Theoretical investigation of the self-trapped hole in alkali halides. I. Long-range effects within the model hamiltonian approach
A small-radius polaron model of the self-trapped hole (Vk-center) in alkali halide crystals is presented. Along with the usual contributions, the electronic polarization is also included in accordance with the electronic polaron theory of Toyozawa. It is shown that the exact solution of the problem within the Landau-Pekar approximation leads to multi-hole quantum states accompanied by the relevant electronic and lattice polarizations. As an example the KCl crystal is considered, for which the Vk-center structure as well as the self-trapping energy are computed. While solving our equations, the local symmetry of the defect is taken into account allowing us to consider a comparatively spread …
Effective diffusion coefficient and diffusion-controlled reactions in insulating solids with defects
Abstract The expressions for effective diffusion coefficient are obtained in the mean field approximation for two-phase system for spatial dimensions of 1, 2 and 3. The existence of potential barrier for diffusion on the phase boundary was taken into account via the boundary conditions. Obtained formulae could be applied in the theory of diffusion-controlled reactions and for interpreting the experimental data on defect diffusion in two-phase media.
Theoretical analysis of hole self-trapping in ionic solids: Application to the KCl crystal.
A method for the calculation of the hole self-trapping (ST) energy in ionic crystals is proposed. It combines model-Hamiltonian and quantum-chemical approaches. An artificial path for the ST process has been suggested containing (a) a free hole not interacting with the lattice vibrations; (b) a free-hole wave packet localized in a small crystal volume in the form of the real ST state, all crystal ions being in their perfect lattice positions; (c) the final ST state of the hole, accompanied with a corresponding lattice relaxation, including strong displacements of ions belonging to the hole region. Some intermediate states might be adopted between (a) and (b) in order to simplify the calcula…
Explicit expressions for totally symmetric spherical functions and symmetry-dependent properties of multipoles
Closed expressions for matrix elements 〈 lm' | A (G)| lm 〉, where | lm 〉 are spherical functions and A (G) is the average of all symmetry operators of point group G, are derived for all point groups (PGs) and then used to obtain linear combinations of spherical functions that are totally symmetric under all symmetry operations of G. In the derivation, we exploit the product structure of the groups. The obtained expressions are used to explore properties of multipoles of symmetric charge distributions. We produce complete lists of selection rules for multipoles Q l and their moments Q lm , as well as of numbers of independent moments in a multipole, for any l and m and for all PGs. Periodic…