Lattice dynamics of ${\mathrm{KTa}}_{1\mathrm{-}\mathrm{x}}$${\mathrm{Nb}}_{\mathrm{x}}$${\mathrm{O}}_3$ solid solutions in the cubic phase

We have calculated the phonon dispersion curves of mixed crystals of ${\mathrm{KTaO}}_3$ and ${\mathrm{KNbO}}_3$ for various niobium concentrations. In our calculations, a nonlinear shell model is used, in which the fourth-order anharmonic core-shell interaction of the oxygen ions is taken into account in the self-consistent phonon approximation. The measured phonon dispersion curves, their temperature dependence, and, in particular, the temperature dependence of the ferroelectric soft-mode frequency for different niobium concentrations between 0 and 100 at. % are well reproduced by our calculations in which only two coupling parameters depend on the niobium concentration in a systematic way. These two parameters are temperature independent and characterize the linear and nonlinear polarizability of the oxygen ions. All other coupling parameters are temperature and concentration independent.