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Deformation behavior of Al-rich metallic glasses under nanoindentation
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Deformation behavior of Al-rich metallic glasses under nanoindentation Hui Guo, Chuanbin Jiang, Baijun Yang, Jianqiang Wang ∗ Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China
a r t i c l e
i n f o
Article history: Received 26 August 2016 Received in revised form 15 October 2016 Accepted 18 October 2016 Available online xxx Keywords: Metallic glasses Inhomogeneous deformation Free volume Nanoindentation
a b s t r a c t To clarify the deformation behavior of Al-rich metallic glasses (MGs), two kinds of Al-rich MGs (i.e. bulk and ribbon samples) with different frozen-in excess volume have been analyzed under nanoindentation. It was found that, with the decrease of frozen-in excess volume, the serration behavior becomes inconspicuous together with the increase of hardness. Further, shear transformation zones (STZs), related to the occurrence of shear banding, have been evaluated by different methods: the cooperative shearing model (CSM), the rate-jump method (RJM) and the dynamic-mechanical response (DMR). In contrast, the STZ volumes, calculated by the RJM, increase from 2.77 nm3 in the bulk to 3.59 nm3 in the ribbon, which are in good agreement with 2.60 nm3 obtained from the icosahedral supercluster medium-range order structure model in Al-rich MGs. This result reflects that an intrinsic correlation exists between the formation of STZs and the medium-range orders (MROs). Moreover, the variation trend of the STZ volume was analyzed in terms of the frozen-in excess volume content. © 2017 Published by Elsevier Ltd on behalf of The editorial office of Journal of Materials Science & Technology.
1. Introduction Aluminum-rich metallic glasses (MGs) have a great potential to be widely used for excellent mechanical properties [1], such as the ultrahigh specific strength, good corrosion resistance [2] and rather low cost. However, similar to conventional MG-forming alloys, there also are brittle behavior caused by highly localized shear banding deformation in Al-rich MGs. To understand the deformation mechanism of Al-rich MGs, a large number of studies have been devoted to the shear banding in melt-spun Al-rich MG ribbons [3,4]. These studies of the deformation behavior are only based upon the Al-rich MG ribbons due to very limited glass formation ability in this class of materials. Since Al-rich bulk metallic glasses (BMGs) with a diameter of 1 mm have been obtained in 2009 [5], they provided a new opportunity for the comprehensive and in-depth understanding of the deformation mechanism. Nanoindentation is one of effective methods for ascertaining the deformation behavior in MGs by its probe with high spatiotemporal and force resolution. Under loading, there are the serrated flow or the pop-in events related to the nucleation and propagation of shear bands in a number of Zr-, Pd- and Cu-based BMGs [6,7]. The
∗ Corresponding author. E-mail address: [email protected] (J. Wang).
characteristics of the serrations are strongly dependent upon the loading rates: a lower loading rate promotes more conspicuous serrations, while a higher loading rate suppresses the appearance of the serrations [6]. This can also be described by the competition between the shear-banding dynamics and the applied rate [8,9]. For MG ribbon and bulk samples with the same composition, more conspicuous serrations appear in ribbon samples containing more concentration of frozen-in volume [10,11]. During deformation of MGs, the sites with larger frozen-in excess volume are easier to form shear transformation zones (STZs), and the agglomeration of STZs evolves into the nucleation site of a shear band [10]. These shear bands are generated and propagated finally contributing to the overall plastic deformation of MGs [12]. The formation of STZs is a key issue in understanding the deformation behavior of MGs. The STZs are the fundamental unit of plasticity, in the form of a small cluster of randomly close-packed atoms that spontaneously and cooperatively reorganize under the action of an applied shear stress [12–14]. It has been recognized that sufficiently small STZs could lead to brittle fracture [15,16]. Recently, Ju et al. [17] revealed a quantized hierarchy of STZs by quasistatic measurements of anelastic relaxation in Al-rich MGs. These reflect the correlation between STZ size and deformation transition mode. However, how many atoms would comprise an STZ remains a controversial issue in MGs. It has been reported that there is a broad distribution of STZ sizes in MGs, which can be
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inferred from a number of experiments [16–20] and simulations [13,21–24], e.g., from a few atoms to several hundred atoms. Moreover, even similar techniques could present considerably different results. For example, in nanoindentation experiments, some studies [16] showed the STZ size of few hundred atoms, while others [17] demonstrated a much smaller STZ size around 20 atoms. To potentially tackle the above problems, in the present study, we selected two kinds of Al-rich MGs (i.e. bulk and ribbon samples) with different frozen-in excess volumes for comparison. The deformation behavior of the two samples was analyzed under nanoindentation. We have calculated the STZ sizes based upon three different methods: the cooperative shearing model (CSM) [25], the rate-jump method (RJM) [16] and the dynamicmechanical response (DMR) [17]. These values have been compared with those derived from an icosahedral supercluster mediumrange order (MRO) structure model in the Al-RE-TM [26]. Finally, an intrinsic correlation between the formation of STZs and the MRO structure was suggested in Al-rich MGs.
Fig. 1. XRD patterns of the Al86 Ni6 Y4.5 Co2 La1.5 bulk and ribbon MGs.
