A simple model was formulated which could be used to assess the statistical significance of grain-boundary character distributions in a material. In particular, the model was developed in order to determine a priori the number of boundaries which needed to be characterized such that the fraction of boundaries of a given type was known to within a certain error. The inclusion of experimental errors in the model accounted for misidentification of boundary types during the characterization process. The model also considered the statistical significance of boundary degradation by boundary type. This was a more restrictive application of the formalism, in that a low probability of degradation (cracking, corrosion, cavitation) on a rare boundary-type could result in very few measurements of degraded boundaries, and therefore to poor statistics. The aim of the model was to determine a priori the number of boundaries which needed to be characterized such that the result would have statistical significance. The model was applied to 2 sets of data on Ni-based alloys in order to show that, for a coincidence-site lattice boundary fraction larger than 0.2 to be known to within a fractional error of less than 0.10, a minimum of 500 boundaries had to be characterized.

A Priori Determination of the Sampling Size for Grain-Boundary Character Distribution and Grain-Boundary Degradation Analysis. B.Alexandreanu, G.S.Was: Philosophical Magazine A, 2001, 81[8], 1951-65