Composition, Elastic Property and Packing Efficiency Predictions for Bulk Metallic Glasses in Binary, Ternary and Quaternary Systems

Borja Soto, Carlos Ernesto; Figueroa Vargas, Ignacio Alejandro; Fonseca Velázquez, José Ramón; Lara Rodriguez, Gabriel Ángel; Verduzco Martínez, Jorge Alejandro

doi:10.1590/1980-5373-MR-2015-0537

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Articles • Mat. Res. 19 (2) • Mar-Apr 2016 • https://doi.org/10.1590/1980-5373-MR-2015-0537 copy

Composition, Elastic Property and Packing Efficiency Predictions for Bulk Metallic Glasses in Binary, Ternary and Quaternary Systems

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract

The results of database based on the efficiency packed model for metallic glasses. The database contains the atomic radii information as well as elastic properties of the most commonly used alloying elements, permitting composition, packing efficiency and elastic property predictions to be made for binary, ternary and quaternary bulk metallic glasses. Twenty different alloys per system (binary, ternary and quaternary) experimentally reported in the literature were compared with those estimated by the database. Comparison charts and diagrams showed good agreement between the composition predictions and those reported from the experimentally processed metallic glasses. The elastic properties predictions could be used to elaborate Blackman diagrams in order to know, in advance, the intrinsic toughness that the investigated alloys might present. The database is intended for designing bulk metallic glasses. Finally, some quaternary alloys were experimentally produced based on the prediction obtained with the database, showing a glassy phase. The microhardness values obtained experimentally of the Zr_57.52Ag_10.62Al_10.62Co_21.24, Zr_57.19Al_10.7Ni_10.7Cu_21.41 and Hf_60.22Al_9.95Cu_9.95Ni_19.89alloys, are 3.8, 4.0 and 3.6 GPa, respectively. The Young´s modulus calculated using microhardness values (E/H_v = 20) are closed to the values obtained by the "mixing rules".

Keywords:
Bulk metallic glasses; Packing efficiency; Glass formation

1 Introduction

Despite new metallic glass systems being continuously investigated and reported, and a broadening of the number of engineering applications for this kind of material, the discovery, development and manufacture of bulk metallic glass (BMG) systems is still a complex and long process. Materials science and engineering states that when a new material is to be produced, prior to this, some properties would be expected from that new material, from its shape, component materials, structure, etc. The other way around would be, knowing the structure, component materials and production of new materials in order to fit some specification. However, for metallic glasses, the structure is still an unsolved puzzle, even though the international community has witnessed their advantageous properties and behaviour i.e. high strength, corrosion and wear resistant, chemical inertness, high toughness, among others.

In 1926, Goldschmidt¹1 Goldschmidt VM. Geochemische Verteilungsgesetze der Elemente VIII. Oslo: Skrifter Norske Videnkaps; 1926. correlated the ability to form a glass with the value of the radius ratio r_A/r_O for oxides A_mO_n. He found that for all the oxides which had been prepared in the vitreous form, the radius ratio was around 0.2 - 0.4. Zachariasen²2 Zachariasen WH. The atomic arrangement in glass. Journal of the American Chemical Society. 1932;54(10):3841-3851. DOI: 10.1021/ja01349a006
https://doi.org/10.1021/ja01349a006... , proposed a model where the SiO₄ polyhedron is repeated to produce a continuous random network (CRN). Regarding the study of BMG structure, different structural models have been proposed in the past 50 years; Bernal's "dense random packing"³3 Bernal JD, Mason J. Packing of spheres: coordination of randomly packed spheres. Nature. 1960;188(4754):910-911. DOI: 10.1038/188910a0
https://doi.org/10.1038/188910a0... model and Miracle's "efficient solute-centred cluster packing"⁴4 Miracle DB. A structural model for metallic glasses. Nature Materials. 2004;3:697-702. doi:10.1038/nmat1219
https://doi.org/10.1038/nmat1219... , amongst many others. The results of the latter are consistent with the high densities measured in bulk metallic glasses. Table 1 summaries some historical ideas pertaining to atomic packing and glass formation.

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Table 1
Summarised historical events of atomic packing and glass formation.

Packing in BMG is very dense with melt viscosities that are several orders of magnitude higher than in pure metallic melts. The dense packing accomplished by structural and chemical atomic ordering below the glass transition temperature also brings the BMG-forming liquids energetically and entropically closer to the corresponding crystalline state. These factors lead to slow crystallisation kinetics and consequentially to high glass forming ability (GFA)¹²12 Axinte E. Metallic glasses from "alchemy" to pure science: Present and future of design, processing and applications of glassy metals. Materials and Design. 2012;35:518-556. DOI: 10.1016/j.matdes.2011.09.028
https://doi.org/10.1016/j.matdes.2011.09... . Since GFA is an influential factor in studying the formation of BMG, the search for systems with sufficiently high GFA is a critical task in this field.

The mechanical behaviour of metallic glasses is also one of the most important topics, attracting a huge amount of research effort. Given its large practical relevance to the implementation of BMG as structural materials in real applications, it is important to know whether a material shows plastic deformation or brittle rupture under certain loading conditions. As a tool for this, the use of Blackman diagrams have been suggested and employed¹³13 Plummer JD, Todd I. Implications of elastic constants, fragility, and bonding on permanent deformation in metallic glass. Appllied Physics Letters. 2011;98(2):021907. http://dx.doi.org/10.1063/1.3540652
https://doi.org/10.1063/1.3540652... to explain the tendency for permanent deformation that a system may exhibit.

The work presented in this manuscript is based on several theoretical models for metallic glasses in terms of glass formation and elastic properties, and is intended to offer an alternative route to design and obtain BMG by estimating the system with GFA from a structural perspective (densest atomic packing) and predict its theoretical elemental elastic properties, from which some indication of plasticity can be obtained. In addition to the above, quaternary alloys were experimentally produced in order to get bulk metallic glasses.

2 Experimental and theoretical calculations

2.1 Theoretical chemical composition calculation

Chemical compositions were calculated based on a sphere-packing scheme (solute-centred clusters occupying an f.c.c. cluster unit cell)⁴4 Miracle DB. A structural model for metallic glasses. Nature Materials. 2004;3:697-702. doi:10.1038/nmat1219
https://doi.org/10.1038/nmat1219... . The Miracle's model includes the calculation of the three-dimensional coordination number N^T, which is obtained for a radius ratio R^* for maximum packing efficiency¹⁴14 Miracle DB, Sanders WS, Senkov O. The influence of efficient atomic packing on the constitution of metallic glasses. Philosophical Magazine. 2003;83(20):2409-2428. DOI: 10.1080/1478643031000098828
https://doi.org/10.1080/1478643031000098... . The efficiency packing was calculated from the chemical composition¹⁴14 Miracle DB, Sanders WS, Senkov O. The influence of efficient atomic packing on the constitution of metallic glasses. Philosophical Magazine. 2003;83(20):2409-2428. DOI: 10.1080/1478643031000098828
https://doi.org/10.1080/1478643031000098... and cluster unit cell length¹⁵15 Miracle DB. The efficient cluster packing model - An atomic structural model for metallic glasses. Acta Materialia. 2006;54(16):4317-4336. DOI: 10.1016/j.actamat.2006.06.002
https://doi.org/10.1016/j.actamat.2006.0... .

2.2 Theoretical elastic properties calculation

The elastic modulus predictions were also carried out for different glassy alloys systems taken from the literature. The estimations were made by applying the "rule of mixtures" approach ¹⁶16 Liu GR. A step-by-step method of rule-of-mixture of fiber and particle-reinforced composite materials. Composite Structure.1998;40(3-4):313-322. doi:10.1016/S0263-8223(98)00033-6
https://doi.org/10.1016/S0263-8223(98)00... ^-¹⁷17 Wang WH. The elastic properties, elastic models and elastic perspectives of metallic glasses. Progress in Materials Science. 2012;57:487-656. once having estimated the composition for the alloy using the efficient cluster-packing model. In the same way as before, theoretical estimations were compared to experimental values reported in the open literature. Twenty different values for Poisson's ratio for typical BMG were taken from ¹⁷17 Wang WH. The elastic properties, elastic models and elastic perspectives of metallic glasses. Progress in Materials Science. 2012;57:487-656.; for these twenty systems elastic constants c₁₁,c₁₂ and c₄₄ were also predicted in order to elaborate a Blackman diagram (plottingc₁₂/c₁₁ vs.c₄₄/c₁₁). The elastic constants c_ij were calculated with 1 - 3 equations¹⁷17 Wang WH. The elastic properties, elastic models and elastic perspectives of metallic glasses. Progress in Materials Science. 2012;57:487-656.^-¹⁸18 Ledbetter H. Handbook of elastic properties of solids liquids and gases. New York: Academic Science; 2001. Vol. 2.

c_{11} = K + (\frac{4}{3}) G

(1)

c_{12} = (3 K - c_{11}) / 2

(2)

c_{44} = G

(3)

The transition between brittle and tough regimes is atν_crit = 0.31 - 0.32¹⁹19 Lewandowski J, Wang WH, Greer AL. Intrinsic plasticity or brittleness of metallic glasses. Philosophical Magazine Letters. 2005;85(2):77–87.. Higher values of ν give higher fracture energy¹⁹19 Lewandowski J, Wang WH, Greer AL. Intrinsic plasticity or brittleness of metallic glasses. Philosophical Magazine Letters. 2005;85(2):77–87.. In other words, the larger the ν is, the more ductile the BMG become, and small variation of ν will significantly change the ductility¹⁷17 Wang WH. The elastic properties, elastic models and elastic perspectives of metallic glasses. Progress in Materials Science. 2012;57:487-656.. Several theoretical compositions obtained from the database were compared to those reported in the literature, and twenty different alloys per system (binary, ternary and quaternary), reported in the literature, are considered here.

