Research Article Cite This: ACS Comb. Sci. 2017, 19, 687-693
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How Many Bulk Metallic Glasses Are There? Yanglin Li,† Shaofan Zhao,† Yanhui Liu,‡ Pan Gong,§ and Jan Schroers*,† †
Department of Mechanical Engineering and Material Science, Yale University New Haven, Connecticut 06511, United States Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China § State Key Laboratory of Materials Processing and Die & Mould Technology, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China ‡
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S Supporting Information *
ABSTRACT: Quantitative prediction of glass forming ability using a priori known parameters is highly desired in metallic glass development; however proven to be challenging because of 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 metals.1 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 dimensions.3 The amorphous structure of BMGs results in unique combinations of properties4 and processabilty,4b,5 which have drawn significant scientific and technological interests.2 Several hundred BMG compositions have been discovered,3 and various theories have been proposed to explain aspects of glass formation and to predict BMG compositions.6 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 multiproperty 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 phases. 7 Even though © 2017 American Chemical Society
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 ΔTx = 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 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 limited,10 they constitute the basic for state of the art BMG alloy development.7g Our work aims to estimate the number of metallic glass forming alloys. For this we considered 32 practical elements (Figure 1) and reduced the number of combinations through empirically estimated metallic glass forming rules. We developed and calibrated such criteria on reported binary Received: March 15, 2017 Revised: August 21, 2017 Published: September 13, 2017 687
DOI: 10.1021/acscombsci.7b00048 ACS Comb. Sci. 2017, 19, 687−693
Research Article
ACS Combinatorial Science
Figure 1. Altogether 32 elements are considered to evaluate the number of possible metallic glass forming alloys. Criteria for elements to be considered in this estimation are that they have been previously reported as a metallic glass alloy constituent and that they are practical (excluding rare earth and toxic elements).
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 < 103 K/s, ribbon formers, with 103 K/s < Rc < 106 K/s, and thin film glass formers, with 106 K/s < Rc < 109 K/ s. All the reported binary systems are summarized and categorized in the Supporting Information (Table 2).12 For criteria to correlate with glass formation, we consider heat of mixing between binary alloy constituents and their atomic size ratio. Both criteria have been suggested by Inoue as glass forming indicators.3 All 490 binary alloy systems are organized by their RS/RL (RS is the small atomic radius and RS is the large atomic radius in a binary alloy system) and enthalpy of mixing ΔHmix values (see Figure 2). For binary alloy systems, we found that ΔHmix values are predominantly related to their alloy systems and to a lesser extend to their compositions. Therefore, we calculated ΔHmix values with the composition of A50B50 for the A−B binary system. ΔHmix is defined as ΔHmix = Σni=1,i≠jΩijcicj. ΔHmix is the mixing enthalpy of liquid alloys, ci and cj are the atomic fraction of the element i and j in the alloy. Ωij is the regular melt interaction parameter between elements i AB and j which can be calculated as Ωij = 4ΔHAB mix. ΔHmix are the enthalpy of mixing of the binary liquid in an A−B system at an equi-atomic composition.13 64 alloys out of the 490 alloy systems have been reported to form metallic glasses and the color indicates their GFA. The strongest distinction between glass and nonglass formers, balanced with including the largest number of known glasses for considered data can be achieved when restricting glass formers to a size ratio of 0.62 < RS/RL < 0.9 (Figure 2). The upper cutoff is identical to what has been suggested by Inoue3 in the past. Using only the size ratio criterion, we identified 286 systems as potential glass formers (of which 59 systems are identified glass formers and 227 as nonglass formers) (see Table 1). As an additional parameter, ΔHmix was analyzed. The strongest distinction between glass and nonglass formers when including the largest value of the reported binary BMGs, is present for
metallic glass formers. Subsequently, we extrapolated those criteria to higher order systems and estimated ∼3 million BMG alloys.
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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 Figure 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: (nk) (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, 4960 ternary systems, 35 960 quaternary systems, and 201 376 quinary systems. To calculate the number of alloys one 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 scale.11 Applying such one atomic percent in one constituents to distinct two alloys, the total number of alloys from 32 elements is ∼1012. 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 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 688
DOI: 10.1021/acscombsci.7b00048 ACS Comb. Sci. 2017, 19, 687−693
Research Article
ACS Combinatorial Science
Figure 2. 490 binary alloy systems organized by their radius ratio RS/ RL and their heat of mixing ΔHmix. Such display reveals the parameters range of binary metallic glasses.
Figure 3. Reduced liquidus temperature ratio dT as a criterion for glass formation: (a) Schematic view of the quantification of deep eutectic using dT and (b) the distribution of dT for 348 reported binary systems.
