The Parameters and Fundamental Zones of Twin-Dependent Triple Junction Distributions
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INTRODUCTION
FOR much of the last century, grain boundaries have been a main focus of materials science research. This has been under the limited assumption that the properties of polycrystalline structure as a whole may be derived from the sum of its parts.[1] While the study of grain boundaries has led to innumerable materials advances, the grain boundary distribution gives incomplete information of the network as a whole. While grain boundaries have various properties on a local scale, corresponding macroscale material properties are likely the result of the grain boundary network.[2] For example, this was demonstrated through studies of grain boundary engineered materials. In these materials, the improvement in properties such as intergranular cracking was shown as the result of the break-up of the random boundary network.[3,4] The grain boundary character distribution (GBCD)[5] provides the relative fraction of grain boundaries without consideration for geometrical or topological correlations within the network.[6] These correlations become particularly important for grain boundary networks with a high fraction of symmetric boundaries such as twin boundaries.[7] Several studies have shown that the percolation threshold for a crystallographically consistent grain boundary network is shifted from that generated by a random network.[8–11] In these studies, boundaries were classified with a binary representation of special vs high-angle random (or general). These studies also indicated that the deviations from the GRADEN B. HARDY, PhD Candidate, and DAVID P. FIELD, Professor, are with the School of Mechanical and Materials Engineering, Washington State University, PO BOX 642920, Pullman, WA 99164-2920. Contact e-mail: [email protected] Manuscript submitted September 6, 2014. METALLURGICAL AND MATERIALS TRANSACTIONS A
random percolation threshold were the result of crystallographic correlations at triple junctions (the intersection of three grains and three grain boundaries). Within the context of special vs random boundaries, it has been further shown that while the GBCD is incapable of reliably describing the boundary network topology, the triple junction distribution can describe network properties.[4,9] Intuitively, this is because the triple junction distribution contains local boundary correlation data and thus serves as the most basic measure of connectivity within the boundary network. Given its geometry, the triple junction has been designated as a first-order constraint and a quadruple node or the intersection of four grains, six boundaries, and four triple junctions as a second-order constraint. Frary and Schuh indicated that at least 75 pct of the correlations within a grain boundary network were accounted for by the triple junction firstorder constraints, whereas the quadruple node secondorder constraints account for the minority fraction.[12,13] Therefore, the triple junction distribution not only describes network topology but it also accounts for the majority of the network constraints. The mentio
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