2.3 Experimental method

Alloys with nominal compositions Zr_57.52Ag_10.62Al_10.62Co_21.24, Zr_57.19Al_10.7Ni_10.7Cu_21.41, and Hf_60.22Al_9.95Cu_9.95Ni_19.89 were prepared with pure elements (purity > 99.99%). The alloys were prepared under Ti-gettered inert atmosphere of argon (high purity > 99.9) using the arc-melting technique. All the ingots were re-melted five times in order to achieve a chemical homogeneity. Then, the molten alloys were poured into a copper mold with an internal cylindrical cavity of 2 mm diameter × 12 mm length by suction casting technique. The structure of the samples was characterized by means of X-ray diffraction with a Siemens D5000 diffractometer, using Cu K_α radiation. Finally, the hardness of the samples was carried out with a HMV-G21D hardness tester, in order to calculate the Young´s modulus values.

3 Results and discussion

3.1 Chemical composition

The prediction for the binary Pd-Si, referred to in Table 2 as alloy 1, being the compositions Pd₈₂Si₁₈ and Pd_82.96Si_17.04, which are the reported and predicted, respectively, showed very good agreement. Other examples are the binaries Co-B, Al-Cu, Co-Zr, Au-Si, where the difference between the reported and predicted composition was small. From the twenty binary alloys investigated, about five showed a significant difference between the reported and predicted compositions. Composition predictions for the twenty different binary alloys were obtained; these alloys are listed in Table 2. It can be observed that the calculated packaging efficiency for the majority of the alloys was approximately 40%. The packing efficiency for Co_77.61B_22.39, Ba_77.7Al_22.3, Ba_77.09Zn_22.91, Ba_77.09Zn_22.91 and Fe_77.79B_22.21binary alloys was about 50%. Figure 1shows the absolute difference between calculated and reported compositions alloys. The absolute difference of chemical composition for most alloys compared is less than 14%. The Ni-Nb (Ni_59.5Nb_40.5, Ni_89.69Nb_10.31, Cu_64.5Zr_35.5 and Cu_90.94Zr_9.06) binary system, showed 30% of difference, approximately.

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Table 2
Predicted and reported alloy compositions for binary systems²⁰20 Yao KF, Chen N. Pd-Si binary bulk metallic glass. Science in China Series G: Physics, Mechanics and Astronomy. 2008;51(4):414-420. DOI: 10.1007/s11433-008-0051-4
https://doi.org/10.1007/s11433-008-0051-...

21 Guo FQ, Poon SJ, Shiflet GJ. CaAl-based bulk metallic glasses with high thermal stability. Appllied Physics Letters. 2004;84(1):37-39. http://dx.doi.org/10.1063/1.1637940
https://doi.org/10.1063/1.1637940...

22 Leonhardt M, Löser W, Lindenkreuz HG. Solidification kinetics and phase formation of undercooled eutectic Ni–Nb melts. Acta Materialia. 1999;47(10):2961-2968.

23 Wang D, Li Y, Sun BB, Sui ML, Lu K, Ma E. Bulk metallic glass formation in the binary Cu-Zr system. Applied Physics Letters. 2004;84(20): 4029-4031.

24 Buschow KH. Thermal stability of amorphous Zr-Cu alloys. Journal of Applied Physics. 1981;52(5):3319-3323.DOI: 10.1063/1.329152
https://doi.org/10.1063/1.329152...

25 WasedaY, Chen HS. A structural study of metallic glasses containing boron (Fe-B, Co-B and Ni-B. Physica Status Solidi.1978;49(1):387-392. DOI: 10.1002/pssa.2210490149
https://doi.org/10.1002/pssa.2210490149...

26 Davies HA, Hull JB. Some aspects of splat-quenching in an inert atmosphere and of the formation of non-crystalline phases in Al-17.3 at. % Cu, germanium and tellurium. Journal of Materials Science. 1974;9:707-717.

27 Nose M, Masumoto T. Characteristics of (Fe, Co and/or Ni)-Zr amorphous alloys. Science Reports of the Research Institute Tohoku University SerA,Physicis,chemistry and metallurgy. 1980;28A:222-236.

28 Chen HS, Jackson KA. The Influence of alloy composition on glass formation and properties. In: Polk DE, Giesen BC. Metallic Glasses. Ohio, USA: Metals Park; 1978. p.74-96.

29 Predecki P, Giessen BC, Grant NJ. New metastable alloy. Transactions of the Metallurgical Society of AIME. 1965;233(7): 1438-1439.

30 Klement W, Willens RH, Duwez P. Non-crystalline structure in solidified gold-silicon alloys. Nature. 1960;187:869-870.

31 Sommer F, Duddek G, Predel B. New glassy alloys. Zeitchrift Metallkude. 1978;69:587-590.

32 St Amand R, Geissen BC. Easy glass formation in simple metal alloys: amorphous metals containing calcium and strontium. Scripta Metallurgica. 1978;12(11):1021-1026. Doi:10.106/0036-9748(78)90017-0
https://doi.org/10.106/0036-9748(78)9001... ^-³³33 Hasegawa R, Ray R. Iron-boron metallic glasses. Journal of Applied Physics. 1978;49:4174-4178. http://dx.doi.org/10.1063/1.325328
https://doi.org/10.1063/1.325328... .

Figure 1
Difference of chemical compositions of binary alloys. (a) Absolute difference of composition predictions for twenty different binary alloys and (b) Difference of solvents predictions for twenty different binary alloys.

Table 3 shows 20 ternary metallic glass compositions reported, it also includes the compositions and packing efficiency calculated with the database. The 4, 5, 7, 11, 15, and 20 alloy systems showed good agreement between calculated and reported ternary compositions as shown inFigure 2. However, for the Cu-Zr-Al, Mg-Gd-Cu and Cu-Zr-Be ternary alloy systems a significant difference was evident. On the other hand, the packing efficiency calculated for the Fe_75.76Y_6.06B_18.18 alloy was exceptional, i.e. 96.41%. In addition, the difference between the calculated and reported composition was very small.

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Table 3
Predicted and reported alloy compositions for ternary systems ³⁴34 Lu S, Tang MB, Xia L. Excellent magnetocaloric effect of a Gd55Al20Co bulk metallic glass. 25Physica B: Condensed Matter. 2011;406(18):3398-3401. http://dx.doi.org/10.1016/j.physb.2011.06.006
https://doi.org/10.1016/j.physb.2011.06....

35 Yu P, Chan KC, Chen W, Xia L. Elastic moduli and mechanical properties of bulk metallic glasses after quasi-static compression. Journal of Alloys and Compounds. 2011;509(34):8518-8521. DOI: 10.1016/j.jallcom.2011.05.113
https://doi.org/10.1016/j.jallcom.2011.0...

36 Soubeyroux JL, Puech S, Blandin J. Effect of silver on the glass forming ability of MgCuGdY bulk metallic glasses. Journal of Alloys and Compounds. 2009;483(1-2) :107-111. DOI : 10.1016/j.jallcom.2008.07.234
https://doi.org/10.1016/j.jallcom.2008.0...

37 Peng H Li SS, Qi YP, Huang TY. Mg–Ni–Gd–Ag bulk metallic glass with improved glass-forming ability and mechanical properties. Intermetallics. 2011;19(7):829-832. doi:10.1016/j.intermet.2010.11.029
https://doi.org/10.1016/j.intermet.2010....

38 Wada T, Qin FX, Wang XM, Yoshimura M, Inoue A, Sugiyama N, et al. Formation and bioactivation of Zr-Al-Co bulk metallic glasses. Journal of Materials Research. 2009;24(9):2941-2948. DOI: http://dx.doi.org/10.1557/jmr.2009.0348
https://doi.org/10.1557/jmr.2009.0348...

