  Water-solid interfaces pervade the natural environment and modern technology.
On some surfaces, water-water interactions induce the formation of partially
dissociated interfacial layers; understanding why is important to model
processes in catalysis or mineralogy. The complexity of the partially
dissociated structures often make it difficult to probe them in a quantitative
manner. Here, we utilize normal incidence x-ray standing waves (NIXSW) to study
the structure of partially dissociated water dimers (H2O-OH) at the Fe2O3(012)
surface (also called (1-102) or R-cut surface); a system simple enough to be
tractable, yet complex enough to capture the essential physics. We find the H2O
and terminal OH groups to be the same height above the surface within
experimental error (1.45 +/- 0.04 Angstrom and 1.47 +/- 0.02 Angstrom,
respectively), in line with DFT-based calculations that predict comparable Fe-O
bond lengths for both water and OH species. This result is understood in the
context of cooperative binding, where the formation of the H-bond between
adsorbed H2O and OH induces the H2O to bind more strongly, and OH to bind more
weakly compared to when these species are isolated on the surface. The surface
OH formed by the liberated proton is found to be in plane with a bulk truncated
(012) surface (-0.01 +/- 0.02 Angstrom). DFT calculations based on various
functionals correctly model the cooperative effect, but overestimate the
water-surface interaction.
