TRANSITION FROM A PROTOTYPIC PHASE INCOMMENSURATELY UNDULATED AT WAVE-NUMBER (H)OVER-CAP TO A FERROIC PHASE UNDULATED AT (H)OVER-CAP 2/

The transition from an artificially undulated prototypic phase to a fe rroic phase is investigated. The wavenumber and amplitude of the proto type undulation are denoted by (h) over cap and U respectively. For si mplicity a single order parameter is assumed, denoted by Q. When U is very small, only one ferroic phase is possible, which is undulated at wavenumber (h) over cap. This has been found before. The present paper finds that an extra term occurs in the averaged free energy function if and only if Q undulates (itself) at (h) over cap/2. This term inclu des Uas a factor. Owing to it, a ferroic phase undulated at (h) over c ap/2 can occur, unless tris very small. The prototypic phase on coolin g changes to the former or latter ferroic phase accordingly to whether U < or > U-c. What expresses U-c is determined. A late part of the pa per takes into account 3 (h) over cap/2 (an overtone) besides (h) over cap/2.