Structure and chemical reactivity of the polar three-fold surfaces of GaPd: A density-functional study

Abstract

The polar threefold surfaces of the GaPd compound crystallizing in the B20 (FeSi-type) structure (space group P2(1)3) have been investigated using density-functional methods. Because of the lack of inversion symmetry the B20 structure exists in two enantiomorphic forms denoted as A and B. The threefold {111} surfaces have polar character. In both nonequivalent (111) and (111) directions several surface terminations differing in structure and chemical composition are possible. The formation of the threefold surfaces has been studied by simulated cleavage experiments and by calculations of the surface energies. Because of the polar character of the threefold surfaces calculations for stoichiometric slabs permit only the determination of the average energy of the surfaces exposed on both sides of the slab. Calculations for nonstoichiometric slabs performed in the grand canonical ensemble yield differences of the surface energies for the possible terminations as a function of the chemical potential in the reactive atmosphere above the surface and predict a transition between Ga- and Pd-terminated surfaces as a function of the chemical potential. The {100} surfaces are stoichiometric and uniquely defined. The calculated surface energies are identical to the average energies of the {100} surfaces of the pure metals. The {210} surfaces are also stoichiometric, with an energy very close to that of the {100} surfaces. Assuming that for the {111} surfaces the energies of different possible terminations are in a proportion equal to that of the concentration-weighted energies of the {111} surfaces of the pure metals, surface energies for all possible {111} terminations may be calculated. The preferable termination perpendicular to the A<111> direction consists of a bilayer with three Ga atoms in the upper and three Pd atoms in the lower part. The surface energy of this termination further decreases if the Pd triplet is covered by additional Ga atom. Perpendicular to the A<111> direction the lowest energy has been found for a bilayer with three Ga atoms per surface cell in the upper layer and one Ga and one Pd in the lower part. The calculated surface energies are in agreement with a simulated cleavage experiment. However, cleavage does not result in the formation of the lowest-energy surfaces, because all possible {111} cleavage planes expose a low-energy surface on one, and a high-energy surface on the other side. The prediction of Ga-terminated surfaces has been tested against the available experimental information. The calculated surface electronic density of states is in very good agreement with photo-emission spectroscopy. Calculated STM images of the most stable surfaces agree with all details of the available experimental images. The chemical reactivity of the most stable surfaces has been studied by the adsorption of CO molecules. The adsorption energies and maximum coverages calculated for the Ga-terminated surfaces permit a reasonable interpretation of the observed thermal desorption spectra, whereas for the Pd-terminated surfaces the calculated adsorption energies are far too high.