2. Materials and methods The Al86 Ni6 Y4.5 Co2 La1.5 master alloy ingots were prepared by arc-melting a mixture of the constituent elements with a purity of better than 99.99% under a Ti-gettered argon atmosphere. In order to ensure compositional homogeneity, the alloy ingots were melted four times. The cylindrical BMG rods of 1 mm in diameter were produced in a copper-mold. For comparison, rapidly solidified ribbons with 0.02 mm × 3 mm were prepared by a single roller melt-spinning technique in an argon atmosphere. The amorphous structure of both bulk and ribbon alloys was confirmed by X-ray diffraction (XRD) using a Rigaku D/max 2400 diffractometer (Tokyo, Japan) with monochromated CuK␣ radiation (=0.1542 nm). The thermal analysis of the bulk and ribbon alloys was characterized using a differential scanning calorimetry (DSC) in a Q2000 under flowing purified argon. DSC was run two times for each alloy from 300 to 773 K at a constant heating rate of 40 K/min. By taking the second scan as a base line, any thermal effects from the structural evolution during heating were investigated. The mechanical properties were characterized by MTS Nanoindenter XP with a Berkovich diamond indenter with a tip radius of ∼20 nm. For the bulk alloy, the cross-section was used to be the indentation surface, while for the ribbon alloy, indentation was performed on the wheel side. Prior to nanoindentation tests, the surfaces of the two alloys mounted in epoxy resin were mechanically polished to a mirror finishing using magnesium oxide solution. All the tests were conducted in a load-controlled mode with a maximum load of 10 mN at loading rates from 0.025 to 0.25 mN/s, and data acquisition rates as high as 20 points per second. At least 16 indents at each loading rate were performed for each alloy with the separation between adjacent indents of 20 m. At 90% unloading, a dwell period of 25 s was imposed to correct for any thermal drift in the system, which was less than 0.05 nm/s. The load–displacement curves were subsequently analyzed and compared as a function of loading rates. 3. Results 3.1. Structural characterization Fig. 1 shows the XRD patterns of the Al86 Ni6 Y4.5 Co2 La1.5 bulk and ribbon MGs. The broad diffractions with no crystalline Bragg diffraction peaks demonstrate the amorphous structure of the two alloys. It has been reported that Al86 Ni6 Y4.5 Co2 La1.5 alloy has a good glass-forming ability, and the BMG rod with the maximum diameter of 1.5 mm has been reported [27,28].
Fig. 2. DSC curves of the Al86 Ni6 Y4.5 Co2 La1.5 bulk and ribbon MGs at a heating rate of 40 K/min. A zoomed-in view of a small region around the Tg is exhibited in the inset of Fig. 2.
Fig. 2 represents the DSC curves of the bulk and ribbon Al86 Ni6 Y4.5 Co2 La1.5 MGs that were normalized using the base lines at a heating rate of 40 K/min. A similar thermal behavior with three obvious exothermic peaks is shown in the two samples. The total exothermic heat of crystallization reactions, Hx (Hx = H1 + H2 + H3 ) is measured to be −149.1 and −159.8 J/g for the bulk and ribbon alloys, respectively. Note that no obvious endothermic transitions can be discerned in Fig. 2. For most of the Al-based MGs, it was not easy to distinguish a glass transition signal from the DSC curves, since the supercooled liquid region was so small that the glass transition signals always partially or even completely overlapped with the crystallization signals [29]. This phenomenon was also observed in the present Al86 Ni6 Y4.5 Co2 La1.5 MG samples. The typical thermodynamic properties are summarized in Table 1. Obviously, the glass transition temperature Tg for the ribbon sample is slightly larger than that for the bulk sample. Considering the bulk and ribbon samples are produced at different cooling rate q, it indicates that the increase in q from about 103 K/s (for bulk) to 106 K/s (for ribbon) causes the increase in Tg . This is in agreement with the relationship of Tg ∝q [30,31]. In order to ascertain the difference in the irreversible structural relaxation behavior between the bulk and the ribbon samples, a zoomed-in view of a small region around Tg is shown in the inset of Fig. 2. The sub-Tg region for the DSC trace of MGs corresponds to the enthalpy released during structure relaxation, which strongly links with the content of frozen-in volume. As Slipenyuk and Eckert experimentally verified [32], the structural relaxation exothermic heat (H0 ) is proportional to the relative change of frozen-in excess volume (f ) frozen in the amorphous alloy,
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Table 1 Thermodynamic properties of the Al86 Ni6 Y4.5 Co2 La1.5 bulk and ribbon MGs measured from DSC. Tg denotes the glass-transition temperature, Tx 1 , Tx 2 and Tx 3 the first, the second and the third crystallization onset temperatures, Tx the supercooled liquid region (Tx = Tx 1 − Tg ), H0 the structural relaxation exothermic heat, H1 , H2 and H3 the exothermic heats of the first, the second and the third crystallization, Hx (Hx = H1 + H2 + H3 ) the total exothermic heat of the crystallization. Alloys
