Nonlinear Lattice Dynamics of Crystals with Structural Phase Transitions

Abstract

Exact periodic solutions are found for three-dimensional lattices with fourth-order on-site electron-ion potentials. Numerical results are presented for ferroelectric SnTe. The coupling of these nonlinear waves with phonons is investigated for phase transitions with finite critical wave vectors. For ${\mathrm{K}}_2$ ${\mathrm{SeO}}_4$ both the paraelectric-incommensurate and the incommensurate-commensurate ferroelectric transitions are analyzed. The cubic power of the nonlinear force leads to a lock-in transition at the wave vector $\frac{2\pi }{3}$.