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Glass forming ability of Zr48Cu36Al16-xAgx alloys determined by three different methods
Journal of Non-Crystalline Solids 515 (2019) 106–112
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Glass forming ability of Zr48Cu36Al16-xAgx alloys determined by three different methods
T
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P. Błyskun , M. Kowalczyk, G. Cieślak, T. Kulik Faculty of Materials Science and Engineering, Warsaw University of Technology, Wołoska 141, 02-507 Warsaw, Poland
A R T I C LE I N FO
A B S T R A C T
Keywords: Metallic glasses Glass forming ability Cone test GFA indicators Oxygen content
This work was focused on the glass forming ability (GFA) of Zr48Cu36Al16-xAgx alloys (x = 0, 2, … 16) examination using three different methods. Critical diameters were determined by both discrete (classic) and continuous (cone test) methods. Several commonly used GFA thermal indicators were investigated as well. Due to oxygen contamination strong influence on the GFA of Zr-based alloys, oxygen content was measured in each prepared alloy by inert gas fusion method. Additionally, the authors discussed the alloy composition influence on the critical diameters and their respective thermal indicators values. These values were compared and their correlation with critical diameters was evaluated in terms of R2 correlation coefficient values. The best correlation was calculated for the θ indicator (R2 = 0.979).
1. Introduction
those temperatures seem to correspond well with the GFA anyway. This is a simple way to evaluate glass forming ability of various compositions and to predict the Dc of an alloy without the necessity of casting multiple bulk samples. However, those numerical values are not always accurate and their correlation with the Dc may be low depending on the actual alloy system and other factors like oxygen contamination [5]. For this reason, many thermal indicators have been created so far and they are very common in the literature. The most accurate ones (i.e. usually well-correlated with the Dc) always consist of only three characteristic temperatures: Tg – glass transition temperature, Tx – crystallization onset temperature and Tl – liquidus temperature. The most often used indicators are listed in Table 1 (all of them were used in this study as well). These GFA indicators exhibit different correlation with the Dc mainly depending on the chemical composition of an alloy. There are many reports in the literature where authors attempted to correlate thermal indicators with the Dc statistically and to reveal the best one within a given elemental system or even the most universal one among every known group of alloys [4,5,7,16,23–25]. As it was mentioned above, the GFA of an alloy strongly depends on its chemical composition. Zr-based alloys exhibit very high glass forming ability, among which the Zr-Cu-Al-Ag system exhibits the highest. Due to that fact it is usually selected for various experiments. There are many works in the literature focused on chemical composition adjustment within this system in order to obtain high GFA, good
Glass forming ability (GFA) is a measure of an alloy susceptibility to effectively avoid crystallization during liquid quenching, thus enabling to obtain amorphous structure in the volume of the material. The first author to widely discuss the GFA of metallic liquids was D. Turnbull [1], just 9 years after the first metallic glass discovery. In his seminal work he already underlined the significant role of possible GFA deterioration caused by contamination. Higher GFA reduces the cooling rate required to vitrify the alloy, i.e. critical cooling rate. Moreover, higher GFA also means higher diameter of a fully glassy ingot that one can obtain with a given casting method, i.e. critical diameter (Dc). Glass forming ability of an alloy can be assessed by many different methods, yet only some of them are commonly used. The most obvious one is to measure the critical diameter of an ingot. It can be executed by the most common discrete method (casting multiple rod-shaped ingots with systematically increased diameter: 1, 2, 3… mm) or less common continuous method (only one cast with a continuous diameter increase: wedge- or cone-shaped ingot [2–4]). These methods allow to determine the Dc which is a direct GFA manifestation. The indirect method of the GFA assessment is the calculation of dimensionless thermal indicators using the characteristic temperatures determined during calorimetric measurements of small samples. There is no direct physical connection between the values determined after vitrifying an alloy and its susceptibility to avoid crystallization, yet
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Corresponding author. E-mail addresses: [email protected] (P. Błyskun), [email protected] (M. Kowalczyk), [email protected] (G. Cieślak), [email protected] (T. Kulik). https://doi.org/10.1016/j.jnoncrysol.2019.04.018 Received 8 January 2019; Received in revised form 4 April 2019; Accepted 17 April 2019 0022-3093/ © 2019 Elsevier B.V. All rights reserved.
Journal of Non-Crystalline Solids 515 (2019) 106–112
P. Błyskun, et al.
determination as well as various thermal indicators calculation. Neither such approach to chemical composition change has been reported in the literature so far, nor such comparative study of the GFA measured by three above-mentioned ways. It was performed in order to determine the chemical composition influence on both the Dc and thermal indicators values simultaneously. As the GFA also depends on the oxygen contamination, its level was carefully examined after each alloy preparation. The Dc and thermal indicators values were statistically correlated to determine which indicators are the most accurate ones in the case of chemical composition change within this particular alloy system.
Table 1 Thermal indicators commonly used to describe and compare the GFA of metallic glasses. No.
