Role of potential-energy scaling in the low-temperature relaxation behavior of amorphous materials

Abstract

Under the assumption that the Kohlrausch-Williams-Watts (KWW) function describes relaxation near the glass transition for amorphous substances, implications are explored for the character of the many-body potential-energy function. The analysis proceeds in several stages: (1) The configuration space is uniquely divided into minimum-containing cells by a steepest-descent construction on the potential hypersurface. (2) Attention is confined to the amorphous region of configuration space by projecting out all cells containing local crystalline patterns. (3) The potential is separated into a hard-core part ${\Phi }_c$ and a ‘‘soft’’ remainder ${\Phi }_s$. (4) ${\Phi }_s$ is coarse grained (smoothed) over a variable scale of lengths l. (5) A master equation is used to describe the relaxation spectrum subject to the interaction smoothed over any l. The demand that KWW relaxation emerge from the last constrains the statistical topography of ${\Phi }_s$. Specifically it requires that on widely separated length scales, multiply branched channels of relatively modest elevation change must exist in ${\Phi }_s$. Furthermore, the separating barriers between these channels tend to be largest in those portions of configuration space sampled by the system at the lowest temperatures, and to scale as lnl.