Crystal-field Splitting in Regular Polyhedron

SONG Zhen; LIU Quan-lin

doi:10.37188/CJL.20220190

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Crystal-field Splitting in Regular Polyhedron

Invited Paper | 更新时间：2023-02-13

- Crystal-field Splitting in Regular Polyhedron
  增强出版
- Chinese Journal of Luminescence Vol. 43, Issue 9, Pages: 1428-1435(2022)
- 作者机构：
  
  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
- 作者简介：
- 基金信息：
  
  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)
- DOI：10.37188/CJL.20220190
  CLC： O482.31
- Published：05 September 2022，
  
  Received：09 May 2022，
  
  Revised：21 May 2022，
- 稿件说明：
移动端阅览
宋振,刘泉林.正多面体中的晶体场劈裂[J].发光学报,2022,43(09):1428-1435.

SONG Zhen,LIU Quan-lin.Crystal-field Splitting in Regular Polyhedron[J].Chinese Journal of Luminescence,2022,43(09):1428-1435.
宋振,刘泉林.正多面体中的晶体场劈裂[J].发光学报,2022,43(09):1428-1435. DOI： 10.37188/CJL.20220190.

SONG Zhen,LIU Quan-lin.Crystal-field Splitting in Regular Polyhedron[J].Chinese Journal of Luminescence,2022,43(09):1428-1435. DOI： 10.37188/CJL.20220190.

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40

/9、90

/9、80

/9和45

/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

能级在不同正多面体中的反转现象。

Abstract

Crystal-field theory plays a fundamental role in understanding the energy levels of rare-earth and transition-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 models 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 40

/9， 90

/9， 80

/9 and 45

In the end， the relative orientations between e

orbitals and the ligands are visualized to present a vivid understanding of the magnitude reverse

关键词

晶体场能级劈裂多面体

Keywords

crystal fieldenergy levelsplittingpolyhedron

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宋振(1986-)，男，山东乳山人，博士，副教授，2014年于北京科技大学获得博士学位，主要从事固体光谱学及发光材料构效关系的研究。. doi: 10.1016/s0925-8388(02)00056-7http://dx.doi.org/10.1016/s0925-8388(02)00056-7

E‐mail： zsong@ustb.edu.cn. doi: 10.1016/s0925-8388(02)00056-7http://dx.doi.org/10.1016/s0925-8388(02)00056-7

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