39 Park ES, Chang HJ, Kim DH. Effect of addition of Be on glass-forming ability, plasticity and structural change in Cu–Zr bulk metallic glasses. Acta Materialia. 2008;56(13):3120-3131. http://dx.doi.org/10.1016/j.actamat.2008.02.044
https://doi.org/10.1016/j.actamat.2008.0...

40 He Q, Cheng YQ, Ma E, Xu J. Locating bulk metallic glasses with high fracture toughness: Chemical effects and composition optimization. Acta Materialia. 2011;59(1):202-215.doi:10.1016/j.actamat.2010.09.025
https://doi.org/10.1016/j.actamat.2010.0...

41 Zhang L, Cheng YQ, Cao AJ, Xu J, Ma E. Bulk metallic glasses with large plasticity: Composition design from the structural perspective. Acta Materialia. 2009;57 (4) :154-1164.

42 Huang XM, Chang CT, Chang ZY, Wang XD, Cao QP, Shen BL, et al. Formation of bulk metallic glasses in the Fe-M-Y-B (M = transition metal) system. Journal of Alloys and Compounds. 2008;460(1-2):708-713. http://dx.doi.org/10.1016/j.jallcom.2007.09.063
https://doi.org/10.1016/j.jallcom.2007.0...

43 Guo G, Bian X, Meng Q, Zhao Y, Li X, Zhang S. Ternary Sm-Al-Co bulk metallic glass with high glass-forming ability. Journal of Alloys and Compounds. 2007;431(1-2):167-170. doi:10.1016/j.jallcom.2006.05.072
https://doi.org/10.1016/j.jallcom.2006.0...

44 Kong HZ, Li Y, Ding J. Magnetic hardening in amorphous alloy Sm60Fe30Al. 10Scripta Materialia. 2001;44(5): 829-834. DOI: 10.1016/S1359-6462(00)00652-7
https://doi.org/10.1016/S1359-6462(00)00...

45 Li S, Wang RJ, Pan MX, Zhao DQ, Wang WH. Heavy rare earth based bulk metallic glasses with high thermal stability. Intermetallic. 2006;14:592-595.

46 Jo CL, Xia L, Ding D, Dong YD. Glass formation ability and kinetics of the GdAl. 5520Ni25 bulk metallic glassChinese PhysicsLetters. 2006;23(3):672-674.

47 Kissinger HE. Reaction kinetics in differential thermal analysis. Analytical Chemistry. 1957;29(11):1702-1706.

48 Zhang B, Zhao DQ, Pan MX, Wang WH, Greer AL. Amorphous metallic plastic. Physical Review Letters. 2005;94:205502

49 Takeuchi A, Inoue A. Size dependence of soft to hard magnetic transition. Materialis Science and Engineering: A. 2004;375-377:1140-1144. doi:10.1016/j.msea.2003.10.201
https://doi.org/10.1016/j.msea.2003.10.2...

50 Wang YT, Xi XK, Fang YK, Zhao DQ, Pan MX, Han BS, et al. Tb nanocrystalline array assembled directly from alloy melt. Applied Physics Letters. 2004; 85(24):5989-5991.

51 Guo FQ, Poon SJ, Shiflet GJ. Metallic glass ingots based on yttrium. Applied Physics Letters. 2003;83(13):2575-2577.

52 Wang J, Li R, Hua N, Huang L, Zhang T. Ternary Fe–P–C bulk metallic glass with good soft-magnetic and mechanical properties. Scripta Materialia. 2011;65(6):536-539.^-⁵³53 Jiang QK, Zhang GQ, Yang L, Wang XD, Saks K, Franz H, et al. La-based bulk metallic glasses with critical diameter up to 30 mm. Acta Materialia. 2007;55(13):4409-4418. DOI: 10.1016/j.actamat.2007.04.021
https://doi.org/10.1016/j.actamat.2007.0... .

Figure 2
Difference of chemical compositions of ternary alloys. (a) Composition predictions of solvents for twenty different ternary alloys and (b) Difference of ternary large solutes for the predicted and calculated alloys.

Table 4 shows the quaternary compositions of BMG reported and calculated. Figure 3 shows good agreement of quaternary compositions. The chemical compositions difference of the alloys reported and calculated was less than 10% for most of the alloy systems studied.

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Table 4
Predicted and reported alloy compositions for quaternary systems³⁶36 Soubeyroux JL, Puech S, Blandin J. Effect of silver on the glass forming ability of MgCuGdY bulk metallic glasses. Journal of Alloys and Compounds. 2009;483(1-2) :107-111. DOI : 10.1016/j.jallcom.2008.07.234
https://doi.org/10.1016/j.jallcom.2008.0... ^,³⁷37 Peng H Li SS, Qi YP, Huang TY. Mg–Ni–Gd–Ag bulk metallic glass with improved glass-forming ability and mechanical properties. Intermetallics. 2011;19(7):829-832. doi:10.1016/j.intermet.2010.11.029
https://doi.org/10.1016/j.intermet.2010.... ^,⁴⁰40 He Q, Cheng YQ, Ma E, Xu J. Locating bulk metallic glasses with high fracture toughness: Chemical effects and composition optimization. Acta Materialia. 2011;59(1):202-215.doi:10.1016/j.actamat.2010.09.025
https://doi.org/10.1016/j.actamat.2010.0... ^,⁴²42 Huang XM, Chang CT, Chang ZY, Wang XD, Cao QP, Shen BL, et al. Formation of bulk metallic glasses in the Fe-M-Y-B (M = transition metal) system. Journal of Alloys and Compounds. 2008;460(1-2):708-713. http://dx.doi.org/10.1016/j.jallcom.2007.09.063
https://doi.org/10.1016/j.jallcom.2007.0... ^,⁵⁴54 Schroers J, Johnson WL. Highly processable bulk metallic glass-forming alloys in the Pt-Co-Ni-Cu-P system. Applied Physics letters. 2004;84(18):3666-3668.

55 Zhang C, Li N, Pan J, Guo SF, Zhang M, Liu L. Enhancement of glass-forming ability and bio-corrosion resistance of Zr-Co-Al bulk metallic glasses by the addition of Ag. Journal of Alloys and Compounds. 2010;504S:S163-S167.

56 Xia L, Chan KC, Tang MB. Enhanced glass forming ability and refrigerant capacity of a Gd55Ni22MnAl bulk metallic glass. 320Journal of Alloys and Compounds. 2011;509(23): 6640-6643. DOI: 10.1016/j.jallcom.2011.03.120
https://doi.org/10.1016/j.jallcom.2011.0...

57 Kawashima A, Zeng Y, Fukuhara M, Kurishita H, Nishiyama N, Miki H, et al. Mechanical properties of a Ni60Pd20PB bulk glassy alloy at cryogenic temperatures. 173Materials Science and Engineering A. 2008;498(1-2):475-481. DOI:10.1016/j.msea.2008.08.033
https://doi.org/10.1016/j.msea.2008.08.0...

58 Zhang L, Cheng YQ, Cao AJ, Xu J, Ma E. Bulk metallic glasses with large plasticity: Composition design from the structural perspective. Acta Materialia. 2009;57(4):1154-1164.

59 Huang XM, Chang CT, Chang ZY, Inoue A, Jiang JZ. Glass forming ability, mechanical and magnetic properties in Fe-W-Y-B alloys. Materials Science and Engineering A. 2010;527(7-8):1952-1956. DOI: 10.1016/j.msea.2009.11.042
https://doi.org/10.1016/j.msea.2009.11.0... ^-⁶⁰60 Jiang QK, Wang XD, Nie XP, Zhang GQ, Ma H, Fecht HJ, et al. Zr-(Cu,Ag)-Al bulk metallic glasses. Acta Materialia. 2008;56(8):1785-1796..

Figure 3
Difference of chemical compositions of ternary alloys. (a) Composition predictions of solvents for twenty different quaternary alloys and (b) Difference of quaternary large solutes for predicted and calculated alloys.

3.2 Elastic properties

The elastic modulus (E) and shear modulus (G) estimations for twenty different alloys were also calculated and compared with those reported in the literature. The corresponding alloys are listed in Tables 5 and 6, respectively and plotted in Figure 4. (It was possible to estimate values for bulk modulus (K), too, but these are not included in this work).

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Table 5
Predicted and reported G for several alloys; alloys 1-12 ¹⁷17 Wang WH. The elastic properties, elastic models and elastic perspectives of metallic glasses. Progress in Materials Science. 2012;57:487-656. and 13-20¹³13 Plummer JD, Todd I. Implications of elastic constants, fragility, and bonding on permanent deformation in metallic glass. Appllied Physics Letters. 2011;98(2):021907. http://dx.doi.org/10.1063/1.3540652
https://doi.org/10.1063/1.3540652... .

