First-principles study of the elastic properties of In-Tl random alloys

Abstract

The composition-dependent lattice parameters and elastic constants of ${\text{In}}_{1\ensuremath{-}x}{\text{Tl}}_{x}(0<x\ensuremath{\le}0.4)$ alloy in face-centered-cubic (fcc) and face-centered-tetragonal (fct) crystallographic phases are calculated by using the first-principles exact muffin-tin orbitals method in combination with coherent-potential approximation. The calculated lattice parameters and elastic constants agree well with the available theoretical and experimental data. For pure In, the fcc phase is mechanically unstable as shown by its negative tetragonal shear modulus ${C}^{\ensuremath{'}}$. With Tl addition, ${C}^{\ensuremath{'}}$ of the fcc phase increases whereas that of the fct phase decreases, indicating that the fcc phase becomes mechanically more stable and the fct phase becomes less stable. In addition, the structural energy difference between the fcc and fct phases decreases with $x$. Both of these effects account for the observed lowering of the fcc-fct martensitic transition temperature upon Tl addition to In. The density of states indicates that the stability of the fct phase relative to the fcc one at low temperatures is due to the particular electronic structure of In and In-Tl alloys.