Static and dynamic critical behaviour of uniaxial ferroelectrics and the phase transition in TGS

Abstract

Abstract Using the Larkin‐Khmelnitskii theory for static critical behaviour it is shown how recent renormalization group calculations on static and dynamic phenomena in uniaxial ferroelectrics can be generalized to the whole critical region. The cross‐over between classical and asymptotic behaviour is described in terms of two additional non‐universal parameters b and t 0 which are defined by microscopic quantities. The critical temperature dependence of the elastic and electrostrictive constants, the dynamic susceptibility, and the ultrasonic attenuation are treated as a ramification of the Larkin‐Khmelnitskii theory. The correlation parameter δ and the kinetic coefficient T exhibit no anomalous behaviour close to T c . The ultrasonic attenuation above T c is shown to be dominated by energy fluctuation. Contradictions in previous interpretations of the data of ferroelectric TGS are removed. At zero temperature T e0 = 4 × 10 −7 s is found for the energy relaxation time and ξ 0 = 3.7 and ξ ∥o = 3.9 Å for the transverse and longitudinal correlation length, respectively. From b = 0.036 and t 0 = 0.04 the size of the critical region of TGS is estimated to t = ( T – T c )/ T c ≈︁ 1.6 × 10 −2 to 1.8 × 10 −3 depending on the quantity which is considered, but the uncertainties in determing t 0 are large.