On the basis of an analysis of data on a large number of compounds exhibiting displacive phase transitions, it is observed (with no known exceptions) that the transition temperature decreases with hydrostatic pressure for those transitions associated with soft zonecenter optic phonons and increases for those transitions associated with soft zone-boundary optic phonons. This difference in behavior is tentatively interpreted in terms of a reversal in the roles of the short-range and long-range forces in the lattice dynamics of the two cases.

Phase transition in squaric acid is discussed on the basis of a pscudospin model for the hydrogen bond system. A strong coupling between the lattice distortion and proton system is introduced in order to account for the twin structure and improper ferroelastic behaviour in the low temperature phase. Anomalous elastic constant and electric susceptibility are calculated and compared with experiments. Isotope effect in the transition temperature is discussed by taking account of the tunneling motion of proton. § I. IntroductionSquaric acid H 2 C40 4 C3, 4-dihydroxy-3-cyclobutane-1, 2-dions, abbreviated as HzSQ) is an unusually strong organic acid. This crystal undergoes a second order antiferrodistortive phase transition at Tc = 97.TC from a tetragonal (high temperature phase) to a monoclinic structure (low temperature phase) confirmed by a birefringence experiment. 1 > From the structural studies by means of X-ray'> and neutron diffraction, 3 J. 4 ) informations on the crystal structure, both above and below T" have been obtained. The structure consists of the layers of planar nwlecules HzC40 1 perpendicular to the b-axis as shown in Fig. 1. Above T,, the protons move in the symmetric double well potential of 0-H-0 bonds, and on the average locate in the midpoints of the bonds. Below T" however, the protons are arranged in an ordered pattern such that each C10 4 is linked by four asymmetric hydrogen bonds with two protons nearer to and other two protons apart from a C40 4 radical. Thus the crystal in the low temperature phase consists of planar ferroelectric layers with the layers antiferroelectrically stacked along the unique monoclinic b-axis. The proton arrangement within each layer is uniform but has two different configurations forming a twin structure accompanied by spontaneous distortions with opposite directions. The twin structure in the monoclinic phase was first reported by Semmingsen. 2 ) Ferroelasticity in H 2SQ has been directly confirmed by observations of Okada.') effect in elastic hysteresis loop under the polarizing microscope by Suzuki and Furthermore, H 2SQ and deuteratecl crystal D 2SQ exhibit a large isotope the transition temperature as T, (H) = 371K and T, (D) = 516K. This factsuggests that the hydrogen bonds play an important role in the phase transition mechanism, and an order-disorder pseudospin model for the proton system such as used for KH2P0 4 will be suitable for this substance. Tncleecl a few theories at Michigan State University on June 27, 2015 http://ptp.oxfordjournals.org/ Downloaded from

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Successive phase transitions in the mixecl crystal with perovskite structure (1x) ABO a +xA'B'O, are discussed on a phenomenological basis. After a short review on the experimental facts, a simple scheme is proposed to predict the phase diagrams of mixed crystals when the model parameters of constituent substances are known. It is shown that the applications of the present scheme to (Ba,_xPbx) TiOa, (Ba,_xSrx) TiOa and Ba (Ti,_xHfx) Oa yield the results which are in good accord with experiments.