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

Abstract 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 Δ S f /( T m − T K ), where Δ S f is the entropy of fusion, T m the melting point, and T K the Kauzmann temperature of a glass-forming liquid. A positive correlation between Δ S f /( T m − T K ) 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 Δ S f /( T m − T K ) was reduced to Δ S f / T m assuming T K ≈ T m /2, and the correlation between Δ S f / T m and kinetic fragility was discussed within the context of recently proposed cluster model of the glass transition.