  The description of distributions related to grain microstructure helps
physicists to understand the processes in materials and their properties. This
paper presents a general statistical methodology for the analysis of
crystallographic orientations of grains in a 3D Laguerre tessellation dataset
which represents the microstructure of a polycrystalline material. We introduce
complex stochastic models which may substitute expensive laboratory
experiments: conditional on the Laguerre tessellation, we suggest interaction
models for the distribution of cubic crystal lattice orientations, where the
interaction is between pairs of orientations for neighbouring grains in the
tessellation. We discuss parameter estimation and model comparison methods
based on maximum pseudolikelihood as well as graphical procedures for model
checking using simulations. Our methodology is applied for analysing a dataset
representing a nickel-titanium shape memory alloy.
