Thermal Expansion of GeTe from First Principles

GeTe, a well-known ferroelectric and thermoelectric material, undergoes a structural phase transition from a rhombohedral to the rocksalt structure at ~600-700 K. We model this phase transition using density functional theory by minimizing the Helmholtz free energy using the elastic and quasi-harmonic approximations and Gruneisen theory. By accounting for up to the fourth order elastic constants and their temperature dependence, we obtain the temperature variation of the structural parameters of rhombohedral GeTe (the lattice constant, the angle between the primitive lattice vectors and the internal atomic displacement) in good agreement with experiment [1]. From the calculated temperature dependence of the transverse optical (TO) mode, which is the primary order parameter for this phase transition, we extracted the critical temperature of 701 K and the critical exponent of 0.17, which are in good agreement with experiment [2]. We find that the divergence of the thermal expansion coefficients near the phase transition in GeTe is induced by acoustic phonon coupling to soft TO modes.

[1] T. Chattopadhyay et al, J. Phys. C 20, 1431 (1987)
[2] E. F. Steigmeier and G. Harbeke, Solid State Commun. 8, 1275 (1970)