Tiling model for glass formation with incremental domain.

As a liquid is supercooled past its freezing point and eventually through a glass transition point, the constituent molecules experience increasing difficulty in undergoing the collective rearrangements necessary to lower the total interaction energy. This inherent sluggishness in glass-formers manifests many observable symptoms which include cooling-rate dependence of thermodynamic properties, and non-exponential relaxation behavior of mechanical and electrical properties. A conceptually simple lattice model of glassy behavior is advocated where for the two-dimensional case, the plane is tiled (covered) by squares of integer size. Each square tile corresponds to well-packed domains of molecules, and the boundaries between domains have a positive misfit energy proportional to the length of the square side.