中心对称矿物中Cu^(2+)六配位的晶场势能和微扰矩阵元计算  

Crystal Field Potential Energy and Minute Interference Matrix Element Calculation on 6-Coordinated Cu^(2+) in Mineral with Symmetric Conter

作　　者：韩照信[1] 张锦刚[1] 栾丽君[1] 

机构地区：[1]长安大学地球科学与国土资源学院,西安710054

出　　处：《地球科学与环境学报》2005年第4期53-57,共5页Journal of Earth Sciences and Environment

基　　金：陕西省科委项目(97D03)

摘　　要：对于离子型或以离子键为主的晶体,其光学和磁学性质可用晶体场理论解释。通过晶场微扰矩阵元的计算,可定量地确定晶场光谱谱带位置。以往资料无矩阵元的计算过程,只是给出了部分积分结果,这不利于在任何对称情况下晶场微扰矩阵元的计算。推导了中心对称矿物的晶场势能算符,计算了积分值,得出了矩阵元以系数Aλx,r2和r4的表达式。并以绿松石的结构数据为基础,计算了Cu2+的晶场微扰矩阵元表达式中的系数Aλx,从而计算了各矩阵元,通过对称矩阵的对角化,最终求得绿松石中Cu2+d轨道能量和晶体场谱带位置计算值。与实验资料对比,符合较好。因此,用晶体场理论和实验资料相结合可定量地阐明具离子键晶体的呈色机制。For the ion model crystals or the erystals in which the ionic bond is dominant,the optic and magnetic features can be interpreted by the crystal field theory. Through the calculation of crystal field minute interference matrix element,the position of crystal field spectra can be defined measurably. Although some calculation results have been given in literatazes, bur the lack of the matrir element calculation procedure is not beneficial for the calculation in any circumstances. This paper deduces the crystal field potential operator on the mineral which has center of symmetry, calculates the integrated value, and gets the matrix element formula expressed by modulus of Aλx, r^2 and r^4 On the bas is of the structure data of turquoise, this paper calculates the modulus Aλx of crystal field minute interference matrix element of Cu^2＋ and calculate the other matrix elements. Through diagonal manipulation of symmetry matrix, as the result, the authors get the d-orbit energy and the position of crystal field spectra of Cu^2＋ in turquoise. Compared with the experiment datas, they are consistent. Therefore, combined with the experiment datas, this method can illustrate the color forming mechanism of ion crystal.

关 键 词：晶场 势能算符 矩阵元计算 d轨道能量 

分 类 号：P574[天文地球—矿物学]