Effects of a Crystal Field on the Orientational Phase Transition in a System of Dipoles: A Mean-Field Study of SO₂-β-Hydroquinone Clathrate

The orientational ordering in a system of dipolar molecules located on a trigonal lattice is studied in the eight-sublattices approximation. Our concrete example is SO₂ molecules in β-hydroquinone clathrate. It is assumed that the molecules interact with each other via effective dipole-dipole interactions, and that the crystal field acting on those molecules is of the form W_A = C_COS[ν(φ-δ_A)], where φ is a rotational angle and A is a sublattice number. If ν is an odd integer, we assume that δ_A may different for different A. The mean electric field which depends on the depolarization field is obtained. Various cases of C, ν, δ_A are investigated. Results are as follows: the possible dipole arrangement is antiferroelectric in all cases; the phase transition for ν = 2, 4, 5, 6 is of second order; if ν = 1, no disordered phase occurs; if ν = 3, the phase transition is weakly of first order excep for special cases; the C dependence of the transition temperature is weak unless ν = 2; δ_A chiefly determines the equilibrium direction. A comparison with experiment suggests that the low-temperature phase of SO₂-β-hydroquinone has ν = 2 or 3, and that interactions between enclosed SO₂ molecules other than dipole-dipole interactions may be also effective.