正多面体中的晶体场劈裂  

Crystal-field Splitting in Regular Polyhedron

作　　者：宋振[1] 刘泉林[1] SONG Zhen;LIU Quan-lin(Beijing Key Laboratory for New Energy Materials and Technologies,School of Materials Science and Engineering,University of Science and Technology Beijing,Beijing 100083,China)

机构地区：[1]北京科技大学材料科学与工程学院,北京市新能源材料与技术重点实验室,北京100083

出　　处：《发光学报》2022年第9期1428-1435,共8页Chinese Journal of Luminescence

基　　金：国家自然科学基金(51832005,51972020);中央高校基本科研业务费专项资金(FRF-IDRY-20-028)资助项目。

摘　　要：晶体场理论是理解稀土/过渡金属离子在无机固体中能级结构的关键。对八面体场,能级表达式及图像解释发展得较为完善,但正四面体、立方体和立方八面体中的能级劈裂情况则需要进一步明确。本文根据微扰理论详细推导了单d电子在上述规则多面体中的晶体场劈裂。基于等键长的几何模型,给出了晶体场势的准确形式。随后构建了久期方程并通过对角化得到了劈裂后的能级。正四面体、八面体、立方体和立方八面体的晶体场劈裂大小分别为40Dq/9、90Dq/9、80Dq/9和45Dq/9。最后,d电子轨道与配位离子的相对取向关系有助于形象地理解e_(g)/t_(2g)能级在不同正多面体中的反转现象。Crystal-field theory plays a fundamental role in understanding the energy levels of rare-earth and transi⁃tion-metal elements in inorganic hosts.It has been fully developed for the octahedral field,both in analytical energy level expression and pictorial understanding.Nevertheless,the crystal field theory for other regular cubic polyhedra,including tetrahedron,cube and cuboctahedron,needs further investigation to show the similarities and differences with the octahedral field.In this work,the detailed crystal-field analysis of one d electron in those regular polyhedra is presented using the perturbation method.The exact crystal-field potentials are derived based on geometrical mod⁃els with equivalent center-ligand bond length.The secular matrices are constructed and diagonalized to give the split energy levels.The crystal-field splittings for regular tetrahedron,octahedron,cube and cuboctahedron are calculated to be 40Dq/9,90Dq/9,80Dq/9 and 45Dq/9.In the end,the relative orientations between e_(g)/t_(2g) orbitals and the li⁃gands are visualized to present a vivid understanding of the magnitude reverse.

关 键 词：晶体场 能级 劈裂 多面体 

分 类 号：O482.31[理学—固体物理]