Abstract
We present a formulation of the statics and dynamics of displacive incommensurately modulated structures with modulation vector q based on a Taylor expansion of the interaction energy and of the dynamical matrix. For a given interaction potential, this approach allows the consistent calculation of the incommensurate distortion and the vibrational frequencies, including the phase and amplitude modes, and the intensities of the modes activated by the distortion. The necessary approximations are discussed; the coupling and selection rules are easily visualized in terms of the space group symmetry of the parent structure. Finally, we work out in detail a simple example of an idealized three-dimensional crystal, calculating the static incommensurate distortion, the $\ensuremath{\Gamma}$ point modes of the modulated structure, and the relative optical intensities of the activated modes.
Published Version
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