Square Tiling Model

The square tiling model has some attractive features reminiscent of real glasses, such as cooperativity, a relaxation spectrum that can be fit by the KWW equation, and a non-Arrhenius temperature-dependence of the longest relaxation time (Fredrickson 1988). However, the existence of an underlying first-order phase transition in real glasses is doubtful, and the characteristic relaxation time of the tiling model fails to satisfy the Adam-Gibbs equation. 

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Figure 4.25 A glassy configuration of the square tiling model on a periodic 50 x 50 square lattice generated by a Monte Carlo simulation. (From Fredrickson 1988, with permission.)...

The cubic bond-orientational order (BOO) model of Trebin and coworkers [45], [46] is an attempt to rectify these theoretical problems. Originally formulated for crystals, the central idea of BOO is that the positional order of the atoms can be lost (due to formation of defect pairs or fluctuations) while still retaining the orientational order of the bonds. An analogous situation would occur for a floor loosely tiled with square tiles. If the sides of the tiles are all aligned properly, but the tiles are not fitted together correctly, orientational order is retained while positional order is lost. 

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