Thermal indicator
Formula
Year established
References
1 2 3 4 5 6 7 8 9 10 11 12 13 14
ΔTxg Trg γ ΔTrg α β1 δ γm φ ξ β2 ω1 ω3 θ
1991 2000 2002 2004 2005 2005 2005 2007 2007 2008 2008 2009 2009 2009
[6] [7] [8] [9] [10] [10] [11] [12] [13] [14] [15] [16] [17] [18]
15 16 17 18 19 20
ω2 γc β′ ω4 Gp χ
Tx – Tg Tg/Tl Tx/(Tg + Tl) (Tx – Tg)/(Tl – Tg) Tx/Tl Tx/Tg + Tg/Tl Tx/(Tl – Tg) (2Tx – Tg)/Tl Tg/Tl[(Tx – Tg)/Tg]0.143 Tg/Tl + (Tx – Tg)/Tx TxTg/(Tl – Tx)2 Tg/Tx – 2Tg/(Tg + Tl) Tl(Tl + Tx)/[Tx(Tl – Tx)] (Tx + Tg)/Tl[(Tx – Tg)/ Tl]0.0728 Tg/(2Tx – Tg) – Tg/Tl (3Tx – 2Tg)/Tl Tg/Tx – Tg/1,3Tl (2Tx – Tg)/(Tl + Tx) [Tg(Tx – Tg)]/(Tl – Tx)2 (Tx – Tg)/(Tl – Tx)[Tx/(Tl – Tx)]1.47
2009 2010 2011 2015 2016 2018
[19] [20] [21] [4] [22] [5]
2. Materials and methods The Zr-Cu-Al-Ag system was selected for the study as it is known for its very high GFA [33]. As described above, silver substitution for aluminium after formula: Zr48Cu36Al16-xAgx (x = 0, 2, 4, 6, 8, 10, 12, 14, 16 at. %) has not been studied in the literature yet. This approach should allow to indicate the alloy with the highest GFA. Using high purity (at least 99.99 wt%) metallic elements master alloys were prepared by arc melting method under argon protective atmosphere, repeated three times to ensure composition homogenization. The alloys oxygen contamination level was measured by inert gas fusion method after arc melting. In each measurement several microsamples were taken from various spots of every ingot and only the average was given as a result. The glass forming ability was examined by means of the Dc and thermal indicators values. The critical diameters were basically determined by cone test using copper mould with taper angle of 10° and diameters range of 2–12 mm. The cone test consisted of cone longitudinal section metallographic observations, where the Dc can be determined using only one ingot (more detailed cone test methodology is available in the previous work [4]). Metallographic observations were performed using Zeiss optical microscope with magnification of 50×. Arbitrary, the last clearly visible crystalline spherulites separated the glass phase from the partially crystalline area, indicating the Dc location. As a comparison, the classic (discrete) method of the Dc evaluation was also performed using various rod-shaped copper moulds (diameters from 1 to 12 mm). The polished cross sections of the rods were studied with Rigaku MiniFlexII X-ray diffractometer in order to indicate ingots with partial crystallinity and separate them from fully glassy ones. To support these XRD studies metallographic observations were done for the rod-shaped samples as well. Both results (the XRD patterns and the microstructure images) were used to determine the Dc in this method. The sample that exhibited single spherulites on the cross section, not detectable by the XRD yet (< 5% of crystallinity, after Kündig et al. [2]), had the diameter considered critical. It should be noted here that the cross section was always made at a distance of at least 1.5 radius from the rod base to avoid the edge effect. The differential thermal analysis (DTA) of fully amorphous cone tips was performed with a heating rate of 0.667 K/s (40 K/min) in order to determine the characteristic temperatures. These values were used to calculate several GFA thermal indicators (formulae in Table 1) for all samples. Indicators vs Dc plots with logarithmic fitting allowed to determine correlation coefficient (R2) for each indicator and arrange them by their applicability in the case of chemical composition changes and slight oxygen contamination level.
mechanical properties or optimum set of both. Silver was substituted for copper to achieve large plasticity of Zr-Cu-Al-Ag alloys by several science groups [26–28], whereas Zhang et al. [29] examined zirconium to copper ratio influence on the GFA of Cu42-xZr42+xAg8Al8 alloys. Simultaneous silver and cobalt substitution for zirconium and copper influence on the GFA of (Cu0.5Zr0.5)95-x-yAl5AgxCoy was studied by Escher et al. [30]. Various Zr-Cu-Al-Ag compositions were examined by Louzguine-Luzgin et al. and their GFA in form of critical diameters was summarized in Ref. [31]. Silver substitution for zirconium and its influence on the GFA (in form of the Dc and thermal indicators values) of Zr70-xCu12.5Ni10Al7.5Agx alloys was investigated by Zhou et al. [32]. However, the most extensive research was done by Zhang et al. [33] as they studied the Zr-Cu-Al-Ag system in three optimisation steps. At first, they revealed that silver substitution for aluminium after the formula: Cu45Zr45Ag10−xAlx (x = 0–7 at. %) results in high glass forming ability when silver and aluminium amounts are equal (x = 5 at. %). Afterwards, they changed the ratio between Al + Ag and Zr + Cu: (Cu0.5Zr0.5)100−x(Ag0.5Al0.5)x (x = 4–20 at. %) to obtain the highest Dc for x = 16 at. %. After that, zirconium for copper substitution: Cu84−xZrxAg8Al8 (x = 42–50 at. %) was investigated and the famous eutectic Zr48Cu36Ag8Al8 composition of very high GFA was finally found. Its Dc was estimated to be up to 25 mm. Zr-based bulk metallic glasses (BMGs) have already been successfully introduced to industry production. Unfortunately, they exhibit a significant drawback which is a GFA loss due to oxygen contamination [2,3,34–39]. In fact, some amount of oxygen may be dissolved in zirconium. However, high oxygen amount causes crystalline zirconiumoxides appearance. These inclusions are not only heterogeneous nucleation sites but also generally decrease Zr-based BMGs mechanical strength by causing an embrittlement [40–42]. Therefore, it is very important to avoid any unnecessary oxygen contamination during alloys preparation process and to use only the purest accessible raw metals. Chen et al. have recently proposed a very interesting Zr-based BMG insensitive to impurities [43]. They explain that the Zr50Ti4Y1Al10Cu25Ni7Co2Fe1 alloy's carefully designed composition is so complex that it hinders crystalline growth, thus stabilizes glassy structure of the alloy. Authors of this work examined silver substitution for aluminium influence on the glass forming ability of Zr48Cu36Al16-xAgx alloys (x = 0, 2, … 16) by three different methods: discrete and continuous Dc
3. Results In the case of the cone test, a preliminary research was necessary as the cone-shaped copper mould used in this work had minimal diameter of 2 mm and there was no reason to cast full ingots of compositions exhibiting the Dc < 2 mm. Therefore, 2 mm rods were cast and cross section X-ray studies were performed on the entire series of nine compositions (Fig. 1). As it was expected, not every composition had 107
Journal of Non-Crystalline Solids 515 (2019) 106–112
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had single spherulites on the cross section, yet not seen as crystalline reflexes on the XRD patterns (< 5% of crystallinity). The Dc values determined by this method are listed in Table 2 as ‘Dc ||’. The largest critical diameter was obtained for Zr48Cu36Al8Ag8 alloy (Dc \/ = 11.3 mm, Dc || = 12 mm), yet the Dc of Zr48Cu36Al6Ag10 alloy was almost as large (Dc \/ = 10.7 mm, Dc || = 10 mm). The Dc values determined by both methods remained similar, although there were some differences: sometimes the Dc \/ was larger than the Dc || and sometimes it was the opposite way. However, the differences were never larger than 0.7 mm. Silver for aluminium substitution significantly affected the Dc values. This dependence is presented in Fig. 4 together with the oxygen content. The critical diameter of the most contaminated alloy was still the highest among the others. It seemed to remain unaffected by the measured oxygen level. Thermal indicators were calculated using characteristic temperatures from Table 2 for each sample. Their values are not presented here as the vast number of individual values would be difficult to interpret. An exemplary indicator ξ was also strongly affected by chemical composition changes and weakly influenced by the measured oxygen levels (Fig. 5). It can be easily observed that in the case of this indicator data points are scattered in a similar manner to those in Fig. 4 with a maximum at x = 8 as well. This is strong indication that ξ is well correlated with the Dc. For more detailed analysis further calculations were required. Both the Dc \/ and Dc || values were used to measure the silver for aluminium substitution influence on the thermal indicators (i.e. their sensitivity to chemical composition changes within this system). Correlation plots with the Dc as abscissa and a thermal indicator as ordinate were built for each indicator (two exemplary plots are shown in Fig. 6 using the Dc \/ values). Logarithmic fitting was used to determine the statistical R2 correlation coefficient values, where close to one values indicate very strong correlation. These values were ordered ascending by the R2 for the Dc \/ values in Table 3. To supplement the current results and improve the statistics, the data from our previous work [4] for similar alloys (x = 7 and 13 at. %) have been added to these correlation results (Fig. 6 and Table 3). Trg, δ, ΔTxg and ΔTrg indicators exhibited the lowest R2 values (< 0.5) showing relatively weak correlation with the Dc, whereas ξ and θ indicators exhibited very strong correlation (R2 ≈ 0,95). Some differences between R2 values determined using critical diameters from the cone test (Dc \/) and from the classic method (Dc ||) were observed. Generally, in the case of good correlation, R2 values were higher for the Dc \/, whereas some R2 values were higher for the Dc || in the case of indicators showing weaker correlation.