Tg (K)
Tx 1 (K)
Tx 2 (K)
Tx 3 (K)
Tx (K)
H0 (J/g)
H1 (J/g)
H2 (J/g)
H3 (J/g)
Hx (J/g)
Bulk Ribbon
510.1 ± 1.3 515.3 ± 1.2
515.6 ± 1.2 522.9 ± 1.3
620.5 ± 1.5 620.5 ± 1.5
680.4 ± 1.6 680.6 ± 1.6
5.5 ± 0.5 7.6 ± 0.7
−5.3 ± 0.1 −5.7 ± 0.1
−29.1 ± 0.1 −31.5 ± 0.1
−69.8 ± 0.2 −73.7 ± 0.2
−50.2 ± 0.2 −54.6 ± 0.2
−149.1 ± 0.2 −159.8 ± 0.2
Table 2 Mechanical properties of the Al86 Ni6 Y4.5 Co2 La1.5 bulk and ribbon metallic alloys, including the maximum depth (hmax ) and the hardness (H). Loading rate (mN/s)
0.25 0.05 0.025 Average
Bulk
Ribbon
hmax (nm)
H (GPa)
hmax (nm)
H (GPa)
282.88 ± 3.05 291.45 ± 3.23 300.34 ± 3.46 291.56 ± 8.73
5.08 ± 0.09 4.87 ± 0.06 4.74 ± 0.09 4.90 ± 0.17
307.60 ± 2.70 316.53 ± 3.20 332.91 ± 3.09 319.01 ± 12.8
4.71 ± 0.07 4.58 ± 0.05 4.44 ± 0.08 4.58 ± 0.13
i.e., H0 = ˇf , where ˇ is a constant. Recently, an expression for the enthalpy release due to relaxation of defect-induced dilatational energy was proposed by Khonik and Kobelev [33], which also shows that the released enthalpy linearly decreases with the relative volume reduction. From the inset of Fig. 2, the released enthalpy of the bulk (ribbon) MG was calculated by integrating from 400 K to 510.1 K (515.3 K) with an accuracy of ±0.1 J/g. The H0 increases from 5.3 J/g (bulk sample) to 5.7 J/g (ribbon sample), i.e. a 7.5% change. This reflects that more free volume is frozen in the ribbon sample. 3.2. Loading rate effect Fig. 3 shows the load–displacement (P–h) curves of the Al86 Ni6 Y4.5 Co2 La1.5 bulk and ribbon MGs under nanoindentation tests with different loading rates (0.025 mN s−1 –0.25 mN s−1 ). With the exception of the curve at 0.25 mN s−1 , all the other curves are plotted on the same axes with their origins offset 50 nm for clarity of presentation. At the lower loading rate of 0.025 mN s−1 , pop-ins became sharper, more horizontal discontinuities. This trend was also observed in the Pd- [6] and Ti-rich [11] MGs. At the same loading rate, the serration behavior is more pronounced for the ribbon sample than that for the bulk sample (see Fig. 3(c)). Similar phenomenon of the ribbon alloys displaying more conspicuous serrations has been detected for many other MGs, such as Zr-Cu-Ni-Al [10] and Ni-Nb-Zr [34] systems. From Fig. 3(a) and (b), the maximum depth (hmax ) at the end of the load holding segment is measured to be larger in the ribbon than that in the bulk. The hardness H is obtained from the corresponding P–h curves based upon the Oliver and Pharr method [35], and summarized in Table 2. The H value decreases from 4.90 GPa (bulk sample) to 4.58 GPa (ribbon sample), i.e. a 6.5% change.
Fig. 3. The load-displacement curves at different loading rates (0.025 mN s−1 to 0.25 mN s−1 ) for the bulk alloy (a), and the ribbon alloy (b), and enlarged P–h curves for the portions as rectangled in (a) and (b) highlighting typical pop-in evolution with different loading rates (c).
4. Discussion 4.1. Correlation between frozen-in excess volume and hardness Further insights into the effect of the frozen-in excess volume on the mechanical properties of the Al86 Ni6 Y4.5 Co2 La1.5 bulk and ribbon MGs can be obtained from numerical simulations of P–h curves. In the free volume theory [36,37], the shear strain rate ␥˙ of MGs is determined by a combination of applied stress , temperature T and free volume accumulation, as described in the following equation:
=f ˙ exp
−
˛*
f
2w sinh
V 2kT
Gm
exp −
kT
(1)
˙ where where the shear strain rate ␥˙ can be expressed as =0.16 ˙ ε, ε˙ is the strain rate [18]. f is the volume fraction of the flow units, and commonly used as 1 when material is applied at low strain rate loading, ˛ is a geometrical factor between 0.5 and 1, ∗ is the critical (hard-sphere) free volume required for an atomic jump, f is the free volume of an atom, w is the frequency of atomic vibration (∼Debye frequency). Further, in Eq. (1), is the applied shear stress, V is the atomic volume (∼1.25∗ ), k is the Boltzmann’s constant (1.38 × 10−23 J/K), T is the temperature and the activation energy for an atomic jump, Gm is roughly estimated to be 8/2 G␥2C s ( C ∼0.0267, ∼3, ˝s ∼ 2∗ here) [25,38].
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Table 3 The estimated STZ volumes of the Al86 Ni6 Y4.5 Co2 La1.5 bulk and ribbon metallic alloys based on three different methods: the cooperative shearing model (CSM) [25], the rate-jump method (RJM) [16] and the dynamic-mechanical response (DMR) [17]. For comparison, the volume of icosahedral supercluster medium-range order (MRO) [26] structure model is also listed.
Fig. 4. Correlation between the hardness H and the normalized free volume f /˛∗ as given by the numerical solution of Eq. (3).
