Tilt and acoustic instabilities in ABX4, A2BX4 and ABX3 perovskite structure types: their role in the incommensurate phases of the organic-inorganic perovskites.

An examination of the tilt modes and other low-frequency modes is made for an isolated, untilted perovskite layer, which maps very simply to the ABX4 perovskites. A sheet of pure tilts exists at the Brillouin Zone boundary at {xi, (1/2), zeta}. An instability is also found at all wavevectors which can be described as continuously varying from pure tilts to pure layer displacements as a function of the wavevector.