Fig. 1. X-ray diffraction patterns of the Zr48Cu36Al16-xAgx (x = 0, 2, … 0.16 at. %) alloys in form of 2 mm rods; good GFA alloys selection for further studies.
high GFA. It appeared that only alloys containing 4–14 at. % were fully amorphous. There were some reflexes from a crystalline phase observed for alloys containing 0–2 and 16 at. % of silver. These alloys, with the Dc lower than 2 mm, were excluded from further testing. Oxygen level measured in the master alloys (x = 4–14 at. %) is presented in Table 2 together with the characteristic temperatures of these alloys and their critical diameters measured by continuous and discrete methods. The oxygen contamination level was quite low in all studied samples (< 400 wt. ppm) compared to other similar works [3,35,39]. The characteristic temperatures responded well to the silver content changes in the alloys. With the silver amount increase, Tg decreased almost uniformly in the entire alloys series. Tx behaved differently as it increased only from x = 4 to 8 and then decreased again to x = 14. Tl values may be slightly surprising as the Zr48Cu36Al8Ag8 composition was considered to be eutectic [33], thus it should exhibit relatively low Tl value. Whereas, Tl determined for the alloy in this work is apparently the highest. Metallographic images illustrating cone test of two exemplary alloys are presented in Fig. 2. Other microstructures looked similar, only the Dc position was different. In the cone tip only a glassy structure was visible, whereas the opposite area was at least partially crystalline in each sample. In the top right hand side microimages one can easily observe large spherulites with diameters up to several hundred micrometers. With the cooling rate increase (lower cone diameters) spherulites size decreased to disappear completely at the critical diameter, which values were carefully measured and are listed in Table 2 as ‘Dc \/’ to differ them from the critical diameters determined by classic method (‘Dc ||’). Discrete method of the Dc determination was also performed for the x = 4–14 series. XRD patterns set together with the corresponding metallographic images of two exemplary alloys are presented in Fig. 3. In the case of this method, the Dc was determined on the sample that
4. Discussion Authors of this work attempted to assess the GFA of Zr48Cu36Al16(x = 4–14 at. %) alloys by three different methods: discrete and continuous Dc determination as well as various thermal indicators calculation. The oxygen contamination level in these alloys was also carefully controlled during ingots preparation as it is known to deteriorate Zr-based BMGs glass forming ability [2,3,34–40]. Oxygen content values measured in the studied samples were relatively low (< 400 xAgx
Table 2 Oxygen content in the Zr48Cu36Al16-xAgx (x = 4–14 at. %) master alloys; characteristic temperatures of these alloys; their critical diameters determined by continuous (Dc \/) and discrete (Dc ||) methods. x [at. %] Oxygen content [wt. ppm] Tg [K] Tx [K] Tl [K] Dc \/ [mm] Dc || [mm]
4 240 ± 45 705 746 1109 3.3 ± 0.1 3 ± 0.5
6 210 ± 15 699 753 1115 6.3 ± 0.1 7 ± 0.5
8 380 ± 5 688 771 1126 11.3 ± 0.1 12 ± 0.5
108
10 191 ± 20 689 755 1099 10.7 ± 0.1 10 ± 0.5
12 257 ± 15 669 746 1108 6.6 ± 0.1 6 ± 0.5
14 268 ± 5 662 727 1118 2.5 ± 0.1 2 ± 0.5
Journal of Non-Crystalline Solids 515 (2019) 106–112
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Fig. 2. Metallographic longitudinal sections of cones: a) Zr48Cu36Al8Ag8, b) Zr48Cu36Al4Ag12.
wt. ppm) [3,35]. Moreover, the variations of oxygen level in the alloys were also rather small what may indicate good repeatability of the preparation process. For these reasons the oxygen contamination influence on the GFA was not generally visible in this work (Figs. 4 and 5). From our last work [39] it is known that the oxygen content strongly influences the GFA of Zr-based alloys and should always be measured. Otherwise, the characteristic temperatures and the Dc values should not be compared with those of other authors as they change significantly with oxygen contamination. The highest Tl value was surprisingly measured for the x = 8 sample, which was expected to exhibit the lowest Tl among other studied samples. This phenomenon could have been caused by the highest oxygen contamination level in this alloy. Generally, impurities decrease the melting temperature, although in this particular case the oxygen impurity behaved differently. It is known that the strong-bonding oxygen decreases atomic mobility in Zr-based alloys causing their mechanical embrittlement [42] and, apparently, increasing their liquidus temperature as well. This proved again that the oxygen level should never be neglected as it not only influences the Dc values but the characteristic temperatures values as well. The critical diameters of the Zr48Cu36Al16-xAgx (x = 4–14 at. %) alloys determined by two different methods (discrete and continuous one) were very similar and the differences did not exceed 0.7 mm (Table 2). This proved that the cone test methodology applied in this
Fig. 4. Silver substitution for aluminium influence on the critical diameters of Zr48Cu36Al16-xAgx (x = 4–14 at. %) alloys determined by cone test and their oxygen contamination level.
work was proper and gave results very similar to those obtained by the discrete method. Silver substitution for aluminium visibly influenced the GFA of the
Fig. 3. XRD patterns and metallographic cross sections of rods: a) Zr48Cu36Al6Ag10, b) Zr48Cu36Al4Ag12. 109
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Table 3 R2 correlation coefficient values calculated for various GFA thermal indicators vs Dc \/ and Dc || of the Zr48Cu36Al16-xAgx (x = 4–14 at. %) alloys, including two additional alloys (x = 7 and 13 at. %) from our former study [4].