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Table 6
Predicted and reported E for several alloys; alloys 1-12¹⁷17 Wang WH. The elastic properties, elastic models and elastic perspectives of metallic glasses. Progress in Materials Science. 2012;57:487-656. and 13-20¹³13 Plummer JD, Todd I. Implications of elastic constants, fragility, and bonding on permanent deformation in metallic glass. Appllied Physics Letters. 2011;98(2):021907. http://dx.doi.org/10.1063/1.3540652
https://doi.org/10.1063/1.3540652... .

Figure 4
Predicted and reported elastic proprieties values for several alloys. (a) Elastic modulus and (b) Shear modulus.

Regarding the Young's modulus, E, the Mg₆₅Cu₂₅Tb₁₀ system reports 51.3 GPa while its predicted value was 54.8 GPa; the Hf₅₅Ni₂₅Al₂₀ reports 117.63 GPa¹³13 Plummer JD, Todd I. Implications of elastic constants, fragility, and bonding on permanent deformation in metallic glass. Appllied Physics Letters. 2011;98(2):021907. http://dx.doi.org/10.1063/1.3540652
https://doi.org/10.1063/1.3540652... and the predicted value is 113.8 GPa (Hf₆₀Ni₃₀Al₁₀). In general, the similarity between the reported and predicted elastic moduli is rather good. However, it can be noticed that some of the composition predictions, even though they did show a slight deviation from those reported in literature, kept a narrow correlation with regards to the elastic modulus values. The elastic property predictions also showed good correlation with the corresponding experimentally reported data (Tables 5,6 and Figure 4). The Mg₆₅Cu₂₅Tb₁₀ ternary system reports a shear modulus, G, of 19.6 GPa¹³13 Plummer JD, Todd I. Implications of elastic constants, fragility, and bonding on permanent deformation in metallic glass. Appllied Physics Letters. 2011;98(2):021907. http://dx.doi.org/10.1063/1.3540652
https://doi.org/10.1063/1.3540652... and its corresponding prediction gives 20.8 GPa (Mg_79.03Cu_10.48Tb_10.48); the quaternary Gd₄₀Y₁₆Al₂₄Co₂₀ reports a G of 23.5 GPa¹⁷17 Wang WH. The elastic properties, elastic models and elastic perspectives of metallic glasses. Progress in Materials Science. 2012;57:487-656. and its predicted value is 27.3 GPa (Gd_63.7Y_9.08Al_18.15Co_9.08).

The Poisson's ratio estimations for twenty different alloys were also calculated and compared with those reported in the literature. The corresponding alloys are listed in Table 7; it also includes the elastic constants ratios (c₄₄/c₁₁ andc₁₂/c₁₁) calculated by the database. The absolute difference percentage of the Poisson's ratio in most alloys compared in this work was between 3.8% - 12%. Compositions 3, 7, and 8, show smaller values than 3%, due to chemical composition similarity. Compositions 10 and 17, show a greater value than 13%, due to greater discrepancy between reported and calculated compositions.

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Table 7
Poisson's ratios for different alloys¹⁷17 Wang WH. The elastic properties, elastic models and elastic perspectives of metallic glasses. Progress in Materials Science. 2012;57:487-656., and their respectively predicted elastic constants ratios.

Figure 5 shows a Blackman diagram constructed using the data from twenty different predicted alloys (listed inTable 7), with the Poisson's ratio. Concerning to the intrinsic toughness estimated for the twenty different predicted alloys, the Poisson's ratio was consistent with the ductile behaviour in most of the alloys. These results could provide an insight into the tough-brittle behaviour that the system might present. Those values at the upper left, such as: Pd₇₅Cu_12.5Si_12.5 (0.216, 0.676, 0.403; c₄₄/c₁₁,c₁₂/c₁₁, Poisson's ratio, respectively) and Ni_71.36Nb_21.48Sn_7.16(0.274, 0.590, 0.371) corresponds to higher Poisson's ratio values (lowc₄₄/c₁₁ and highc₁₂/c₁₁), and so those systems would be expected to display ductile behaviour.

Figure 5
Blackman diagram of twenty different predicted alloys.

The Poisson´s ratio reported and predicted for Ho₃₉Al₂₅Co₂₀Y₁₆ are 0.319 and 0.328, respectively. These are down to the right on the Blackman construction and the transition from brittle to tough behaviour would be expected atv ~ 0.32, which is consistent with the criterion reported.¹⁹19 Lewandowski J, Wang WH, Greer AL. Intrinsic plasticity or brittleness of metallic glasses. Philosophical Magazine Letters. 2005;85(2):77–87.

With the database, it was possible to make other predictions based on elastic properties, such as the kinetic fragility index, m, which was calculated with equation (4)³⁹39 Park ES, Chang HJ, Kim DH. Effect of addition of Be on glass-forming ability, plasticity and structural change in Cu–Zr bulk metallic glasses. Acta Materialia. 2008;56(13):3120-3131. http://dx.doi.org/10.1016/j.actamat.2008.02.044
https://doi.org/10.1016/j.actamat.2008.0... .

$m = 12 (\frac{K}{G} + 0.67)$ (4)

The kinetic fragility index is recently used to know whether an alloy will present high or low GFA⁶³63 Lafi OA, Imran MM. Compositional dependence of thermal stability, glass-forming ability and fragility index in some Se-Te-Sn glasses. Journal of Alloys and Compounds. 2011;509(16):5090-5094.. Since elastic moduli can be potentially correlated to a wide range of physical, mechanical and thermal properties in BMGs, the way the database has been used here may be considered a starting point for how it can be implemented in future studies. Additionally, the database performs three different composition predictions for the ternary systems, the one that considers the gamma sites to be empty, another in which gamma sites are half occupied byβ_γ anti-site defects and the last one that assumes all gamma sites are occupied by the presence ofβ_γ anti-site defects. Thus, the best prediction approach was chosen to be compared with the reported data in the ternary systems.

3.3 Experimental results

In order to test the database, some glass alloys in the form of bulk were experimentally obtained. Figure 6 shows the XRD pattern of the Zr_57.52Ag_10.62Al_10.62Co_21.24, Zr_57.19Al_10.7Ni_10.7Cu_21.41, and Hf_60.22Al_9.95Cu_9.95Ni_19.89alloys. The XRD patterns are constituted by a single broad peak (located between 2θ ~ 35 and 55^o) typical of a metallic glass. These results confirm the usefulness of the work presented in this manuscript, where it was possible to design, model and produce bulk metallic glasses a-priori, reducing the experimental work time associated with standard experimental processes.

Figure 6
XRD patterns of the experimentally obtained bulk metallic glasses.

Table 8 shows packing efficiency values and kinetic fragility index m of alloys produced. The efficiency packing values were between 45% and 50%. According to Angell ⁶¹61 Angell CA. Structural instability and relaxation in liquid and glassy phases near the fragile liquid limit. Journal of Non-Crystalline Solids. 1988;102(1-3):205-221.doi:10.1016/0022-3093(88)90133-0
https://doi.org/10.1016/0022-3093(88)901... ^-⁶²62 Angell CA. Relaxation in liquids, polymers and plastic crystals - strong/fragile patterns and problems. Journal of Non-Crystalline Solids. 1991;131-133(Part 1):13-31., glass-forming liquids can be classified into strong and fragile liquids, depending on their fragility. The upper and lower limits of parameter are theoretically estimated between 16 for ‘strong' systems and 200 for ‘fragile' systems⁶³63 Lafi OA, Imran MM. Compositional dependence of thermal stability, glass-forming ability and fragility index in some Se-Te-Sn glasses. Journal of Alloys and Compounds. 2011;509(16):5090-5094.. The alloys obtained are strong systems with high glass forming ability.

Thumbnail

Table 8
Compositions, packaging efficiency and kinetic index of fragility, calculated with the database for the obtained BMGs.

Table 9 shows compositions calculated by "mixing rules", elastic properties, and elastic constants ratios (c₄₄/c₁₁ andc₁₂/c₁₁). The typical BMGs have Young's modulus E ~ 25 GPa - 250 GPa, shear modulus G ~ 9 GPa - 88 GPa, and bulk modulus K ~ 20 GPa - 243 GPa ¹⁷17 Wang WH. The elastic properties, elastic models and elastic perspectives of metallic glasses. Progress in Materials Science. 2012;57:487-656..

Thumbnail

Table 9
Elastic properties calculated with the "mixing rules" for the obtained BMGs.

A good correlation between microhardness, H_v, and Young's modulus, E, has been reported elsewhere¹⁷17 Wang WH. The elastic properties, elastic models and elastic perspectives of metallic glasses. Progress in Materials Science. 2012;57:487-656., in that work, it is reported an E/H_v ~20.

The microhardness values obtained experimentally in this work of Zr_57.52Ag_10.62Al_10.62Co_21.24, Zr_57.19Al_10.7Ni_10.7Cu_21.41 and Hf_60.22Al_9.95Cu_9.95Ni_19.89alloys, are 3.8, 4.0 and 3.6 GPa, respectively. If these values are substituted in the E/H_v = 20 relationship found in the previous research¹⁷17 Wang WH. The elastic properties, elastic models and elastic perspectives of metallic glasses. Progress in Materials Science. 2012;57:487-656., then the Young´s modulus values calculated are 76, 80 and 73 GPa. These values are closed to the calculated values with the "mixing rules" (table 9).

