Study on the effect of glass transition temperature on fragility parameter in metallic glass-forming liquids

The frequently used m_0.33, determined by the glass transition temperature T_g,0.33 at a heating rate q = 0.33 K/s in numerous studies, is compared with the Angell fragility parameter m_η, derived from T_g,η at a viscosity of η = 10¹² Pa s. Although m_0.33 exhibits an overall increasing trend with m_η, it does not accurately quantify the degree of deviation from the Arrhenius relation of η. Several counterexamples indicate that a larger m_0.33 can correspond to a smaller m_η. For 23 kinds of metallic glass-forming liquids, T_g,0.33 corresponds to viscosities ranging from 7.7 × 10⁷ Pa s to 1.5 × 10¹² Pa s. Consequently, m_0.33 is determined under non-uniform viscosity standards, making it unsuitable for accurately evaluating the departure of η from Arrhenius temperature dependence. However, m_0.33 can be converted to m_η by multiplying by a factor λ = (T_g,η/T_g,0.33) × [(T_g,0.33-T₀)/(T_g,η-T₀)]², where T₀ is the kinetic ideal glass transition temperature. The ratio T_g,η/T_g,0.33 is 0.962, with a high R² = 0.979. By using T_g,η ≈ 0.962T_g,0.33, a simpler approximate expression can be given as m_η ≈ 0.962 × {(1-χ)/(0.962-χ)}²m_0.33, where χ is T₀/T_g.