Crystal-field splitting of energy levels of rare-earth ions Dy3+(4f9) and Yb3+(4f13) in M(II) sites in the fluorapatite crystal Sr5(PO4)3F

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Abstract
We have calculated a set of crystal-field parameters, B nm , for Dy 3+ through Yb 3+ ions in M (II) sites in the crystal Sr 5 (PO 4 ) 3 F (SFAP). The B nm parameters were derived from lattice-sum calculations and from analyses of the optical spectra reported for Ho 3+ , Er 3+ , and Tm 3+ individually doped into SFAP. These parameters were used to predict starting values, which were then semiempirically fitted for the crystal-field splitting of the multiplet manifolds of the sextet states of Dy 3+ (4f 9 ), 6 H J , and 6 F J and the doublet states of Yb 3+ (4f 13 ) having manifolds 2 F 7/2 and 2 F 5/2 . The results are compared with an analysis of the absorption and fluorescence spectra of Dy 3+ and Yb 3+ individually doped into SFAP. The rms deviation between 44 calculated and observed Stark levels of Dy 3+ in Dy:SFAP is 10 cm −1 . Without fitting of any parameters, the predicted crystal-field splitting of the Yb 3+ multiplet manifolds is in reasonable agreement with the observed spectra for Yb:SFAP.