Structural modulation of the commensurate phases of betaine calcium chloride dihydrate (BCCD) within a model with nearest neighbour anharmonic couplings

The structural modulation of the four-fold phase of BCCD has been studied b y neutron and X-ray difraction, and the discrepancies between the results g iven by both techniques are quite remarkable. Although neutron measurements show that the modulation is clearly anharmonic and the effect of third ord er satellites is essential to describe the structural modulation, the inten sity of these satellites is very low in the case of X-rays. In the present work the theoretical structural modulation is analyzed within the framework of a symmetry based semi-microscopic model in the mean-field approximation . The model takes into account the three degrees of freedom associated with the lowest energy phonon branches as well as the anharmonic interactions b etween nearest neighbours to reproduce the essential experimental features of the phase diagram. Although the model is not able to predict the structu ral modulation at the atomic level, the well defined symmetry of the variab les allows a comparison of the theoretical and experimental modulations.