Mobility of F Centers in Alkali Halides

Abstract

The migration of F centers in alkali halides is important both for characterizing their chemical reactivity and as a benchmark for theoretical methods. In order to provide a solid basis for the assessment of theoretical methods, we reviewed the available experimental literature on the migration of F centers in NaCl, KCl, NaBr, and KBr. The migration of the F center through the bulk, across the (100) surface, and from the surface into the bulk was modeled. The activation enthalpy for the migration of an F center was calculated using dispersion-corrected generalized gradient approximation (GGA) functionals and a self-consistent dielectric-dependent global hybrid method based on plane-wave functions for the bulk and the (100) surface. The geometries of the transition states were characterized, and the position of the defect electron was determined. The influence of the theoretical methodology and the temperature dependence of the lattice parameter on the migration barrier was investigated. For the description of the bulk, thermal corrections were considered to enhance comparability with the experiment. The calculated migration enthalpies of 1.31, 1.46, and 1.32 eV for NaCl, KCl, and KBr, respectively, agree well with experimental measurements. For NaBr, a migration enthalpy of 0.93 eV is predicted. While only a direct hopping process between neighboring anion sites is found for the bulk, there are two possible pathways for some surfaces. The migration barrier on the surface and from the surface into the bulk is predicted to be lower than that in the bulk in all cases.

3D-to-2D Transition of Anion Vacancy Mobility in CsPbBr3 under Hydrostatic Pressure

“…The lattice vectors were kept fixed at the values determined previously for the pristine bulk, thus neglecting the pΔV contribution to the change in enthalpy, as is commonly done when considering solid state systems. 81,82 The paths are nonlinear in general, and they should not be confused with the sticks in Figure 1a. The resulting potential energy profiles of the minimum enthalpy paths are shown in Figure 1b.…”

“…Having identified all 1-NN sets of SEPS in the Pnma structure, the minimum enthalpy paths taken by a vacancy as it hops between a pair of sites belonging to each set were calculated using the CINEB method, following which the transition state structures were optimized further using the dimer method. The lattice vectors were kept fixed at the values determined previously for the pristine bulk, thus neglecting the pΔV contribution to the change in enthalpy, as is commonly done when considering solid state systems. , The paths are nonlinear in general, and they should not be confused with the sticks in Figure a. The resulting potential energy profiles of the minimum enthalpy paths are shown in Figure b.…”

Nitrogen Activation on Defective Potassium Chloride and Sodium Chloride

“…For N 2 migration below the surface (Figure b), the energy barrier is slightly larger, 1.87 eV. In both cases, the barrier is higher than for desorption or migration of the F center simulated on the same level of theory . However, the same trend for the energy difference between the two available migration paths is observed with and without adsorbed nitrogen.…”

“…Therefore, migration of adsorbed nitrogen was modeled for several paths across the pristine KCl (100) surface and from the terrace into the defect cavity. Additionally, the exchange with the neighboring chloride anion analogous to the mechanism of the F center diffusion , was studied.…”

“…Unless denoted otherwise, the GGA functional PBE with D3­(BJ) dispersion correction , was employed for geometry optimizations, as in our previous studies of defective alkali halides. ,, This method overestimates the experimental 0 K lattice parameter of KCl by about 1.5% and reproduces the low-temperature value for NaCl.…”