\emph{In Situ} Synchrotron Studies of a Model Catalyst: WO$_x$/$\alpha$-Fe$_2$O$_3$

Statistically averaging surface-sensitive X-ray techniques are employed to elucidate the surface morphology of a model oxide-supported heterogeneous catalyst, tungsten oxide (WO$_x$) on hematite ($\alpha$-Fe$_2$O$_3$). Atomically flat $\alpha$-Fe$_2$O$_3$ (0001) single crystals were coated with sub-monolayer WO$_x$ by atomic layer deposition (ALD). \emph{In situ} X-ray standing wave (XSW) imaging with X-ray fluorescence (XRF) was used to determine W position relative to bulk-like cation lattice sites under nominally reducing and oxidizing chemical conditions. X-ray absorption fine structure (XAFS) reveals details of W coordination, bond length, and chemical state on WO$_x$-coated hematite single crystals and nanopowders. Synchrotron characterization results are compared with morphologies predicted by density functional theory (DFT) calculations for clean WO$_x$/$\alpha$-Fe$_2$O$_3$ surfaces. Thermodynamics and atomic configurations for H$_2$O and CO adsorption are also predicted. Excited-state self-consistent field (SCF) calculations are used to model X-ray photoelectron spectroscopy (XPS) results.