An Extraordinary Type of Thermal Behavior of Soft Modes when T→Tc-0. Extraordinary Types, Caused by It, of T Dependence of Electric and Elastic Properties near Tc

A second-order transition between a prototypic and a commensurate ferroic phase is considered. The concept of the “catastrophe indices” of the soft modes is introduced for their thermal behavior when T → T c -0 (it is assumed that the ferroic phase occurs below T c ). Presented are some cases where the catastrophe indices are all 1 and some cases where the indices are not all 1 . A general theory is constructed which manifests that a nonunity catastrophe index causes certain extraordinary types (which differ according to different values of faintness index) of T dependence of electric susceptibility (κ) and elastic compliance near T c . One of these types is: κ∝( T - T c ) -1 at T > T c , κ∝( T c - T ) -2 at T < T c . Another is: κ=temp.indep.at T > T c , κ∝( T c - T ) -1 at T < T c .