The elastic constants ratios were used to plot a Blackman diagram. Figure 7 shows the Blackman diagram of alloys mentioned above with their corresponding Poisson's ratio. It shows the values at the upper left (lowc₄₄/c₁₁ and highc₁₂/c₁₁) and high Poisson´s ratio values, suggest ductile behaviour.

Figure 7
Blackman diagram of the experimentally obtained bulk metallic glasses.

4 Conclusions

The results of the database presented here for estimating composition and elemental elastic properties in metallic glasses have been able to closely approach those experimentally determined and reported in the literature. They additionally provide valuable information regarding the mechanical behaviour that these alloys might present. This illustrates the usefulness of these theoretical models. In relation to the packing efficiency calculations, particularly those obtained for the quaternary systems, it can be noticed that some other factors such as chemical affinity, bonding and/or the enthalpies of mixing, must play a key role in the BMG-forming systems. The database enclosing the methods used in this work has been developed; incorporates the elemental elastic constants for the most common alloying elements as well as their atomic radii information. The quaternary alloys experimentally obtained are strong systems with high glass forming ability, which is consistent with the Miracle´s model and kinetic fragility index m. The Young's modulus estimated with microhardness values are closed to those calculated by the "mixing rules". The Poisson´s ratio and Blackman diagram, suggest ductile behaviour of the BMGs obtained.

Acknowledgements

The authors would like to acknowledge the financial support from SEP CONACYT 178289 for funding the project. A. Tejeda-Cruz, S. García-Galán, J. Morales-Rosales, C. Flores-Morales, C. Delgado, G. Aramburo, O. Novelo and J. M. Garcia-León are also acknowledged for their technical support.

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Publication Dates

Publication in this collection
08 Mar 2016
Date of issue
Mar-Apr 2016

History

Received
08 Sept 2015
Reviewed
25 Nov 2015
Accepted
16 Dec 2015

This is an Open Access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Who	When	What	Related to
Goldschmidt¹1 Goldschmidt VM. Geochemische Verteilungsgesetze der Elemente VIII. Oslo: Skrifter Norske Videnkaps; 1926.	1926	Tetrahedral configurations were necessary for the formation of a glass	Oxides of the type A_mO_n
Zachariasen²2 Zachariasen WH. The atomic arrangement in glass. Journal of the American Chemical Society. 1932;54(10):3841-3851. DOI: 10.1021/ja01349a006 https://doi.org/10.1021/ja01349a006...	1932	Continuous random network (CRN)	SiO₄
Sun⁵5 Sun KH. Fundamental condition of glass formation. Journal of the American Ceramic Society. 1947;30(9):277-281. DOI: 10.1111/j.1151-2916.1947.tb19654.x https://doi.org/10.1111/j.1151-2916.1947...	1946	Model to obtain long range or network of atoms to form a glassy phase	Oxides of the type M-O single bound
Bernal, Mason³3 Bernal JD, Mason J. Packing of spheres: coordination of randomly packed spheres. Nature. 1960;188(4754):910-911. DOI: 10.1038/188910a0 https://doi.org/10.1038/188910a0...	1959	Model of dense random packing (DRP) or rigid spheres	Bernal holes
Polk⁶6 Polk D. The structure of glassy metallic alloys. Acta Metallurgica. 1972;20(4):485-491. Doi: 10.1016/0001-6160(72)90003-X https://doi.org/10.1016/0001-6160(72)900...	1972	Model to describe transition metal – metalloid glassy systems	Metallic glasses
Egami Waseda⁷7 Egami T, Waseda YJ. Atomic size effect on the formability of metallic glasses. Journal of Non-Crystalline Solids. 1984;64(1-2):113-134.	1984	Relation between glass formability and atomic size mismatch	Binary metallic glassy alloys
Granato⁸8 Granato AV. Thermodynamic properties of liquid and amorphous monatomic metals from an interstitialcy model. Journal of Non-Crystalline Solids. 1993;156-158(Part 1):402-406. DOI: 10.1016/0022-3093(93)90206-D https://doi.org/10.1016/0022-3093(93)902...	1993	The main roles of interstitial atoms is in destabilising the crystalline phase	Frozen glassy and liquid states alloys
Egami⁹9 Egami T. Universal criterion for metallic glass formation. Materials Science and Engineering. 1997;226-228:261-267. doi:10.1016/S0921-5093(97)80041-X https://doi.org/10.1016/S0921-5093(97)80...	1997	Topological instability applied to local atomic structure	Metallic elements and alloys
Senkov, Miracle¹⁰10 Senkov ON, Miracle DB. Effect of the atomic size distribution on glass forming ability of amorphous metallic alloys. Materials Research Bulletin. 2001;36(12):2183-2198. DOI: 10.1016/S0025-5408(01)00715-2 https://doi.org/10.1016/S0025-5408(01)00...	2001	Interstitial model for glass formation	Prediction of glass formation
Egami¹¹11 Egami T. Atomistic mechanism of bulk metallic glass formation. Journal of Non-Crystalline Solids. 2003;317(1-2):30-33. doi:10.1016/S0022-3093(02)02003-3 https://doi.org/10.1016/S0022-3093(02)02...	2003	Identified several conditions that would favour multicomponent bulk metallic glass formation	Prediction of BMG-formation
Miracle⁴4 Miracle DB. A structural model for metallic glasses. Nature Materials. 2004;3:697-702. doi:10.1038/nmat1219 https://doi.org/10.1038/nmat1219...	2004	Model to determine the alloy constituent concentration based on a topological atomistic approach	Dense packing of atomic clusters for glass formation

Table 2 Predicted and reported alloy compositions for binary systems²⁰20 Yao KF, Chen N. Pd-Si binary bulk metallic glass. Science in China Series G: Physics, Mechanics and Astronomy. 2008;51(4):414-420. DOI: 10.1007/s11433-008-0051-4
https://doi.org/10.1007/s11433-008-0051-...

21 Guo FQ, Poon SJ, Shiflet GJ. CaAl-based bulk metallic glasses with high thermal stability. Appllied Physics Letters. 2004;84(1):37-39. http://dx.doi.org/10.1063/1.1637940
https://doi.org/10.1063/1.1637940...

22 Leonhardt M, Löser W, Lindenkreuz HG. Solidification kinetics and phase formation of undercooled eutectic Ni–Nb melts. Acta Materialia. 1999;47(10):2961-2968.

23 Wang D, Li Y, Sun BB, Sui ML, Lu K, Ma E. Bulk metallic glass formation in the binary Cu-Zr system. Applied Physics Letters. 2004;84(20): 4029-4031.

24 Buschow KH. Thermal stability of amorphous Zr-Cu alloys. Journal of Applied Physics. 1981;52(5):3319-3323.DOI: 10.1063/1.329152
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25 WasedaY, Chen HS. A structural study of metallic glasses containing boron (Fe-B, Co-B and Ni-B. Physica Status Solidi.1978;49(1):387-392. DOI: 10.1002/pssa.2210490149
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26 Davies HA, Hull JB. Some aspects of splat-quenching in an inert atmosphere and of the formation of non-crystalline phases in Al-17.3 at. % Cu, germanium and tellurium. Journal of Materials Science. 1974;9:707-717.

27 Nose M, Masumoto T. Characteristics of (Fe, Co and/or Ni)-Zr amorphous alloys. Science Reports of the Research Institute Tohoku University SerA,Physicis,chemistry and metallurgy. 1980;28A:222-236.

28 Chen HS, Jackson KA. The Influence of alloy composition on glass formation and properties. In: Polk DE, Giesen BC. Metallic Glasses. Ohio, USA: Metals Park; 1978. p.74-96.

29 Predecki P, Giessen BC, Grant NJ. New metastable alloy. Transactions of the Metallurgical Society of AIME. 1965;233(7): 1438-1439.

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31 Sommer F, Duddek G, Predel B. New glassy alloys. Zeitchrift Metallkude. 1978;69:587-590.

32 St Amand R, Geissen BC. Easy glass formation in simple metal alloys: amorphous metals containing calcium and strontium. Scripta Metallurgica. 1978;12(11):1021-1026. Doi:10.106/0036-9748(78)90017-0
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https://doi.org/10.1063/1.325328... .

