  We show how van der Waals (vdW) forces outcompete covalent and ionic forces
to control ferroelectric ordering in CuInP2S6 nanoflakes as well as in CuInP2S6
and CuBiP2Se6 crystals. While the self-assembly of these 2D layered materials
is clearly controlled by vdW effects, this result indicates that the internal
layer structure is also similarly controlled. Using up to 14 first-principles
computational methods, we predict that the bilayers of both materials should be
antiferroelectric. However, antiferroelectric nanoflakes and bulk materials are
shown to embody two fundamentally different types of inter-layer interactions,
with vdW forces strongly favouring one and strongly disfavouring the other
compared to ferroelectric ordering. Strong specific vdW interactions involving
the Cu atoms control this effect. Thickness-dependent significant cancellation
of these two large opposing vdW contributions results in a small net effect
that interacts with weak ionic contributions to control ferroelectric ordering.
