  Achieving the formation of target open crystalline lattices from colloidal
particles is of paramount importance for their potential application in
photonics. Examples of such desired structures are the diamond, tetrastack, and
pyrochlore lattices. Here, we demonstrate that the self-assembly of tetravalent
patchy particles results in the selective formation of cubic tetrastack
crystals, both in the bulk and in the systems subjected to external fields
exerted by the solid substrate. It is demonstrated that the presence of an
external field allows for the formation of well-defined single crystals with a
low density of defects. Moreover, depending on the strength of the applied
external field, the mechanism of epitaxial growth changes. For weakly
attractive external fields, the crystallization occurs in a similar manner as
in the bulk, since the fluid does not wet the substrate. Nonetheless, the
formed crystal is considerably better ordered than the crystals formed in bulk,
since the surface induces the ordering in the first layer. On the other hand,
it is demonstrated that the formation of well-ordered cubic tetrastack crystals
is considerably enhanced by the increase in external field strength, and the
formation of the thick crystalline film occurs via a series of layering
transitions.
