Structural relationships between spontaneous strain and acoustic properties in ferroelastics

A number of structural relationships between the spontaneous strain and acoustic properties of ferroelastic materials is described. Zero-velocity pure transverse acoustic modes are shown to occur in mutually perpendicular pairs at second-order phase transitions. These soft modes have propagation and displacement directions situated in ferroelastic domain wall planes. The resultant ferroelastic spontaneous strain is shown to result from the appropriate summation of pure shear strains produced by these soft modes and characterised by a two-dimensional acoustic strain tensor which is proportional to the difference between the spontaneous strain tensors of two strain-compatible ferroelastic orientation states.