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Scripta Materialia 68 (2013) 183–186

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Nanoindentation study of chemical effects on the activation volumecontrolling shear band initiation in metallic glasses

Loıc Perriere,⇑ Sophie Nowak, Sophie Brossard, Minh-Thanh Thai, Marc Bletry andYannick Champion

Institut de Chimie et des Materiaux Paris-Est, CNRS-UPEC, 2 rue Henri Dunant, 94320 Thiais, France

Received 24 July 2012; revised 9 October 2012; accepted 9 October 2012Available online 16 October 2012

Planar flow melt spinning was used to prepare six Zr-based metallic glasses. Evidence of the effect of chemistry was found bystructural and thermal characterizations. A clear influence of chemistry was also observed on the mechanical behaviour, with dif-ferences in hardness and Young’s modulus measured by nanoindentation being noted. Using a statistical analysis of the data, theactivation volume controlling initiation of shear bands in the localized deformation process was obtained, and a correlation betweenthis volume and the intrinsic alloy properties is emphasized.� 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Metallic glass; Melt spinning; Nanoindentation; Shear bands

Metallic glass (MG) alloys continue to be the sub-ject of intense study owing to their great potential due totheir extreme strength, high resilience and functional prop-erties [1]. In addition, above the glass transition tempera-ture, Tg, viscoplastic behaviour allows unusually easy netshape processing of parts, as long as this temperature is be-low the temperature of crystallization, Tx [2–4]. Indeed,MGs represent a real breakthrough in metallurgy, but theirdevelopment is strongly hindered by the lack of macro-scopic ductility below Tg. In fact, plasticity occurs in themajority of MGs, but is localized in a few thin shear bands;extended development of one of these bands leads to rapidmacroscopic failure. Accordingly, macroscopic ductilitywould be expected if shear bands are multiplied and spa-tially confined, as in partially devitrified glasses [5] or innanopillars [6]. For the first case, random distribution ofsmall-sized crystallites in the glass phase generates multipli-cation and deviation of shear bands, both of which areresponsible for delays in localization. For the second, theeffect is clearly size dependent and there is evidence of theeffect of the chemistry (intrinsic effect) on the phenomenon.In any case, improvement in ductility would be obtained bya better understanding of the process of shear band forma-tion and evolution in order to control these processes.

In this study, we examine the effect of chemistry onthe formation of shear bands in Zr-based MGs and par-

1359-6462/$ - see front matter � 2012 Acta Materialia Inc. Published by Elhttp://dx.doi.org/10.1016/j.scriptamat.2012.10.013

⇑Corresponding author. Tel.: +33 (0) 1 56 70 30 38; fax: +33 (0) 1 5670 30 43; e-mail: perriere@icmpe.cnrs.fr

tially devitrified MGs in order to examine potential cor-relations between chemistry (intrinsic effect) and shearband initiation. The first correlation is studied by intro-ducing a small variation of alloy composition by theaddition of W (refractory) and Sn (soft) in alloysZr57Cu20Al10Ni8Ti5 and Zr50Cu50. The second is evalu-ated from the measurement of the macroscopic activa-tion volumes, v, characterizing the thermally activatedprocess controlling shear band formation. As proposedby Argon [7], the activation volume is simply relatedby an elementary shear to the volume of the sheartransformation zone (STZ), a concept that has provedrelevant to describing both heterogeneous and homoge-neous deformation [8,9]. Measurements were carried outusing nanoindentation which allows investigation ofdeformation when materials are macroscopically brittle.These experiments reveal the effects of indentation sizeand time scale on activation volume, which require pro-posing a relevant analysis to evaluate a comparablemacroscopic activation volume.

A low content (i.e. <4 at.%) of solute atoms havingdifferent atomic radii and bonding energies comparedto the MG constituents is added to MG alloys. Fromthese additions changes are expected in the local atomicarrangement (i.e. spatial atomic distribution, free vol-ume content) and the atomic bonding strength (fromchanges in the local electronic structure).

Sn and W have similar atomic radii, but fairly differentbonding energies: a strong impact on the local structure

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Figure 1. XRD patterns of Zr57Cu20Al10Ni8Ti5 (1), Zr50.3Cu29.8Al7.5-

Ni8.1Sn0.3W4 (3) and Zr48Cu48Sn2W2 (5) (numbered according to Table 1).� denotes peaks corresponding to ZrW2 precipitates, and � to W precipitates.