N°. alloy	Reported composition	Predicted composition	%Pack. Eff.	N°. alloy	Reported Composition	Predicted Composition	%Pack. Eff.
1	Pd₈₂Si₁₈	Pd_82.96Si_17.04	44.76	11	Al₉₁Er₉	Al_91.22Er_8.78	41.38
2	Pd₈₁Si₁₉	Pd_82.96Si_17.04	44.76	12	Au_81.4Si_18.6	Au_81.98Si_18.02	41.69
3	Pd₈₀Si₂₀	Pd_82.96Si_17.04	44.76	13	Au₈₃Si₁₇	Au_81.98Si_18.02	41.69
4	Ca_66.4Al_33.6	Ca_79.86Al_20.14	44.76	14	Au₈₀Si₂₀	Au_81.98Si_18.02	41.69
5	Ni_59.5Nb_40.5	Ni_89.69Nb_10.31	45.75	15	Au₇₅Si₂₅	Au_81.98Si_18.02	41.69
6	Cu_64.5Zr_35.5	Cu_90.94Zr_9.06	42.22	16	Ba₇₂Al₂₈	Ba_77.7Al_22.3	51.85
7	Cu₉₀Zr₁₀	Cu_90.94Zr_9.06	42.22	17	Ba₇₆Ga₂₄	Ba_77.05Ga_22.95	50.37
8	Co₇₇B₂₃	Co_77.61B_22.39	51.65	18	Ba₇₆Zn₂₄	Ba_77.09Zn_22.91	50.46
9	Al_82.7Cu_17.3	Al_84.22Cu_15.78	41.75	19	Ca_87.5Ag_12.5	Ca_80.06Ag_19.94	46.17
10	Co₉₁Zr₉	Co_91.22Zr_8.78	41.14	20	Fe₇₈B₂₂	Fe_77.79B_22.21	52.07

Table 3 Predicted and reported alloy compositions for ternary systems ³⁴34 Lu S, Tang MB, Xia L. Excellent magnetocaloric effect of a Gd55Al20Co bulk metallic glass. 25Physica B: Condensed Matter. 2011;406(18):3398-3401. http://dx.doi.org/10.1016/j.physb.2011.06.006
https://doi.org/10.1016/j.physb.2011.06....

35 Yu P, Chan KC, Chen W, Xia L. Elastic moduli and mechanical properties of bulk metallic glasses after quasi-static compression. Journal of Alloys and Compounds. 2011;509(34):8518-8521. DOI: 10.1016/j.jallcom.2011.05.113
https://doi.org/10.1016/j.jallcom.2011.0...

36 Soubeyroux JL, Puech S, Blandin J. Effect of silver on the glass forming ability of MgCuGdY bulk metallic glasses. Journal of Alloys and Compounds. 2009;483(1-2) :107-111. DOI : 10.1016/j.jallcom.2008.07.234
https://doi.org/10.1016/j.jallcom.2008.0...

37 Peng H Li SS, Qi YP, Huang TY. Mg–Ni–Gd–Ag bulk metallic glass with improved glass-forming ability and mechanical properties. Intermetallics. 2011;19(7):829-832. doi:10.1016/j.intermet.2010.11.029
https://doi.org/10.1016/j.intermet.2010....

38 Wada T, Qin FX, Wang XM, Yoshimura M, Inoue A, Sugiyama N, et al. Formation and bioactivation of Zr-Al-Co bulk metallic glasses. Journal of Materials Research. 2009;24(9):2941-2948. DOI: http://dx.doi.org/10.1557/jmr.2009.0348
https://doi.org/10.1557/jmr.2009.0348...

39 Park ES, Chang HJ, Kim DH. Effect of addition of Be on glass-forming ability, plasticity and structural change in Cu–Zr bulk metallic glasses. Acta Materialia. 2008;56(13):3120-3131. http://dx.doi.org/10.1016/j.actamat.2008.02.044
https://doi.org/10.1016/j.actamat.2008.0...

40 He Q, Cheng YQ, Ma E, Xu J. Locating bulk metallic glasses with high fracture toughness: Chemical effects and composition optimization. Acta Materialia. 2011;59(1):202-215.doi:10.1016/j.actamat.2010.09.025
https://doi.org/10.1016/j.actamat.2010.0...

41 Zhang L, Cheng YQ, Cao AJ, Xu J, Ma E. Bulk metallic glasses with large plasticity: Composition design from the structural perspective. Acta Materialia. 2009;57 (4) :154-1164.

42 Huang XM, Chang CT, Chang ZY, Wang XD, Cao QP, Shen BL, et al. Formation of bulk metallic glasses in the Fe-M-Y-B (M = transition metal) system. Journal of Alloys and Compounds. 2008;460(1-2):708-713. http://dx.doi.org/10.1016/j.jallcom.2007.09.063
https://doi.org/10.1016/j.jallcom.2007.0...

43 Guo G, Bian X, Meng Q, Zhao Y, Li X, Zhang S. Ternary Sm-Al-Co bulk metallic glass with high glass-forming ability. Journal of Alloys and Compounds. 2007;431(1-2):167-170. doi:10.1016/j.jallcom.2006.05.072
https://doi.org/10.1016/j.jallcom.2006.0...

44 Kong HZ, Li Y, Ding J. Magnetic hardening in amorphous alloy Sm60Fe30Al. 10Scripta Materialia. 2001;44(5): 829-834. DOI: 10.1016/S1359-6462(00)00652-7
https://doi.org/10.1016/S1359-6462(00)00...

45 Li S, Wang RJ, Pan MX, Zhao DQ, Wang WH. Heavy rare earth based bulk metallic glasses with high thermal stability. Intermetallic. 2006;14:592-595.

46 Jo CL, Xia L, Ding D, Dong YD. Glass formation ability and kinetics of the GdAl. 5520Ni25 bulk metallic glassChinese PhysicsLetters. 2006;23(3):672-674.

47 Kissinger HE. Reaction kinetics in differential thermal analysis. Analytical Chemistry. 1957;29(11):1702-1706.

48 Zhang B, Zhao DQ, Pan MX, Wang WH, Greer AL. Amorphous metallic plastic. Physical Review Letters. 2005;94:205502

49 Takeuchi A, Inoue A. Size dependence of soft to hard magnetic transition. Materialis Science and Engineering: A. 2004;375-377:1140-1144. doi:10.1016/j.msea.2003.10.201
https://doi.org/10.1016/j.msea.2003.10.2...

50 Wang YT, Xi XK, Fang YK, Zhao DQ, Pan MX, Han BS, et al. Tb nanocrystalline array assembled directly from alloy melt. Applied Physics Letters. 2004; 85(24):5989-5991.

51 Guo FQ, Poon SJ, Shiflet GJ. Metallic glass ingots based on yttrium. Applied Physics Letters. 2003;83(13):2575-2577.

52 Wang J, Li R, Hua N, Huang L, Zhang T. Ternary Fe–P–C bulk metallic glass with good soft-magnetic and mechanical properties. Scripta Materialia. 2011;65(6):536-539.^-⁵³53 Jiang QK, Zhang GQ, Yang L, Wang XD, Saks K, Franz H, et al. La-based bulk metallic glasses with critical diameter up to 30 mm. Acta Materialia. 2007;55(13):4409-4418. DOI: 10.1016/j.actamat.2007.04.021
https://doi.org/10.1016/j.actamat.2007.0... .

N°. alloy	Reported composition	Predicted composition	%Pack. Eff.	N°. alloy	Reported composition	Predicted composition	%Pack. Eff.
1	Gd₅₅Al₂₀Co₂₅	Gd_60.24Al_13.25Co_26.51	65.64	11	Sm₆₀Al₁₀Fe₃₀	Sm_60.24Al_13.25Fe_26.51	65.64
2	Cu₄₆Zr₄₆Al₈	Cu_76.86Zr_7.71Al_15.43	60.64	12	Gd₅₆Al₂₄Co₂₀	Gd_60.24Al_13.25Co_26.51	65.64
3	Mg₆₅Gd₂₅Cu₁₀	Mg_73.53Gd_8.11Cu_24.32	59.28	13	Gd₅₅Al₂₅Ni₂₀	Gd_60.24Al_13.25Ni_26.51	65.64
4	Mg₇₅Gd₁₀Ni₁₅	Mg_73.53Gd_8.82Ni_17.65	71.81	14	Nd₆₀Al₁₀Co₃₀	Nd_56.81Al_10.8Co_32.39	45.7
5	Zr₅₈Al₁₂Co₃₀	Zr_56.81Al_10.8Co_32.39	45.7	15	Ce₇₀Al₁₀Cu₂₀	Ce_69.44Al_15.28Cu_15.28	61.57
6	Cu_47.5Zr₄₀Be_12.5	Cu_76.86Zr_7.71Be_15.43	69.74	16	Pr₆₀Al₁₀Fe₁₀	Pr_63.68Al_12.11Fe_24.21	67.15
7	Zr₅₈Al₁₂Cu₃₀	Zr_56.81Al_10.8Cu_32.39	45.7	17	Tb₆₅Al₁₀Fe₂₅	Tb_60.24Al_13.25Fe_26.51	60.59
8	Hf₆₂Al₁₃Ni₁₅	Hf_66.67Al_11.11Ni_22.22	67.22	18	Y₅₆Al₂₄Co₂₀	Y_60.24Al_13.25Co_26.52	65.64
9	Fe₇₂Y₆B₂₂	Fe_75.76Y_6.06B_18.18	96.41	19	Fe₈₀P₁₁C₉	Fe_72.46P_13.77C_13.77	37.79
10	Sm₅₅Al₂₅Co₂₀	Sm_60.24Al_13.25Co_26.51	65.64	20	La₆₂Al₁₄Cu₂₄	La_60.24Al_13.25Cu_26.51	65.64

