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对各向异性多晶试样的X射线衍射测量给出一组描述单个面法线取向分布的函数(极图)。用以前文章里所叙述的方法(把晶粒取向函数展开成广义勒让德函数的级数),从一组这些面法线分布就可以推导出试样里所有晶粒的取向分布。表征晶粒取向的展开系数W_(1mn)必须满足试样所具有的晶体学的和统计学的对称元的限制条件。当晶粒属于立方晶系时,不仅要求某些W_(1mn)等于零,而且剩下的不等于零的W_(1mn)应该彼此线性相关(对于给定的1和m)。用计算机从数值上解出了表示W_(1mn)的线性相关的矩阵方程式,结果用一个表格给出。
X-ray diffraction measurements of anisotropic polycrystalline samples give a set of functions (pole figures) describing the normal distribution of single faces. Using the method described in the previous article, which expands the grain orientation function to the generalized Legendre function, the orientation distribution of all the grains in the sample can be derived from a set of these surface normal distributions. The expansion coefficient W_ (1mn) characterizing the grain orientation must satisfy the crystallographic and statistical symmetry constraints possessed by the specimen. When the grains belong to a cubic system, not only do some W_ (1mn) be equal to zero, but also the remaining W_ (1mn) that is not equal to zero should be linearly related to each other (for a given 1 and m). A numerical solution of the matrix of linear correlations representing W_ (1mn) is given by the computer and the results are given in a table.