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Electronegativity difference as a factorfor evaluating the thermal stability ofAl-rich metallic glassesC.S. Ma a , J. Zhang a , X.C. Chang a , W.L. Hou a & J.Q. Wang aa Shenyang National Laboratory for Materials Science, Institute ofMetal Research, Chinese Academy of Sciences, Shenyang, China

Version of record first published: 04 Dec 2008

To cite this article: C.S. Ma, J. Zhang, X.C. Chang, W.L. Hou & J.Q. Wang (2008): Electronegativitydifference as a factor for evaluating the thermal stability of Al-rich metallic glasses, PhilosophicalMagazine Letters, 88:12, 917-924

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Philosophical Magazine LettersVol. 88, No. 12, December 2008, 917–924

Electronegativity difference as a factor for evaluating the thermal

stability of Al-rich metallic glasses

C.S. Ma, J. Zhang, X.C. Chang, W.L. Hou and J.Q. Wang*

Shenyang National Laboratory for Materials Science, Institute of Metal Research, ChineseAcademy of Sciences, Shenyang, China

(Received 29 May 2007; final version received 2 October 2008)

This article proposes a factor, the critical electronegativity difference �xcri, tocorrelate alloy composition with thermal stability and glass-forming ability ofAl–Ni–RE (RE: Rare Earth element) ternary metallic glasses. The Al-richmetallic glasses with �x4�xcri exhibit glassy behavior, whereas alloys with�x5�xcri are nanocrystalline. Nanoglassy alloys occur when �x��xcri. Thebest glass formers are located near �xcri. Furthermore, an equation has beendeduced to calculate �xcri with varying RE covalent atomic radius.

Keywords: electronegativity; crystallization; metallic glasses

1. Introduction

Although a large number of easy-glass-forming metallic alloys have been discovered inrecent years, most of the search process is rather tedious and costly. Therefore, itis important to find theoretical or empirical criteria to evaluate and predict the Glass-Forming Ability (GFA) and the thermal stability of alloy compositions. Great progresshas been made on Bulk Metallic Glasses (BMGs) from the viewpoint of topology [1]and chemistry (mainly including mixing enthalpy [2], electron valence [3], andelectronegativity [4,5]). Compared to the BMGs with high GFA, Al-based marginalglass-forming systems are, to date, the only ones for which one cannot obtain bulk sampleswith a thickness exceeding 1mm. They have some unique characteristics: (1) all the glassformers in this system have off-eutectic compositions; (2) the rules or criteria suitable forcharacterizing BMGs, such as the ‘three empirical rules’ [2], the Trg parameter [6], and the‘confusion principle’ [7], are not applicable to Al-based Metallic Glasses (MGs). Hence,it is essential to discover effective factors and find more specific guidelines for developingAl-based BMGs.

Glass formation of the basic ternary alloy systems, Al–Ni–RE (RE: Rare Earthelement), showing a relatively wide glass-forming range and a good GFA in Al-richsystems, has been studied extensively. It is recognized that the reported thickness ofAl–Ni–RE samples varies dramatically with the RE element [6–9]. Among the factorsinfluencing GFA, the mixing enthalpy of the Al–RE atomic pair and the electron valencefor the RE element are almost the same (�38 kJ/mol and 3, respectively) for all REelements [10,11]. Apparently, the main differences between the RE elements lie in their

*Corresponding author. Email: jqwang@imr.ac.cn

ISSN 0950–0839 print/ISSN 1362–3036 online

� 2008 Taylor & Francis

DOI: 10.1080/09500830802526596

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atomic size and electronegativity. A number of studies have been performed on therelationship between the atomic size and the GFA in Al-rich systems. Miracle et al. [12]and Senkov and Miracle [13] reported that there exists a special atomic-radius ratiocorresponding to the maximum packing efficiency, and the atomic-size distributionplot of Al-based MGs has a concave downward shape, which is typical for ordinaryamorphous alloys. Sa Lisboa et al. [14] proposed a topological lambda criterion(� ¼

PZi¼B CijðRi=RAlÞ

3� 1j, where B to Z represents different solute elements with

corresponding atomic concentration Ci and atomic radius Ri), from which threecrystallization categories can be distinguished on the basis of critical � value:nanocrystalline, glassy, and nanoglassy. On the other hand, Louzguine and Inoue [4]found that the supercooled liquid region, �Tx (the temperature difference between thetemperature of the onset of crystallization Tx and the glass-transition temperature Tg) inAl–RE–Ni–Co alloys, increases linearly with increasing electronegativity of the REelement within a certain composition range. The lower the difference between theconstituent elements, the wider the range of the supercooled liquid region becomes [5].However, the evaluation and prediction of thermal stability and GFA in Al-rich alloysystems is rather difficult, since the interrelationship between the component’s electro-negativity and glass formation has not yet been well elaborated.

