A Structural Measure of Effective- (Fictive-) Temperature and its Basis in Statistical Mechanics

The concept of fictive-temperature has long been utilized to characterize the processing dependence of glass structure, and has recently been shown to be predictive of metallic glass ductility. Some theories have hypothesized that it is actually a real temperature related to the configurational degrees of freedom of the glass, i.e. an "effective-temperature," notably the shear-transformation-zone (STZ) and soft-glassy-rheology (SGR) theories. Here we derive a thermodynamic integration scheme for calculating effective-temperature based on a 2-temperature hypothesis. To test this scheme we simulate a binary Cu-Zr metallic glass modeled with an EAM potential. Measures of the energy fluctuations associated with both the fast and slow degrees of freedom are measured during the glass quench. The resulting effective-temperature is consistent with estimates of fictive-temperature obtained from simulation in more heuristic ways. The results indicate that effective-temperature can be understood as a purely structural quantity. The method provides a means to measure the effective-temperature in the absence of fluctuations induced by shear and without resorting computationally expensive and impractical methods for explicitly measuring the configurational entropy.