Free Energy of Displacive Ferroelectrics

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Abstract
A power series for the free energy is derived in the linear anharmonic approximation. This free energy is expressed in terms of a complete set of microscopic order parameters which determine the ionic displacements in the ferroelectric transition. In general this complete set of microscopic order parameters is larger than the set of order parameters used in the phenomenological free energy of Devonshire. However, for those ferroelectric crystals which are characterized by only one soft optical branch, this larger set may be reduced to the same number as used by Devonshire. Such a reduction is explicitly carried out for the perovskite structure and the resulting expression is the same as that derived phenomenologically by Devonshire with the coefficients expressed in terms of microscopic lattice parameters.