Precrystallization of fluids induced by patterned substrates

It is shown that a fluid near a topographically patterned wall exhibits cry stallization below the bulk freezing point (so-called precrystallization). In detail, a periodic array of fixed hard spheres is considered as a wall p attern. The actual type of the pattern corresponds to a face-centred-cubic (fcc) lattice cut along the (111), (100) or (110) orientation, a hexagonal- close-packed (hcp) solid with (110) orientation as well as a rhombic lattic e distorted with respect tb the triangular one. The fluid is represented by mobile hard spheres of the same diameter as the fixed wall spheres. By com puter simulation we find complete wetting by a crystalline sheet proceeding via a cascade of layering transitions as the bulk freezing point is approa ched for the fee (111) and hcp (110) cases, provided that the wall crystal lattice exactly matches that of the coexisting bulk crystal. On the other h and, there is incomplete wetting for the fee (100) and (110) cases. The fre ezing of the first layer starts at lower bulk pressures for a lattice with a larger lattice constant as compared to that of the coexisting bulk crysta l. A rhombic pattern either results in incomplete wetting by a solid sheet, which is unstable as a bulk phase, or prevents wetting completely. Using a phenomenological theory we derive scaling relations for the thickness of t he crystalline layer which are confirmed by the simulation data. We further more show that the Lindemann rule of bulk freezing can be applied also for interfacial freezing transitions.