Fig. 5. Silver substitution for aluminium influence on the exemplary ξ indicator determined for Zr48Cu36Al16-xAgx (x = 4–14 at. %) alloys and their oxygen contamination level.
Zr48Cu36Al16-xAgx (x = 4–14 at. %) alloys what can be observed in Figs. 4 and 5. This was inverted parabolic dependence with a maximum of both the Dc \/ and ξ indicator values near the x = 8 alloy, proving that this particular composition indeed exhibited the best GFA among other similar compositions studied in the current research and in other references [33]. It can be noticed that the left hand sides of the Figs. 4 and 5 plots are steeper than the right hand sides. This indicates that the aluminium influence on the Zr48Cu36Al16-xAgx alloys GFA is stronger than the silver influence. I.e. 2 at. % of Al (x = 14) was enough to exceed the Dc = 2 mm threshold, whereas in the case of silver twice larger Ag addition was necessary (x = 4). Moreover, the Dc values of x = 12 and 10 are significantly larger than those of x = 4 and 6, respectively. Since aluminium has very similar atomic radius to silver [44] this influence difference must be explained by the enthalpies of mixing (ΔHmix). ΔHmix of Zr-Al (−44 kJ/mol) and Cu-Al (−1 kJ/mol) are more negative than Zr-Ag (−20 kJ/mol) and Cu-Ag (+2 kJ/mol) [44]. This is the most probable reason why aluminium is a better glass stabilizer than silver in these alloys, although both of them are necessary to obtain good GFA. The values of thermal indicators generally increased with the Dc increment (an example in Fig. 6b), only ω1 and β′ changed the opposite way (an example in Fig. 6a). Similar behaviour of these two indicators has already been reported by Long et al. for a huge database of various alloys [5] so this is probably the way they behave. Statistical correlation of the Dc and thermal indicators values allowed to determine the most accurate indicators in the case of chemical composition changes in the Zr-Cu-Ag-Al system. The calculated R2 correlation coefficient values (Table 3) ranged significantly: from 0.053
Thermal indicator
R2 for Dc \/
R2 for Dc ||
Trg δ ΔTxg ΔTrg Gp β2 γc ω2 χ ω4 α ω3 β′ ω1 γm β1 φ γ ξ θ
0.088 0.248 0.272 0.429 0.660 0.663 0.676 0.680 0.696 0.713 0.789 0.798 0.842 0.843 0.868 0.882 0.907 0.921 0.939 0.960
0.081 0.252 0.271 0.412 0.620 0.703 0.641 0.643 0.655 0.677 0.824 0.835 0.804 0.804 0.831 0.850 0.859 0.896 0.859 0.953
for Trg to 0.979 for θ indicator. Some indicators (Trg, δ, ΔTxg and ΔTrg) exhibited none or low sensitivity to the studied chemical composition changes (R2 < 0.5) but most of them exhibited good correlation. The R2 values of each indicator determined for the Dc \/ and the Dc || differed slightly but it was obviously the direct consequence of the Dc differences already described above. Generally, the obtained R2 values were very high compared to other similar works [4,5]. This proves that most of selected indicators reacted very well to the GFA changes. Considering silver for aluminium substitution as a chemical composition change, ξ and θ indicators were the most accurate ones in describing the GFA (R2 > 0.95). In the current study, the best indicator was θ (R2 = 0.979 for the Dc \/), although it is not generally accepted as the universal GFA indicator in the similar correlation reports [4,5,16,23,24]. However, the ξ indicator was actually recognized as a reliable criterion in work of Gu et al. [24]. On the other hand, χ and ω4 have been recently proposed (Ref. [4,5], respectively) as indicators exhibiting high correlation with the Dc even for a range of various alloys. Their average R2 values (0.728 and 0.749, respectively) obtained in the current work prove that their universality does not cover every alloy system with the same reliability.
5. Summary The effect of chemical composition change on the Dc and thermal indicators values of the Zr48Cu36Al16-xAgx (x = 0–16 at. %) alloys has
Fig. 6. Selected indicators values: a) ω1, b) θ vs Dc \/ of the Zr48Cu36Al16-xAgx (x = 4–14 at. %) alloys, including two data points from our former study [4]. 110
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been reported. The oxygen content seemed to be a GFA significant influencing factor, thus it should always be known during any careful GFA analysis to reveal the full picture of the studied phenomena (e.g. chemical composition influence on the GFA of a system). The silver for aluminium substitution influence on the Dc values was strong, yet aluminium affected the GFA stronger than silver probably due to its more negative ΔHmix with the main alloying components (Zr and Cu). The GFA of alloys containing 0–2 and 16 at. % of silver did not exceed the lower cone test limit (Dc > 2 mm), thus they were excluded from further investigations. The critical diameters determined by the discrete method gave very similar results to those of the continuous method (the differences were lower than 0.7 mm). The highest critical diameter values (Dc \/ = 11.3 mm, Dc || = 12 mm) were obtained for the Zr48Cu36Al8Ag8 alloy proving its highest GFA among other alloys in this system. Most of the thermal indicators were clearly affected by the chemical composition changes. They generally exhibited good correlation with the Dc. The highest correlation coefficients were obtained for the θ (R2 = 0.979) and ξ (R2 = 0.961) indicators. They exhibited high sensitivity to chemical composition changes of the Zr48Cu36Al16xAgx alloys. ξ has already been reported elsewhere as a proper indicator in describing the GFA of various alloys and it exhibited very high R2 value in this study as well, thus it may actually be proposed as a potentially reliable GFA indicator.
[11]
[12] [13]
[14] [15]
[16]
[17]
[18] [19]
[20]
[21]
Declarations of interest
[22]
None. [23]
CRediT authorship contribution statement
[24]
P. Błyskun: Investigation, Data curation, Visualization, Writing original draft. M. Kowalczyk: Methodology, Formal analysis, Writing review & editing. G. Cieślak: Resources, Investigation, Validation. T. Kulik: Funding acquisition, Conceptualization, Supervision, Project administration.
