  Despite its importance in atmospheric science, much remains unknown about the
microscopic mechanism of heterogeneous ice nucleation. In this work, we perform
hybrid Monte Carlo simulations of the heterogeneous nucleation of ice on a
range of generic surfaces, both flat and structured, in order to probe the
underlying factors affecting the nucleation process. The structured surfaces we
study comprise one basal plane bilayer of ice with varying lattice parameters
and interaction strengths. We show that what determines the propensity for
nucleation is not just the surface attraction, but also the orientational
ordering imposed on liquid water near a surface. In particular, varying the
ratio of the surface's attraction and orientational ordering can change the
mechanism by which nucleation occurs: ice can nucleate on the structured
surface even when the orientational ordering imposed by the surface is weak, as
the water molecules that interact strongly with the surface are themselves a
good template for further growth. We also show that lattice matching is
important for heterogeneous nucleation on the structured surface we study. We
rationalise these brute-force simulation results by explicitly calculating the
interfacial free energies of ice and liquid water in contact with the
nucleating surface and their variation with surface interaction parameters.
