Crossover from classical to 3d-Ising critical behaviour near the antiferrodistortive phase transition of lawsonite.

Results of X-ray scattering intensities and peak profiles of lawsonite single crystals are presented in a wide temperature range including the antiferrodistortive phase transition Cmcm - (Tc 270 K) → Pmcn. In the integrated intensities of the superlattice reflections above Tc pronounced pretransitional tails similar to those detected recently in birefringence [P. Sondergeld et al., Phys. Rev. B62, 6143 (2000)] and in excess entropy data [S. A. Hayward et al., Eur. J. Min. 14, 1145 (2002)] are observed. These tails correspond to diffuse Lorentzian shaped scattering peaks. The temperature variation of the diffuse scattering intensity and profile can be well described within a Landau-Ginzburg model. In combination with entropy data we obtain a complete set of free energy parameters. Using these coefficients we are able to fit the spontaneous part and the precursor tails of the integrated intensities, the excess birefringence and entropy in a broad temperature range outside a temperature interval of about ±3 K around Tc. In the vicinity of Tc the experimental data are in excellent agreement with the predictions of a crossover model, the effective critical exponent αeff(τ) varying from the classical (αeff = 0.5) to the 3d Ising limit (αeff = 0.11). Lawsonite therefore represents an ideal system to study the crossover from classical to critical behavior