the crystal lattice matching criterion of the two slab in the interface area

[njuxyh]

Hi all:
recently i saw a arXiv named "electrical contacts to monolayer black phosphorus: a first principles investigation" http://http://arxiv.org/abs/1404.7207
and saw the monolayer black phosphorus and the cu(111) interface, as mentioned in the manuscript, the lattice constant a=4.58 angstrom,
as i know, according to the Figure in the manuscript shows (see attachment),  the cu (111) lattice constant in the bulk phase is about 5.10 angstrom.
of course, there are some surface reformation after the cu (111) is cleaved, but the lattice of cu (111) surface do not change to about 4.5 angstromm,

so one question is how does the two lab crystal lattice match? is there a criterion of good matching for the difference between two lattice?

     

[zh]

In principle, two lattices should be matched as much as possible. You can extend the supercells of two slabs in the planar directions to make them be matched as much as possible.