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

TL;DR

This paper develops a statistical approach to model and analyze the distribution of grain orientations in 3D polycrystalline materials conditioned on Laguerre tessellations, reducing reliance on costly experiments.

Contribution

It introduces complex stochastic interaction models for grain orientations conditioned on Laguerre tessellations, with methods for parameter estimation and model validation.

Findings

Successful modeling of grain orientation distributions in a nickel-titanium alloy.

Effective parameter estimation and model comparison techniques demonstrated.

Graphical procedures for model checking using simulations provided.

Abstract

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.