Method for fitting crystal field parameters and the energy level fitting for Yb3+ in crystal Sc2O3

doi:10.1088/1674-1056/19/8/087501

中国物理B ›› 2010, Vol. 19 ›› Issue (8): 87501-087501.doi: 10.1088/1674-1056/19/8/087501

Method for fitting crystal field parameters and the energy level fitting for Yb³⁺ in crystal Sc₂O₃

宁凯杰¹, 肖进¹, 丁丽华¹, 周文龙¹, 张庆礼², 刘文鹏², 殷绍唐², 江海河³

(1)Crystal Lab, Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Hefei 230031, China; (2)Crystal Lab, Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Hefei 230031, China; Anhui Provincial Key Lab of Optical Devices and Materials, Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Hefei 230031, China; (3)Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei 230031, China

收稿日期:2009-10-27 修回日期:2009-12-08 出版日期:2010-08-15 发布日期:2010-08-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 50772112 and 50872135), the Natural Science Foundation of Anhui Province of China (Grant No. 08040106820), the Knowledge Innovation Program of the Chinese Academy of Sciences (Grant No. YYYJ-1002).

Method for fitting crystal field parameters and the energy level fitting for Yb³⁺ in crystal Sc₂O₃

Zhang Qing-Li(张庆礼)^a)b)^†,Ning Kai-Jie(宁凯杰)^a), Xiao Jin(肖进)^a), Ding Li-Hua(丁丽华)^a),Zhou Wen-Long(周文龙)^a),Liu Wen-Peng(刘文鹏)^a)b),Yin Shao-Tang(殷绍唐)^a)b), and Jiang Hai-He(江海河)^c)

^a Crystal Lab, Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Hefei 230031, China; ^bAnhui Provincial Key Lab of Optical Devices and Materials, Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Hefei 230031, China; ^c Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei 230031, China

Received:2009-10-27 Revised:2009-12-08 Online:2010-08-15 Published:2010-08-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 50772112 and 50872135), the Natural Science Foundation of Anhui Province of China (Grant No. 08040106820), the Knowledge Innovation Program of the Chinese Academy of Sciences (Grant No. YYYJ-1002).

摘要/Abstract

摘要： A method to compute the numerical derivative of eigenvalues of parameterized crystal field Hamiltonian matrix is given, based on the numerical derivatives the general iteration methods such as Levenberg–Marquardt, Newton method, and so on, can be used to solve crystal field parameters by fitting to experimental energy levels. With the numerical eigenvalue derivative, a detailed iteration algorithm to compute crystal field parameters by fitting experimental energy levels has also been described. This method is used to compute the crystal parameters of Yb³⁺ in Sc₂O₃ crystal, which is prepared by a co-precipitation method and whose structure was refined by Rietveld method. By fitting on the parameters of a simple overlap model of crystal field, the results show that the new method can fit the crystal field energy splitting with fast convergence and good stability.

Abstract: A method to compute the numerical derivative of eigenvalues of parameterized crystal field Hamiltonian matrix is given, based on the numerical derivatives the general iteration methods such as Levenberg–Marquardt, Newton method, and so on, can be used to solve crystal field parameters by fitting to experimental energy levels. With the numerical eigenvalue derivative, a detailed iteration algorithm to compute crystal field parameters by fitting experimental energy levels has also been described. This method is used to compute the crystal parameters of Yb³⁺ in Sc₂O₃ crystal, which is prepared by a co-precipitation method and whose structure was refined by Rietveld method. By fitting on the parameters of a simple overlap model of crystal field, the results show that the new method can fit the crystal field energy splitting with fast convergence and good stability.

Key words: crystal field parameter, numerical derivative of matrix eigenvalue, Yb³⁺:Sc₂O₃, simple overlap model

中图分类号: (Crystal and ligand fields)

71.70.Ch

61.50.Ah (Theory of crystal structure, crystal symmetry; calculations and modeling) 61.66.Fn (Inorganic compounds) 71.70.Ej (Spin-orbit coupling, Zeeman and Stark splitting, Jahn-Teller effect)

张庆礼, 宁凯杰, 肖进, 丁丽华, 周文龙, 刘文鹏, 殷绍唐, 江海河. Method for fitting crystal field parameters and the energy level fitting for Yb³⁺ in crystal Sc₂O₃[J]. 中国物理B, 2010, 19(8): 87501-087501.

Zhang Qing-Li(张庆礼),Ning Kai-Jie(宁凯杰), Xiao Jin(肖进), Ding Li-Hua(丁丽华),Zhou Wen-Long(周文龙),Liu Wen-Peng(刘文鹏),Yin Shao-Tang(殷绍唐), and Jiang Hai-He(江海河). Method for fitting crystal field parameters and the energy level fitting for Yb³⁺ in crystal Sc₂O₃[J]. Chin. Phys. B, 2010, 19(8): 87501-087501.

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Method for fitting crystal field parameters and the energy level fitting for Yb³⁺ in crystal Sc₂O₃

Method for fitting crystal field parameters and the energy level fitting for Yb³⁺ in crystal Sc₂O₃

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