Symmetry-based model for the modulated phases of betaine calcium chloride dihydrate

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Abstract
A symmetry-based model for betaine calcium chloride dihydrate (BCCD) is presented. BCCD is a crystal with many modulated phases that can be commensurate or incommensurate. In our model, BCCD is viewed as formed of layers, perpendicular to which the crystal is modulated. The free energy is expanded in terms of amplitudes of symmetry modes of these layers. Which symmetry modes must appear in the free energy is determined through experimental data on the phonon-dispersion relation. For a previous related work, the phonon-dispersion relation was not yet available and the necessary assumption of which modes should be included proved to be incorrect. In the free energy, competing interactions between the symmetry modes lead to different phases. The phase sequence derived from this model corresponds fairly well to what is found in experiment, but incommensurate and higher-order commensurate phases are overemphasized. The polarity of the phases determined by the model agrees with experimental data.