  Atomic structure of a mono-dispersive hematite ($\alpha$-Fe$_2$O$_3$)
nanocube $(0 1\bar1 2)$ surface was determined with synchrotron X-ray
diffraction. The $\alpha$-Fe$_2$O$_3$ nanocubes were prepared through a
hydrothermal process and a single layer of nanocubes was deposited on a silicon
substrate with a drop cast method. The alignment of nanocubes with their $(0
1\bar1 2)$ surfaces parallel to the substrate is confirmed with grazing
incidence X-ray diffraction. Specular crystal truncation rods (CTR's) from
as-prepared and vacuum annealed nanocube surfaces have been measured and they
are drastically different from previously reported CTR's from macroscopic
single crystal $(0 1\bar1 2)$ surfaces. The measured CTR's from nanocube
surfaces are explained well with the atomic structure models of half of atoms
in top Fe layer being missing while extra oxygen-layers cover the half-missing
Fe layer. An acidic environment during hydrothermal nanocube synthesis process
is proposed as the main cause of the difference.
