium

The lattice dynamics, second- and third-order elastic constants, and the anisotropic thermal expansion of hexagonal titanium are worked out using Keating's approach. The ten third-order elastic constants are calculated using five third-order parameters. The experimental measurements on the pressure derivatives of the second-order elastic constants in titanium are in good agreement with the calculated values. The low- and high-temperature limits γ̄L and γ̄H of the lattice thermal expansion are calculated and compared with those obtained from the thermal-expansion data of titanium. The lattice dynamics of titanium is found to be similar to that of zirconium. © 1973 The American Physical Society.