The Elastic Properties of Crystals with Jahn—Teller Structural Phase Transitions

In the first two chapters we have described how the Jahn—Teller effect gives rise to local distortions around a degenerate center and how the degenerate states of different Jahn—Teller sites interact. We have shown that interstitial interaction makes the ground state of the crystal correspond to a certain packing of “frozen” (in contrast with the case of an isolated center) local Jahn—Teller distortions. With increasing temperature the correlations of the Jahn—Teller distortions become weaker, and a transition to a disordered phase occurs. This structural phase transition associated with the cooperative Jahn—Teller effect is naturally determined by the lowest electronic state of the lattice sites and by the character of their vibronic coupling. In this chapter we discuss the main types of conceptually different situations produced by the cooperative Jahn—Teller effect and examine the elastic anomalies accompanying this structural phase transition.