The symmetry and structure of crystalline surfaces

We discuss the relationship between symmetry and atomic structure at crystalline surfaces, proposing a general structural definition of flat, stepped and kinked facets based upon chains of atoms rather than planes of atoms. We demonstrate that surface chirality derives ultimately from the reduction in symmetry incurred by truncating a bulk crystalline solid, rather than from the presence of kinks. Our analysis allows us, for example, to identify the stepped bcc surfaces as chiral even in the absence of kink sites; this class of surface promises a more stable environment for heterogeneous asymmetric catalysis than the kinked fcc surfaces considered in the literature hitherto.