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A general approach is presented for the incommensurate states and incommensurate (IC)-commensurate (C) transitions in ferroelectrics. An emphasis is put on the determination of the free energy as a function of the IC wave vector as well as on the role played by harmonics. The Levanyuk-Sannikov model for an improper ferroelectric material (NH 4 ) 2 BeF 4 is studied in details from this point of view, and the IC-C transition of this model is shown to be of second order. Some possible extensions of the model are suggested to have a first-order IC-C transition.
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Shiba et al. (1978) studied this question.
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