Spectral graph theory for characterization and homogenization of grain boundary networks
Spectral graph theory for characterization and homogenization of grain boundary networks
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DOI：
10.1016/j.actamat.2017.11.054
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发表时间：
2018-03-01
期刊：
影响因子：
9.4
通讯作者：
Critchfield, Tyler R.
中科院分区：
文献类型：
--
作者：
Johnson, Oliver K.;Lund, Jarrod M.;Critchfield, Tyler R.
晶界网络(GBN)对结构材料和功能材料的性能都有深远的影响。然而，现有的表征其复杂结构的方法几乎普遍依赖于对GB的二进制分类，要么是“特殊的”，要么是“一般的”，这忽略了GB类型和性质的丰富和连续的光谱。此外，事实证明，描述GB的聚合网络结构是复杂的，传统方法侧重于局部结构，也依赖于二元GB分类，例如通过评估有多少“特殊”或“一般”边界在三重结点或四重节点处相交。在这里，我们基于谱图理论为GBN开发了新的结构度量，该度量既编码了全局网络拓扑结构，又编码了组成GB属性的全谱，从而实现了对任意GBN的高保真表征。利用这些度量，我们导出了一种新的GBN扩散系数的结构-性质关系。这个表达式中的主导项提供了一个有效和准确的近似，其对应的光谱度量揭示了影响感兴趣属性的主导微结构特征。这一项的谱指数作为一种全局有序参数，揭示了GBN的一个基本结构转变。这项工作提供了一个新的框架来表征GBN的结构，比以前可能的更具一般性，并促进了新的缺陷敏感结构-特性模型的开发。(C)2017 Acta Materialia Inc.由Elsevier Ltd.出版。保留所有权利。
Grain boundary networks (GBNs) have a profound influence on the properties of both structural and functional materials. However, existing methods to characterize their complex structure have almost universally relied upon a binary classification of GBs as either "special" or "general", which ignores the rich and continuous spectrum of GB types and properties. Furthermore, characterizing the aggregate network structure of GBs has proven complicated, with traditional methods focusing on local structure and also relying on a binary GB taxonomy, e.g. by evaluating how many "special" or "general" boundaries meet at triple junctions or quadruple nodes. Here we develop new structural metrics for GBNs, based on spectral graph theory, that encode both global network topology and the full spectrum of constituent GB properties, enabling high-fidelity characterization of arbitrary GBNs. Using these metrics, we derive an new structure-property relation for GBN diffusivity. The dominant term in this expression provides an efficient and accurate approximation, whose corresponding spectral metrics reveal the dominant microstructural features influencing the property of interest. The spectral index of this term serves as a type of global order parameter that reveals a fundamental structural transition in GBNs. This work provides a new framework to characterize the structure of GBNs in greater generality than previously possible and facilitates the development of new defect-sensitive structure-property models. (C) 2017 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.