[25]
[26]
[27]
Acknowledgments [28]
This work was financially supported by the National Science Center [grant number 2015/17/B/ST8/00618]. Authors would also like to thank Miss Agata Myśliborska-Błyskun for providing language help.
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Glass forming ability of Zr48Cu36Al16-xAgx alloys determined by three different methods
T
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P. Błyskun , M. Kowalczyk, G. Cieślak, T. Kulik Faculty of Materials Science and Engineering, Warsaw University of Technology, Wołoska 141, 02-507 Warsaw, Poland
A R T I C LE I N FO
A B S T R A C T
Keywords: Metallic glasses Glass forming ability Cone test GFA indicators Oxygen content
This work was focused on the glass forming ability (GFA) of Zr48Cu36Al16-xAgx alloys (x = 0, 2, … 16) examination using three different methods. Critical diameters were determined by both discrete (classic) and continuous (cone test) methods. Several commonly used GFA thermal indicators were investigated as well. Due to oxygen contamination strong influence on the GFA of Zr-based alloys, oxygen content was measured in each prepared alloy by inert gas fusion method. Additionally, the authors discussed the alloy composition influence on the critical diameters and their respective thermal indicators values. These values were compared and their correlation with critical diameters was evaluated in terms of R2 correlation coefficient values. The best correlation was calculated for the θ indicator (R2 = 0.979).
1. Introduction
those temperatures seem to correspond well with the GFA anyway. This is a simple way to evaluate glass forming ability of various compositions and to predict the Dc of an alloy without the necessity of casting multiple bulk samples. However, those numerical values are not always accurate and their correlation with the Dc may be low depending on the actual alloy system and other factors like oxygen contamination [5]. For this reason, many thermal indicators have been created so far and they are very common in the literature. The most accurate ones (i.e. usually well-correlated with the Dc) always consist of only three characteristic temperatures: Tg – glass transition temperature, Tx – crystallization onset temperature and Tl – liquidus temperature. The most often used indicators are listed in Table 1 (all of them were used in this study as well). These GFA indicators exhibit different correlation with the Dc mainly depending on the chemical composition of an alloy. There are many reports in the literature where authors attempted to correlate thermal indicators with the Dc statistically and to reveal the best one within a given elemental system or even the most universal one among every known group of alloys [4,5,7,16,23–25]. As it was mentioned above, the GFA of an alloy strongly depends on its chemical composition. Zr-based alloys exhibit very high glass forming ability, among which the Zr-Cu-Al-Ag system exhibits the highest. Due to that fact it is usually selected for various experiments. There are many works in the literature focused on chemical composition adjustment within this system in order to obtain high GFA, good
Glass forming ability (GFA) is a measure of an alloy susceptibility to effectively avoid crystallization during liquid quenching, thus enabling to obtain amorphous structure in the volume of the material. The first author to widely discuss the GFA of metallic liquids was D. Turnbull [1], just 9 years after the first metallic glass discovery. In his seminal work he already underlined the significant role of possible GFA deterioration caused by contamination. Higher GFA reduces the cooling rate required to vitrify the alloy, i.e. critical cooling rate. Moreover, higher GFA also means higher diameter of a fully glassy ingot that one can obtain with a given casting method, i.e. critical diameter (Dc). Glass forming ability of an alloy can be assessed by many different methods, yet only some of them are commonly used. The most obvious one is to measure the critical diameter of an ingot. It can be executed by the most common discrete method (casting multiple rod-shaped ingots with systematically increased diameter: 1, 2, 3… mm) or less common continuous method (only one cast with a continuous diameter increase: wedge- or cone-shaped ingot [2–4]). These methods allow to determine the Dc which is a direct GFA manifestation. The indirect method of the GFA assessment is the calculation of dimensionless thermal indicators using the characteristic temperatures determined during calorimetric measurements of small samples. There is no direct physical connection between the values determined after vitrifying an alloy and its susceptibility to avoid crystallization, yet
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Corresponding author. E-mail addresses: [email protected] (P. Błyskun), [email protected] (M. Kowalczyk), [email protected] (G. Cieślak), [email protected] (T. Kulik). https://doi.org/10.1016/j.jnoncrysol.2019.04.018 Received 8 January 2019; Received in revised form 4 April 2019; Accepted 17 April 2019 0022-3093/ © 2019 Elsevier B.V. All rights reserved.
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determination as well as various thermal indicators calculation. Neither such approach to chemical composition change has been reported in the literature so far, nor such comparative study of the GFA measured by three above-mentioned ways. It was performed in order to determine the chemical composition influence on both the Dc and thermal indicators values simultaneously. As the GFA also depends on the oxygen contamination, its level was carefully examined after each alloy preparation. The Dc and thermal indicators values were statistically correlated to determine which indicators are the most accurate ones in the case of chemical composition change within this particular alloy system.
Table 1 Thermal indicators commonly used to describe and compare the GFA of metallic glasses. No.
