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How Many Bulk Metallic Glasses Are There? Yanglin Li, Shaofan Zhao, Yanhui Liu, Pan Gong, and Jan Schroers ACS Comb. Sci., Just Accepted Manuscript • DOI: 10.1021/acscombsci.7b00048 • Publication Date (Web): 13 Sep 2017 Downloaded from http://pubs.acs.org on September 14, 2017
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How Many Bulk Metallic Glasses Are There? Yanglin Lia, Shaofan Zhaoa, Yanhui Liub, Pan Gongc, Jan Schroers*,a a
Department of Mechanical Engineering and Material Science, Yale University, New Haven,
Connecticut, 06511, USA b
Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
c
State Key Laboratory of Materials Processing and Die & Mould Technology, Huazhong
University of Science and Technology, Wuhan, Hubei, 430074, China
Corresponding author:
[email protected] Abstract: Quantitative prediction of glass forming ability using a priori known parameters is highly desired in metallic glass development; however proven to be challenging due to the complexity of glass formation. Here we estimate the number of potential metallic glasses (MGs) and bulk metallic glasses (BMGs) forming systems and alloys, from empirically determined alloy design rules based on a priori known parameters. Specifically, we take into account atomic size ratio, heat of mixing, and liquidus temperature, which we quantify on binary glasses and centimeter-sized BMGs. When expanding into higher order systems that can be formed among 32 practical elements, we reduce the composition space for BMG formation using developed criteria by 106 times and estimate ~3 million binary, ternary, quaternary and quinary BMGs alloys. Keywords: bulk metallic glasses, combinatorial materials science, complex alloys, statistical analysis
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Introduction Glass formation is a common phenomenon present in most material classes and relatively new for metals1. A metallic glass is formed when crystallization is avoided upon melt cooling. Central in quantifying glass forming ability (GFA) is the critical cooling rate. Alloys that vitrify upon cooling with rates of 1000 K/s or less are called bulk metallic glasses (BMGs)2. These alloys have received particular attention since they can be formed in bulk dimensions3. The amorphous structure of BMGs results in unique combinations of properties4 and processabilty4b,
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which
have drawn significant scientific and technological interests2. Several hundred BMG compositions have been discovered3, and various theories have been proposed to explain aspects of glass formation and to predict BMG compositions6. However, both scientifically and technologically it would be empowering to know how many BMG forming alloys potentially exist as it would inform the development of appropriate techniques to discover them. From an application point of view it would allow to estimate the potential toolbox to meet the specific, typically multi-property requirements. A wide range of theories have been developed to predict, out of the vast compositional space, alloys that could form metallic glasses. Such theories can be divided into two groups. One is based on properties that are associated with physical properties of the glass, the associated supercooled liquid, and even competing crystalline phases, such as viscosity, fragility, density, liquidus temperature Tl, glass transition temperature Tg, crystallization temperature Tx
,
and
structure and density of states of competing crystalline phases7. Even though correlations of these parameters with metallic glass formation have been identified, such correlations only focus on one specific aspect and cannot predict the complex glass formation, hence have limited predictable potential. Combinations of such quantities have been used as indicators for glass formation such as the reduced glass transition temperature Trg = Tg/Tl, the supercooled liquid region ∆Tx = Tx–Tg, parameter S = (Tx–Tg)/(Tl–Tg), and parameter γ = Tx/(Tl+Tg)2, 8. Most prominent is the so-called Turnbull criteria, Trg = Tg/Tl. Even though these strategies are very insightful and essential in understanding metallic glass formation, they rely on parameters that are only known after the glass has been discovered and are cumbersome to measure. Hence, theories rely on above quantities are of limited use in quantitative predictions of glass forming compositions. The other group of theories correlate glass forming ability with a priori known
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quantities, such as the atomic size of the constituent elements, heat of mixing, and electronegativity
3, 6b, 9
. Even though correlation of above individual quantities with glass
forming ability is limited10, they constitute the basic for state of the art BMG alloy development7g. Our work aims to estimate the number of metallic glass forming alloys. For this we considered 32 practical elements (Fig. 1) and reduced the number of combinations through empirically estimated metallic glass forming rules. We developed and calibrated such criteria on reported binary metallic glass formers. Subsequently, we extrapolated those criteria to higher order systems and estimated ~3 million BMG alloys.
Results and discussion Our strategy to estimate the number of metallic glass forming alloys is based on reducing the overall compositional space through specific glass forming indicators. We consider 32 elements (colored in blue in Fig. 1) as practical metallic glass constituent elements to evaluate the number of possible metallic glass forming alloys. The 32 elements all have been reported previously as constituents in glass forming alloys. We restrict the previously reported elements to those that are “practical”. Therefore, we exclude rare earth elements and high costs elements such as Sc, Ta, Ru, and Rh, in spite of their identified capability in forming metallic glass.
The number of all possible alloy combinations from the element candidates (set S), can be calculated according to, the number of k-combinations from a given set S of size n: (n is the number of elements and k is the total element number allowed in the alloy system). The 32 elements yield 496 binary alloy systems, 4,960 ternary systems, 35,960 quaternary systems and 201,376 quinary systems. In order to calculate the number of alloys on has to decide on a “grid”. From a literature survey we concluded that a reasonable grid is one atomic percent as it has been widely reported that glass forming compositions exhibit different properties (hence different alloys) on that scale11. Applying such one atomic percent in one constituents to distinct two alloys, the total number of alloys from 32 elements is ~1012.
In order to identify the fraction of alloys, within above vast number, that form metallic glasses, we need to identify criteria. Specifically, we performed statistical analysis on published data of
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metallic glass formation, and used data of binary glass alloys to identify statistically significant parameters that can be used as predictors for glass formation. We assume that the majority of binary systems that form metallic glasses from the 32 practical elements have been already identified. To quantify the glass forming ability, the glass formers are categorized into three groups based on their critical cooling rate (Rc): bulk glass formers, with Rc