Table 1. Number of Binary Systems Obey Criteria and the Number of Those That Are Reported Glasses using RS/RL, ΔHmix, dT, and Their Combinations criteria
RS/ RL
obey criteria 286 positive cases 59 |reported − obey| + | 227 reported − positive| total binary systems: 490
ΔHmix
dT
RS/RL and ΔHmix
217 49 168
112 45 67
136 46 90
RS/RL, ΔHmix, and dT 62 34 32
of the 32 elements. This assumption is based on the fact that deep eutectic systems are easy to characterize and data would therefore exist. The strongest distinction between glass and nonglass formers, when including the largest number of known glasses is present within considered alloys is present when restricting glass formation to dT ≥ 0.2. Overall, 112 systems are predicted from dT ≥ 0.2 alone, of which 45 are glass forming systems and 67 nonglass forming system (Table 1). Altogether, 62 systems out of the 490 systems obey all three criteria, dT ≥ 0.2, 0.62 < RS/RL < 0.9, and ΔHmix ≤ −15 kJ/mol. Out of the 62 systems obeying all three criteria, 34 systems are glass formers and 28 systems are nonglass formers. To quantify which of the various criteria is best suited to estimate the number of glass formers we use the best compromise between the accuracy of predicting the overall number of binary systems, which is quantified by the difference of the number of reported binary systems (64) and the number of systems obeying the criteria, and the quality of this prediction. The quality of the prediction is estimated by many of the systems obey the criteria are predicting a known glass former accurately. Among the considered criteria, RS/RL, ΔHmix, and dT are best suited in estimating the number of binary glass formers. Above consideration only revealed best-suited criteria to correlate with metallic glass formation. However, it is not clear if RS/RL, ΔHmix, or dT scale with GFA. Therefore, we divided the 64 known binary glass formers into bulk glass former, ribbon glass formers and film glass formers and plotted their corresponding RS/RL, ΔHmix, and dT (Figure 4a−c). For all three parameters, no correlation with GFA, when considering errors set by standard deviation can be observed. This finding reveals that RS/RL, ΔHmix, or dT, are able to some extent to distinguish between glass formers and nonglass formers, however, no conclusion about the actual GFA can be made.
reported glasses: 64
−15 kJ/mol. Using only this criterion, we identified 217 systems as potential glass formers (of which 49 are identified glass formers and 168 as nonglass formers). Combining these two criteria, we identified 136 systems as potential glass formers (of which 46 are identified glass formers and 90 as nonglass formers). If we assume that the 46 identified binary systems represent all binary glass forming systems from the 32 considered elements, the two criteria overestimate the binary glass forming systems significantly. To more accurately predict glass formation, additional criteria have to be identified and considered. Widely used has been Trg = Tg/Tl.8b To increase Trg, a low Tl is beneficial, which has been manifested in the widely confirmed finding that BMGs are typically present at, or close to, deep eutectic compositions.3 To quantify the depth of a eutectic temperature for alloy AxB(1‑x), we used the reduced liquidus temperature ratio dT = 1−Tl/Tl0 (Tl is the experimentally determined liquidus temperature, Tl0 is the composition weighted and linear interpolation of the melting temperature of the pure elements Tl0 = TmAx + TmB(1−x) (Figure 3a). ASM alloy phase diagram database provide data to calculate dT for 348 alloys out of the 490 systems. We assume that besides the 348 binary alloy systems, which are summarized in ASM database no other significant deep eutectic, dT ≥ 0.2 exist for binary systems out 689
DOI: 10.1021/acscombsci.7b00048 ACS Comb. Sci. 2017, 19, 687−693
Research Article
ACS Combinatorial Science
Figure 4. Evaluation of considered criteria in terms of their correlation with GFA (a−c) and their correlation with each other for considered binary systems (d−f). Radius ratio RS/RL (a), heat of mixing ΔHmix (b), and reduced liquidus temperature ratio dT (c) for the considered binary metallic glass system of different glass forming ability show no significant correlation with GFA. Weak correlation among each other is revealed for RS/RL vs ΔHmix (d), RS/RL vs dT (e), and ΔHmix vs dT (f), with correlation coefficient r = 0.099, −0.222, −0.039, respectively.
