FIRST TYPE OF FERROELECTRICITY GENERATED BY UNDULATED-PROTOTYPIC TO FERROIC TRANSITION .2. F=2

Before this paper, ferroelectricity generated by undulated-prototypic to ferroic transition was abbreviated as U-ferroelectricity. This pape r deals with U-ferroelectricity of type I and of f = 2 (f denotes fain tness index). A case study is made. The prototypic phase when homogene ous is assumed tetragonal. The order parameters are two real variables , Q(alpha) and Q(beta). The free energy function can be expanded into a power series in electric field, as Psi = Phi - E theta' - (1/2)E(2) Phi '' -..., which defines Phi, Phi', etc. A theory is given; it clari fies that the combination of the following term within Phi (not Phi') and the following delta undulation is responsible for the generation o f U-ferroelectricity: Term [Q(beta)(partial derivative(xx)(2)-partial derivative(yy)(2))Q(alpha)-Q(alpha) (partial derivative(xx)(2)-partial derivative(yy)(2))Q(beta)] and delta = U cos((h) over cap x+U' cos((h ) over cap y+<(theta)over cap>').