  Despite the rapid pace of computationally and experimentally discovering new
two-dimensional layered materials, a general criteria for a given compound to
prefer a layered structure over a non-layered one remains unclear. Articulating
such criteria would allow one to identify materials at the verge of an
inter-dimensional structural phase transition between a 2D layered phase and 3D
bulk one, with potential applications in phase change memory devices. Here we
identify a general stabilization effect driven by vibrational entropy that can
favor 2D layered structures over 3D bulk structures at higher temperatures,
which can manifest in ordered vacancy compounds where phase competition is
tight. We demonstrate this vibrational-entropy stabilization effect for three
prototypical ordered vacancy chalcogenides, ZnIn2S4 and In2S3, and Cu3VSe4,
either by vacancy rearrangement or by cleaving through existing vacancies. The
relative vibrational entropy advantage of the 2D layered phase originates
mainly from softened out-of-plane dilation phonon modes.
