Second order elastic anomalies in barium titanate from cubic to tetragonal phase transition

The anomalies of the second order elastic constants have been derived for barium titanate for the phase transition from cubic to tetragonal. The equilibrium values of the components of the order parameter and the strain variables have been obtained from the stability conditions. The fluctuations in the order parameter have been derived from the Landau-Khalatnikov equations. Expression for the shift in the zero point energy in the tetragonal phase is obtained and is shown to be proportional to (T -T<SUB>c</SUB>)<SUP>2</SUP>. The anomalies for all the second order elastic constants have been derived and relations among them reported. It is shown that the second order elastic anomalies suffer a discontinuity at the transition temperature