In this work, a basic Al–Ni–RE alloy system was selected on account of the variety andavailability of experimental data, to systematically investigate the influence of electro-negativity on the thermal stability and GFA in this system. It is anticipated that thecorrelation found between them will serve as a useful gauge for designing and predictingthe properties of Al-rich ternary amorphous alloys.

2. Results and discussion

Electronegativity reflects the bonding nature of atomic pairs in alloys and can be relatedwith bond type or bond length. To find the relationship between componentelectronegativity and supercooled liquid region, a parameter, �x, quantifying electro-negativity differences among the elements, is introduced as follows [15]:

�x ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXni¼1

Ciðxi � xÞ2

sð1Þ

x ¼Xni¼1

Cixi; ð2Þ

where n is the number of components; xi is the Pauling electronegativity of element i;Ci is the concentration of element i; x is the average electronegativity of alloys.

Figure 1 shows the relationship between the electronegativity difference �x andthe supercooled liquid region �Tx of Al–Ni–RE (RE¼Gd,Y,Ce, La) metallic glasses. Thedetailed data concerning thermal characteristics and calculated �x values in the Al–Ni–RE glasses are listed in Table 1. The value of �Tx for nanocrystalline alloys was set to bezero since no observable glass-transition signal can be detected upon reheating. It isobvious that there exists a critical eletronegativity difference �xcri in each system. When�x4�xcri, the glassy alloys exhibit a distinct supercooled liquid region and undergo the

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eutectic crystallization. Nanoglassy behavior occurs when �x��xcri. The alloys with�x5�xcri display the unresolved Tg followed by the nanocrystalline process. Hence, �xcricould be used as a tool to distinguish the crystalline behavior of Al-rich metallic glasses. Bycomparison, note that the �xcri values in these systems are around 0.14, slightly varyingfrom 0.135 for Al–Ni–Gd systems to 0.145 for Al–Ni–La. Furthermore, when a REcovalent atomic radius parameter is introduced, a linear relationship is observed betweenthe electronegativity difference �xcri and the RE covalent atomic radius RRE, asdemonstrated by the solid line in Figure 2. This relationship is expressed by anapproximation formula:

�xcri ¼ 1:245RRE � 0:065: ð3Þ

In order to reveal how closely the estimated values for the regression line correspond to theactual experimental data, the statistical parameter, R2, known as the coefficient ofdetermination ranging from 0 to 1, was calculated using this regression mode. As is clear inthe graph, the R2 value is as high as 0.98 for this fit, suggesting that there is a solidcorrelation between �xcri and RRE.

From simple calculations using Equation (3), the factor �xcri can be obtained for anyother ternary Al–Ni–RE system and utilized to predict the crystalline type. A numberof experimental results available in the literature, support the predictive validity in otherAl–Ni–RE alloys. For example, the calculated value of �xcri is about 0.139 in Al–Ni–Ndsystems. Nanocrystalline Al86Ni9Nd5 (�x¼ 0.138) alloy turned into glassy Al85Ni10Nd5(�x¼ 0.141) when as low as 1% alloy composition changed [19].

0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18−5

0

5

10

15

20

25

30

35GlassyNanocrystallineNanoglassyBest glass former

ΔTx

(K)

Δx

Δx =0.137

Al–Ni–Y

(b)

0.11 0.12 0.13 0.14 0.15 0.16

0

5

10

15

20

25

30Glassy Nanocrystalline Nanoglassy Best glass former

ΔTx (

K)

Δx

Δx =0.135

Al–Ni–Gd

(a)

0.12 0.13 0.14 0.15 0.16−202468

10121416182022

GlassyNanocryrstallineNanoglassyBest glass former

Δx

Δx =0.145 Al–Ni–La

(d)

0.13 0.14 0.15 0.16 0.17−202468

1012141618202224

GlassyNanocrystallineBest glass former

ΔTx (

K)

ΔTx (

K)

Δx

Δx =0.142

Al–Ni–Ce

(c)

Figure 1. Relationship between �x and �Tx for Al–Ni–RE (RE¼Gd,Y,Ce, and La).

