Two-Dimensional Glass Amorphous Graphene

To further highlight the differences in the crystalUne and liquid states Table 9.1 lists the entropies of melting calculated in both two- and three-dimensions from the present work (taken at the respective coexistence curve maxima) and from previous work focussed on relatively simple models hard and soft spheres, a Lennard-Jones potential, and the one-component plasma [102]. The absolute values reported here are larger (and consistent with known values for the conformal systems Si and Ge [103]). However, the ratio of the three- and two-dimensional system values appears consistent throughout, reflecting the more ordered nature of the liquid state when confined to two dimensions. 

Column 4 shows the ratios of the respective three- and two-dimensional transition entropy changes 

One of the simplest models which displays a reentrant crystal/fluid coexistence curve (in both two- and three-dimensions [93, 94]) is a gaussian core model (GCM) [108-111] in which the interaction energy between a pair of particles i and j separated by a distance ry is expressed as 

Several expanded forms, and subsequent modifications, are present in the literature [119] (also, see [116, 120, 121] for reviews). 

All basic MD annealing strategies systematically remove kinetic energy. For a-G they generate configurations dominated by five-, six- and seven-membered rings and in which all three- and four-membered rings are quenched out. A small number 

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