Theory of Incommensurate Phase Transitions when the Soft Mode System Comprises Only a Nondegenerate Zero-Wavenumber Mode, as in NaNO2

Even when the (unmodulated) soft mode system comprises only a nondegenerate mode and hence the antisymmetrized square of the representation for it does not exist, incommensurate phases are possible. A theory is constructed for a substance like NaNO 2 as an example. The same new thought is applied as recently done to K 2 SeO 4 . No ad hoc extra transition parameter needs to be brought in. “Lifshitz invariants” and other important terms are logically produced. Phases incommensurate along none or some of the x , y and z axes are deduced. The conditions are found that determine to which ferroic phase the prototypic phase should change by a second-order transition, Also, the mechanism is explained of the second transition, seen in NaNO 2 , from the phase incommensurate along the x axis to the totally commensurate ferroic phase.