Statistical physics of grain-boundary engineering.
Statistical physics of grain-boundary engineering.
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晶界工程统计物理。
DOI：
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发表时间：
2005
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通讯作者：
Elizabeth A. Holm
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作者：
E. McGarrity;P. Duxbury;Elizabeth A. Holm
逾渗理论现在是多晶材料分析的标准，其中晶界可以分为两个不同的类别，即具有有利性质的"好"边界和严重降低材料性能的"坏"边界。晶界工程（GBE）致力于通过设计体积分数c和良好晶界的排列来改善材料行为。GBE材料中的两个关键分解过程是强连接的颗粒聚集体的渗流的开始和弱晶界的连接路径的开始。利用真实的多晶微结构，我们发现在二维中强聚集渗流的阈值c（SAP）和弱边界渗流的阈值c（WBP）是相等的，其值为c（SAP）= c（WBP）= 0.38（1），比规则六方晶粒结构的阈值c（RH）= 2sin（pi/18）= 0.347（1）稍高。.在三维空间中，强的聚集渗流和弱的边界渗流分别发生在不同的位置，我们发现c（SAP）= 0.12（3）和c（WBP）= 0.77（3）。高T（c）材料的临界电流和结构系统的内聚能与统计物理中的临界流形问题有关。我们开发了GBE材料中的临界流形理论，该理论具有三个不同的区域：（i）低浓度，其中随机流形理论适用，（ii）临界浓度，其中换算标度理论适用，以及（iii）高浓度，c> c（SAP），其中周期性弹性介质理论适用。制度（iii）可能是最重要的实际上，其特征在于一个临界长度L（c），这是在临界流形上的分裂区域的大小。在高对比度ε-> 0的极限下，我们发现在二维L（c）成正比gc/（1-c），而在三维L（c）成正比gexp [B（0）c/（1-c）]/[c（1-c）]（1/2），其中g是平均晶粒尺寸，ε是弱边界与强边界的结合能之比，并且B（0）是1阶常数。GBE材料的许多性质可以与L（c）相关，L（c）在二维中在接近c = 1时代数地发散，但在三维中在该极限处指数地发散。我们强调，GBE渗流过程和临界流形行为是非常不同的二维相比，三维。因此，使用二维模型来理解大块GBE材料的行为可能会产生误导。
Percolation theory is now standard in the analysis of polycrystalline materials where the grain boundaries can be divided into two distinct classes, namely "good" boundaries that have favorable properties and "bad" boundaries that seriously degrade the material performance. Grain-boundary engineering (GBE) strives to improve material behavior by engineering the volume fraction c and arrangement of good grain boundaries. Two key percolative processes in GBE materials are the onset of percolation of a strongly connected aggregate of grains, and the onset of a connected path of weak grain boundaries. Using realistic polycrystalline microstructures, we find that in two dimensions the threshold for strong aggregate percolation c(SAP) and the threshold for weak boundary percolation c(WBP) are equivalent and have the value c(SAP) = c(WBP) =0.38 (1) , which is slightly higher than the threshold found for regular hexagonal grain structures, c(RH) =2 sin (pi/18) =0.347... . In three dimensions strong aggregate percolation and weak boundary percolation occur at different locations and we find c(SAP) =0.12 (3) and c(WBP) =0.77 (3) . The critical current in high T(c) materials and the cohesive energy in structural systems are related to the critical manifold problem in statistical physics. We develop a theory of critical manifolds in GBE materials, which has three distinct regimes: (i) low concentrations, where random manifold theory applies, (ii) critical concentrations where percolative scaling theory applies, and (iii) high concentrations, c> c(SAP) , where the theory of periodic elastic media applies. Regime (iii) is perhaps most important practically and is characterized by a critical length L(c) , which is the size of cleavage regions on the critical manifold. In the limit of high contrast epsilon-->0 , we find that in two dimensions L(c) proportional, gc/ (1-c) , while in three dimensions L(c) proportional, g exp [ b(0) c/ (1-c) ] / [c (1-c) ](1/2) , where g is the average grain size, epsilon is the ratio of the bonding energy of the weak boundaries to that of the strong boundaries, and b(0) is a constant which is of order 1. Many of the properties of GBE materials can be related to L(c) , which diverges algebraically on approach to c=1 in two dimensions, but diverges exponentially in that limit in three dimensions. We emphasize that GBE percolation processes and critical manifold behavior are very different in two dimensions as compared to three dimensions. For this reason, the use of two dimensional models to understand the behavior of bulk GBE materials can be misleading.