In situ observation of the polytypic phase transition 2H-12R in PbI₂: investigations of the thermodynamic structural and dielectric properties

Abstract

A reversible phase transition between the two polytypic phases 2H and 12R was found in PbI2 near 367K which proves that these polytypes are thermodynamic equilibrium phases and not the result of growth processes. Disordered stackings were observed in samples which were annealed at temperatures above 420K. The phase transition is kinetically hindered with an activation energy of 3.8 eV. The character of the phase transition is first order with a latent heat of around 276 J mol-1. The absence of dielectric anomalies with electric fields along the hexagonal c axis indicates that dipole-dipole interactions are not involved in the transition mechanism. The nature of the inter-layer forces are exclusively based on short-range interactions leading to a description of the phase transition in terms of pseudo-spin models. The elastic energy released during the phase transition is 1.2 J mol-1 as determined from the observed jump of the c lattice parameter. A thermodynamic description of the phase transition leads to the conclusion that its driving forces are related to the gain of phonon energy and elastic energy during the transformation. The entropy gain is due to the differences of the phonon frequencies between the two phases. Higher polytypes, if thermodynamically stable phases, can be described as mixtures of structural elements of the basic polytypes with additional stabilisation energies. The temperature evolution of the free energies of the different phases is anticipated. The experimental results are expressed in terms of the Landau theory which shows that the phase transition 2H-12H must be first order as observed. The Landau theory also explains the disordered polytype as a common para-phase for all ordered polytypes. Further insight into the origin of polytypism can be derived from the current understanding of ANNNI models.