Light
yield, time response, afterglow, and thermoluminescence of
Ce-doped garnet scintillators and persistent luminescent materials
are controlled by a complex interplay between recombination and trapping/detrapping
processes. Extensive research has contributed to a good qualitative
understanding of how traps, impurities, and the presence of Ce4+ affect the materials properties. In this work we present
a quantitative model that can explain the thermoluminescence and afterglow
behavior of complex garnets. In particular, the model allows the determination
of capture rates and effective capture radii for electrons by traps
and recombination centers in Lu1Gd2Ga3Al2O12:Ce garnet ceramics. The model relies
on solving a set of coupled rate equations describing charge carrier
trapping and recombination in garnet ceramics doped with Ce and also
codoped with a known concentration of an intentionally added electron
trap, Yb3+. The model is supported by analysis of a complete
set of experimental data on afterglow, rise-time kinetics, and X-ray
excited luminescence which show that thermoluminescence/afterglow
are governed by trapping/detrapping processes following interactive
kinetics with dominant recombination channel. The underlying reason
for dominant recombination is the presence of a small fraction of
Ce4+ (≈2 ppm in the 0.2% Ce-doped sample) which
have a very high capture cross section (≈2.7 Å effective
radius) because of the Coulomb attractive nature of this recombination
center. The quantitative insights on capture cross sections and concentrations
of Ce4+ help to better understand the optical properties
of Ce-doped garnet scintillators and persistent luminescent materials
and serve in optimizing synthesis procedures by tuning the Ce3+/Ce4+ ratio by codoping with divalent cations
and annealing in an oxygen-containing atmosphere.