Considering the√shear stress is relevant to indention hardness, described as H ≈ 3 3 [39], at a fixed shear strain rate, Eq. (1) can be rearranged as √ ˛∗ Gm ˙ 6 3kT −1 exp H= + (2) sinh V f 2wf kT −3 /s, ˙ In the case of the current Al-rich MG, ␥∼10 w ∼ 9.37 × 1012 /s, ∗ ∼0.02 nm3 , V ∼0.025 nm3 , G ∼30 GPa and Gm ∼2.08 × 10−21 J (T is taken to be 300 K). Considering the absolute value of free volume in MGs, f , is rather difficult to be obtained, herein, the normalized free volume is adopted from Spaepen [36] as f /˛∗ . Correspondingly, the quantitative relationship between the normalized free volume f /˛∗ and hardness H is established as
H = 1.72 sin h−1 8.74 × 10−17 exp
˛∗ f
(3)
The numerical solution of Eq. (3) is plotted in Fig. 4, in which the correlation between the hardness, H, and the normalized free volume, f /˛∗ is obtained. Interestingly, such a relationship could be effectively confirmed in the reported data of hardness (H = 3.89 GPa) and normalized free volume (˛∗ /f = 38.8) of Al86.8 Ni3.7 Y9.5 [3,40]. Further, from Fig. 4, it is noted that, within the region of f /˛∗ ≈ 2.4%–2.7%, the curve is approximately linear, i.e. the hardness linearly decreases with the increase of the normalized free volume. Correspondingly, the hardness change from the bulk to the ribbon samples can be expressed as |bulk -ribbon | |Hbulk − Hribbon | f ≈ f Hbulk bulk
(4)
f
At present, it is almost impossible to obtain the absolute value of free volume in MGs. Previous works suggested that the relative change of frozen-in excess volume could be approximately treated as that of free volume per atomic volume [32,41,42]. Thus, from Eq. (4), we might as well calculate the hardness change between the bulk and the ribbon from the angle of the change of their structural relaxation exothermic heat. The hardness change is estimated to be ∼7.5% in the two samples, which is close to the experimental one (∼6.5%). This reflects an interconnection between the frozen-in excess volume and hardness. 4.2. STZs for plastic flow of Al-rich MGs To reveal the characteristics of STZs in MGs, to date, several main methods have been proposed: the cooperative shearing model (CSM) [25], the rate-jump method (RJM) [16] and the dynamicmechanical response (DMR) [17]. The DMR method was probing a
STZ (nm3 )
Models
Eqs.
CSM RJM DMR MRO
Eq. (6) Eq. (8) Eq. (11) V ≈ 2.1817a3
STZ (atoms)
Bulk
Ribbon
Bulk
Ribbon
5.00 2.77 0.27 2.60
5.05 3.59 0.29
250 218 13 216
252 282 14 216
subset of STZs activated during their pre-straining. Unlike the DMR method derived from the homogeneous deformation mode of MGs, the CSM and RJM methods are both based upon inhomogeneous flow mode of MGs. The CSM method based on the concept of the potential energy landscape was proposed to effectively interpret the plastic deformation of MGs well below Tg . RJM method also indicates its flow localization tendency while undergoing plastic deformation. And the RJM method is the further development of the CSM method by considering strain-rate sensitivity measurements in nanoindentation. Though it has been widely applied, RJM method has its limitations since the STZ volume can only be calculated from this method if strain rate sensitivity is greater than zero. It has not been confirmed that the STZ size of one certain composition might be changed under different experiment methods. Now one question arises very naturally: does the STZ size intrinsically exist or depend on the calculation method? Next, from the above methods, we begin to analyze the characteristics of STZs in Al-rich MGs. 4.2.1. CSM Normally, the formation of STZ is associated with the shear-flow energy barrier W. For an STZ at finite stress 0 < CT < C0, W can be defined as [25]:
W = 4RG0 C2 1 −
CT C0
3/2 ˝
(5)
where ˝ is the STZ volume, C is the average elastic limit (∼0.0267), is a correction factor arising from the matrix confinement (∼3). CT and C 0 are the threshold shear resistances at temperature T and 0 K. G0 is the shear modulus at 0 K. R actually varies from 1/4 to 2 /32 as CT decreases from C 0 to 0. For the cooperative shearing model (CSM) of Johnson and Samwer [25] from Eq. (5), the barrier W can be obtained: W = 8/2 C2 G˝ while T = Tg and CT = 0. Considering the glasstransition temperature of the amorphous material is recognized to be a good measure of the shear-flow barrier, W ≈ 37kTg [43], thus, the STZ volume can be determined by: ˝=
2 W 8 C2 G
≈ 9.8 × 10−3
Tg G
(6)
From Table 1, Tg values are taken as 510.1 K and 515.3 K, respectively. According to Eq. (6), the STZ volumes are estimated to be 5.00 nm3 (bulk sample) and 5.05 nm3 (ribbon sample), respectively, as listed in Table 3. By comparison, it can be noted that the STZ volume of the Al86 Ni6 Y4.5 Co2 La1.5 bulk sample is very close to that of the ribbon sample. The average atomic volume (= Mi /( i NA )) was calculated based on the molar atomic weight (Mi ) and density ( i ) of the i-th component element, where NA is Avogadro’s number. Due to the average atomic volume of 0.02 nm3 in Al-rich MGs, we obtained their effective numbers of atoms participating in a STZ as 250 atoms for the bulk sample and 252 atoms for the ribbon sample.
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4.2.3. DMR The first quantitative model of STZ behavior was developed by Argon, in which the free energy F for STZ activation was calculated in terms of the elastic constants of the MGs as [12,17,44]
F =
1 0 2 (1+ ) 2 7 − 5 + ˇ + 30 (1 − ) 9 (1 − ) 2␥0 G
× G02 ˝
(10)
where is the Poisson’s ratio, 0 is the resistance of the STZ itself to shear, G is the shear modulus, 0 /G = 0.027 [44]. ˇ2 relates the hydrostatic stress to shear strain and is approximately equal to 1. The characteristic strain, 0 ≈ 0.2 [17]. The characteristic activation energy F would be equal to EC (=ATC , where the A ≈ 3.13 × 10−3 eV/K, TC is the value of the crystallization onset temperature)[45,46]. Thus, the volume of the STZ is changed as: Fig. 5. Logarithmic hardness vs logarithmic equivalent strain rates, are determined for the strain rate sensitivity, where in identification of STZ volumes of plastic flow of bulk and ribbon MGs.
