Quantum-chemical analysis of the thermodynamic isotope effect in quasi-one-dimensional H-bonded Pb(H/D)PO₄ ferroelectrics

Abstract

The thermodynamics of the structural phase transition of H-bonded ferroelectric materials, Pb(H/D)PO₄, were considered in terms of the pseudo-spin Ising model with inclusion of tunneling and longrange effects. The pseudo-spin Hamiltonian parameters needed for analysis of the transition were determined by a procedure based on an independent quantum chemical method. A simplified scheme for the selection of model clusters was proposed, which allows the application of various quantum chemical methods, including high-level methods (CCSD/6-311+G** and so on), in the calculations of double-well potential profiles and Slater parameters. The calculation results were discussed in terms of two statistic models: molecular field approximation (MFA) and Bethe cluster method (BCM). The theoretical estimates of critical transition temperature for both systems are discussed and it is shown that the (semi)quantitative reproduction of experimental data is possible only in terms of BCM taking into account the tunneling effects. The explanation is given for the observed isotope effect caused by very pronounced increase in the critical transition temperature upon deuteration (ΔT_с ≈ 140 K). The crucial role belongs to the difference between tunneling effects in the ferroelectric crystals in question. It is emphasized that the observed differences between the crystal lattice and H/D bond geometries, including the mutual orientation of the bonds, must be accurately included in the calculations.