ELASTIC ANOMALIES OF BARIUM-TITANATE

The anomalies of the second-, third-, and fourth-order elastic constan ts have been derived for barium titanate and related compounds for the phase transition from cubic to tetragonal and from the tetragonal to the orthorhombic phases. The equilibrium values of the three component s of the order parameter and the strain variables in the two phases ha ve been obtained from the stability conditions. The fluctuations in th e order parameter in the two phases have been derive from the Landau-K halatnikov equations. Expressions have been given for the shift in the zero point energy in the tetragonal and orthorhombic phases, and thes e are shown to be proportional to (T-T(c))2. The anomalies for all the second-order elastic constants have been derived for both phases, and relations among them have been reported. It is shown that the elastic anomalies suffer a discontinuity at the transition temperature for bo th the phases. Our expressions give the temperature variation of the t hird-order elastic and fourth-order elastic constants for the phase tr ansition from the tetragonal to the orthorhombic phase.