发光学报2022，Vol.43Issue(9)：1428-1435,8.DOI:10.37188/CJL.20220190
正多面体中的晶体场劈裂
Crystal-field Splitting in Regular Polyhedron
摘要
Abstract
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 eg/t2g 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Key words
crystal field/energy level/splitting/polyhedron分类
数理科学引用本文复制引用
宋振,刘泉林..正多面体中的晶体场劈裂[J].发光学报,2022,43(9):1428-1435,8.基金项目
国家自然科学基金(51832005,51972020) （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Supported by National Natural Science Foundation of China(51832005,51972020) （FRF-IDRY-20-028）
Fundamental Research Funds for The Cen-tral Universities(FRF-IDRY-20-028) （FRF-IDRY-20-028）
