The low-index surfaces of the AlPd compound crystallizing in the B20 (FeSi-type) structure have been investigated using ab initio density functional methods. The space group of the B20 structure is $P{2}_{1}3$, with four threefold rotational axes along the $\langle 111\rangle$ directions and three twofold screw axes along the $\langle 100\rangle$ directions, but no inversion symmetry. The B20 structure exists in two enantiomorphic forms related by inversion. The termination of the structure perpendicular to the twofold screw axes is uniquely defined: The corrugated {100} surfaces are formed by the characteristic zigzag Al-Pd chains separated by shallow troughs. Perpendicular to the $\langle 210\rangle$ directions the structure consists of slightly puckered planes containing Al and Pd in equal numbers. The {210} surfaces shows pseudo-fivefold symmetry. Their structure is shown to be closely related to that of the {110} surfaces of the B2 structure. Both the {100} and {210} surfaces undergo some structural relaxation, but no reconstruction changing their $(1\times 1)$ periodicity. While perpendicular to the $\langle$100$\rangle$ and $\langle$210$\rangle$ directions only one surface termination is possible, perpendicular to the threefold $\langle$111$\rangle$ directions there are several possible surface terminations differing in structure and chemical composition. Because of the lack of inversion symmetry the threefold {111} surfaces have polar character. The (111) and $\left(\overline{1}\overline{1}\overline{1}\right)$ surfaces are not equivalent; the (111) surfaces of one enantiomorph are identical to the $\left(\overline{1}\overline{1}\overline{1}\right)$ surfaces of the other form (and vice versa). In both the (111) and $\left(\overline{1}\overline{1}\overline{1}\right)$ directions several surface terminations are possible. The formation of threefold surfaces has been studied by simulated cleavage experiments and by calculations of the surface energies of all possible terminations. Perpendicular to the $\langle 111\rangle$ direction the lowest energy has been found for a bilayer with three Al atoms per surface cell in the upper layer and one Al and one Pd in the lower part. The preferable termination perpendicular to the $\langle \overline{1}\overline{1}\overline{1}\rangle$ direction is more symmetric; it consists again of a bilayer with three Al 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 Al atom. The calculated surface energies permit us to perform a Wulff construction of the equilibrium shape of AlPd crystallites. {100} and {210} facets together occupy 77$\%$ of the surface area in about equal proportion. The high anisotropy of the energy of the {111} surfaces results in the substantial difference of the surface areas of the opposite threefold facets.

• Received 24 August 2012

DOI:https://doi.org/10.1103/PhysRevB.87.035436