Analyses of glass-transition behavior of Pd-based metallic glass with linear solution to non-linear differential equation

The glass transition in of Pd82Si18, Pd40Ni40P20 (number indicated at.%) and Pd40Cu30Ni10P20 metallic glasses has been analysed by carrying out numerical calculations to a linear differential equation, which relates to a non-linear differential equation proposed by Beukel and Sietsma. The linear solutions are obtained from the non-linear differential equation based on free volume theory by taking into consideration a function form Mackey–Glass model and a concept of effective equilibrium free volume, the latter of which is introduced to account for the lack of atomic transportation near glass-transition temperature (Tg). The calculation results to the linear solutions were plotted in free volume (x)—temperature (T) and dx/dT–T diagrams, and compared with those by Beukel and Sietma model. It is found that the calculation results of the linear solutions reproduces those of the Beukel and Sietma model with respects to the values of dx/dT in dx/dT–T diagram: sharp increasing at around Tg and overshooting slightly higher than Tg. In addition, the changes in free volume on heating are interpreted with chemical reactions in order to account for the implication of the linear model by introducing a concept of effective equilibrium free volume.