4.2.2. RJM Based on Eq. (5), Pan et al. [16] proposed that the activation volume V* can be obtained by direct differentiation of the activation energy W, V* = −(∂W/∂ CT ). Thus, the volume of the STZ can be expressed as ˝=−
C0
6RG0 ␥2C
1−
CT C0
1/2 V
∗
(7)
Here the constant R is approximately equal to 1/4. Both CT and C 0 can be obtained from the related relation [25]: CT /GT = C 0 C 1 (T/Tg )2/3 , where C 0 = 0.036, C 1 = 0.016, G0 = 1.1GT , GT is the threshold shear resistance at temperature T (unit: K). In Eq. (7), V* can be derived from the strain rate sensitivity, V* =kT/(m), under nanoindentation tests. Thus, the volume of the STZ is changed as ˝=
kT 2 2R G0 ␥ mH √ C C0 3
1−
CT C0
(8)
1/2
˙ where m is the strain rate sensitivity (m = ∂ log H/∂ log , H P/A(hc )) and is the critical shear stress upon the traditional ten√ sile or compressive tests, ≈ H/(3 3) (H was detected in Table 2). The equivalent strain rate is from: 1 dh h˙ 1 ˙ ε= = = h dt h 2
P˙ h˙ − P H
≈
1 P˙ 2P
(9)
The corresponding strain rate sensitivity m is derived by lining up the hardness vs equivalent strain rate in a log-log scale and measuring the slope of the straight line (Fig. 5). In Fig. 5, the error bars represent the statistical variations of the hardness from the 16 indents at each loading rate. The hardness increases linearly with the increase in loading rate, consistent with the results in Fig. 3 and Table 2. The values of m are from 0.029 in the bulk sample to 0.024 in the ribbon sample. Combining Eq. (8) with (9), we have calculated the STZ volume in Al-rich MGs, as listed in Table 3. The STZ volumes of the Al86 Ni6 Y4.5 Co2 La1.5 MG vary from 2.77 nm3 (for the bulk sample) to 3.59 nm3 (for the ribbon sample). According to the dense-packing hard-sphere model of MGs, an average atomic radius statistically
1/3
can be estimated as R = Ai ri3 = 1.447 Å, in which Ai and ri are the atomic fraction and the atomic radius of each element, respectively. Correspondingly, we get the STZ sizes of about 218 atoms (for the bulk sample) and 282 atoms (for the ribbon sample).
˝=
3.13 × 10-3 × TC 41+5 +0.0675 90(1− )
×0.04G
(11)
In Eq. (11), generally, for Al-rich MGs, = 0.34, G = 30 GPa. From Table 1, the first crystallization onset temperatures of Al-rich bulk and ribbons MGs under investigation are about 515.6 K and 522.9 K, respectively. Thus, the STZ volumes ˝ of the Al86 Ni6 Y4.5 Co2 La1.5 MG are estimated to be 0.27–0.29 nm3 for the two samples. Considering the average atomic volume of 0.02 nm3 in Al-rich MGs, we obtained the effective numbers of atoms participating in an STZ of the bulk and ribbon as 13–14 atoms, as listed in Table 3. Recently, Atzmon and Ju [40] studied an elastic relaxation in a bent Al86.8 Ni3.7 Y9.5 MG, and modeled the relaxation time to estimate the value of STZ volume to be about 0.28–0.42 nm3 . They further quantized the sizes of STZs in the range of 14–21 atoms. These values are a little higher than those of the Al86 Ni6 Y4.5 Co2 La1.5 MGs estimated by DMR. From Table 3, it is clear that, the values of STZ volume calculated are much sensitive to the flow model used, i.e. 5.00–5.05 nm3 (CSM method), 2.77–3.59 nm3 (RJM method) and 0.27–0.29 nm3 (DMR method). The number of atoms n has a wide range for the bulk and ribbon MGs, i.e. 250–252 atoms (CSM method), 218–282 atoms (RJM method) and 13–14 atoms (DMR method). The obtained STZ size in turn explains the more conspicuous serrations in ribbon with large-sized STZ. Obviously, 30% enlargement on the STZ volume relying on the RJM method, from 2.77 to 3.59 nm3 , could explain the significant improvement of ductility in the ribbon one [47,48]. Frozen-in excess volume plays an important role in the evolution of STZs by providing fertile regions. Annealing effect was continuously imposed on the bulk, eliminating frozen-in volume. However, it does not reach an agreement on the correlation between the frozen-in excess volume content and STZ volume [48–50]. Pan et al. [48] found that as annealing embrittles the sample, the derived STZ size decreases. Recently, Jiang et al. [49] also demonstrated that there was a positive interplay between shear transformations and frozen-in excess volume. The development of amorphous plasticity was dominated by STZs, and the frozen-in excess volume fertilized shear transformations that further contribute to plasticity. While Choi et al. [50] reported a negative effect of frozen-in excess volume on STZ volume. Here, an enhancement of frozen-in excess volume on the STZ volume is reported, more investigations still need to be carried out to look insights into the frozen-in excess volume effect on STZ volume. What’s more, the STZ volumes obtained from CSM method are about 1.5 times and 15 times of those from the RJM method and DMR method, respectively. This difference could be attributed to the characteristics of the calculation methods. The RJM method is based on plastic flow, which according to the CSM method, corresponds to percolations of the meta-basin. Therefore, it is not surprising to obtain a very large number of atoms for the estimated STZ size. While the DMR method focuses on the ‘pop-in’ phenomena
