The Unreconstructed {\alpha}-Al$_{2}$O$_{3}$(0001) Surface is Inhomogeneous and Rough
Alumina (Al$_{2}$O$_{3}$) is a key material for thin-film growth and heterogeneous catalysis, where the atomic surface structure critically impacts performance. Using noncontact atomic force microscopy (nc-AFM) combined with density functional theory (DFT) calculations, we challenge the common assumption that the unreconstructed $\alpha$-Al$_{2}$O$_{3}$(0001) surface is atomically flat and uniformly Al-terminated. This widely accepted bulk termination satisfies polarity compensation requirements but results in highly undercoordinated surface Al cations at the surface. Despite substantial inward relaxation of these Al cations, we find that the (1 ${\times}$ 1) surface remains inherently metastable, relative to the thermodynamically stable $(\sqrt{31} \times \sqrt{31})R\pm9\deg$ surface reconstruction that forms at high temperatures above 1000 {\deg}C. Nc-AFM imaging of the unreconstructed surface reveals a rough and disordered morphology, with only nanometer-scale regions exhibiting the ordered Al-terminated (1 $\times$ 1) structure. Our results show that the unreconstructed Al$_{2}$O$_{3}$(0001) surface is intrinsically inhomogeneous, reconciling conflicting experimental observations and challenging the validity of commonly used atomistic models.