Developments in Ceramic Materials Research

Optical Fluoride and Oxysulfide Ceramics: Preparation and Characterization 87
the matrix element U (2) for all the transitions is equal or close to zero and most contribution to
the line strengths of the electronic transitions comes from U (6) and to a lesser extent from U (4) .
Hence, only dipole–dipole mechanism of cross-relaxational energy transfer is allowed.
The same situation occurs for the case of energy migration over the 4 F3/2 manifold of the Nd 3+
ion where U (2) for the 4 F3/2→ 4 I9/2 transition is also equal to zero. The dipole–dipole nature of
the above-mentioned processes were confirmed elsewhere [63]. If we use now the
dependence 1n Itr(t) as a function of t 1/2 (Figure 31b), this graph is linearized, which proves
Forster-like decay law and its slope can be used to determine the γ macroparameter (γ=0.03
μs −1/2 ) for 0.5 wt% of the Nd 3+ ion (NA=1.31×10 20 cm −3 ) and s=6. The value of the quenching
microparameter CDA for the 4 F3/2 level determined from the slope of the decay curve at the
disordered stage can be calculated using Eq. (5) and is equal to 3.8×10 −39 cm 6 /s. Similar
analysis of fluorescence decay curves are provided for the La2O2S:Nd 3+ (1 wt%)
(NA=2.03×10 20 cm −3 ) ceramic sample. The measured fluorescence kinetics exhibits
nonexponential decay at T=300 K (Figure 32a). Exponential decay at the far stage of the
decay curve gives τfin=50.3 μs (1/τmeas.=19881 s −1 ) and points out the presence of energy
migration over the donors to acceptors, because the radiative decay time for the La2O2S:Nd 3+
crystal measured in Ref. [48] at zero-concentration limit is equal to τR=95 μs. The kinetics
decay at the Forster (disordered stage) can be found by multiplying the measured curve by
exp(+t/τfin) (Figure 32b), where τfin is the measured lifetime at the far stage of kinetics decay
and accounts for both intracenter decay and energy migration. The same slope in
terms of the coordinates [lg(−ln I(t))] and [lgt] was observed (Figure 33a) and, hence, the
dipole–dipole interaction was found for La2O2S: Nd 3+ as well. The γ parameter was obtained
from the slope of the graph presented in Figure 33b and is equal to γ=0.07 μs −1/2 . The
obtained value of CDA=2.2×10 −39 cm 6 /s in La2O2S: Nd 3+ was found to be 1.8 times smaller
than in Gd2O2S:Nd 3+ .
The CDA microparameter in oxysulfide ceramics was found to be rather high and to
exceed by two orders of magnitude the quenching microparameter for the 4 F3/2 metastable
level of the Nd 3+ ion in the LaF3 crystal (CDA=1.4×10 −41 cm 6 /s at 300 K) [63]. The reason
according to Refs. [62] and [64] may be the much higher absorption and emission crosssections
of electronic transitions in oxysulfide ceramics comparing to LaF3. The latter
exhibits itself, for example, in several times higher radiative rates in the ceramics.
The boundary time between the so called ordered stage of the decay and the disordered
one can be calculated from the formula [65]
In the Gd2O2S:Nd 3+ crystal it was found to be 744 ns for Rmin (Nd–Nd)=3.76 Å taken
from the data for Nd2O2S crystal [66]. The value of tbound1 is rather small in Gd2O2S:Nd 3+
because of large value of CDA and small Rmin. The latter is smaller than, for example, in
LaF3:Nd 3+ (Rmin=4.151 Å) [63], and even smaller than in SrF2:Nd 3+ (Rmin=4.09 Å) [67], in
CaF2:Nd 3+ (Rmin=3.85 Å) [67], and CdF2:Nd 3+ (Rmin=3.82 Å) [67]. For La2O2S: Nd 3+ at
T=300 K the boundary time was calculated to be tbound1=1.3 μs which is approximately two
times longer than in Gd2O2S:Nd 3+ due to 1.8 times lower value of the CDA microparameter.
(6)