A Model of an Incommensurate-Commensurate Phase Transition

A phase transition in an incommensurate structure induced by a soft mode with the wave vector k near the Brillouin zone boundary k c is investigated. The soft mode belongs to the lower branch of two split phonon branches degenerate at k c . It is shown that this general feature of the phonon spectrum leads with decreasing temperature to the shift of k toward k c and finally to the lock-in transition into a commensurate phase. The present model is appropriate for ammonium fluoroberyllate, for example, and differs qualitatively from those recently suggested for potassium selenate and metal chalcogenides.