The surface morphology of CuFeS$_2$: A hybrid-exchange density functional study

The surface morphology of CuFeS$_2$ has been determined using hybrid-exchange density functional theory calculations. The (110) surface is identified to be the most stable non-polar surface with a surface energy of 0.58 Jm$^{-1}$. The polar (112)/($\overline{112}$) surface pair is shown to be remarkably stable and thermodynamically preferred to the (110) surface if certain defects are included. The stability of the polar (112)/($\overline{112}$) surface pair is attributed to a combination of geometric and electronic mechanisms localised to the (112) surface which combine to neutralise the electrostatic dipole perpendicular to the surface. The former entails a partial reversal of the surface atomic layer sequence while the latter involves dispersion of charge from the subsurface anions to neighbouring cations. Because of its stability, (112) and ($\overline{112}$) facets always form a significant portion of the Wulff construction regardless of the growth conditions.