摘要
最小二乘法是求解精确晶格参数的基本方法。讨论了使用和不使用校正函数情形下的科恩最小二乘法,给出了所有晶系的法方程、晶格参数、误差估计的计算公式,以及计算晶格参数、校正函数参数的阻尼最小二乘迭代算法,该方法具有普适性,有大的收敛范围和快的收敛速度。作为应用例子,计算了数个不同晶系晶体的晶格参数,说明最小二乘法是获得高精度晶格参数的计算方法;用阻尼最小二乘法计算了ChuG校正函数的参数,表明该方法是获得校正函数参数的有效方法。
The least square method is an essential method to compute lattice parameters with high precision. The Cohen＇s least square method with or without a corrective function of diffraction angle is discussed. The normal equations of seven crystal systems, formulas to compute lattice parameters and estimate error are given. The modified Levenberg-Marquardt iteration algorithm, which is commonly applicable, with wide convergent range and fast convergent speed to compute the lattice parameters and corrective function parameters, is also given. As examples, the lattice parameters of several crystals belonging to the different crystal systems were computed, and the results showed that the least square method is a method to obtain accurate lattice parameters, and the parameters of the corrective function ChuG was computed with the modified Levenberg-Marquardt method, which shows that the method is effective to compute the corrective function parameters.
出处
《量子电子学报》
CAS
CSCD
北大核心
2009年第2期177-186,共10页
Chinese Journal of Quantum Electronics
基金
国家自然科学基金(50872135)
安徽省优秀青年科技基金(08040106820)资助项目
关键词
材料
晶格参数
科恩最小二乘法
法方程
衍射角校正函数
阻尼最小二乘法
materials
lattice parameter
Cohen＇s least square method
normal equation
corrective function of diffraction angle
Levenberg-Marquardt method