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Table 1. Summary of thermal characteristics for the Al–Ni–RE (RE¼Gd,Y,Ce, and La) ternarymetallic glasses. Tg, Tx, and �Tx denote the glass-transition temperature, crystallizationtemperature, and supercooled liquid region, respectively. ‘—’ stands for alloys with unobservableglass transition; ‘*’ represents the values estimated from figures in the references. N/A denotes valuesthat cannot be directly taken from the context in the references. Crystallization types are:NC: nanocrystalline; G: glassy; and NG: nanoglassy. The best glass formers are indicated in italics.�x denotes the electronegative difference among the elements. � is a topological instabilityparameter [24].

Composition Tg (�C) Tx (

�C) �Tx (�C) �x �

Crystallizationtype Ref.

Al87Gd10Ni3 258 N/A 22* 0.136 0.109 G [16]Al85Gd8Ni7 261 N/A 27* 0.140 0.103 G [16]Al82Gd7Ni11 N/A N/A 14* 0.147 0.107 G [7]Al83Gd7Ni10 N/A N/A 13* 0.144 0.104 G [7]Al84Gd7Ni9 N/A N/A 12* 0.141 0.100 G [7]Al82Gd11Ni7 N/A N/A 10* 0.156 0.133 G [7]Al83Gd10Ni7 N/A N/A 13* 0.151 0.123 G [7]Al84Gd9Ni7 N/A N/A 20* 0.146 0.113 G [7]Al86Gd7Ni7 231 N/A 8* 0.134 0.093 NG [16]Al85Gd7Ni8 N/A N/A 25* 0.138 0.097 NG [7]Al88Gd9Ni3 — N/A 0 0.131 0.099 NC [16]Al90Gd7Ni3 — N/A 0 0.119 0.080 NC [16]Al88Gd5Ni7 — N/A 0 0.121 0.073 NC [16]Al87Gd6Ni7 — N/A 0 0.128 0.083 NC [16]Al87Gd3Ni10 — N/A 0 0.117 0.064 NC [16]Al86Gd4Ni10 — N/A 0 0.125 0.074 NC [16]Al85Gd5Ni10 — N/A 0 0.132 0.084 NC [16]Al87Gd7Ni6 — N/A 0 0.131 0.090 NC [7]Al88Gd7Ni5 — N/A 0 0.127 0.086 NC [7]Al75Y13.3Ni11.6 387.4 401.7 14.3 0.174 0.172 G [17]Al77Y12.3Ni10.7 369.6 379.6 10 0.168 0.159 G [17]Al78Y11.7Ni10.3 356.7 362.6 5.9 0.164 0.151 G [17]Al79Y11.2Ni9.8 347.8 356.2 8.4 0.160 0.145 G [17]Al81Y10.1Ni8.9 321.1 324.6 3.5 0.152 0.131 G [17]Al82Y9.6Ni8.4 307.2 315.7 8.5 0.148 0.124 G [17]Al83Y9.1Ni7.9 278.5 287.6 9.1 0.144 0.117 G [17]Al84Y8.5Ni7.5 274.5 284.4 9.9 0.140 0.110 G [17]Al83.5Y11Ni5.3 275 303 28 0.144 0.127 G [18]Al85Y9Ni6 273.4 284 10.6 0.137 0.110 NG [17]Al85Y10Ni5 278.8 287 8.2 0.138 0.116 NG [17]Al86.5Y9Ni4.5 239 253 14 0.131 0.105 NG [18]Al85Y8Ni7 — 267.6 0 0.136 0.103 NC [17]Al86Y7.5Ni6.5 — 240.7 0 0.131 0.097 NC [17]Al87Y6.9Ni6.1 — 225.1 0 0.126 0.089 NC [17]Al88Y6.4Ni5.6 — 192.3 0 0.121 0.083 NC [17]Al85Y3Ni12 — 250 0 0.122 0.071 NC [17]Al85Y4Ni11 — 247 0 0.125 0.077 NC [17]Al85Y5Ni10 — 232 0 0.128 0.084 NC [17]Al85Y6Ni9 — 252 0 0.131 0.090 NC [17]Al85Y7Ni8 — 247 0 0.134 0.097 NC [17]Al89.5Y7Ni3.5 — 150 0 0.116 0.081 NC [18]Al88Y8Ni4 — 192 0 0.124 0.093 NC [18]

(continued )

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Table 1. Continued.

Composition Tg (�C) Tx (

�C) �Tx (�C) �x �

Crystallizationtype Ref.

