Shell model calculations of the adsorption and diffusion of K +, Cl −, and KCl on KCl(0 0 1)

Abstract

Equilibrium adsorption positions and diffusion pathways of the ions K + and Cl − as well as of the molecule KCl on the terrace of the (0 0 1) surface of KCl were determined by shell model calculations allowing relaxations of the crystal lattice in the vicinity of the adsorbed species. For the ions each one adsorption position was found, in which the ions are located above the hollow site at the center of a slightly distorted square formed by two cations and two anions of the uppermost surface layer of the KCl crystal. Adsorption energies of −1.52 eV for K + and −1.61 eV for Cl − were calculated. Jumps of the ions occur from these positions to adjacent hollow positions in the ±[1 0 0] and ±[0 1 0] directions with a jump distance of a 0/2. The activation energies for the jumps result as 0.142 for K + and 0.152 eV for Cl − and the mean diffusion lengths as x s K ( nm ) = 0.315 exp [ 1.379 ( eV ) / 2 kT ] and x s Cl ( nm ) = 0.315 exp [ 1.462 ( eV ) / 2 kT ] . For the KCl molecule four distinct adsorption minima with energies between −0.932 and −0.825 eV were found. Because of the smaller lattice relaxation caused by the molecule the adsorption energies are considerably lower than for the single ions. In the position with the largest adsorption energy the ions of the admolecule are again placed above adjacent hollow sites. In two more adsorption positions only one ion is at the hollow site and the other one in a top position above an oppositely charged ion of the surface. In the fourth position with the smallest adsorption energy both ions are in top positions. Jumps between the different adsorption positions proceed by rotations of the molecule, in which one of its ions remains essentially attached to a local minimum position. The diffusion and desorption of a KCl molecule was studied by a Monte Carlo method, resulting in a mean diffusion length x s (nm) = 0.39 exp[0.84 (eV)/2 kT], which agrees rather well with an experimental value of x s exp ( nm ) = 0.20 exp [ 0.82 ( eV ) / 2 kT ] . Values for the mean stay time as well as for the surface diffusion coefficient are derived.