To further characterize the effectiveness of using a combination of the three criteria, RS/RL, ΔHmix, and dT, we evaluated their correlations with each other (Figure 4d−f). The pairwise scatter plots reveal a very weak correlation quantified in correlation coefficients r(ΔHmix, RS/RL) = 0.099, r(dT, RS/ RL) = −0.222, and r(ΔHmix, dT) = −0.039. This finding is surprising. Even though RS/RL, ΔHmix, and dT describe somehow different aspects of glass formation, such as kinetics and packing, thermodynamics, and phase stability, and relative stability of liquid and crystals, respectively. It has been widely accepted that these aspects are all interconnected.3,7a For example, a low dT originates from high stability of liquid (large negative heat of mixing in liquid phase, ΔHmix) compare to the solid, suggesting a correlation between ΔHmix and dT. Our findings might underline the complex nature of glass formation and the challenge in describing glass formation in a closed-form expression. As the above criteria are insufficient to distinguish between MGs and BMGs, we also considered an additional database to explore specific predictors for BMGs. For this, we considered bulk metallic glass formers with a critical casting diameter of at least 10 mm (see Table 3 in the Supporting Information). As
oppose to MGs, which are present over the whole range, BMGs tend to form at specific ratio of RS/RL [0.9, 0.81, 0.72, 0.63] (see Figure 5). The radius ratio of second largest atom over largest atom R2/RL is plotted against the radius ratio of the third largest atom over the largest atom R3/RL in the BMG system. Those values are similar to those calculated using Miracle’s efficiently packing solute-centered atomic clusters model.9b Atoms that are similar in size within one alloy (within 3%) can be treated as topologically identical. To estimate the number of BMGs we require RS/RL to be within ±0.02 of [0.9, 0.81, 0.72, 0.63]. For the heat of mixing we observe best correlation when requiring for at least one pair obeying ΔHmix ≤ −15 kJ/mol. All the other pairs can be as high as 5 kJ/mol. We use the design rules determined from the analysis of binary systems, to extrapolate into higher order systems. We apply as general MG design rules as follows: (1) All pairs satisfy 0.62 < RS/RL < 0.9 or RS/RL ≥ 0.97 (topologically identical). (2) Min([ΔHmix]) of all element pairs ← 15 kJ/mol, and Max([ΔHmix]) of all element pairs 0.2 out of the 490 systems. Specifically, we multiply the number of higher order systems obeying above criteria with 112/490. For BMGs we use above criteria however modify Rule 1 by the following steps: (1a) All pair of RS/RL are within ±0.02 of either of values [0.9, 0.8, 0.71, 0.63] or RS/RL ≥ 0.97. (1b) More than 3 different atom sizes (RL, R2, R3) are needed for good glass forming systems. To estimate the number of BMG forming alloys, we need to define the minimum compositional difference distinguishing two alloys and the compositional range of BMG formation. It has been often observed that small compositional changes of 1 at% can change glass forming ability and other properties14 of a metallic glass. Hence, we assume a one atomic percent grid, resulting in 99 binary alloys, 4851 ternary alloys, 156 849 quaternary alloys, and 3 764 376 quinary alloys per system. We furthermore assume a bulk glass forming range of 10% for metallic constituents and for 5% for metalloids.3 For MGs, we assume a 20% range. The numbers of MG and BMG systems and alloys from 32 element candidates are listed in the Table 2. An interesting result is the relatively small difference in numbers between BMGs and MGs. Even though from an application point of view, the difference between MGs (103 K/s < Rc< 106 K/s) and BMGs (Rc < 103 K/s) might be large, this difference in rates is relatively small when considering the range of critical cooling rates for metals ranging from less than 1 K/s for best glass formers15 to 1013 K/s and above for pure metals.1a The predictive structural model16 well explains the formation of BMG in discovered alloys at certain composition range. Utilizing this model to obtain efficient packing for all elements, we can get glass forming composition range for packing efficiency 100% ± 1% and alloy systems falling into the radius
Figure 6. Current BMG development status: ∼106 potential BMGs alloys identified, compared with ∼105 BMGs alloys, which have been experimentally considered and ∼103 BMGs discovered.