184 L. Perriere et al. / Scripta Materialia 68 (2013) 183–186

and energy of the MG is therefore expected from the addi-tion of one or both of these elements. The solute atomswere added to the intensively studied Zr57Cu20Al10Ni8Ti5alloy [10], which has a high glass-forming ability (GFA),and 20 mm diameter bars were produced. The binary alloyZr50Cu50 was also studied; this has a lower GFA and a lesscomplex chemistry than the other alloy studied here.Highly refractory W is rarely used to produce MGs as it ad-versely affects the GFA [11]. Although W has a negative,though low, mixing enthalpy with Zr (��9 kJ mol�1),the large positive mixing enthalpy with Cu (22 kJ mol�1)prohibits direct insertion of this element and some devitri-fication is to be expected. Sn has a high mixing enthalpywith W (26.5 kJ mol�1); it is an extremely soft metal witha melting point about one-sixth that of W.

To ensure the formation of MG or MG with limiteddevitrification, alloys were produced by planar flow meltspinning with a quenching rate of 106 K s�1, into the formof ribbons �40 lm thick and �10 mm wide. Metals werefirst mixed and melted under a He atmosphere in awater-cooled copper crucible heated by electromagneticinduction. W was added in the form of the binary eutecticZrW2 prepared beforehand by arc-melting. Six differentcompositions were prepared (Table 1). The amorphousstate of the ribbons was confirmed by X-ray diffraction(XRD) using an X’Pert PRO MPD diffractometer (PANa-lytical, the Netherlands). The thermodynamic properties(Tg, Tx, liquidus temperature Tl, and heat of crystalliza-tion) of MGs were characterized by differential scanningcalorimetry (DSC) using a 404 F1 Pegasus calorimeter(Netzsch, Germany). 15 mg of specimens were heated upto the liquidus temperature at a rate of 0.167 K s�1 inalumina crucibles. Nanoindentation was performed witha Triboscope nanoindenter (Hysitron, USA), using adiamond Berkovich indenter (E = 1141 GPa, v = 0.07).The maximum indentation load used was 8000 mN at aloading rate of 1.6 mN s�1. Activation volumes werecalculated from constant-load tests at 8000 mN afterloading at a rate of 16 mN s�1 and measuring the depthvariation over 5 s. At least 10 indents were made on eachribbon for evaluation of the mechanical and rheologicalproperties. Prior to analysis, measurements were carriedout on the reference Zr57Cu20Al10Ni8Ti5 MG in bulk andribbon forms which gave the same values, confirming thatnanoindentation performed on ribbons �40 lm thick isconsistent.

Compositions without W (Zr57Cu20Al10Ni8Ti5, Zr58.4

Cu24.5Al6.4Ni6.7Sn4 and Zr50Cu50) are fully amorphous(Fig. 1). As explained above, addition of W leads to someprecipitation, and reflections identified as ZrW2 werefound for alloys containing W and Al (Zr50.3Cu29.8Al7.5

Ni8.1Sn0.3W4 and Zr44Cu44Al8Sn2W2) (Fig. 1). In theMG with W and no Al (Zr48Cu48Sn2W2), the precipitatesare pure W (Fig. 1). The volume fraction of crystallites islow since W is identified in all crystallites and its content isless than 4 at.% in alloys. In addition, it should be notedthat DSC shows similar thermal evolution between fullyand partially crystallized MGs, in particular a largeexothermic peak corresponding to crystallization isobserved, supporting the low level of devitrification inMG containing W. Tg values are reported in Table 1.The domain of stable supercooled liquid, DTx = Tx � Tg,and the reduced glass transition temperature, Trg =

Tg/Tl, have been added in order to obtain informationabout the variation of GFA with composition.

From the nanoindentation loading–unloading curve,hardness, H, and Young modulus, E, are calculatedaccording to the Oliver and Pharr approach [12] by:

H ¼ F max

ACmax

ð1Þ

E ¼ @p@h� 1

CffiffiffiffiffiffiffiffiffiffiffiACmax

p ð2Þ

The load–depth curve is fitted using the parabolic law:F ¼ C � h2. ACmax is calculated from the contact depthhD, obtained from the load–depth curve: ACmax

¼ 24:5ð1:24 � hDÞ2 according to Ref. [13] and the correction pro-posed by Charleux et al. [14], taking into account thepile-up produced around the indent when materials deformplastically by shearing. It is emphasized that the pile-upand/or indent size may have a significant effect, with, forexample, higher values of hardness and Young’s modulusobserved with decreasing load [14,15]. The yield stressand hardness are related by Tabor’s rule, rY � H=3:3[12] for MGs exhibiting an average maximum elastic defor-mation: eel ¼ E=rY � 2%, and this behaviour was con-firmed by macroscopic testing in compression onZr57Cu20Al10Ni8Ti5 [10]. The yield stress, rY, is then calcu-lated with the following relation:

rY ¼F max

3:3 � 24:5 � ð1:24hDÞ2: ð3Þ

Measured values of E and H and calculated values ofrY are reported in Table 1. The macroscopic activationvolumes are obtained from the constant-load experi-ments (Fig. 2), in which depth variation as a functionof time provides information on the local flow rate. Ina thermally activated flow process, the local shear rateis defined by:

_c ¼ _c � exp �Q� svkT

� �; ð4Þ

where Q is the activation energy characterizing the en-ergy barrier for atomic displacement, s is the local shearstress applied on the activation volume, v, derived by:

v ¼ kT@ln _c@s

� �T

¼ffiffiffi3p

kT@ln_s@r

� �T

: ð5Þ

Table 1. Chemical compositions, thermodynamic and mechanical properties, and values of the activation volume extrapolated at Dh = 7 nm,vhomogeneous.

