  We have used low-energy electron diffraction and microscopy to compare the
growth of graphene on hydrogen-free Ge(111) and Ge(110) from an atomic carbon
flux. Growth on Ge(110) leads to significantly better rotational alignment of
graphene domains with the substrate. To explain the poor rotational alignment
on Ge(111), we have investigated experimentally and theoretically how the
adatom reconstructions on Ge interact with graphene. We find that the ordering
transition of the adatom reconstruction of Ge(111) is not significantly
perturbed by graphene. Density functional theory calculations show that
graphene on reconstructed Ge(110) has large-amplitude corrugations, whereas it
is remarkably flat on reconstructed Ge(111). We argue that the absence of
corrugations prevents graphene islands from locking into a preferred
orientation.
