Developments in Ceramic Materials Research

Optical Fluoride and Oxysulfide Ceramics: Preparation and Characterization 83
In the first approximation, the experimental data on nontradiative energy transfer kinetics due
to the multipole interaction between ions, for which electronic excitation prior to emission or
quenching keeps its position unchanged [55], [56] and [57], can be analyzed in terms of the
theory of direct energy transfer (DET) when the process of energy migration over the donors
to the acceptors can be neglected. The quantity in Eq. (1) is then equal to zero, and the
nonradiative transfer kinetics is reasonably described by a two-stage process. During the
initial stage, i.e., the so called ordered stage, decay proceeds with the maximal possible rate
for a given activator and is described by the simple exponential law [58]:
where the quenching rate is given by
and the sum is evaluated over all the sites of the acceptor sublattice, taking into account its
occupation cA=nA/nmax. For Nd 3+ doped laser crystals the unexcited Nd 3+ ions whose
concentration is much greater than the concentration of excited ions, can act as acceptors, i.e.,
nA=n(Nd 3+ ), and s=6 for the dipole–dipole interaction, s=8 for the dipole–quadrupole
interaction, s=10 for the quadrupole–quadrupole interaction, and so on.
From a certain instant t1 onward, the ordered stage goes over to the so-called Forster or
disordered stage, which means that acceptor ensemble is stochastic or disordered due to
accidental occupation of acceptor sublattice positions.
For the analysis of the disordered stage of the kinetics decay the following equations for
the static nonradiative energy transfer can be used [56] and [58]:
where
and Γ(x) is the gamma function. These expressions were derived by integration, assuming a
continuous medium and neglecting the particle sizes or the crystal lattice constant.
The intra center decay time τ can be found from the fluorescence kinetics measured in a
diluted sample. Fluorescence of the optical samples for the transitions from the 4 F3/2 manifold
are excited by tunable LiF: F2→F2 + color center laser pumped by YAG:Nd laser (tp=10 ns,
f=12 Hz). High throughput MDR-2 monochromator and a PMT-83 are used for fluorescence
selection and detection. A Tektronix TDS 3032B digital oscilloscope is employed for
fluorescence kinetics measurements. The fluorescence kinetics of the 4 F3/2 manifold in the
Gd2O2S:Nd 3+ (0.1 wt%) optical crystal ceramics measured under laser excitation at 893.5 nm
for 1.08 μm fluorescence detection at 300 K exhibits exponential decay (τ=107 μs) in the
measured temperature range 77–300 K (Figure 29a).
(2)
(3)
(4)
(5)