Vibrational anharmonicity and the elastic phase transition of indium-thallium alloys

The anharmonic behaviour of the long wavelength acoustic modes in In-Tl alloys in the vicinity of the elastic, f.c.c. to f.c.t. phase transition has been determined from the composition, temperature, hydrostatic and uniaxial pressure dependences of ultrasound wave velocities in single crystals containing between 10 at. % and 30 at. %Tl. The hydrostatic pressure derivatives show that the soft acoustic mode of f.c.c. alloys softens while that of the f.c.t. alloys stiffens with pressure. An empirical equation of state has been constructed for the f.c.c. alloys. A large negative mode Gruneisen parameter found for the soft transverse acoustic phonon (wave vector $\langle$110$\rangle$, polarization $\langle$1$\overline{10}\rangle$) for f.c.c. alloys near the transition reflects the marked vibrational anharmonicity of the soft mode. The pressure effects on ultrasound wave velocity have been used to determine sets of independent, room temperature third order elastic constants for several alloy compositions. The third order invariants in the elastic strain energy have been evaluated to assess quantitatively the applicability of Landau theory, in conjunction with the soft mode concept, to an elastic phase transition. The relative magnitudes of the third order invariants conform to the nearly second order character of the phase transition. However, the first order character has been established by a marked hysteresis in ultrasonic wave velocities as crystals are cycled by temperature or pressure through the transition. There is a third order invariant in the order parameter: Landau theory predicts correctly the first order nature of the transition.