formation by assuming 25 research groups focus on the study of amorphous metals and prepare and characterize 2 alloys per day for the last 30 years (200 working days each year). For the number of discovered BMGs (here we distinct between 1 at% nearby composition as a different BMG), we estimate ∼103 BMGs discovered. Comparing these numbers (Figure 6) reveals that only a minute fraction ∼0.1% out of the potential BMG forming compositions have been identified. This low fraction, which originates from the absence of predictable theories to identify glass formers and from the inefficiency of currently used experimental alloy development methods. One strategy might be the use of combinatorial methods paired with high-throughput characterization methods, to replace currently used sequential trial-and-error methods.20 In some cases, a 1000-fold increases in fabrication and characterization rate has been reported.20f
Table 2. Numbers of MG and BMG Systems (Considering 32 Elements) Using Empirically Determined Rules numbers of systems
numbers of alloys
type
ternary
quaternary
quinary
ternary
quaternary
quinary
BMGs MGs
113 378
1096 3939
3305 24 004
5537 37 027
263 040 3 781 193
2 564 680 149 086 170
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DOI: 10.1021/acscombsci.7b00048 ACS Comb. Sci. 2017, 19, 687−693
ACS Combinatorial Science
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CONCLUSIONS We estimate the number of BMG forming alloys. For this a statistical analysis of known binary metallic glasses was performed to develop three criteria to estimate the number of potentially metallic glass forming alloys in higher order systems. These are atomic size ratio, 0.62 < RS/RL < 0.9, heat of mixing, ΔHmix ≤ −15 kJ/mol, and a deep eutectic liquidus temperature, dT ≥ 0.2. We used these criteria and further considered 119 bulk metallic glass formers (dc ≥ 10 mm) to identify criteria indicating BMG formation. With this approach we considered binary, ternary, quarternary, and quinary alloy systems for which we identified ∼5000 higher ordered systems and ∼3 million potential BMG forming alloys. This number is larger when considering that only ∼105 composition have been explored thus far for BMG formation and less than a thousand BMG have been identified. This finding reveals the potential of BMG alloy development but also highlights limitations of current alloy development strategies.
ACKNOWLEDGMENTS
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REFERENCES
(1) (a) Zhong, L.; Wang, J. W.; Sheng, H. W.; Zhang, Z.; Mao, S. X. Formation of monatomic metallic glasses through ultrafast liquid quenching. Nature 2014, 512 (7513), 177−180. (b) Schroers, J. CONDENSED-MATTER PHYSICS Glasses made from pure metals. Nature 2014, 512 (7513), 142−143. (c) Kelton, K. F.; A.L, G. Nucleation in Condensed Matter; Pergamon Press 2010. (2) Johnson, W. L. Bulk glass-forming metallic alloys: Science and technology. MRS Bull. 1999, 24 (10), 42−56. (3) Inoue, A. Stabilization of metallic supercooled liquid and bulk amorphous alloys. Acta Mater. 2000, 48 (1), 279−306. (4) (a) Ashby, M. F.; Greer, A. L. Metallic glasses as structural materials. Scr. Mater. 2006, 54 (3), 321−326. (b) Schroers, J. Processing of Bulk Metallic Glass. Adv. Mater. 2010, 22 (14), 1566− 1597. (c) Chen, W.; Liu, Z.; Ketkaew, J.; Mota, R. M. O.; Kim, S. H.; Power, M.; Samela, W.; Schroers, J. Flaw tolerance of metallic glasses. Acta Mater. 2016, 107, 220−228. (5) Chiu, H. M.; Kumar, G.; Blawzdziewicz, J.; Schroers, J. Thermoplastic extrusion of bulk metallic glass. Scr. Mater. 2009, 61 (1), 28−31. (6) (a) Laws, K. J.; Miracle, D. B.; Ferry, M. A predictive structural model for bulk metallic glasses. Nat. Commun. 2015, 6, 8123. (b) Zhang, K.; Dice, B.; Liu, Y. H.; Schroers, J.; Shattuck, M. D.; O’Hern, C. S. On the origin of multi-component bulk metallic glasses: Atomic size mismatches and de-mixing. J. Chem. Phys. 2015, 143, 054501. (c) Perim, E.; Lee, D.; Liu, Y.; Toher, C.; Gong, P.; Li, Y.; Simmons, W. N.; Vlassak, J. J.; Schroers, J.; Curtarolo, S.; et al. Spectral descriptors for bulk metallic glasses based on the thermodynamics of competing crystalline phases. Nat. Commun. 