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I.

INTRODUCTION

DEPENDING on the temperature dependence of the relaxation time s (or, equivalently, the viscosity g = G¥s, where G¥ is the dynamic shear modulus) in the temperature range between Tg and Tm, where Tg is the glass transition temperature and Tm is the melting (usually liquidus) temperature, glass-forming liquids are divided into strong and fragile liquids. When the logarithm of the relaxation time of a supercooled liquid is plotted vs an inverse absolute temperature, T, reduced by Tg (i.e., log(s) vs Tg/T), all glass-forming liquids have the same relaxation time of sg = 103 s at T = Tg (in accord to this definition of Tg).[1] With an increase in temperature above Tg, liquids with strong directional bonding and high stability of intermediate range order, such as silica or germania, show almost a linear, Arrhenius, dependence of log(s) on Tg/T over the entire temperature range above Tg. These liquids are called strong liquids. At the same time, molecular liquids and many metallic glasses, which lack a strong directional bonding character and therefore possess a high configurational degeneracy and suffer rapid degradation of intermediate range order above Tg, show a very rapid decrease in log(s) with a decrease in Tg/T in the temperature range of Tg £ T £ Tm and a weak dependence above Tm. These liquids are called fragile liquids. Examples of extremely fragile liquids are o-terphenyl, toluene, pure metals, and marginal metallic glasses. OLEG N. SENKOV, Senior Scientist, is with UES, Inc., Dayton, OH 45432. Contact e-mail: [email protected] DANIEL B. MIRACLE, Senior Scientist, is with the Air Force Research Laboratory, Materials and Manufacturing Directorate, Wright-Patterson AFB, OH 45433. This article is based on a presentation given in the symposium ‘‘Bulk Metallic Glasses VI,’’ which occurred during the TMS Annual Meeting, February 15–19, 2009, in San Francisco, CA, under the auspices of TMS, the TMS Structural Materials Division, TMS/ASM: Mechanical Behavior of Materials Committee. Article published online September 3, 2009 METALLURGICAL AND MATERIALS TRANSACTIONS A

Stronger liquids are generally better glass formers because they have higher viscosity/relaxation time at T < Tm, and therefore slower kinetics of crystallization, than more fragile liquids.[2–4] Almost all bulk metallic glasses show intermediate fragile behavior.[5] Slow kinetics of crystallization due to high viscosity/high relaxation time of supercooled liquid can also be important for enhancing the GFA of bulk metallic glasses. The fragile behavior of supercooled glass-forming liquids can generally be described by an empirical Vogel–Fulcher–Tamman (VFT) equation:[6] s ¼ s1 exp½A=ðT  To Þ

½1

where s¥, A, and To are the fitting parameters. An approach to quantify liquid fragility defines a fragility index m as the slope of the log10 s (or log10 g) vs Tg/T curve near Tg:[7]   d log10 s  d log10 g  m ¼        ½2 d Tg T  d Tg T  T¼Tg

T¼Tg

According to this definition, more fragile liquids have higher m values. Sin