Table 4 Predicted and reported alloy compositions for quaternary systems³⁶36 Soubeyroux JL, Puech S, Blandin J. Effect of silver on the glass forming ability of MgCuGdY bulk metallic glasses. Journal of Alloys and Compounds. 2009;483(1-2) :107-111. DOI : 10.1016/j.jallcom.2008.07.234
https://doi.org/10.1016/j.jallcom.2008.0... ^,³⁷37 Peng H Li SS, Qi YP, Huang TY. Mg–Ni–Gd–Ag bulk metallic glass with improved glass-forming ability and mechanical properties. Intermetallics. 2011;19(7):829-832. doi:10.1016/j.intermet.2010.11.029
https://doi.org/10.1016/j.intermet.2010.... ^,⁴⁰40 He Q, Cheng YQ, Ma E, Xu J. Locating bulk metallic glasses with high fracture toughness: Chemical effects and composition optimization. Acta Materialia. 2011;59(1):202-215.doi:10.1016/j.actamat.2010.09.025
https://doi.org/10.1016/j.actamat.2010.0... ^,⁴²42 Huang XM, Chang CT, Chang ZY, Wang XD, Cao QP, Shen BL, et al. Formation of bulk metallic glasses in the Fe-M-Y-B (M = transition metal) system. Journal of Alloys and Compounds. 2008;460(1-2):708-713. http://dx.doi.org/10.1016/j.jallcom.2007.09.063
https://doi.org/10.1016/j.jallcom.2007.0... ^,⁵⁴54 Schroers J, Johnson WL. Highly processable bulk metallic glass-forming alloys in the Pt-Co-Ni-Cu-P system. Applied Physics letters. 2004;84(18):3666-3668.

55 Zhang C, Li N, Pan J, Guo SF, Zhang M, Liu L. Enhancement of glass-forming ability and bio-corrosion resistance of Zr-Co-Al bulk metallic glasses by the addition of Ag. Journal of Alloys and Compounds. 2010;504S:S163-S167.

56 Xia L, Chan KC, Tang MB. Enhanced glass forming ability and refrigerant capacity of a Gd55Ni22MnAl bulk metallic glass. 320Journal of Alloys and Compounds. 2011;509(23): 6640-6643. DOI: 10.1016/j.jallcom.2011.03.120
https://doi.org/10.1016/j.jallcom.2011.0...

57 Kawashima A, Zeng Y, Fukuhara M, Kurishita H, Nishiyama N, Miki H, et al. Mechanical properties of a Ni60Pd20PB bulk glassy alloy at cryogenic temperatures. 173Materials Science and Engineering A. 2008;498(1-2):475-481. DOI:10.1016/j.msea.2008.08.033
https://doi.org/10.1016/j.msea.2008.08.0...

58 Zhang L, Cheng YQ, Cao AJ, Xu J, Ma E. Bulk metallic glasses with large plasticity: Composition design from the structural perspective. Acta Materialia. 2009;57(4):1154-1164.

59 Huang XM, Chang CT, Chang ZY, Inoue A, Jiang JZ. Glass forming ability, mechanical and magnetic properties in Fe-W-Y-B alloys. Materials Science and Engineering A. 2010;527(7-8):1952-1956. DOI: 10.1016/j.msea.2009.11.042
https://doi.org/10.1016/j.msea.2009.11.0... ^-⁶⁰60 Jiang QK, Wang XD, Nie XP, Zhang GQ, Ma H, Fecht HJ, et al. Zr-(Cu,Ag)-Al bulk metallic glasses. Acta Materialia. 2008;56(8):1785-1796..

N°. alloy	Reported composition	Predicted composition	%Pack. Eff.	N°. alloy	Reported Composition	Predicted Composition	%Pack. Eff.
1	Pt_57.5Cu_14.7Ni_5.3P_22.5	Pt_60.76Cu_9.81Ni_9.81P_19.62	50.23	11	Zr₅₃Ag₉Al_23.5Co_14.5	Zr_57.52Ag_10.6Al_10.62Co_21.24	45.37
2	Ce₆₈Al₁₀Nb₂Cu₂₀	Ce_52.56Al_11.86Nb_11.86Cu_23.72	46.64	12	Gd₅₅Al₂₀Mn₃Ni₂₂	Gd_53.01Al_11.75Mn_11.75Ni_23.49	48.27
3	Mg_58.5Y₂ Gd₉Cu_30.5	Mg_67.83Y_8.04Gd_8.04Cu_16.09	52.92	13	Zr₆₁Ti₂Al₁₂Cu₂₅	Zr_60.39Ti_9.9Al_9.9Cu_19.8	48.39
4	Mg₇₄Gd₁₀Ag₁Ni₁₅	Mg_67.83Gd_8.04Ag_8.04Ni_16.09	58.13	14	Ni₆₀Pd₂₀P₁₇B₃	Ni_67.18Pd_8.2P_8.2B_16.41	66.95
5	Mg₇₃Gd₁₀Ag₂Ni₁₅	Mg_67.83Gd_8.04Ag_8.04Ni_16.09	58.13	15	Fe_67.7Dy₆Mo_3.76B_22.6	Fe_75.68Dy_6.08Mo_6.08B_12.16	61.51
6	Mg₇₁Gd₁₀Ag₄Ni₁₇	Mg_67.83Gd_8.04Ag_8.04Ni_16.09	58.13	16	Fe₆₈Y₆W₄B₂₂	Fe_76.15Y_5.96W_5.96B_11.92	61.78
7	Mg₇₀Gd₁₀Ag₅Ni₁₅	Mg_67.83Gd_8.04Ag_8.04Ni_16.09	58.13	17	Zr₄₆Ag_8.4Al₈Cu_37.6	Zr_57.52Ag_10.62Al_10.62Cu_21.24	44.7
8	Mg₆₉Gd₁₀Ag₆Ni₁₅	Mg_67.83Gd_8.04Ag_8.04Ni_16.09	58.13	18	Fe₆₈Y₆Mo₄B₂₂	Fe_76.15Y_5.96Mo_5.96B_11.92	61.94
9	Mg₆₈Gd₁₀Ag₇Ni₁₅	Mg_67.83Gd_8.04Ag_8.04Ni_16.09	58.13	19	Fe₇₀Y₆Ni₂B₂₂	Fe_76.15Y_5.96Ni_5.96B_11.92	66.48
10	Zr₅₃Ag₅Al_23.5Co_18.5	Zr_57.52Ag_10.62Al_10.62Co_21.24	45.37	20	Fe₆₆Y₆Co₆B₂₂	Fe_76.15Y_5.96Co_5.96B_11.92	66.27

N°. alloy	Reported composition	Predicted composition	Reported G (GPa)	Predicted G (GPa)
1	Cu₆₀Zr₂₀Hf₁₀Ti₁₀	Cu_70.99Zr_14.51Hf_7.25Ti_7.25	36.9	44.2
2	Mg₆₅Cu₂₅Tb₁₀	Mg_79.03Cu_10.48Tb_10.48	19.6	20.8
3	Gd₄₀Y₁₆Al₂₄Co₂₀	Gd_63.7Y_9.08Al_18.15Co_9.08	23.5	27.3
4	Er₅₀Al₂₄Co₂₀Y₆	Er_64.61Al_17.7Co_8.85Y_8.85	27	31.8
5	Ca₆₅Mg₁₅Zn₂₀	Ca_69.44Mg_15.28Zn_15.28	10.1	14.3
6	Ho₃₉Al₂₅Co₂₀Y₁₆	Ho_64.4Al_17.8Co_8.9Y_8.9	26.2	30.5
7	Ho₅₅Al₂₅Co₂₀	Ho_51.61Al_32.26Co_16.13	25.42	34.1
8	Er₅₅Al₂₅Co₂₀	Er_56.25Al_29.17Co_14.58	27.08	34.4
9	Mg₆₅Cu₂₅Gd₁₀	Mg_80.65Cu_9.68Gd_9.68	19.3	20.5
10	Mg₆₅Cu₂₅Y₁₀	Mg_80.65Cu_9.68Y_9.68	19.4	20.8
11	Ca₆₅Li_9.96Mg_8.54Zn_16.5	Ca_53.7Li_11.58Mg_11.58Zn_23.15	8.95	16.4
12	Ni₆₀Nb₃₅Sn₅	Ni_71.36Nb_21.48Sn_7.16	66.3	63.7
13	Mg_58.8Cu_30.5Y₁₁	Mg_80.65Cu_9.68Y_9.68	20.4	20.8
14	Fe₆₅Mo₁₄C₁₅B₆	Fe_66.99Mo_8.25C_16.51B_8.25	73	79
15	Zr_46.25Cu_46.25Al_7.5	Zr_56.81Cu_32.39Al_10.8	34.3	37.1
16	Mg₅₇Cu₃₁Y_6.6Nd_5.4	Mg_67.84Cu_16.08Y_8.04Nd_8.04	20.7	22.6
17	Hf₅₀Ni₂₅Al₂₅	Hf₆₀Ni₃₀Al₁₀	47	43.4
18	Hf₅₅Ni₂₅Al₂₀	Hf₆₀Ni₃₀Al₁₀	43.7	43.4
19	Zr_45.25Cu_46.25Al_7.5Sn₁	Zr_45.25Cu_46.25Al_7.5Sn₁	35.7	42.2
20	Zr₆₄Cu₂₆Al₁₀	Zr_63.68Cu_24.21Al_12.11	28.7	35.8

