Third-order elastic constants and low-temperature lattice thermal expansion of the high-temperature structural material TiAl

We have derived the expressions for the 12 third-order elastic constants for a tetragonal system by the method of homogeneous deformation which are used to determine the third-order elastic constants of TiAl. These third-order elastic constants are used to determine the low-temperature limit of the volume thermal expansion of TiAl. The value of C-333 was calculated to be a high value. The high value of the third-order elastic constant C-333 shows a marked anisotropy in the crystal. The low-temperature limit is found to be negative, indicating a negative volume thermal expansion down to zero kelvin.