Monte carlo simulation of the mixed alkali effect with cooperative jumps

In our previous works on molecular dynamics (MD) simulations of lithium metasilicate (Li2SiO3), it has been shown that the long time behavior of the lithium ions in Li2SiO3 has been characterized by the component showing the enhanced diffusion (Levy flight) due to cooperative jumps. It has also been confirmed that the contribution of such component decreases by interception of the paths in the mixed alkali silicate (LiKSiO3). Namely, cooperative jumps of like ions are much decreased in number owing to the interception of the path for unlike alkali-metal ions. In the present work, we have performed a Monte Carlo simulation using a cubic lattice in order to establish the role of the cooperative jumps in the transport properties in a mixed alkali glass. Fixed particles (blockage) were introduced instead of the interception of the jump paths for unlike alkali-metal ions. Two types of cooperative motions (a pull type and a push type) were taken into account. Low-dimensionality of the jump path caused by blockage resulted in a decrease of a diffusion coefficient of the particles. The effect of blockage is enhanced when the cooperative motions were introduced.