Empirically derived cubic-field energy-level schemes of fluorescence of Tb3+ in CaF2(I) are analyzed and compared with those theoretically derived. The x values for the 5D4, 7F3, 7F4, and 7F5 states are derived to the first order for a weak cubic field, and the energies are calculated to the second order. The second-order energies when added to the theoretical first-order levels of Lea, Leask, and Wolf at the calculated x values give energy levels in agreement with the empirical schemes to within 10%, substantiating the cubic crystal-field assignment for this crystal. The ratio of fourth- to sixth-order cubic crystal-field parameters (A4〈r4〉/A6〈r6〉) is found to be −11.5.
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Calculated for values of A4〈r4〉=−210 cm−1 (7F3 and 7F5 states); 7F4, A4〈r4〉=−120 cm−1; and A6〈r6〉=19 cm−1 (7F3 and 7F5 states); A6〈r6〉=10 cm−1 (7F4 state).
The energy designation of the 7F states are as follows: 7F6, ground state (corresponding to 000 cm−1 of Ref. 13) is −300 cm−1; 7F5(1700)+1684 cm−1; 7F4+2970 cm−1; 7F3(3970)+3968 cm−1; 7F2+4680 (Exp. center of gravity of observed lines); 7F1+5140 cm−1; 7F0+5370 cm−1; estimated.
Matrix elements linking 5D4 are only those of magnitude ≳2 cm−1=ΔE″ to states below 40 000-cm−1, elements <2 cm−1=ΔE″ and linking states >40 000 cm−1 excluded. Matrix elements for 5D4 state are calculated for values of A4〈r4〉=−420 cm−1 and A6〈r6〉=38 cm−1.
Table V
Theoretical energy-level values (cm−1) Tb3+ in CaF2.a
Using A4〈r4〉/A6〈r6〉≅−9.1 and A4〈r4〉 ≅ −173 cm−1.
Assuming Γ1 level terminates line No. 12 (Ref. 7) from 20 116-cm−1 level, the center of gravity of the 7F4 crystal-field-split levels becomes 3009 cm−1
Centers of gravity: 4I11/2–2262 cm−1; 4I9/2–234 cm−1; 4I13/2–4202 cm−1 [center of gravity for 4I11/2 level (first) was chosen at 2237 cm−1 instead of 2262 cm−1, on the assumption that the 2352 (Γ7) empirical level was not the Γ7 cubic field level, to get good empirical-to-theoretical deviations for the remaining levels]. x value, E value, and W are defined by Lea, Leask, and Wolf.12.
Centers of gravity: 4I11/2–2164 cm−1; 4I9/2–195 cm−1; 4I13/2–4150 cm−1; 4I15/2–6225 cm−1. Center of gravity for 4I11/2 was chosen at 2164 cm−1 instead of 2194 cm−1 under the assumption the 2283 cm−1 empirical level was not the Γ7 cubic-field level. The x values, E values, and scale factors W are defined by Lea, Leask, and Wolf.12
Tables (16)
Table I
Operator-equivalent factors for Tb3+ in CaF2 (accuracy: 3 significant figures).
Calculated for values of A4〈r4〉=−210 cm−1 (7F3 and 7F5 states); 7F4, A4〈r4〉=−120 cm−1; and A6〈r6〉=19 cm−1 (7F3 and 7F5 states); A6〈r6〉=10 cm−1 (7F4 state).
The energy designation of the 7F states are as follows: 7F6, ground state (corresponding to 000 cm−1 of Ref. 13) is −300 cm−1; 7F5(1700)+1684 cm−1; 7F4+2970 cm−1; 7F3(3970)+3968 cm−1; 7F2+4680 (Exp. center of gravity of observed lines); 7F1+5140 cm−1; 7F0+5370 cm−1; estimated.
Matrix elements linking 5D4 are only those of magnitude ≳2 cm−1=ΔE″ to states below 40 000-cm−1, elements <2 cm−1=ΔE″ and linking states >40 000 cm−1 excluded. Matrix elements for 5D4 state are calculated for values of A4〈r4〉=−420 cm−1 and A6〈r6〉=38 cm−1.
Table V
Theoretical energy-level values (cm−1) Tb3+ in CaF2.a
Using A4〈r4〉/A6〈r6〉≅−9.1 and A4〈r4〉 ≅ −173 cm−1.
Assuming Γ1 level terminates line No. 12 (Ref. 7) from 20 116-cm−1 level, the center of gravity of the 7F4 crystal-field-split levels becomes 3009 cm−1
Centers of gravity: 4I11/2–2262 cm−1; 4I9/2–234 cm−1; 4I13/2–4202 cm−1 [center of gravity for 4I11/2 level (first) was chosen at 2237 cm−1 instead of 2262 cm−1, on the assumption that the 2352 (Γ7) empirical level was not the Γ7 cubic field level, to get good empirical-to-theoretical deviations for the remaining levels]. x value, E value, and W are defined by Lea, Leask, and Wolf.12.
Centers of gravity: 4I11/2–2164 cm−1; 4I9/2–195 cm−1; 4I13/2–4150 cm−1; 4I15/2–6225 cm−1. Center of gravity for 4I11/2 was chosen at 2164 cm−1 instead of 2194 cm−1 under the assumption the 2283 cm−1 empirical level was not the Γ7 cubic-field level. The x values, E values, and scale factors W are defined by Lea, Leask, and Wolf.12