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

• Main Author: Brassington, Michael Paul
• Published: University of Bath 1982
• Subjects: 669; Metallurgy & metallography
• Online Access: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.238579

The anharmonic character of indium-thallium alloys in the vicinity of the fee to fct elastic phase transition has been determined from the composition, temperature, hydrostatic pressure and uniaxial stress dependences of ultrasound wave velocities in single crystals grown by the zone levelling method and containing between 10at% and 30at% Tl. Both the pulse echo overlap and the pulse superposition ultrasonic techniques were employed. The hydrostatic pressure derivatives of second order elastic constants (SOEC), derived from the experimental results, have illuminated the effect of hydrostatic compression on the fcc-fct boundary of the In-Tl phase diagram and enabled the construction of an empirical, room temperature equation of state for fcc alloys. Mode Gruneisen parameters evaluated for these alloys strongly reflect the effects of increased levels of vibrational anharmonicity and the softening of the transverse acoustic phonon, wave vector q and polarised e, in that increasingly large negative parameters were recorded for this mode as the phase transition was approached. A small but significant thermal hysteresis was found to be associated with the structural transition in In-22at% Tl while the effect of temperature on the hydrostatic pressure derivatives of the SOEC of In-25at% Tl was observed to be negligible, at least for temperatures far from the transition temperature Tc. The hydrostatic and uniaxial stress derivatives of ultrasound velocities in five In-Tl alloys were used to evaluate five complete sets of independent, room temperature, third order elastic constants (TOEC). These results have allowed the evaluation of third order invariants in the free energy expansion with respect to irreducible strains and so for the first time permitted a critical, quantitative assessment of the applicability of Landau theory, in conjunction with the soft phonon concept, to a first-order elastic phase transition. This theory is found to fit experimental observations well. The relative magnitudes of third order invariants conform to the nearly second-order character of the phase transformation and to the negligible volume change associated with it. From trends in the third order invariants, Landau theory suggests that the second-order character of the elastic phase transition increases with the Tl content of the alloy, such that In-31at% Tl, for which Tc ≈ OK, should exhibit a structural transformation which is most nearly of second order.