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提出了一个方法,用这个方法可以从x射线衍射测量获得的一组面法线分布,推导出在各向异性多晶试样里晶体的取向分布。它是以前提出来的分析具有纤维织构试样的类似方法的推广。因此它表示了一个适用于具有任意对称元的试样的极图转换问题的完全一般的解。面法线分布函数被展开成球谐函数的级数,它的系数Q_(1m)可以由实验衍射数据的数字积分而确定。晶体分布函数被展开成广义球谐函数的级数,它作为对称陀螺(Symmetrictop)的薛定锷波方程的解而出现。晶体分布函数的系数W_(1mn)是作为Q_(1m)的线性组合而获得。研究了由存在于试样里的晶体学的或者统计学的对称元引起的W_(1mn)的对称性质。以前在纤维织构分析方面提出的估计级数截断误差的方法和用最小二乘法减小实验误差的方法,经过适当推广后,在这里仍然适用。此外也指出了由于晶体的不完整性或者有限的尺寸而造成的衍射线变宽的影响至少可以近似地被修正。
A method is proposed by which the orientation distribution of crystals in an anisotropic polycrystalline sample can be deduced from a set of surface normal distributions obtained from x-ray diffraction measurements. It is an extension of a similar approach previously proposed for the analysis of samples with fibrous textures. It therefore represents a completely general solution to the problem of pole mapping for samples with arbitrary symmetry. The surface normal distribution function is expanded to the order of the spherical harmonic function, and its coefficient Q_ (1m) can be determined by the numerical integration of the experimental diffraction data. The crystal distribution function is expanded to the series of the generalized spherical harmonic function, which appears as the solution to the Schrödinger equation of Symmetryop. The coefficient W_ (1mn) of the crystal distribution function is obtained as a linear combination of Q_ (1m). The symmetry properties of W_ (1mn) caused by the crystallographic or statistical symmetry elements present in the sample were investigated. The previous methods of estimating the series truncation error and the method of least-squares reduction of experimental errors proposed in fiber texture analysis are properly applied here and still apply here. It has also been pointed out that the effect of the broadening of the diffraction lines due to the imperfections or the limited dimensions of the crystal can be at least approximately corrected.