Method for fitting crystal field parameters and the energy level fitting for Yb^(3+) in crystal Sc_2O_3  

作　　者：张庆礼 宁凯杰 肖进 丁丽华 周文龙 刘文鹏 殷绍唐 江海河 

机构地区：[1]Crystal Lab,Anhui Institute of Optics and Fine Mechanics,Chinese Academy of Sciences [2]Anhui Provincial Key Lab of Optical Devices and Materials,Anhui Institute of Optics and Fine Mechanics,Chinese Academy of Sciences [3]Hefei Institutes of Physical Science,Chinese Academy of Sciences

出　　处：《Chinese Physics B》2010年第8期582-589,共8页中国物理B（英文版）

基　　金：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：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 Yb^3＋ 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.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 Yb^3＋ 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.

关 键 词：crystal field parameter numerical derivative of matrix eigenvalue Yb^3＋Sc2O3 simple overlap model 

分 类 号：O741[理学—晶体学]