Molecular dynamics study of the α–β transition in quartz: elastic properties, finite size effects, and hysteresis in the local structure
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The α–β transition in quartz is investigated by molecular dynamics simulations in the constant stress ensemble. Based on a frequently used two-body interaction potential for silica, it is found that anomalies in the elastic constants are at least in semiquantitative agreement with experiment despite the fact that no anomaly in the c/a ratio is observed in the simulations. A finite-size scaling analysis shows that first-order Landau theory is applicable to the employed model potential surface. This statement also applies to the susceptibility below the transition temperature Ttr, which has not yet been measured experimentally. Examination of the local order near Ttr reveals that the deformation of SiO4 tetrahedral units is equally large in the β phase as in the α phase. However, large hysteresis effects can be observed in the local structure for distances r > 4 Å. The results are in agreement with the picture of a first-order displacive phase transformation which is driven by the motion of deformed tetrahedral SiO4 units. Yet, the fast oscillations of oxygen atoms are around (time-dependent) positions that do not correspond to the ideal oxygen positions in β-quartz. The averaged configurations resemble the ideal structure only if averaged over at least a few nanoseconds.
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