Order parameter coupling and Debye-Waller factor at the phase transition in NiTiO3

NiTiO3 undergoes a second order phase transition from an (ordered) ilmenite structure <(R(3)over bar)> to a disordered corundum-like structure <(R(3)over bar c)>. The primary order parameter is of the order-disorder type (cation exchange, A(2g) symmetry). In addition there are displacive degrees of freedom of A(2g) and A(1g) symmetry. Their variation with temperature was derived from neutron powder diffraction experiments. The coupling between the various order parameters was analysed in the framework of Landau theory. No consistency could be achieved if only lowest order coupling terms are considered. In principle, agreement may be obtained by including higher order terms, however, the large number of free parameters involved in this case are regarded as a mere parametrisation of the problem. Instead various order-disorder phase transition theories were applied. Most of them show large discrepancies with the observed data. The best approximations, though not really satisfactory, are obtained for (i) a generalized Bragg Williams approach which takes into account the thermal entropy and (ii) the quasi-chemical approach which takes into account short range order effects. In the latter case the number of nearest neighbours is close to 2, i.e. the system exhibits a quasi one-dimensional behaviour in agreement with earlier considerations of the elementary exchange process. Finally, an excellent fit to all data is achieved by dividing the whole temperature region into two parts: a low temperature one governed by the law of mass action (no correlations), and a high temperature one close to T-c governed by a general critical power law (with beta approximate to 0.1). The critical behaviour of the various mean square displacements derived from the Debye-Waller factors can be explained semi-quantitatively within Landau theory and confirms the assumptions about the order parameter coupling.