Alloy Composition (at.%) Structure Tg (K) Trg DTxg (K) E (GPa) H (GPa) rY (GPa) vhomogeneous

(A3)

1 Zr57Cu20Al10Ni8Ti5 Amorphous 675 0.596 32 80.7 ± 0.7 5.46 ± 0.09 1.65 ± 0.03 2052 Zr58.4Cu24.5Al6.4Ni6.7Sn4 Amorphous 721 0.614 20 92.0 ± 1.9 6.16 ± 0.20 1.87 ± 0.06 1943 Zr50.3Cu29.8Al7.5Ni8.1Sn0.3W4 Amorphous + ZrW2 715 0.611 45 94.9 ± 1.8 6.15 ± 0.13 1.86 ± 0.04 1704 Zr50Cu50 Amorphous 681 0.560 25 84.0 ± 0.8 5.60 ± 0.06 1.70 ± 0.02 1905 Zr48Cu48Sn2W2 Amorphous + W 748 0647 22 91.2 ± 1.8 6.03 ± 0.13 1.83 ± 0.04 1896 Zr44Cu44Al8Sn2W2 Amorphous + ZrW2 723 0.608 31 99.4 ± 1.2 6.09 ± 0.05 1.84 ± 0.01 167

Figure 2. Depth as a function of time at constant load forZr58.4Cu24.5Al6.4Ni6.7Sn4 (2). The solid line represents the fit forDh = f(t). Inset: logarithm of the applied stress vs. logarithm of thestrain rate. The slope is the strain-rate sensivity, m.

L. Perriere et al. / Scripta Materialia 68 (2013) 183–186 185

ffiffiffi3p

is the Taylor’s factor which relates the macroscopicapplied stress, r, to the shear stress, s, in a von Mises plas-ticity criterion (similarly to ultrafine-grained metals[16,17]). The strain rate is calculated from the indentationrate as _e ¼ _h=h. The load is initially applied up to8000 mN and kept constant, while the depth variation is re-corded as a function of time. As shown in Figure 2, theexperimental data fit a log function: hfit ¼ Aþ B � lnðtÞ.From Eq. (3), values of ln(r) are plotted as a function ofthe calculated Inð_eÞ, giving the strain rate sensitivity,m ¼ @lnr=@ln_e, from the slope of the curve (inset ofFig. 2). The macroscopic activation volume is then ob-tained by:

V ¼ffiffiffi3p

kTmr

ð6Þ

Multiple measurements for each MG reveal a largerange of depth variations over the holding time andfor the same load. The various depths are randomly ob-served in a series of experiments and the calculated dif-ference in v can vary by a factor of 5. This means thatfor a load–time couple, there corresponds a series ofstress–strain rate couples and as well as a series ofstrain-rate sensitivities and activation volumes. Thisobservation should be expected since MG deformationis heterogeneous in nature below Tg. Formation andpropagation of a shear band is evidenced in nanoinden-tation by the well-known serration effect visible in theloading part of the curve. In a small and confined vol-ume of matter and for a given load–time condition,the total number of shear bands formed to produce plas-tic flow most likely depends on random factors such assurface structure and orientation, statistical distributionand orientation of “atomic clusters”, the free volume

forming the glass, and stress-induced heat release. Aprobability function (the analytical form of which wouldrequire further analysis) for the formation of n shearbands would depend on these factors and the loadingconditions. The consequence of this is, first, that valuesof strain-rate sensitivity and activation volume for a gi-ven load–time couple and their dependence on depthvariation cannot be estimated from the mean value ofa series of nanoindentations on a given alloy; and, sec-ond, values for various samples measured from singleexperiments are not directly comparable. Focusing ona relevant estimation of the activation volume, one drawfrom the following approximation:

