A more realistic approach toward the differential equation governing the glass transition phenomenon

In this contribution, the non-linear differential equation governing the glass transition phenomena of metallic glasses has been investigated analytically through a powerful mathematical tool known as the Adomian decomposition method. Unlike the previous works in this context, no simplifying assumption has been made so that the approach is more realistic. Furthermore and as a salient advantage, the method is free of discretization, linearization and perturbation. For the sake of exemplification, the resulted general solution was tested for the alloy Zr41.2Ti13.8Cu12.5Ni10Be22.5 and the relevant “free volume vs. temperature” curves were obtained. In addition, as another illustrative example, the glass transition temperature for the alloy Pd40Ni40P20 was estimated by the proposed scheme. The employed approach was successful to predict the glass transition temperature for the test case alloys closer to the experimental values than those of by the prior mathematical works in the literature.