Phonon dispersion relations and thermal expansion of erbium

The lattice dynamics, second- and third-o rder elastic constants, and the temperature variation of the lattice thermal expansion of erbium are worked out on the basis of Keating's method. The ten third-order elastic constants are calculated using four third-order anharmonic parameters. The model used here reproduces the measured pressure derivatives of the second-order elastic constants of erbium well. The low- and high-temperature limits γ̄L and γ̄H of the lattice thermal expansion are evaluated and the calculated γ̄H is compared with that obtained from the thermal expansion and specific heat data. The dispersion relations in erbium are found to be similar to those in holmium.