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prior to the steady plastic flow, a much smaller number of 10–20 atoms is obtained. In this section, we will provide a comparison about the effectiveness of these flow models for Al-rich MGs. Note that, in essence, the origin of STZs is related to the closely packed atomic cluster. For comparison, it becomes important to provide the possible eigenvalue about the STZs size in Al-rich MGs from the angle of topological glassy structure. Icosahedral cluster structure is regarded as one of the most recognized frame structure. And the local icosahedral order was observed in metallic glasses by means of Angstrom-beam electron diffraction of a single icosahedron [51]. For the Al-transition metal (TM)-rare earth (RE) glassy alloys, it has been recognized that there is the icosahedral supercluster medium-range order (MRO) structure based upon RE- or TM-centered clusters with the icosahedral fivefold packing [26,52]. In the icosahedral supercluster, there are 12 RE(TM)-centered clusters on the vertex of the icosahedral supercluster, one RE(TM)-centered clusters in the center, TM(RE) atoms located at RE(TM)-centered cluster tetrahedral interstices in the icosahedral supercluster [26]. Here, we set the edge length of an icosahedral supercluster MRO as a (the distance between the RE(TM)-centered clusters on the vertex and the RE(TM)-centered can be calculated by a clusters in the center), and then the cluster √ cubic box with minimum edge length L=(1+ 5)a/2. The volume is √ 3L2 − a2 /12 ≈ 2.1817a3 for V=20 × (1/3) × (1/2) × ( 3/2)a2 × an icosahedral supercluster MRO. Thus, for a given a ∼1.06 nm, the volume V of the Al86 Ni6 Y4.5 Co2 La1.5 MG is determined to be 2.60 nm3 and the number of atoms in the MRO is ∼216. In contrast, only the range of 2.77–3.59 nm3 values is very close to the volume value of 2.60 nm3 obtained by MRO. The type of MRO clusters could have a potential association with the STZ size. More experimental work and computational simulation need to be carried out to further gain insight into the intrinsic correlation between the structure unit and deformation unit. 5. Conclusion The deformation behavior of the Al86 Ni6 Y4.5 Co2 La1.5 bulk and ribbon MGs have been investigated under nanoindentation. It was indicated that from ribbon to bulk sample, with the decrease of frozen-in volume, the serration behavior becomes inconspicuous together with the increase of hardness. We have estimated the STZ sizes based on three different models: CSM, RJM and DMR. It was found that the STZ volumes, calculated by the RJM, increase from 2.77 nm3 in the bulk to 3.59 nm3 in the ribbon. However, the STZ volumes are calculated to be close for the two samples as 5.00–5.05 nm3 using CSM method and 0.27–0.29 nm3 using DMR method. On the whole, the STZ volumes from RJM method is in agreement with 2.60 nm3 obtained from the icosahedral supercluster MRO structure model in Al-rich MGs. Moreover, an increase in the STZ volumes from the bulk to the ribbon was analyzed in terms of the frozen-in excess volume content. We believe that these results may improve the understanding of the plasticity mechanism of MGs.
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This work was supported by the National Natural Science Foundation of China (Nos. 51131006 and 51471166) and the National Key Research and Development Program of China (No. 2016YFB1100204). Special thanks are indebted to Prof. J. Xu and Dr. Z.Q. Song for helpful discussion, Prof. H.W. Yang and Dr. F.X. Bai
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Deformation behavior of Al-rich metallic glasses under nanoindentation Hui Guo, Chuanbin Jiang, Baijun Yang, Jianqiang Wang ∗ Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China
a r t i c l e
i n f o
Article history: Received 26 August 2016 Received in revised form 15 October 2016 Accepted 18 October 2016 Available online xxx Keywords: Metallic glasses Inhomogeneous deformation Free volume Nanoindentation
a b s t r a c t To clarify the deformation behavior of Al-rich metallic glasses (MGs), two kinds of Al-rich MGs (i.e. bulk and ribbon samples) with different frozen-in excess volume have been analyzed under nanoindentation. It was found that, with the decrease of frozen-in excess volume, the serration behavior becomes inconspicuous together with the increase of hardness. Further, shear transformation zones (STZs), related to the occurrence of shear banding, have been evaluated by different methods: the cooperative shearing model (CSM), the rate-jump method (RJM) and the dynamic-mechanical response (DMR). In contrast, the STZ volumes, calculated by the RJM, increase from 2.77 nm3 in the bulk to 3.59 nm3 in the ribbon, which are in good agreement with 2.60 nm3 obtained from the icosahedral supercluster medium-range order structure model in Al-rich MGs. This result reflects that an intrinsic correlation exists between the formation of STZs and the medium-range orders (MROs). Moreover, the variation trend of the STZ volume was analyzed in terms of the frozen-in excess volume content. © 2017 Published by Elsevier Ltd on behalf of The editorial office of Journal of Materials Science & Technology.
