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 ${\overline{\gamma }}_L$ and ${\overline{\gamma }}_H$ 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.