Anharmonicity and mode softening inNb3Sn

The elastic shear-mode softening in ${\mathrm{Nb}}_3$Sn has been investigated within the framework of a previously developed coupled-mode Landau theory with anharmonic effects included consistently in the quasiharmonic and anisotropic-elastic-continuum approximation. Anharmonic effects enter through the third- and fourth-order elastic constants, which have been determined as a function of temperature from empirical data and from thermodynamic conditions. A strong enhancement of the electronically driven instability by the anharmonic phonon-phonon interaction is found. The third-order elastic constants of ${\mathrm{Nb}}_3$Sn and of ${\mathrm{V}}_3$Si are of opposite sign. The third- and fourth-order constants of ${\mathrm{Nb}}_3$Sn are smaller than for ${\mathrm{V}}_3$Si. In spite of this, the anharmonic enhancement of the shear-mode softening in ${\mathrm{Nb}}_3$Sn is still larger than previously determined for ${\mathrm{V}}_3$Si.