Mean-square-displacement distribution in crystals and glasses: An analysis of the intrabasin dynamics

In the energy landscape picture, the dynamics of glasses and crystals is usually decomposed into two separate contributions: interbasin and intrabasin dynamics. The intrabasin dynamics depends partially on the quadratic displacement distribution on a given metabasin. Here we show that such a distribution can be approximated by a Gamma function, with a mean that depends linearly on the temperature and on the inverse second moment of the density of vibrational states. The width of the distribution also depends on this last quantity, and thus the contribution of the boson peak in glasses is evident on the tail of the distribution function. It causes the distribution of the mean-square displacement to decay slower in glasses than in crystals. When a statistical analysis is performed under many energy basins, we obtain a Gaussian in which the width is regulated by the mean inverse second moment of the density of states. Simulations performed in binary glasses are in agreement with such a result.