Thermal indicator
Formula
Year established
References
1 2 3 4 5 6 7 8 9 10 11 12 13 14
ΔTxg Trg γ ΔTrg α β1 δ γm φ ξ β2 ω1 ω3 θ
1991 2000 2002 2004 2005 2005 2005 2007 2007 2008 2008 2009 2009 2009
[6] [7] [8] [9] [10] [10] [11] [12] [13] [14] [15] [16] [17] [18]
15 16 17 18 19 20
ω2 γc β′ ω4 Gp χ
Tx – Tg Tg/Tl Tx/(Tg + Tl) (Tx – Tg)/(Tl – Tg) Tx/Tl Tx/Tg + Tg/Tl Tx/(Tl – Tg) (2Tx – Tg)/Tl Tg/Tl[(Tx – Tg)/Tg]0.143 Tg/Tl + (Tx – Tg)/Tx TxTg/(Tl – Tx)2 Tg/Tx – 2Tg/(Tg + Tl) Tl(Tl + Tx)/[Tx(Tl – Tx)] (Tx + Tg)/Tl[(Tx – Tg)/ Tl]0.0728 Tg/(2Tx – Tg) – Tg/Tl (3Tx – 2Tg)/Tl Tg/Tx – Tg/1,3Tl (2Tx – Tg)/(Tl + Tx) [Tg(Tx – Tg)]/(Tl – Tx)2 (Tx – Tg)/(Tl – Tx)[Tx/(Tl – Tx)]1.47
2009 2010 2011 2015 2016 2018
[19] [20] [21] [4] [22] [5]
2. Materials and methods The Zr-Cu-Al-Ag system was selected for the study as it is known for its very high GFA [33]. As described above, silver substitution for aluminium after formula: Zr48Cu36Al16-xAgx (x = 0, 2, 4, 6, 8, 10, 12, 14, 16 at. %) has not been studied in the literature yet. This approach should allow to indicate the alloy with the highest GFA. Using high purity (at least 99.99 wt%) metallic elements master alloys were prepared by arc melting method under argon protective atmosphere, repeated three times to ensure composition homogenization. The alloys oxygen contamination level was measured by inert gas fusion method after arc melting. In each measurement several microsamples were taken from various spots of every ingot and only the average was given as a result. The glass forming ability was examined by means of the Dc and thermal indicators values. The critical diameters were basically determined by cone test using copper mould with taper angle of 10° and diameters range of 2–12 mm. The cone test consisted of cone longitudinal section metallographic observations, where the Dc can be determined using only one ingot (more detailed cone test methodology is available in the previous work [4]). Metallographic observations were performed using Zeiss optical microscope with magnification of 50×. Arbitrary, the last clearly visible crystalline spherulites separated the glass phase from the partially crystalline area, indicating the Dc location. As a comparison, the classic (discrete) method of the Dc evaluation was also performed using various rod-shaped copper moulds (diameters from 1 to 12 mm). The polished cross sections of the rods were studied with Rigaku MiniFlexII X-ray diffractometer in order to indicate ingots with partial crystallinity and separate them from fully glassy ones. To support these XRD studies metallographic observations were done for the rod-shaped samples as well. Both results (the XRD patterns and the microstructure images) were used to determine the Dc in this method. The sample that exhibited single spherulites on the cross section, not detectable by the XRD yet (< 5% of crystallinity, after Kündig et al. [2]), had the diameter considered critical. It should be noted here that the cross section was always made at a distance of at least 1.5 radius from the rod base to avoid the edge effect. The differential thermal analysis (DTA) of fully amorphous cone tips was performed with a heating rate of 0.667 K/s (40 K/min) in order to determine the characteristic temperatures. These values were used to calculate several GFA thermal indicators (formulae in Table 1) for all samples. Indicators vs Dc plots with logarithmic fitting allowed to determine correlation coefficient (R2) for each indicator and arrange them by their applicability in the case of chemical composition changes and slight oxygen contamination level.
mechanical properties or optimum set of both. Silver was substituted for copper to achieve large plasticity of Zr-Cu-Al-Ag alloys by several science groups [26–28], whereas Zhang et al. [29] examined zirconium to copper ratio influence on the GFA of Cu42-xZr42+xAg8Al8 alloys. Simultaneous silver and cobalt substitution for zirconium and copper influence on the GFA of (Cu0.5Zr0.5)95-x-yAl5AgxCoy was studied by Escher et al. [30]. Various Zr-Cu-Al-Ag compositions were examined by Louzguine-Luzgin et al. and their GFA in form of critical diameters was summarized in Ref. [31]. Silver substitution for zirconium and its influence on the GFA (in form of the Dc and thermal indicators values) of Zr70-xCu12.5Ni10Al7.5Agx alloys was investigated by Zhou et al. [32]. However, the most extensive research was done by Zhang et al. [33] as they studied the Zr-Cu-Al-Ag system in three optimisation steps. At first, they revealed that silver substitution for aluminium after the formula: Cu45Zr45Ag10−xAlx (x = 0–7 at. %) results in high glass forming ability when silver and aluminium amounts are equal (x = 5 at. %). Afterwards, they changed the ratio between Al + Ag and Zr + Cu: (Cu0.5Zr0.5)100−x(Ag0.5Al0.5)x (x = 4–20 at. %) to obtain the highest Dc for x = 16 at. %. After that, zirconium for copper substitution: Cu84−xZrxAg8Al8 (x = 42–50 at. %) was investigated and the famous eutectic Zr48Cu36Ag8Al8 composition of very high GFA was finally found. Its Dc was estimated to be up to 25 mm. Zr-based bulk metallic glasses (BMGs) have already been successfully introduced to industry production. Unfortunately, they exhibit a significant drawback which is a GFA loss due to oxygen contamination [2,3,34–39]. In fact, some amount of oxygen may be dissolved in zirconium. However, high oxygen amount causes crystalline zirconiumoxides appearance. These inclusions are not only heterogeneous nucleation sites but also generally decrease Zr-based BMGs mechanical strength by causing an embrittlement [40–42]. Therefore, it is very important to avoid any unnecessary oxygen contamination during alloys preparation process and to use only the purest accessible raw metals. Chen et al. have recently proposed a very interesting Zr-based BMG insensitive to impurities [43]. They explain that the Zr50Ti4Y1Al10Cu25Ni7Co2Fe1 alloy's carefully designed composition is so complex that it hinders crystalline growth, thus stabilizes glassy structure of the alloy. Authors of this work examined silver substitution for aluminium influence on the glass forming ability of Zr48Cu36Al16-xAgx alloys (x = 0, 2, … 16) by three different methods: discrete and continuous Dc
3. Results In the case of the cone test, a preliminary research was necessary as the cone-shaped copper mould used in this work had minimal diameter of 2 mm and there was no reason to cast full ingots of compositions exhibiting the Dc < 2 mm. Therefore, 2 mm rods were cast and cross section X-ray studies were performed on the entire series of nine compositions (Fig. 1). As it was expected, not every composition had 107
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had single spherulites on the cross section, yet not seen as crystalline reflexes on the XRD patterns (< 5% of crystallinity). The Dc values determined by this method are listed in Table 2 as ‘Dc ||’. The largest critical diameter was obtained for Zr48Cu36Al8Ag8 alloy (Dc \/ = 11.3 mm, Dc || = 12 mm), yet the Dc of Zr48Cu36Al6Ag10 alloy was almost as large (Dc \/ = 10.7 mm, Dc || = 10 mm). The Dc values determined by both methods remained similar, although there were some differences: sometimes the Dc \/ was larger than the Dc || and sometimes it was the opposite way. However, the differences were never larger than 0.7 mm. Silver for aluminium substitution significantly affected the Dc values. This dependence is presented in Fig. 4 together with the oxygen content. The critical diameter of the most contaminated alloy was still the highest among the others. It seemed to remain unaffected by the measured oxygen level. Thermal indicators were calculated using characteristic temperatures from Table 2 for each sample. Their values are not presented here as the vast number of individual values would be difficult to interpret. An exemplary indicator ξ was also strongly affected by chemical composition changes and weakly influenced by the measured oxygen levels (Fig. 5). It can be easily observed that in the case of this indicator data points are scattered in a similar manner to those in Fig. 4 with a maximum at x = 8 as well. This is strong indication that ξ is well correlated with the Dc. For more detailed analysis further calculations were required. Both the Dc \/ and Dc || values were used to measure the silver for aluminium substitution influence on the thermal indicators (i.e. their sensitivity to chemical composition changes within this system). Correlation plots with the Dc as abscissa and a thermal indicator as ordinate were built for each indicator (two exemplary plots are shown in Fig. 6 using the Dc \/ values). Logarithmic fitting was used to determine the statistical R2 correlation coefficient values, where close to one values indicate very strong correlation. These values were ordered ascending by the R2 for the Dc \/ values in Table 3. To supplement the current results and improve the statistics, the data from our previous work [4] for similar alloys (x = 7 and 13 at. %) have been added to these correlation results (Fig. 6 and Table 3). Trg, δ, ΔTxg and ΔTrg indicators exhibited the lowest R2 values (< 0.5) showing relatively weak correlation with the Dc, whereas ξ and θ indicators exhibited very strong correlation (R2 ≈ 0,95). Some differences between R2 values determined using critical diameters from the cone test (Dc \/) and from the classic method (Dc ||) were observed. Generally, in the case of good correlation, R2 values were higher for the Dc \/, whereas some R2 values were higher for the Dc || in the case of indicators showing weaker correlation.
