Analysis of Experimental Grain Boundary Distributions Based on Boundary-Space Metrics

Abstract

Grain boundary distributions in the space of macroscopic boundary parameters are basic statistical characteristics of boundary networks. To avoid artifacts caused by the currently used computation method, it is proposed to utilize the kernel density estimation technique and to determine boundary distributions based on metric functions defined in the boundary space. A distribution is calculated at points of interest by summing areas of boundaries that fall within specified distances from these points. The new method is illustrated on experimental data of a nickel-based superalloy.DOI: 10.1007/s11661-014-2325-y Ó The Author(s) 2014. This article is published with open access at Springerlink.com A variety of properties of polycrystalline materials are affected by grain boundaries. To explore relationships between boundary structures and material properties, the boundaries need to be investigated at both atomic and ''macroscopic'' levels. Studies at the atomic scale are limited by experimental capabilities, but the macroscopic boundary parameters (i.e., misorientations between neighboring grains and directions of boundary plane normals [1] ) can be relatively easily determined. Experimental methods of three-dimensional microstructure characterization have been improved greatly over the last decade, and large sets of boundary parameters are being collected, e.g., References 2, 3. The sizes of resulting data sets allow for statistical analyses of boundaries.One of the most basic statistical characteristics of a boundary network is the distribution of grain boundaries with respect to the macroscopic boundary parameters. In relevant reports published so far (e.g., References 4 through 8), the distributions have been computed using a method [4] based on partition of a certain domain in the boundary parameter space into equivolume bins. Although this method has been successfully applied to various materials, it has deficiencies leading to artifacts in computed distributions, and complicating estimation of the reliability of the distributions.This note presents an alternative approach to computation of the boundary distributions. Suggestions given in Reference 9 are followed to adapt the kernel density estimation technique and to replace the partition of the boundary space by probing the distributions at selected points and counting boundaries that are not farther from those points than an assumed limiting distance defined in the boundary space. It is shown that this change of the computation method leads to significant improvements in the quality of resulting distributions. The new method also allows for a direct estimation of the reliability of the distributions. In the following, deficiencies of the hitherto used approach are discussed. Then, the new approach is described and confronted with the old one. Both methods are applied to grain boundary data of a nickel-based superalloy. For simplicity, only cubic ðm " 3mÞ crystal symmetry is considered; similar analysis can be performed for other holohedral symmetries.The gra...

Three-dimensional characterization of grain boundaries in pure nickel by serial sectioningviamechanical polishing

“…The minimum value in the AE3 section is about 200 MRD. These numbers are quite reliable as their relative errors vary between 6 and 20%; here and below, the relative error of a distribution at a given point is estimated as " ¼ 1=ð fnvÞ 1=2 , where f denotes the value of the distribution, n is the number of distinct grain boundaries in the network, and v stands for the volume determined by m and p (Glowinski & Morawiec, 2014). The AE3 section in Fig.…”

“…Li et al, 2009;Glowinski & Morawiec, 2014;Beladi et al, 2014;Saylor et al, 2003). A considerable part of this collection is related to facecentered cubic (f.c.c.)…”

“…Most of the boundary distributions published so far, including that reported by Li et al (2009), were obtained using a method based on dividing the five-dimensional space of boundary parameters into equi-volume bins and summing areas of mesh segments falling into a specific bin (Saylor et al, 2003). However, several deficiencies of that method were recently pointed out (Glowinski & Morawiec, 2014). Briefly, elongated shapes of some bins and lack of correspondence between bin dimensions and experimental resolutions lead to artifacts that hinder analysis of the distributions.…”

“…These artifacts are significantly reduced, and the quality of the distributions is improved, when the binning is abandoned in favor of the kernel density estimation (KDE) (Glowinski & Morawiec, 2014). With KDE, the distribution is probed in points uniformly dispersed in the boundary space, and areas of boundaries that are no farther (in terms of a metric defined in that space) from a given point than an assumed limiting radius are summed.…”

“…metals having significant fractions of AE3 boundaries. This applies to fine-grained pure nickel with a unimodal grain size distribution (Li et al, 2009), and also to superalloy IN100 (Glowinski & Morawiec, 2014) and austenite (Beladi et al, 2014).…”