Theory of Lattice Dynamics ofNb3Sn-Type Compounds

We present a method of calculating electron screening in the tight-binding approximation and constructing the dynamical matrix for the $\beta$-W compounds. We show that, in the cubic phase, no long-wavelength optical mode is temperature dependent except ${\Gamma }_{12}$ which has a weak temperature variation. By the method of long waves, we calculate the elastic constants, particularly $c_{11}-c_{12}$, as a function of temperature, obtaining a fair agreement with experiment. We infer that the cubic to tetragonal phase transition is due to the instability of the $c_{11}-c_{12}$ shear mode, associated with which is a tetragonal distortion of ${\Gamma }_{12}$ symmetry, in agreement with the neutron-scattering experiment of Shirane and Axe.