N°. alloy	Reported composition	Predicted composition	Reported E (GPa)	Predicted E (GPa)
1	Cu₆₀Zr₂₀Hf₁₀Ti₁₀	Cu_70.99Zr_14.51Hf_7.25Ti_7.25	101.1	117.7
2	Mg₆₅Cu₂₅Tb₁₀	Mg_79.03Cu_10.48Tb_10.48	51.3	54.8
3	Gd₄₀Y₁₆Al₂₄Co₂₀	Gd_63.7Y_9.08Al_18.15Co_9.08	62.2	70.3
4	Er₅₀Al₂₄Co₂₀Y₆	Er_64.61Al_17.7Co_8.85Y_8.85	71.1	81.7
5	Ho₃₉Al₂₅Co₂₀Y₁₆	Ho_64.4Al_17.8Co_8.9Y_8.9	69.1	78.4
6	Tm₃₉Zr₁₅Al₂₅Co₂₀	Tm_64.65Zr_8.84Al_17.68Co_8.84	75	86.5
7	Yb_62.5Zn₁₅Mg_17.5Cu₅	Yb_54.13Zn_11.47Mg_22.94Cu_11.47	26.5	50.3
8	Pr₅₅Al₂₅Co₂₀	Pr_56.25Al_29.17Co_14.58	45.9	71.9
9	Ho₅₅Al₂₅Co₂₀	Ho_51.61Al_32.26Co_16.13	66.64	89
10	Er₅₅Al₂₅Co₂₀	Er_56.25Al_29.17Co_14.58	70.72	90.2
11	Mg₆₅Cu₂₅Gd₁₀	Mg_80.65Cu_9.68Gd_9.68	50.6	54
12	Ca₆₅Li_9.96Mg_8.54Zn_16.5	Ca_53.7Li_11.58Mg_11.58Zn_23.15	23.4	41.5
13	Mg_58.8Cu_30.5Y₁₁	Mg_80.65Cu_9.68Y_9.68	53.9	54
14	Zr_46.25Cu_46.25Al_7.5	Zr_56.81Cu_32.39Al_10.8	93.81	99
15	Mg₅₇Cu₃₁Y_6.6Nd_5.4	Mg_67.84Cu_16.08Y_8.04Nd_8.04	54.4	59.5
16	Hf₅₀Ni₂₅Al₂₅	Hf₆₀Ni₃₀Al₁₀	125.6	113.8
17	Cu₄₇Zr₄₇Al₆	Cu_67.57Zr_24.32Al_8.11	92.4	113.6
18	Hf₅₅Ni₂₅Al₂₀	Hf₆₀Ni₃₀Al₁₀	117.63	113.8
19	Zr_45.25Cu_46.25Al_7.5Sn₁	Zr_45.25Cu_46.25Al_7.5Sn₁	97.3	112.8
20	Zr₆₄Cu₂₆Al₁₀	Zr_63.68Cu_24.21Al_12.11	78.85	95.5

N°. alloy	Reported composition	Predicted composition	Reported v	Predicted v	v % Difference ABS	Predicted *c₁₂ / c₁₁*	Predicted *c₄₄ /c₁₁*
1	Zr₆₅Al₁₀Ni₁₀Cu₁₅	Zr_57.19Al_10.7Ni_10.7Cu_21.41	0.355	0.374	5.1	0.598	0.268
2	Nd₆₀Al₁₀Co₁₀Fe₂₀	Nd_56.36Al_10.91Co_10.91Fe_21.82	0.306	0.346	11.6	0.528	0.315
3	Pd_77.5Cu₆Si_16.5	Pd₇₅Cu_12.5Si_12.5	0.411	0.403	2.0	0.676	0.216
4	Gd₄₀Y₁₆Al₂₄Co₂₀	Gd_63.7Y_9.08Al_18.15Co_9.08	0.321	0.340	5.6	0.515	0.324
5	Ca₆₅Mg₁₅Zn₂₀	Ca_69.44Mg_15.28Zn_15.28	0.300	0.337	11.0	0.509	0.328
6	Ce₇₀Al₁₀Ni₁₀Cu₁₀	Ce_52.56Al_11.86Ni_23.72Cu_11.86	0.313	0.356	12.1	0.552	0.299
7	Pr₆₀Al₁₀Ni₁₀Cu₂₀	Pr_56.14Al_10.97Ni_10.97Cu_21.93	0.360	0.363	0.8	0.571	0.286
8	Ho₃₉Al₂₅Co₂₀Y₁₆	Ho_64.4Al_17.8Co_8.9Y_8.9	0.319	0.328	2.7	0.489	0.341
9	Tm₄₀Zr₁₅Al₂₅Co₂₀	Tm_64.65Zr_8.84Al_17.68Co_8.84	0.307	0.330	7.0	0.492	0.339
10	Yb_62.5Zn₁₅Mg_17.5Cu₅	Yb_54.13Zn_11.47Mg_22.94Cu_11.47	0.276	0.368	25.0	0.582	0.279
11	La₅₅Al₂₅Co₂₀	La_61.54Al_19.23Co_19.23	0.327	0.356	8.1	0.553	0.298
12	Pr₅₅Al₂₅Co₂₀	Pr_56.25Al_29.17Co_14.58	0.324	0.359	9.7	0.560	0.294
13	Tb₅₅Al₂₅Co₂₀	Tb_61.54Al_19.23Co_19.23	0.302	0.347	13.0	0.533	0.311
14	Dy₅₅Al₂₅Co₂₀	Dy_61.54Al_19.23Co_19.23	0.304	0.343	11.4	0.523	0.318
15	Ho₅₅Al₂₅Co₂₀	Ho_61.54Al_19.23Co_19.23	0.311	0.340	8.5	0.513	0.325
16	Er₅₅Al₂₅Co₂₀	Er_56.25Al_29.17Co_14.58	0.306	0.343	10.8	0.521	0.319
17	Mg₆₅Cu₂₅Gd₁₀	Mg_67.57Cu_24.32Gd_8.11	0.310	0.373	16.9	0.596	0.270
18	Mg₆₅Cu₂₅Y₁₀	Mg_67.57Cu_24.32Y_8.11	0.329	0.372	11.6	0.593	0.271
19	Ca₆₅Li_9.96Mg_8.54Zn_16.5	Ca_53.7Li_11.58Mg_11.58Zn_23.15	0.307	0.329	6.7	0.490	0.340
20	Ni₆₀Nb₃₅Sn₅	Ni_71.36Nb_21.48Sn_7.16	0.385	0.371	3.8	0.590	0.274

Alloy	Efficiency packing %	Kinetic fragility index, m
Zr_57.52 Ag_10.62Al_10.62 Co_21.24	45.37	40.1
Zr_57.19Al_10.7 Ni_10.7 Cu_21.41	46.56	40.8
Hf_60.22Al_9.95Cu_9.95Ni_19.89	49.8	46

Alloy	Elastic proprieties (GPa)			Elastic constants ratios
Alloy	E	G	K	c₁₂/c₁₁	c₄₄/c₁₁
Zr_57.52Ag_10.62Al_10.62Co_21.24	71.4	40.9	109.3	0.591	0.272
Zr_57.19Al_10.7Ni_10.7Cu_21.41	83.8	40.1	109.5	0.597	0.268
Hf_60.22Al_9.95Cu_9.95Ni_19.89	77.8	37.8	119.5	0.640	0.240

ABM, ABC, ABPol UFSCar - Dep. de Engenharia de Materiais, Rod. Washington Luiz, km 235, 13565-905 - São Carlos - SP- Brasil. Tel (55 16) 3351-9487 - São Carlos - SP - Brazil
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