摘要
本文按最低对称的三斜晶系导出以直接测定值θ与点阵参数间的误差方程式,并以台劳级数线性化,由最小二乘得到法方程式,因而得到低对称晶系矿物点阵参数的最小二乘法精密计算公式。利用本文推导的公式与传统的柯亨最小二乘法公式,分别计算了七个三斜晶系矿物的点阵参数,二者存在不容忽视的差值。
So far the calculation of formula lattice parameters using X-ray powder diffrac-tion pattern for low-symmetric systems with least square method and its error equa-tions are built mainly on the equation of 1/d^2 and the reciprocal lattice parameters,and the calculation of lattice parameters is carried out under the condition thatthe sum of residual squares V^2 1/d^2 is minimal. But, according to least squaretheory, the error equations should be built on the equation of directly determinedelements θ and the lattice parameters, and the calculation of lattice parametersshould be carried out under the condition that the sum of residual squares V_θ~2 isminimal. Only in this way, can the best estimates of lattice parameters be obtained,and the estimates from the above method are only approximate estimates. In this paper, from the lowest-symmetric system-triclinic crystal System, theerror equation is built on the equation of directly determined elements θ and thelattice parameters, and is linearized with Taylor's Series. According to least square theory, the calculation of lattice parameters shouldbe carried out under the condition that the sum of residual squares V_θ~2 is minimal.Only in this way can the best estimates of lattice parameters be obtained.
关键词
晶系
点阵
参数
最小二乘法
低对称
lattices
parameter
least square methods
X-ray diffraction low-sym-metric crystal system