Al89Ce5.5Ni5.5 — 200 0 0.134 0.078 NC [19]Al87Ce4.33Ni8.67 — 213 0 0.135 0.076 NC [19]Al86Ce4Ni10 — 233 0 0.136 0.077 NC [19]Al85Ce5Ni10 254 270 16 0.145 0.088 G [19]Al84Ce6Ni10 278 295 17 0.153 0.098 G [19]Al85Ce7.5Ni7.5 271 285 14 0.157 0.106 G [19]Al85Ce4Ni11 — 259 0 0.139 0.080 NC [19]Al84Ce4Ni12 — 280 0 0.142 0.084 NC [19]Al83Ce7Ni10 301 321 20 0.161 0.109 G [19]Al87Ce6Ni7 227 244 17 0.144 0.088 G [20]Al86Ce6Ni8 244 263 19 0.147 0.091 G [20]Al85Ce6Ni9 258 279 21 0.150 0.095 G [20]Al84Ce6Ni10 269 287 18 0.153 0.098 G [20]Al83Ce6Ni11 300 319 19 0.156 0.102 G [20]Al88La4Ni8 — 183 0 0.133 0.078 NC [8]Al88La5Ni7 — 204 0 0.139 0.087 NC [8]Al87La4Ni9 — 205 0 0.136 0.081 NC [8]Al87La5Ni8 — 226 0 0.142 0.090 NC [8]Al86La5Ni9 225 239 14 0.145 0.094 NG [8]Al86La6Ni8 245 259 14 0.151 0.103 G [8]Al86La4Ni10 — 199 0 0.139 0.084 NC [8]Al85La6Ni9 256 272 16 0.154 0.106 G [8]Al85La5Ni10 243 260 17 0.148 0.097 G [8]Al84La5Ni11 265 282 17 0.151 0.101 G [8]Al84La6Ni10 273 289 16 0.157 0.110 G [8]Al90La4Ni6 — N/A 0 0.126 0.071 NC [21]Al89La5Ni6 — N/A 0 0.135 0.083 NC [21]Al87La6Ni7 N/A N/A 20 0.148 0.100 NG [22]

0.158 0.160 0.162 0.164 0.166 0.168 0.170 0.1720.132

0.134

0.136

0.138

0.140

0.142

0.144

0.146

0.148

Ele

ctro

nega

tivity

diff

eren

ce

RE covalent atomic radius (nm)

RE=Gd

Y

Ce

La

Figure 2. Relationship between �xcr and covalent atomic radius.

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Figure 3 demonstrates the compositional triangles for Al–Ni–RE (RE¼Gd,Y,Ce, and

La) systems, for which thermal crystallization results are available in the literature

(Table 1). A remarkable distribution of points around the �xcri line is obtained: alloys

reported to be glassy fall above (�x4�xcri), while nanocrystalline alloys lie below

(�x5�xcri) this newly derived dividing line. This case is very similar to � criterion defined

by Sa Lisboa et al. [14], in which crystallization type can be discerned by �0.1 line in

Al-based MGs: alloys exhibit glass behavior when �40.1, while nanocrystalline

when �50.1, and nanoglassy when �� 0.1. To further manifest the correlation between

GFA and �xcri, the best glass formers reported so far in their respective systems

were marked as stars in Figure 3. Note that the best glass formers in these systems

are located at nanocrystalline Al87Ni7Gd6 (300 mm) [7], nanoglassy Al85Ni5Y10 (120 mm)

[9], glassy Al85Ni10Ce5 (90 mm) [19], and nanoglassy Al86Ni9La5 (780mm) alloy [8],

respectively. Apparently, the alloy compositions are not fully consistent with Sa Lisboa’s

� criterion [14] in which alloys arrested to be the best glass formers in Al-rich systems

are nanoglassy with �� 0.1. By comparison, the best glass formers are located much

nearer to the �xcri line than the �0.1 line.

80 85 90 95 100

0

5

10

15

20 0

5

10

15

20GlassyNanocrystallineNanoglassyBest glass former

Y (at.%)

(b)

80 85 90 95 100

0

5

10

15

20 0

5

10

15

20GlassyNanocrystalline Nanoglassy Best glass former

Gd (at.%

)

Ni (

at.%

)

Ni

Ni (

at.%

)

Ni (

at.%

)

Al (at.%) Al (at.%)

Al (at.%) Al (at.%)

Δx 0.135

Δx 0.142 Δx 0.145

Δx 0.137

(a)

80 85 90 95 100

0

5

10

15

20 0

5

10

15

20GlassyNanocrystallineBest glass former

Ce (at.%

)

(c)

80 85 90 95 100

0

5

10

15

20 0

5

10

15

20

La (at.%)

Glassy Nanocrystalline Nanoglassy Best glass former

(d)

λ0.1line

λ0.1line λ0.1line

λ0.1line

Figure 3. Compositional triangles for Al–Ni–RE (RE¼Gd,Y,Ce, and La) systems. The plottedpoints, corresponding to actual compositions reported in the literature, selectively distribute aroundthe �xcri (� ) and �0.1 (—) lines depending upon crystallization behavior.