@ln_s@r� ln_s2 � ln_s1

r2 � r1

ð7Þ

with:

ln_e2 � ln_e1 ¼ �lnh0 þ Dh

h0

� �þ ln

t2

t1

� �� ln

t2

t1

� �� Dh

h0

ð8Þ2 2

r2 � r1 ¼F

3:3 � 24:5� h0 � ðh0 þ DhÞ

h20 � ðh0 þ DhÞ2

� � F3:3 � 24:5

� 2Dh � h0

h40

ð9Þ

that:

m � �MkT2� 3:3 � 24:5

F� h2

0 �h0 � lnðt1=t2Þ

Dh� 1

� �ð10Þ

It follows that the variation of v as a function of Dh canbe approximated by an equation of the formv � A � ðB=Dhþ 1Þ. This was verified from the plot of vas a function of 1/Dh for the data recorded for the variousMG alloys (Fig. 3). One can conclude that, first, macro-scopic activation volumes are only comparable for differ-ent alloys at a given Dh (assuming that the number ofshear bands is the same at a given Dh for various alloys).Second, at a given Dh, deformation is localized in a fewshear bands corresponding to a low volume fraction ofthe total impacted matter and where the flow rate is largerthan the average measured strain rate. Accordingly, themacroscopic activation volume measured in such condi-tions cannot be straightforwardly and quantitatively re-lated to the actual thermally activated process at theatomic scale. Further reliable analysis is needed to definea relevant Dh and associated v. For example, Dh could bearbitrarily chosen as �10 nm which is the average shearband thickness. More quantitatively, it should be notedthat the larger the depth variation corresponding to largerstrain rate, the larger the value of the correlation factor,R2, of the hfit curve. This can be easily attributed to the ser-ration effect, which is known to be less detectable as the

Figure 4. Evolution of the apparent activation volume, vhomogeneous as afunction of the Young’s modulus, E; digits refer to the alloys (Table 1).

Figure 3. Activation volumes as a function of 1/Dh; digits refer to thealloys (Table 1).

186 L. Perriere et al. / Scripta Materialia 68 (2013) 183–186

strain rate increases [18]. R2 was found to vary as a func-tion of the indent depth following: R2 ¼ 0:265=Dhþ 0:963,and gives Dh � 7 nm for R2 = 1, which would correspondto the absence of serration or a so-called apparent homo-geneous deformation. It is worth noting that this depthvariation is of the order of the shear band thickness.The activation volumes for homogeneous deformation,vhomogeneous (Table 1), were then defined by extrapolatingthe value of v from the fitted curve (Fig. 3) at Dh = 7 nm.It can be seen that these volumes are of the order of thosemeasured in the homogeneous deformation domainaround Tg in Zr-based MG [19], which is consistent withapparent homogeneous deformation conditions.

A clear impact of the chemistry and/or the partial devit-rification on the activation volume is thus emphasized(20% variation is observed for the maximum difference).In contrast, no particular rules can be deduced regardingthe magnitude of the activation volume and the composi-tion. For instance, a very complex alloy such as (2) hassame the vhomogeneous as the simplest one (4). Moreover,no major effect is observed due to partial crystallizationand a similar trend is observed regarding v as a functionof Dh for these alloys. This suggests that crystallites haveno real impact on the mechanism of shear band initiation.The complexity in alloy composition increased for partiallycrystallized MGs and the absence of long-range order doesnot allow a direct correlation between vhomogeneous and alloycomposition. The Young’s modulus was used as a relevantparameter to compare these alloys. It should be noted thatE is analogous to an energy density and is affected by smallchemical variations producing local changes in atomicbonding distance and energy. Plotting vhomogeneous as a func-tion of E (Fig. 4) reveals a linear relationship. Indirectly,Dubach et al. [20] showed a similar linear trend for a Zr-

based alloy at various temperatures: they observed a de-crease in E and increase in activation volume when the tem-perature increases with inhomogeneous deformation. It isaccepted that STZ characteristics, such as the energy bar-rier density for activation, and physical properties, suchas Poisson’s ratio, are relevant indicators for evaluatingthe deformability of MGs [21]. The present results showan association between these parameters and a relevantactivation volume, and its evolution with local chemistry,which should be of interest in terms of the current modelsfor designing MG alloys.

A series of six Zr-based MGs was prepared in ribbonform using planar flow melt spinning. Zr57Cu20Al10Ni8Ti5and Zr50Cu50 alloys were slightly modified by addition ofSn and W, in order to modify the local chemistry. The effectof chemistry variation was studied through structural(XRD) and thermal (DSC) analyses. Clear differences wereobserved between amorphous alloys in terms of both Tg

and GFA. The effect of composition change was observedon the mechanical behaviour, investigated by nanoinden-tation, which showed notable differences in hardness andYoung’s modulus values. The activation volume control-ling the shear band initiation was evaluated by means ofconstant-load tests: values of 167–205 A3 were determineddepending on the alloy. A linear correlation between theelementary processes of shear band formation (vhomogeneous)and the Young’s modulus, E, has been emphasized.

Authors would like to thank the French MoD forfunding this work.

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