Ferroelastic and ferroelectric phase transition in a molecular crystal : tanane - 2. — Phenomenological model and piezoelectric resonance study of the soft acoustic mode

We report in this article a low frequency acoustic resonance study of the elastic anomaly associated with the ferroelastic and ferroelectric phase transition of tanane. The critical behaviour of the elastic constant $$ compared to that of the dielectric susceptibility [MATHS] allows a discussion to be given of the singularities associated with such a phase transition in terms of three linearly coupled variables : - An Ising order parameter η which describes the short range molecular ordering. - A shear strain of the lattice uxy. - And a lattice component of the polarization : pz opposite to the pseudo-spin component : p'z due to the permanent dipole moment of the molecule. We also discuss the dynamics of this coupled system and the dispersion of its dielectric and acoustic response functions. The observed damping of the acoustic modes coupled to the molecular ordering thus provides an estimate of the relaxation time characteristic of this order-disorder phase transition : [MATHS] τ*η ~ 10-9 s × T/T - Tc