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It is well known that the amorphous state is metastable thermodynamically.In the case of solidification from melt, the amorphous phase competes kineticallyand thermodynamically with the corresponding solid solutions and intermetalliccompounds [23]. Factors destabilizing the solid solutions or compounds can lead toan increase in GFA. Egami and Waseda [24] first proposed a topological instabilitymodel that successfully described the minimum solute concentrations for amorphizationby rapid quenching of binary systems. The minimum solute concentration, locates atwhichever average atomic-level elastic strains throughout this system, equal the criticalvalue for topological instability of the single-phase, which is the crystalline solid solutionof the same composition as the liquid. Sa Lisboa et al. [14] further extended the modeland put forward a � criterion, in which �0.1 line were closely related to the crystallinebehavior and GFA in Al-based glass-former alloys. On the other hand, it is noted thatelements with similar electronegativity tend to form solid solutions whilst, with theincrease of the electronegativity difference among constituent elements, the formation ofcompounds would be feasible. It is reasonably expected that there exists an optimumelectronegativity configuration among components. Thus, apart from the atomic sizefactor, the eletronegativity difference plays an important role in dominating GFA orcrystallization behavior as well. Figure 3 simultaneously presents such effects resultingfrom �xcri and �

0.1 line in Al-rich compositional triangle. It can be seen that �xcri and�0.1 has the similar tendency to distinguish the GFA and crystallization behavior in thetypical Al–Ni–RE glass-formation range (80–90 at% Al, 5–15 at% TM, 3–15 at% RE).However, it could be worthwhile noting that the actual radius of Ni and Al vary muchwith Al-based systems and compositions since d-orbital of TM atoms hybridize stronglywith the s and/or p orbital of Al atoms in the Al-rich amorphous alloys. For example,the bond length of Al–Ni in Al89La6Ni5 is 0.243 nm, but that in Al87Y8Ni5 is 0.268 nm[25–27]. The change in atomic radii could have an influence on the validity of � criterion.With regard to electronegative, it represents per se the attraction of a neutral atom ina stable molecule for electrons [28]. Recent studies have further indicated that theelectronegativity includes the ionization potential and electron affinity, and theionization potential is fairly related to the covalent radius [29], from which, it isreasonable to infer that the eletronegativity is associated with not only chemical effect(which is a pervasive concept in mind), but also atomic size effect. Such an analysis isconfirmed by the present results that, during differentiating the GFA and crystallizationbehavior in the Al-rich glasses, there exhibits a similar tendency for �xcri and �

0.1 line,whereas the best glass formers are located much nearer �xcri (Figure 3). Thereby, �xcrcould be served as a more useful tool to predict or design best glass-former compositionsin the Al-based systems.

Normally �Tx are used as an indicator of the GFA for metallic glasses; in fact, it isa quantitative measure of glass stability, which is defined as the resistance of glassestowards devitrification upon reheating above Tg. GFA is specified as the ease by whichmelts can be cooled to form amorphous alloys without the precipitation of any crystalduring solidification. Some results have shown that GFA and glass thermal stability arerelated but are independent properties [30]. This concept was further confirmed inour results, in which the best GFA in Al-rich MGs is not always accompanied by thehighest thermal stability in Al–Ni–RE system (Figure 3). This gives us an important hintthat �Tx is a reflection of thermal stability, but could not be used solely as a criterion forevaluating and predicting GFA.

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3. Conclusions

The relationship between the electronegativity difference and the supercooled liquidregion has been investigated for Al–Ni–RE ternary metallic glasses. It was found thata critical electronegativity difference �xcr exists in each system, which can distinguishthe crystallization behavior and locate the best glass former. It can serve as a usefultool for designing and predicting the properties of Al–Ni–RE ternary glass-formingalloys.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos.50471076) and the National Key Basic Research Program of China (No. 2007CB613906). Thanksare due to H. Yang for helpful discussions.

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