Ultrasonic study of phonon mode softening and melting in indium-thallium alloys

Measurements of ultrasonic wave velocities have been made between room temperature and the melting point in single crystals of indium, the fct 11.5-at.%-Tl and 15-at.%-Tl alloys and the fcc 27-at.%-Tl alloy. The object has been to test Ida's theory of melting on the basis of lattice instability and also suggestions that melting may take place by a phonon-mode-softening process. Contrary to the predictions of the both these hypotheses, it is found that for these materials longitudinal-acoustic modes stiffen somewhat near the melting point, while transverse modes exhibit no measurable premelting effects. The temperature dependence of the elastic stiffness tensor components of each material have been obtained. For the fct crystals the modulus $\frac{(C_{11}-C_{12})}{2}$ decreases as the temperature is raised: the [110], $\overrightarrow{\mathrm{q}}\parallel \left[1\mathrm{}\overline{1}0\right]$ acoustic-phonon mode in these fct crystals is softening in the vicintiy of the Brillouin zone center, a result which is consistent with an incipient martensitic transition, although the crystals melt before such a transition can occur. In the 15-at.%-Tl alloy, which at its melting point is very close to the fcc-fct phase boundary, $\frac{(C_{11}-C_{12})}{2}$ is very small: the [110], $\overrightarrow{\mathrm{q}}\parallel \left[1\mathrm{}\overline{1}0\right]$ mode is particularly soft. In all the fct crystals studied the modulus $\frac{(C_{11}-C_{12})}{2}$ tends to zero not at the melting point but at a higher temperature: this convergence above the melting point is also found in the elastic-constant pairs ($C_{11}$ and $C_{33}$) and ($C_{44}$ and $C_{66}$) (in a cubic crystal $C_{11}=C_{33}$ and $C_{44}=C_{66}$. It is concluded that acoustic-mode softening is not a prelude to melting in the way that it is to the martensitic transition in these indium-thallium alloys.