Atomic step disorder on polycrystalline surfaces leads to spatially inhomogeneous work functions

Structural disorder causes materials surface electronic properties, e.g. work function ($\phi$) to vary spatially, yet it is challenging to prove exact causal relationships to underlying ensemble disorder, e.g. roughness or granularity. For polycrystalline Pt, nanoscale resolution photoemission threshold mapping reveals a spatially varying $\phi= 5.70\pm 0.03$~eV over a distribution of (111) textured vicinal grain surfaces prepared by sputter deposition and annealing. With regard to field emission and related phenomena, e.g. vacuum arc initiation, a salient feature of the $\phi$ distribution is that it is skewed with a long tail to values down to 5.4 eV, i.e. far below the mean, which is exponentially impactful to field emission via the Fowler-Nordheim relation. We show that the $\phi$ spatial variation and distribution can be explained by ensemble variations of granular tilts and surface slopes via a Smoluchowski smoothing model wherein local $\phi$ variations result from spatially varying densities of electric dipole moments, intrinsic to atomic steps, that locally modify $\phi$. Atomic step-terrace structure is confirmed with scanning tunneling microscopy (STM) at several locations on our surfaces, and prior works showed STM evidence for atomic step dipoles at various metal surfaces. From our model, we find an atomic step edge dipole $\mu=0.12$ D/edge atom, which is comparable to values reported in studies that utilized other methods and materials. Our results elucidate a connection between macroscopic $\phi$ and nanostructure that may contribute to the spread of reported $\phi$ for Pt and other surfaces, and may be useful toward more complete descriptions of polycrystalline metals in models of field emission and other related vacuum electronics phenomena, e.g. arc initiation.