Glass transition, structural relaxation, and theories of viscosity: a molecular dynamics study of amorphous CaAl2Si2O8

Abstract

Molecular dynamics (MD) simulation provides a unique window into the dynamics of amorphous silicates of geochemical importance. Of special interest are theories of the glass transition and viscosity when an equilibrium liquid passes through the metastable supercooled liquid state to become a nonequilibrium glass. Viscosity increases enormously in a small temperature range around the glass transition temperature. Twenty MD simulations utilizing 1300 particles were conducted for CaAl2Si2O8 at temperatures in the range 1700 to 5000 K along the ∼ 1 GPa isobar. A pairwise potential with Coulombic and Born-Mayer interaction was used in the evaluation of forces. Simulation durations range from 50 to 150 ps. Previously, structures, thermodynamic properties, and tracer diffusivities were determined as a function of temperature for liquid and glass (Morgan and Spera, 2001). Here, the focus is upon atomic cooperative motion at the nanometer scale and theories of viscosity illuminated by correlation analysis and tagged particle dynamics. Dramatic differences in the dynamics of particles monitored by the nongaussian component of atom self-diffusivity, the van Hove correlation function and the intermediate scattering function appear near the (computer) glass transition temperature Tg = 2800 K. At T < Tg, the van Hove correlation function for oxygen and calcium exhibits a double-peaked structure characteristic of hopping diffusion through correlated jumps involving neighboring particles to nearest neighbor sites in an otherwise “frozen” structure. The crossover between continuous (hydrodynamic-like) motion and hopping motion shows up in the time dependence of the mean square displacement as a function of temperature and in the temporal decay of microscopic density fluctuations given by the intermediate scattering function. A particle and its neighbors remain trapped for a finite waiting time before undergoing a cooperative thermally activated rearrangement that is based on an elementary hop. The waiting time distribution is strongly temperature dependent and related to the dramatic increase in structural relaxation time as temperature approaches Tg. Three models for the glass transition—the Adam-Gibbs configurational entropy model, mode-coupling theory, and the stochastic trapping diffusion model—are discussed in light of the MD simulations. Although each model offers novel insight into the glass transition and the relationship between structural relaxation and atomic-scale dynamics, no single model is complete. The MD simulations are consistent with a picture of “dynamic heterogeneity” as the cause of the sluggish dynamics as an equilibrium liquid becomes deeply supercooled. At some temperature above the Kauzmann temperature (TK) where the extrapolated entropy of supercooled liquid equals that of crystalline solid, long-lived, highly cooperative, collective particle motions take place in restricted regions of three-dimensional space. Subsets of particles exhibit faster or slower than average relaxation rates. The relationship of dynamic heterogeneity viewed in three-dimensional Euclidean space to its analog in 6N-dimensional-phase space remains to be elucidated. Specifically, the lifetime and sizes of cooperatively rearranging regions as a function of temperature needs further study. Self-organization of cooperatively rearranging regions demands further investigation as well.