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The description of distributions related to grain microstructure helpsphysicists to understand the processes in materials and their properties. Thispaper presents a general statistical methodology for the analysis ofcrystallographic orientations of grains in a 3D Laguerre tessellation datasetwhich represents the microstructure of a polycrystalline material. We introducecomplex stochastic models which may substitute expensive laboratoryexperiments: conditional on the Laguerre tessellation, we suggest interactionmodels for the distribution of cubic crystal lattice orientations, where theinteraction is between pairs of orientations for neighbouring grains in thetessellation. We discuss parameter estimation and model comparison methodsbased on maximum pseudolikelihood as well as graphical procedures for modelchecking using simulations. Our methodology is applied for analysing a datasetrepresenting a nickel-titanium shape memory alloy.

Fitting the grain orientation distribution of a polycrystalline material conditioned on a Laguerre tessellation