A Bayesian approach to 2D triple junction modeling

We propose a Bayesian analytical approach to evaluate the 2D local transition probabilities model developed by Frary and Schuh in 2004 [1]. Their model characterizes the statistical properties of high-angle and low-angle interface networks in polycrystalline ensembles. The motivation for this work is to analyze the approach presented in Ref. [1] under a Bayesian premise. The model of Frary and Schuh [1] considers the percolation angular threshold for interfacial networks, Θt, to be a deterministic quantity; we, on the other hand, relax this assumption and presume the threshold angle to be a random variable. The physical justification for this is that there could be uncertainties in the microstructure network or measurement errors, for example, and thus Θt should not be a constant value. As a result, the fraction of boundaries to be classified as special, P, also becomes a random variable. We assume P to follow a Beta(z, 1 − z) distribution, where z ∈∈ (0, 1) is an adjustable parameter. Comparison of the error analysis between the Bayesian and non-Bayesian approaches, to the experimental results reported by Frary and Schuh [1], suggests that our model accounts for slightly more variation than the non-Bayesian approach.