Shapes of grain inclusions in crystals.
Shapes of grain inclusions in crystals.
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晶体中晶粒夹杂物的形状。
DOI：
10.1103/physrevb.32.12
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发表时间：
1985
期刊：
影响因子：
--
通讯作者：
Rottman
中科院分区：
文献类型：
--
作者：
He;Jayaprakash;Rottman
研究了嵌入相同材料的简单立方晶体中并相对于[001]轴旋转小角度的颗粒（具有固定体积）的“平衡”形状。 Read 和 Schockley 的晶界位错模型用于计算作为取向函数的晶界能。然后通过武尔夫结构从该能量中找到颗粒形状。针对泊松比 \ensuremath{\nu} 和表征核心能量的常数的不同值，分析了形状的各个方面。这种零温度形状的一个新颖特征是弯曲部分，其在斜率不连续的边缘处与小平面相交。对于小的 \ensuremath{\nu} ，形状本质上是一个平滑弯曲的旋转椭球体，在 (100)、(010)、(1\ifmmode\bar\else\textasciimacron\fi{}00) 和 (01\ifmmode\bar\else\textasciimacron\fi{}0) 平面上有四个等效的椭圆面。对于较大的 \ensuremath{\nu} 值，两个光滑部分可以在赤道平面处以斜率不连续性相交。在相变语言中，除了一阶相变之外，我们还发现了三重点，并且在 \ensuremath{\nu} 的狭窄范围内还发现了临界点。定性地探讨了非零温度的影响以及核心能量对位错特征的依赖性。
The ``equilibrium'' shape of a grain (with fixed volume) embedded in a simple-cubic crystal of the same material and rotated by a small angle with respect to the [001] axis is studied. The dislocation model of grain boundaries of Read and Schockley is used to compute the grain-boundary energy as a function of orientation. The grain shape is then found from this energy via the Wulff construction. Various aspects of the shape are analyzed for different values of both Poisson's ratio \ensuremath{\nu} and a constant characterizing the core energy. One novel feature in this zero-temperature shape is curved portions which meet facets at edges where there is a discontinuity in slope. For small \ensuremath{\nu} the shape is essentially a smoothly curved ellipsoid of revolution with four equivalent elliptical facets on the (100), (010), (1\ifmmode\bar\else\textasciimacron\fi{}00), and (01\ifmmode\bar\else\textasciimacron\fi{}0) planes. For large values of \ensuremath{\nu} two smooth parts can meet at the equatorial plane with a slope discontinuity. In phase-transition language we find, besides first-order transitions, triple points and, in a narrow regime in \ensuremath{\nu}, critical points. Effects of nonzero temperature and the dependence of the core energy on the character of the dislocation are explored qualitatively.