Simulations d'une structure cristalline incommensurable à caractère désordonné

Incommensurate crystal structures do not display three-dimensional periodicity. Discovered in the 1960's, a mathematical model has been established in 1974 only. Incommensurate structures belong to the big family of aperiodic structures. The modulation of incommensurate structures manifests itself as satellite reflections around the main peaks on X-rays diffractograms. Short range order correlations in crystals lead to diffuse scattering between Bragg peaks in the diffraction pattern. The computing power available today allows for very time consuming simulations of the incommensurate or disordered crystal structures. Simulations based on Monte-Carlo and the molecular dynamic techniques have been performed. The former is based on stochastic algorithms, whereas the latter is deterministic. This PhD thesis strove to combine these two methods, using a four-isomermodel, in order to study the incommensurate, disordered polymorph of p-azoxydiphenetol (PAP), which crystallises below 356 K. One of the main features of the PAP molecule is its dative bond. A Monte-Carlo program, using true empirical potentials, has been developed in order to explain the behaviour of PAP. This code (6000 lines), written in C, uses the GSL and OpenMP libraries. Using numerical and experimental tools, this thesis provides explanations for the origin, from an atomic point of view, of the incommensurate and disordered behaviour of PAP. Calculations have been performed on the clusters of École Polytechnique Fédérale de Lausanne. Simulated diffraction patterns have been compared to experimental data, collected before and during this study. Moreover, a set of differential scanning calorimetry (DSC) measurements has been carried out during this work, the results of which have been analysed based on Arrhenius's law. For a better understanding of the role played by the dative bond, and the relation between the complexity of the molecule and the structure, DFT and ab initio calculations have been performed. This work has successfully woven the results from different experimental and numerical techniques into a comprehensive model for this very complex system indeed.