多晶材料晶胞参数的X射线线对法最小二乘方程稳定性判别解法

DISCRIMINATION OF STABILITY OF THE LEAST SQUARE EQUATIONS IN DETERMINATION OF LATTICE PARAMETER OF POLYCRYSTALLINE MATERIALS FROM PAIRS OF X RAY DIFFRACTION LINES

晶胞参数是多晶材料晶体结构的重要参数。测定两条衍射线之间的衍射角差的线对法在实验技术上比较简便，系统误差小，可得到较精确的结果。但线对法求解晶胞参数时，最小二乘方程的某些系数组合可使误差严重积累。这些病态方程组解出的晶胞参数误差很大。本研究提出一种用逆矩阵范数数值对线对法最小二乘方程组的稳定性进行判别，选择常态方程而求解晶胞参数的方法。

Lattice parameters are the important crystal structural parameters of polycrystalline materials.The pair line method by measuring the difference of angles between two diffraction lines is rather simple and convenient technically and is easy to obtain accurate results.But combination of some coefficients in the least square equations can lead to a serious accumulation errors.The results obtained by these defective equations will have a large error.A method for solving the normal state equations to obtain the lattice parameters by using of the inverse matrix to discriminate the stability of the pair line least square equations is given in this paper.Practical example process that the method is quite explicit and accurate,and reliable results can be obtained.