Energy migration in randomly doped crystals : geometrical properties of space and kinetic laws

Abstract

The kinetics of energy migration in the excited states of doped crystals are calculated using a percolation model. Special care has been taken in the case where an annihilation process controls the density n of excitations at time t. In this case the number I of fusions per unit of time follows the laws : I ∼ t-α (with α = 1 - d(1 - ε)/2) at short times, I ∼ t-β (with β= 1 + d(1 + ε)/2) at longer times, I ∼ t-2 at very long times. d is the spectral dimension of Alexander and Orbach, and ε is related to the other classical percolation exponents through ε = β/(β + γ). The applicability of this theory to randomly doped crystals with short-range interactions is then discussed. A new experimental result which has been obtained in a naphthalene D 8 crystal doped with naphthalene H8 is given. These experimental and theoretical results are in relatively good agreement