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Inherent transition parameters for a crystal which has several basis atoms related to each other by some symmetry operations have been studied from a group-theoretical point of view. These parameters are classified according to their symmetry properties. Some of these parameters, though belonging to the same irreducible representations as the components of the polarization, do not represent any polar quantities but nevertheless can be made use of to explain the appearance of spontaneous polarization in improper ferroelectric crystals.
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Takagi et al. (1973) studied this question.
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