Fragility of metallic glass-forming liquids: A simple thermodynamic connection

Fragility measures the degree by which the viscosity or relaxation time of a glass-forming liquid deviates from the Arrhenius behavior. We will demonstrate that kinetic fragility of a glass-forming liquid is quantitatively related to ΔSf/(Tm − TK), where ΔSf is the entropy of fusion, Tm the melting point, and TK the Kauzmann temperature of a glass-forming liquid. A positive correlation between ΔSf/(Tm − TK) and the kinetic fragility was found to hold in metallic glass-forming liquids, where both thermodynamic and kinetic data are available. It will be demonstrated that such correlation is consistent with the energy landscape model of the glass transition. Furthermore, the thermodynamic fragility index ΔSf/(Tm − TK) was reduced to ΔSf/Tm assuming TK ≈ Tm/2, and the correlation between ΔSf/Tm and kinetic fragility was discussed within the context of recently proposed cluster model of the glass transition.