The glass transition temperature Tg divided by the liquidus temperature Tl, Trg = Tg/Tl. The larger it is, the more readily a melt forms glass, with about 2/3 or more taken as a guideline.
Japanese name: 換算ガラス転移温度
Reduced glass transition temperature appears in 1 practice question across 1 topic, including Glasses and amorphous materials.
The reduced glass transition temperature Trg is the glass transition temperature Tg divided by the liquidus temperature Tl, both expressed in absolute temperature. When a melt is cooled, crystals can form below Tl, but once it has cooled to Tg the atoms can hardly move and crystals can no longer form. In other words, the temperature span of the supercooled liquid in which crystallization is a risk runs from Tl to Tg, and a larger Trg means that this span is narrower and that the liquid is more viscous within it. For this reason Trg has been used as a simple index of how easily a liquid forms a glass (glass-forming ability).
In 1969 Turnbull used the theory of homogeneous nucleation to estimate what values of Trg make glass formation easy. Assuming that the viscosity of the liquid reaches about 10¹² Pa·s at Tg and varies with temperature in a certain way, the result is that in liquids with Trg greater than about 2/3 the rate of crystal nucleation during cooling is very small, and they form glasses easily even when cooled slowly. Liquids with Trg of about 1/2 need very fast quenching to form a glass. Pure metals are thought to have very small Trg and do not form glasses with ordinary rapid quenching.
In metallic glass alloys, moving the composition close to a deep eutectic lowers Tl greatly while Tg changes little, so Trg increases. For example, an alloy with Tg of 650 K and Tl of 1000 K has Trg of 0.65. If the composition can be changed to lower Tl to 900 K, Trg becomes about 0.72, and glass formation can be expected to become easier. In fact, most bulk metallic glasses have Trg of about 0.6 or more, and a trend has been reported for alloys with smaller critical cooling rates to have larger Trg. Lowering the liquidus temperature by using many components is an idea consistent with Inoue's empirical rules.
Trg is simple and convenient, but it does not always rank glass-forming ability correctly. Not only nucleation but also the rate of crystal growth matters, and Tg varies by several K to more than ten K with heating rate, while Tl also depends on measurement conditions. For metallic glasses, therefore, other indices are used alongside it, such as ΔTx (the width of the supercooled liquid region), the difference between Tg and the temperature Tx at which crystallization starts on heating, and γ, expressed as Tx/(Tg + Tl). The usual approach is to compare several indices and finally confirm by actually casting the alloy and finding the maximum thickness that becomes glass.
Answer: A. The alloy with Tg = 625 K and Tl = 940 K
Calculating Trg gives 625/940 ≈ 0.665 for the alloy with Tg = 625 K and Tl = 940 K, about 0.538 for the alloy with Tg = 700 K and Tl = 1300 K, and about 0.512 for the alloy with Tg = 420 K and Tl = 820 K. The narrower the temperature span from Tl to Tg, the more quickly the melt passes through the supercooled-liquid range in which crystals can nucleate and grow, and the liquid in that range is also more viscous, so glass forms more easily. Turnbull estimated that crystallization is strongly suppressed once Trg reaches about 2/3 or more. The alloy with the highest Tg or the lowest Tl is not necessarily the one chosen; what matters is their ratio. This is an empirical guideline with exceptions.
Yes. For pure substances and compounds the melting point Tm is used, and the ratio is sometimes written Tg/Tm. In alloys the temperature at which solid starts to melt differs from the temperature at which it is fully molten, so the liquidus temperature Tl, at which it becomes fully liquid, is generally used as the upper limit of the range where crystallization must be avoided.
No. 2/3 is a guide from nucleation theory, and actual glass-forming ability also depends on the rate of crystal growth, heterogeneous nucleation on impurities and the cooling rate. Some alloys with large Trg form glasses poorly, and some show the opposite.
Yes. For many crystalline polymers there is an empirical rule that Tg is about 1/2 to 2/3 of the melting point Tm (in absolute temperature). For poly(ethylene terephthalate) (PET), for example, Tg is about 350 K and Tm about 530 K, a ratio of about 0.66.
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