A new correlation between the characteristics temperature and glass-forming ability for bulk metallic glasses

A new criterion or parameter χ given by Tx-TgTl-Tx×TxTl-Txa\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {\frac{{T_{\text{x}} - T_{\text{g}} }}{{T_{\text{l}} - T_{\text{x}} }}} \right) \times \left( {\frac{{T_{\text{x}} }}{{T_{\text{l}} - T_{\text{x}} }}} \right)^{a}$$\end{document} (wherein Tg is the glass transition temperature, Tx the onset crystallization temperature, Tl the liquidus temperature or the offset temperature of melting and a a fitting exponent) has been suggested to predict the glass-forming ability (GFA) of bulk metallic glasses (BMGs). Regression analysis between the critical diameter Dmax and this criterion yielded a value of a = 1.47. There exists a linear relationship between χ and Dmax with a coefficient of determination R2 = 0.43, and this correlation can be expressed by the approximation formula: Dmax=0.33±0.30+15.0±0.70χ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$D_{\hbox{max} } = \left( {0.33 \pm 0.30} \right) + \left( {15.0 \pm 0.70} \right)\chi$$\end{document}. The comparisons of the χ parameter with the currently available parameters based on characteristic transformation temperatures of BMGs clearly confirmed that the new criterion exhibits the best ability for appraising the GFA of the alloys. Finally, evaluated glass-forming tendencies of four previously reported Zr-based BMGs using this χ parameter were compared with their corresponding experimental results.