Calculating activation energy of amorphous phase with the Lambert W function

Abstract

A new approach for determining the activation energy of amorphous alloys is developed. Setting the second order differential coefficient of heterogeneous reaction rate equation of non-isothermal heating as zero at extreme points of DSC curve, we obtain the new correlation taking form: $$ \gamma_{1} = Lambertw\left( {\gamma_{3} e^{{ - \gamma_{2} }} } \right) + \gamma_{2} $$ where γ1,γ2 and γ3 are symbols comprising parameters, and Lambertw(…) is the Lambert W function symbol. Through this function, the activation energy can be calculated with DSC test at single heating rate without the isoconversion assumption. To evaluate the feasibility of calculating the activation energy with the new method, the glass transition activation energy of as-cast Pd40Ni40P20 amorphous alloy is measured. The value is 1.6 eV, which agrees well with the result of viscosity measurements. Thus, it is a good possibility that the new approach can be used to determine the activation energy of amorphous phase.