Study On Ferroelastic Phase Transition And Pure Mode Axis Of Cubic System By Slowness Surfaces

Structural phase transition contains ferroelastic phase transition in which spontaneous strain is the only order parameter. The studies on ferroelastic phase transition have some guidance significance to the development and application of crystals. In this paper, the slowness surfaces of cubic system crystals have been drawn by using Matlab. The piezoelectric effect has been considered. On the basis of the slowness surfaces of cubic system crystals, the pure mode axes have been studied. The main contents of the paper are described as follows:Firstly, the elastic stiffness coefficients must meet the relations which are the stability conditions of cubic system. We draw the slowness surfaces of cubic system considering all the possible relations of the elastic stiffness coefficients. The results are summarized as follows. The ferroelastic phase transitions of cubic system only have relation with the elastic stiffness cofficients c44and c11-c12/2.When c44is the least one of all the elastic stiffness coefficients, the direction of the maximum slowness is in any direction of the XZ plane. When c11-c12/2is the least one, the direction of the maximum slowness is along the direction [1,0,1]. The slowness surfaces of cubic system have been drawn withc44â†'0, c11-c12â†'0, respectively. We can find that the spontaneous strains of c44â†'0are S4+S5+S6, S4(S5)(S6), S4-S5, S6, S4, S5, S6.The spontaneous strains of c11-c12â†'0are St+S2-2S3, S1-S2, S3, S1-S2.When the spontaneous strains appear in the crystals, the symmetry of crystals will change. According to Curie principle and group theory, the symmetry group of each ferroelastic phase has been determined.Secondly, only non-centrosymmetric crystals-23,43m classes have the piezoelectric effect which has some impact on ferroelastic phase transitions. The elastic stiffness cofficients of23,43m classes are calculated when there is a piezoelectric effect. The slowness surface and the direction of the maximum slowness of cubic systems have been drawn with the piezoelectric effect by using Matlab. The ferroelastic phase transitions correspond to c44E or c11E-c12E/2.When c11E-c12E/2is the least one of all the elastic stiffness coefficients, the direction of the maximum slowness with the piezoelectric effect are the same as that with the piezoelectric effect ignored. When c44E is the least one, the direction of the maximum slowness with the piezoelectric effect changes from the arbitary directions in XZ plane to the direction of axis Z. Finally,the dierction is called pure mode axis for the propagation of the elastic waves when the direction of the energy velocity is in agreement with that of the phase velocity. The direction of the energy velocity is the normal direction of the three dimensional slowness surfaces.The direction of the phase velocity is the direction of the wave-vector. The pure mode axes of two kinds of crystals which are c44E and c11E-c12E/2being the least one,respectively,have been drawn and the coordinates have been obtained by means of Matlab.