在正交集团O上定义的定向分布函数的张量里埃扩展
1Department of Science and Mathematics, Glenville State University, Glenville, WV 26351, USA.
概括
这项研究扩展了面向分布函数 (ODF) 的张量里埃扩展,包括不恰当的点群,增强了复杂晶体对称性的纹理分析. 新方法准确地表示了超出标准旋转组SO的对称性的多晶体.
科学领域:
- 连续机械学的连续力学.
- 材料科学是一种材料科学.
- 晶体学 晶体学是指结晶学.
背景情况:
- 经典的纹理分析在旋转组SO上使用方向分布函数 (ODF).
- 这种方法对于由不适当的点群定义的晶体对称性是有限的.
- 曼和杜先前的工作为SO上的ODF建立了张量里埃扩展 (tensor Fourier expansions).
研究的目的:
- 将张量里埃扩展过程扩展到对直角组O(3) 上定义的ODF.
- 开发一种分析具有属于21个不恰当点组中的任何一个晶体对称的多晶体的方法.
- 为材料科学中的纹理分析提供一个更全面的框架.
主要方法:
- 考虑在直角组O上定义的方向分布函数 (ODF).
- 扩展了将经典ODF扩展重写成张量里叶扩展的系统程序.
- 适用于以不适当的点群定义的晶体对称性的多晶体.
主要成果:
- 介绍了一种推导在O(3) 上的ODF的张量里埃扩展的一般程序.
- 该方法成功地容纳了21个不适当的点组,克服了基于SO3的分析的局限性.
- 提供了说明性示例,以证明开发的程序的适用性.
结论:
- 开发的张量里埃膨胀法为具有复杂对称性的多晶体的纹理分析提供了强大的框架.
- 这项工作显著推进了对晶体结构的理解和计算处理.
- 这些发现对于连续力学和材料分析的基本问题至关重要.
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