Fig. 1. X-ray diffraction patterns of the Zr48Cu36Al16-xAgx (x = 0, 2, … 0.16 at. %) alloys in form of 2 mm rods; good GFA alloys selection for further studies.
high GFA. It appeared that only alloys containing 4–14 at. % were fully amorphous. There were some reflexes from a crystalline phase observed for alloys containing 0–2 and 16 at. % of silver. These alloys, with the Dc lower than 2 mm, were excluded from further testing. Oxygen level measured in the master alloys (x = 4–14 at. %) is presented in Table 2 together with the characteristic temperatures of these alloys and their critical diameters measured by continuous and discrete methods. The oxygen contamination level was quite low in all studied samples (< 400 wt. ppm) compared to other similar works [3,35,39]. The characteristic temperatures responded well to the silver content changes in the alloys. With the silver amount increase, Tg decreased almost uniformly in the entire alloys series. Tx behaved differently as it increased only from x = 4 to 8 and then decreased again to x = 14. Tl values may be slightly surprising as the Zr48Cu36Al8Ag8 composition was considered to be eutectic [33], thus it should exhibit relatively low Tl value. Whereas, Tl determined for the alloy in this work is apparently the highest. Metallographic images illustrating cone test of two exemplary alloys are presented in Fig. 2. Other microstructures looked similar, only the Dc position was different. In the cone tip only a glassy structure was visible, whereas the opposite area was at least partially crystalline in each sample. In the top right hand side microimages one can easily observe large spherulites with diameters up to several hundred micrometers. With the cooling rate increase (lower cone diameters) spherulites size decreased to disappear completely at the critical diameter, which values were carefully measured and are listed in Table 2 as ‘Dc \/’ to differ them from the critical diameters determined by classic method (‘Dc ||’). Discrete method of the Dc determination was also performed for the x = 4–14 series. XRD patterns set together with the corresponding metallographic images of two exemplary alloys are presented in Fig. 3. In the case of this method, the Dc was determined on the sample that
4. Discussion Authors of this work attempted to assess the GFA of Zr48Cu36Al16(x = 4–14 at. %) alloys by three different methods: discrete and continuous Dc determination as well as various thermal indicators calculation. The oxygen contamination level in these alloys was also carefully controlled during ingots preparation as it is known to deteriorate Zr-based BMGs glass forming ability [2,3,34–40]. Oxygen content values measured in the studied samples were relatively low (< 400 xAgx
Table 2 Oxygen content in the Zr48Cu36Al16-xAgx (x = 4–14 at. %) master alloys; characteristic temperatures of these alloys; their critical diameters determined by continuous (Dc \/) and discrete (Dc ||) methods. x [at. %] Oxygen content [wt. ppm] Tg [K] Tx [K] Tl [K] Dc \/ [mm] Dc || [mm]
4 240 ± 45 705 746 1109 3.3 ± 0.1 3 ± 0.5
6 210 ± 15 699 753 1115 6.3 ± 0.1 7 ± 0.5
8 380 ± 5 688 771 1126 11.3 ± 0.1 12 ± 0.5
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10 191 ± 20 689 755 1099 10.7 ± 0.1 10 ± 0.5
12 257 ± 15 669 746 1108 6.6 ± 0.1 6 ± 0.5
14 268 ± 5 662 727 1118 2.5 ± 0.1 2 ± 0.5
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Fig. 2. Metallographic longitudinal sections of cones: a) Zr48Cu36Al8Ag8, b) Zr48Cu36Al4Ag12.
wt. ppm) [3,35]. Moreover, the variations of oxygen level in the alloys were also rather small what may indicate good repeatability of the preparation process. For these reasons the oxygen contamination influence on the GFA was not generally visible in this work (Figs. 4 and 5). From our last work [39] it is known that the oxygen content strongly influences the GFA of Zr-based alloys and should always be measured. Otherwise, the characteristic temperatures and the Dc values should not be compared with those of other authors as they change significantly with oxygen contamination. The highest Tl value was surprisingly measured for the x = 8 sample, which was expected to exhibit the lowest Tl among other studied samples. This phenomenon could have been caused by the highest oxygen contamination level in this alloy. Generally, impurities decrease the melting temperature, although in this particular case the oxygen impurity behaved differently. It is known that the strong-bonding oxygen decreases atomic mobility in Zr-based alloys causing their mechanical embrittlement [42] and, apparently, increasing their liquidus temperature as well. This proved again that the oxygen level should never be neglected as it not only influences the Dc values but the characteristic temperatures values as well. The critical diameters of the Zr48Cu36Al16-xAgx (x = 4–14 at. %) alloys determined by two different methods (discrete and continuous one) were very similar and the differences did not exceed 0.7 mm (Table 2). This proved that the cone test methodology applied in this
Fig. 4. Silver substitution for aluminium influence on the critical diameters of Zr48Cu36Al16-xAgx (x = 4–14 at. %) alloys determined by cone test and their oxygen contamination level.
work was proper and gave results very similar to those obtained by the discrete method. Silver substitution for aluminium visibly influenced the GFA of the
Fig. 3. XRD patterns and metallographic cross sections of rods: a) Zr48Cu36Al6Ag10, b) Zr48Cu36Al4Ag12. 109
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Table 3 R2 correlation coefficient values calculated for various GFA thermal indicators vs Dc \/ and Dc || of the Zr48Cu36Al16-xAgx (x = 4–14 at. %) alloys, including two additional alloys (x = 7 and 13 at. %) from our former study [4].
