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

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

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.

Keywords: crystal field parameter numerical derivative of matrix eigenvalue Yb³⁺:Sc₂O₃ simple overlap model

Received: 27 October 2009
Revised: 08 December 2009
Accepted manuscript online:

PACS:	71.70.Ch	(Crystal and ligand fields)
	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)

Fund: 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).

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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 2010 Chin. Phys. B 19 087501

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Calculating Hamiltonian parameters for Yb³⁺ in a low-symmetry lattice site, and fitting the structure and levels of Yb³⁺:RETaO₄ (RE=Gd, Y, and Sc)
Zhang Qing-Li (张庆礼), Ning Kai-Jie (宁凯杰), Ding Li-Hua (丁丽华), Liu Wen-Peng (刘文鹏), Sun Dun-Lu (孙敦陆), Jiang Hai-He (江海河), Yin Shao-Tang (殷绍唐). Chin. Phys. B, 2013, 22(6): 067105.

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

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