2016, 7, 12315. (7) (a) Busch, R.; Schroers, J.; Wang, W. H. Thermodynamics and kinetics of bulk metallic glass. MRS Bull. 2007, 32 (8), 620−623. (b) Shadowspeaker, L.; Busch, R. On the fragility of Nb-Ni-based and Zr-based bulk metallic glasses. Appl. Phys. Lett. 2004, 85 (13), 2508− 2510. (c) Koster, U.; Meinhardt, J.; Roos, S.; Liebertz, H. Formation of quasicrystals in bulk glass forming Zr-Cu-Ni-Al alloys. Appl. Phys. Lett. 1996, 69 (2), 179−181. (d) Chen, M. W.; Zhang, T.; Inoue, A.; Sakai, A.; Sakurai, T. Quasicrystals in a partially devitrified Zr65Al7.5Ni10Cu12.5Ag5 bulk metallic glass. Appl. Phys. Lett. 1999, 75 (12), 1697− 1699. (e) Scudino, S.; Kuhn, U.; Schultz, L.; Breitzke, H.; Luders, K.; Eckert, J. Formation of quasicrystals in ball-milled amorphous Zr-TiNb-Cu-Ni-Al alloys with different Nb content. J. Mater. Sci. 2004, 39 (16−17), 5483−5486. (f) Inoue, A.; Takeuchi, A. Recent development and application products of bulk glassy alloys. Acta Mater. 2011, 59 (6), 2243−2267. (g) Perim, E.; Lee, D.; Liu, Y. H.; Toher, C.; Gong, P.; Li, Y. L.; Simmons, W. N.; Levy, O.; Vlassak, J. J.; Schroers, J.; Curtarolo, S. Spectral descriptors for bulk metallic glasses based on the thermodynamics of competing crystalline phases. Nat. Commun. 2016, 7, 12315. (8) (a) Johnson, W. L.; Na, J. H.; Demetriou, M. D. Quantifying the origin of metallic glass formation. Nat. Commun. 2016, 7, 10313. (b) Turnbull, D. Under What Conditions Can a Glass Be Formed. Contemp. Phys. 1969, 10 (5), 473. (c) Lu, Z. P.; Liu, C. T. A new glassforming ability criterion for bulk metallic glasses. Acta Mater. 2002, 50 (13), 3501−3512. (d) Donald, I. W.; Davies, H. A. Prediction of GlassForming Ability for Metallic Systems. J. Non-Cryst. Solids 1978, 30 (1), 77−85. (e) Wang, N.; Ji, L.; Yao, W. J.; Zheng, Y. P. Correlation between fragility and eutectic instability and glass-forming ability in binary metallic glasses under growth controlled conditions. J. Appl. Phys. 2012, 111 (10), 103525. (f) Schroers, J. On the formability of bulk metallic glass in its supercooled liquid state. Acta Mater. 2008, 56 (3), 471−478.
METHODS Database Construction. A comprehensive literature study was performed to collect reported binary MGs and the reported BMGs with dc ≥ 10 mm. The atomic radii of elements used for calculation are listed in Table 1 (Supporting Information). The heat of mixing data obtained from previous paper13 are listed in Table 2 (Supporting Information). The eutectic compositions and the liquidus temperature at the eutectic composition for binary MGs are extracted from ASM Alloy Phase Diagram Database.21 Binary MG systems considered are listed in Table 2 (Supporting Information). This includes 64 binary systems. The critical cooling rate Rc for binary MGs are carefully validated. The MGs are categorized into 3 groups based on their critical cooling rate Rc: bulk form, with Rc < 103 K/s and dc ≥ 1 mm; ribbon form, prepared by melt spinning or splat quenching with 103 K/s < Rc < 106 K/s; thin film form, prepared by vapor quenching or sputtering with 106 K/s < Rc < 109 K/s. The reported BMGs (at least one alloy with dc ≥ 10 mm) are summarized in Table 3 (Supporting Information), including 59 systems and 119 ally compositions. ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acscombsci.7b00048. Thirty-two practical elements and their atomic radii used in the present work, binary glasses systems and their reduced liquid temperature ratio, radius ratio, heat of mixing and the glass forming ability classified as bulk, ribbon, and film form, and lists of BMG systems with dc > 10 mm and some representative composition and their preparation method and resulting maximum rod diameter (PDF)
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The authors acknowledge primary financial support from the NSF-DMREF No. 1774632. We also want to thank Sungwoo Sohn and Naijia Liu for their helpful discussion on data analysis.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Yanglin Li: 0000-0002-6983-8296 Notes
The authors declare no competing financial interest. 692
DOI: 10.1021/acscombsci.7b00048 ACS Comb. Sci. 2017, 19, 687−693
Research Article
ACS Combinatorial Science
upon heating and cooling in Cu50Zr50 metallic glass thin films. Acta Mater. 2016, 121, 68−77. (h) Yao, J. H.; Hostert, C.; Music, D.; Frisk, A.; Bjorck, M.; Schneider, J. M. Synthesis and mechanical properties of Fe-Nb-B thin-film metallic glasses. Scr. Mater. 2012, 67 (2), 181−184. (21) Villars, P.; Okamoto, H.; Cenzual, K. ASM Alloy Phase Diagrams Database; ASM International: Materials Park, OH, USA, 2006.
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DOI: 10.1021/acscombsci.7b00048 ACS Comb. Sci. 2017, 19, 687−693