1. Introduction Aluminum-rich metallic glasses (MGs) have a great potential to be widely used for excellent mechanical properties [1], such as the ultrahigh specific strength, good corrosion resistance [2] and rather low cost. However, similar to conventional MG-forming alloys, there also are brittle behavior caused by highly localized shear banding deformation in Al-rich MGs. To understand the deformation mechanism of Al-rich MGs, a large number of studies have been devoted to the shear banding in melt-spun Al-rich MG ribbons [3,4]. These studies of the deformation behavior are only based upon the Al-rich MG ribbons due to very limited glass formation ability in this class of materials. Since Al-rich bulk metallic glasses (BMGs) with a diameter of 1 mm have been obtained in 2009 [5], they provided a new opportunity for the comprehensive and in-depth understanding of the deformation mechanism. Nanoindentation is one of effective methods for ascertaining the deformation behavior in MGs by its probe with high spatiotemporal and force resolution. Under loading, there are the serrated flow or the pop-in events related to the nucleation and propagation of shear bands in a number of Zr-, Pd- and Cu-based BMGs [6,7]. The
∗ Corresponding author. E-mail address: [email protected] (J. Wang).
characteristics of the serrations are strongly dependent upon the loading rates: a lower loading rate promotes more conspicuous serrations, while a higher loading rate suppresses the appearance of the serrations [6]. This can also be described by the competition between the shear-banding dynamics and the applied rate [8,9]. For MG ribbon and bulk samples with the same composition, more conspicuous serrations appear in ribbon samples containing more concentration of frozen-in volume [10,11]. During deformation of MGs, the sites with larger frozen-in excess volume are easier to form shear transformation zones (STZs), and the agglomeration of STZs evolves into the nucleation site of a shear band [10]. These shear bands are generated and propagated finally contributing to the overall plastic deformation of MGs [12]. The formation of STZs is a key issue in understanding the deformation behavior of MGs. The STZs are the fundamental unit of plasticity, in the form of a small cluster of randomly close-packed atoms that spontaneously and cooperatively reorganize under the action of an applied shear stress [12–14]. It has been recognized that sufficiently small STZs could lead to brittle fracture [15,16]. Recently, Ju et al. [17] revealed a quantized hierarchy of STZs by quasistatic measurements of anelastic relaxation in Al-rich MGs. These reflect the correlation between STZ size and deformation transition mode. However, how many atoms would comprise an STZ remains a controversial issue in MGs. It has been reported that there is a broad distribution of STZ sizes in MGs, which can be
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inferred from a number of experiments [16–20] and simulations [13,21–24], e.g., from a few atoms to several hundred atoms. Moreover, even similar techniques could present considerably different results. For example, in nanoindentation experiments, some studies [16] showed the STZ size of few hundred atoms, while others [17] demonstrated a much smaller STZ size around 20 atoms. To potentially tackle the above problems, in the present study, we selected two kinds of Al-rich MGs (i.e. bulk and ribbon samples) with different frozen-in excess volumes for comparison. The deformation behavior of the two samples was analyzed under nanoindentation. We have calculated the STZ sizes based upon three different methods: the cooperative shearing model (CSM) [25], the rate-jump method (RJM) [16] and the dynamicmechanical response (DMR) [17]. These values have been compared with those derived from an icosahedral supercluster mediumrange order (MRO) structure model in the Al-RE-TM [26]. Finally, an intrinsic correlation between the formation of STZs and the MRO structure was suggested in Al-rich MGs.
Fig. 1. XRD patterns of the Al86 Ni6 Y4.5 Co2 La1.5 bulk and ribbon MGs.
2. Materials and methods The Al86 Ni6 Y4.5 Co2 La1.5 master alloy ingots were prepared by arc-melting a mixture of the constituent elements with a purity of better than 99.99% under a Ti-gettered argon atmosphere. In order to ensure compositional homogeneity, the alloy ingots were melted four times. The cylindrical BMG rods of 1 mm in diameter were produced in a copper-mold. For comparison, rapidly solidified ribbons with 0.02 mm × 3 mm were prepared by a single roller melt-spinning technique in an argon atmosphere. The amorphous structure of both bulk and ribbon alloys was confirmed by X-ray diffraction (XRD) using a Rigaku D/max 2400 diffractometer (Tokyo, Japan) with monochromated CuK␣ radiation (=0.1542 nm). The thermal analysis of the bulk and ribbon alloys was characterized using a differential scanning calorimetry (DSC) in a Q2000 under flowing purified argon. DSC was run two times for each alloy from 300 to 773 K at a constant heating rate of 40 K/min. By taking the second scan as a base line, any thermal effects from the structural evolution during heating were investigated. The mechanical properties were characterized by MTS Nanoindenter XP with a Berkovich diamond indenter with a tip radius of ∼20 nm. For the bulk alloy, the cross-section was used to be the indentation surface, while for the ribbon alloy, indentation was performed on the wheel side. Prior to nanoindentation tests, the surfaces of the two alloys mounted in epoxy resin were mechanically polished to a mirror finishing using magnesium oxide solution. All the tests were conducted in a load-controlled mode with a maximum load of 10 mN at loading rates from 0.025 to 0.25 mN/s, and data acquisition rates as high as 20 points per second. At least 16 indents at each loading rate were performed for each alloy with the separation between adjacent indents of 20 m. At 90% unloading, a dwell period of 25 s was imposed to correct for any thermal drift in the system, which was less than 0.05 nm/s. The load–displacement curves were subsequently analyzed and compared as a function of loading rates. 3. Results 3.1. Structural characterization Fig. 1 shows the XRD patterns of the Al86 Ni6 Y4.5 Co2 La1.5 bulk and ribbon MGs. The broad diffractions with no crystalline Bragg diffraction peaks demonstrate the amorphous structure of the two alloys. It has been reported that Al86 Ni6 Y4.5 Co2 La1.5 alloy has a good glass-forming ability, and the BMG rod with the maximum diameter of 1.5 mm has been reported [27,28].