Fig. 5. Silver substitution for aluminium influence on the exemplary ξ indicator determined for Zr48Cu36Al16-xAgx (x = 4–14 at. %) alloys and their oxygen contamination level.
Zr48Cu36Al16-xAgx (x = 4–14 at. %) alloys what can be observed in Figs. 4 and 5. This was inverted parabolic dependence with a maximum of both the Dc \/ and ξ indicator values near the x = 8 alloy, proving that this particular composition indeed exhibited the best GFA among other similar compositions studied in the current research and in other references [33]. It can be noticed that the left hand sides of the Figs. 4 and 5 plots are steeper than the right hand sides. This indicates that the aluminium influence on the Zr48Cu36Al16-xAgx alloys GFA is stronger than the silver influence. I.e. 2 at. % of Al (x = 14) was enough to exceed the Dc = 2 mm threshold, whereas in the case of silver twice larger Ag addition was necessary (x = 4). Moreover, the Dc values of x = 12 and 10 are significantly larger than those of x = 4 and 6, respectively. Since aluminium has very similar atomic radius to silver [44] this influence difference must be explained by the enthalpies of mixing (ΔHmix). ΔHmix of Zr-Al (−44 kJ/mol) and Cu-Al (−1 kJ/mol) are more negative than Zr-Ag (−20 kJ/mol) and Cu-Ag (+2 kJ/mol) [44]. This is the most probable reason why aluminium is a better glass stabilizer than silver in these alloys, although both of them are necessary to obtain good GFA. The values of thermal indicators generally increased with the Dc increment (an example in Fig. 6b), only ω1 and β′ changed the opposite way (an example in Fig. 6a). Similar behaviour of these two indicators has already been reported by Long et al. for a huge database of various alloys [5] so this is probably the way they behave. Statistical correlation of the Dc and thermal indicators values allowed to determine the most accurate indicators in the case of chemical composition changes in the Zr-Cu-Ag-Al system. The calculated R2 correlation coefficient values (Table 3) ranged significantly: from 0.053
Thermal indicator
R2 for Dc \/
R2 for Dc ||
Trg δ ΔTxg ΔTrg Gp β2 γc ω2 χ ω4 α ω3 β′ ω1 γm β1 φ γ ξ θ
0.088 0.248 0.272 0.429 0.660 0.663 0.676 0.680 0.696 0.713 0.789 0.798 0.842 0.843 0.868 0.882 0.907 0.921 0.939 0.960
0.081 0.252 0.271 0.412 0.620 0.703 0.641 0.643 0.655 0.677 0.824 0.835 0.804 0.804 0.831 0.850 0.859 0.896 0.859 0.953
for Trg to 0.979 for θ indicator. Some indicators (Trg, δ, ΔTxg and ΔTrg) exhibited none or low sensitivity to the studied chemical composition changes (R2 < 0.5) but most of them exhibited good correlation. The R2 values of each indicator determined for the Dc \/ and the Dc || differed slightly but it was obviously the direct consequence of the Dc differences already described above. Generally, the obtained R2 values were very high compared to other similar works [4,5]. This proves that most of selected indicators reacted very well to the GFA changes. Considering silver for aluminium substitution as a chemical composition change, ξ and θ indicators were the most accurate ones in describing the GFA (R2 > 0.95). In the current study, the best indicator was θ (R2 = 0.979 for the Dc \/), although it is not generally accepted as the universal GFA indicator in the similar correlation reports [4,5,16,23,24]. However, the ξ indicator was actually recognized as a reliable criterion in work of Gu et al. [24]. On the other hand, χ and ω4 have been recently proposed (Ref. [4,5], respectively) as indicators exhibiting high correlation with the Dc even for a range of various alloys. Their average R2 values (0.728 and 0.749, respectively) obtained in the current work prove that their universality does not cover every alloy system with the same reliability.
5. Summary The effect of chemical composition change on the Dc and thermal indicators values of the Zr48Cu36Al16-xAgx (x = 0–16 at. %) alloys has
Fig. 6. Selected indicators values: a) ω1, b) θ vs Dc \/ of the Zr48Cu36Al16-xAgx (x = 4–14 at. %) alloys, including two data points from our former study [4]. 110
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been reported. The oxygen content seemed to be a GFA significant influencing factor, thus it should always be known during any careful GFA analysis to reveal the full picture of the studied phenomena (e.g. chemical composition influence on the GFA of a system). The silver for aluminium substitution influence on the Dc values was strong, yet aluminium affected the GFA stronger than silver probably due to its more negative ΔHmix with the main alloying components (Zr and Cu). The GFA of alloys containing 0–2 and 16 at. % of silver did not exceed the lower cone test limit (Dc > 2 mm), thus they were excluded from further investigations. The critical diameters determined by the discrete method gave very similar results to those of the continuous method (the differences were lower than 0.7 mm). The highest critical diameter values (Dc \/ = 11.3 mm, Dc || = 12 mm) were obtained for the Zr48Cu36Al8Ag8 alloy proving its highest GFA among other alloys in this system. Most of the thermal indicators were clearly affected by the chemical composition changes. They generally exhibited good correlation with the Dc. The highest correlation coefficients were obtained for the θ (R2 = 0.979) and ξ (R2 = 0.961) indicators. They exhibited high sensitivity to chemical composition changes of the Zr48Cu36Al16xAgx alloys. ξ has already been reported elsewhere as a proper indicator in describing the GFA of various alloys and it exhibited very high R2 value in this study as well, thus it may actually be proposed as a potentially reliable GFA indicator.
[11]
[12] [13]
[14] [15]
[16]
[17]
[18] [19]
[20]
[21]
Declarations of interest
[22]
None. [23]
CRediT authorship contribution statement
[24]
P. Błyskun: Investigation, Data curation, Visualization, Writing original draft. M. Kowalczyk: Methodology, Formal analysis, Writing review & editing. G. Cieślak: Resources, Investigation, Validation. T. Kulik: Funding acquisition, Conceptualization, Supervision, Project administration.
[25]
[26]
[27]
Acknowledgments [28]
This work was financially supported by the National Science Center [grant number 2015/17/B/ST8/00618]. Authors would also like to thank Miss Agata Myśliborska-Błyskun for providing language help.
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