Fundamentals in ferroelectric transition of TGS

Abstract

An extended Landau type-model has been used to find the three-terms polynomial expansion of the Gibbs free energy, that describe the second-order phase transition in pure TGS crystal. Temperature dependence of the coefficients was calculated using experimental susceptibilities and polarization, measured on a large temperature range. In a second version of the model, the influence of the external electric field was considered. The third coefficient δ E gets negative values near the Curie point. Gibbs free energy curves G E ( P, T), versus polarization, show peculiar behaviour depending on an external electric field, in the temperature range 3–5°C near the Curie point. The share contribution of the electric field 1.5 kV/cm, exceed 100% at Δ T= T C− T <1.5°C. All curves become asymmetrical and the external barriers of the double minimum potential, for Δ T⩽4°C, show turning points for values smaller than k B T. The central barrier, at Δ T<25°C, is about two orders of magnitude smaller than k B T. The energy corresponding to the internal field E int≈ P S/3 ε 0, is higher or comparable to k B T, only at Δ T⩾10°C. The equation of state E( P, T), which is supposed to represent the hysteresis loop P( E), does not give the right order of magnitude of the measured coercive field. On this ground and according to some other literature data, we conclude that the free energy G( P, T) of TGS is a non-analytical function. Some other models, taking into account short and long-range interaction, have to be considered.