Method for fitting crystal field parameters and the energy level fitting for Yb3+ in crystal Sc2O3 |
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Authors: | Zhang Qing-Li Ning Kai-Jie Xiao Jin Ding Li-Hu Zhou Wen-Long Liu Wen-Peng Yin Shao-Tang and Jiang Hai-He |
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Institution: | Crystal Lab, Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Hefei 230031, China; 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; Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei 230031, China |
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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. |
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Keywords: | crystal field parameter numerical derivative of matrix eigenvalue Yb3+:Sc2O3 simple overlap model |
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