Transitions from Artificially Incommensurately Undulated Prototypic Phases to Ferroic Phases

Abstract

In this paper, unlike in previous ones, it is assumed that prototypic phases are not homogeneous but artificially incommensurately undulated. Transitions from such prototypic phases to ferroic phases are investigated. As is well known, free energy functions are composed of order parameters, spatial differentiations and coefficients. Unlike previously, not only order parameters are undulated. By prototype undulation, even coefficients are undulated. Those gradient-linear terms which would be extinguished by spatial averaging if prototypic phases were homogeneous, can play important roles. Three cases are studied, one of which is the simplest case conceivable, and in the other two the free energy function contains ∂ z ( Q 2 α - Q 2 β ) and ∂ z ( Q α Q β ) respectively. An expression of a rise of the transition temperature is obtained. In the latter two cases, expressions of nonzero and non-π phase differences are obtained.