Fig. 2. DSC curves of the Al86 Ni6 Y4.5 Co2 La1.5 bulk and ribbon MGs at a heating rate of 40 K/min. A zoomed-in view of a small region around the Tg is exhibited in the inset of Fig. 2.
Fig. 2 represents the DSC curves of the bulk and ribbon Al86 Ni6 Y4.5 Co2 La1.5 MGs that were normalized using the base lines at a heating rate of 40 K/min. A similar thermal behavior with three obvious exothermic peaks is shown in the two samples. The total exothermic heat of crystallization reactions, Hx (Hx = H1 + H2 + H3 ) is measured to be −149.1 and −159.8 J/g for the bulk and ribbon alloys, respectively. Note that no obvious endothermic transitions can be discerned in Fig. 2. For most of the Al-based MGs, it was not easy to distinguish a glass transition signal from the DSC curves, since the supercooled liquid region was so small that the glass transition signals always partially or even completely overlapped with the crystallization signals [29]. This phenomenon was also observed in the present Al86 Ni6 Y4.5 Co2 La1.5 MG samples. The typical thermodynamic properties are summarized in Table 1. Obviously, the glass transition temperature Tg for the ribbon sample is slightly larger than that for the bulk sample. Considering the bulk and ribbon samples are produced at different cooling rate q, it indicates that the increase in q from about 103 K/s (for bulk) to 106 K/s (for ribbon) causes the increase in Tg . This is in agreement with the relationship of Tg ∝q [30,31]. In order to ascertain the difference in the irreversible structural relaxation behavior between the bulk and the ribbon samples, a zoomed-in view of a small region around Tg is shown in the inset of Fig. 2. The sub-Tg region for the DSC trace of MGs corresponds to the enthalpy released during structure relaxation, which strongly links with the content of frozen-in volume. As Slipenyuk and Eckert experimentally verified [32], the structural relaxation exothermic heat (H0 ) is proportional to the relative change of frozen-in excess volume (f ) frozen in the amorphous alloy,
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Table 1 Thermodynamic properties of the Al86 Ni6 Y4.5 Co2 La1.5 bulk and ribbon MGs measured from DSC. Tg denotes the glass-transition temperature, Tx 1 , Tx 2 and Tx 3 the first, the second and the third crystallization onset temperatures, Tx the supercooled liquid region (Tx = Tx 1 − Tg ), H0 the structural relaxation exothermic heat, H1 , H2 and H3 the exothermic heats of the first, the second and the third crystallization, Hx (Hx = H1 + H2 + H3 ) the total exothermic heat of the crystallization. Alloys
Tg (K)
Tx 1 (K)
Tx 2 (K)
Tx 3 (K)
Tx (K)
H0 (J/g)
H1 (J/g)
H2 (J/g)
H3 (J/g)
Hx (J/g)
Bulk Ribbon
510.1 ± 1.3 515.3 ± 1.2
515.6 ± 1.2 522.9 ± 1.3
620.5 ± 1.5 620.5 ± 1.5
680.4 ± 1.6 680.6 ± 1.6
5.5 ± 0.5 7.6 ± 0.7
−5.3 ± 0.1 −5.7 ± 0.1
−29.1 ± 0.1 −31.5 ± 0.1
−69.8 ± 0.2 −73.7 ± 0.2
−50.2 ± 0.2 −54.6 ± 0.2
−149.1 ± 0.2 −159.8 ± 0.2
Table 2 Mechanical properties of the Al86 Ni6 Y4.5 Co2 La1.5 bulk and ribbon metallic alloys, including the maximum depth (hmax ) and the hardness (H). Loading rate (mN/s)
0.25 0.05 0.025 Average
Bulk
Ribbon
hmax (nm)
H (GPa)
hmax (nm)
H (GPa)
282.88 ± 3.05 291.45 ± 3.23 300.34 ± 3.46 291.56 ± 8.73
5.08 ± 0.09 4.87 ± 0.06 4.74 ± 0.09 4.90 ± 0.17
307.60 ± 2.70 316.53 ± 3.20 332.91 ± 3.09 319.01 ± 12.8
4.71 ± 0.07 4.58 ± 0.05 4.44 ± 0.08 4.58 ± 0.13
i.e., H0 = ˇf , where ˇ is a constant. Recently, an expression for the enthalpy release due to relaxation of defect-induced dilatational energy was proposed by Khonik and Kobelev [33], which also shows that the released enthalpy linearly decreases with the relative volume reduction. From the inset of Fig. 2, the released enthalpy of the bulk (ribbon) MG was calculated by integrating from 400 K to 510.1 K (515.3 K) with an accuracy of ±0.1 J/g. The H0 increases from 5.3 J/g (bulk sample) to 5.7 J/g (ribbon sample), i.e. a 7.5% change. This reflects that more free volume is frozen in the ribbon sample. 3.2. Loading rate effect Fig. 3 shows the load–displacement (P–h) curves of the Al86 Ni6 Y4.5 Co2 La1.5 bulk and ribbon MGs under nanoindentation tests with different loading rates (0.025 mN s−1 –0.25 mN s−1 ). With the exception of the curve at 0.25 mN s−1 , all the other curves are plotted on the same axes with their origins offset 50 nm for clarity of presentation. At the lower loading rate of 0.025 mN s−1 , pop-ins became sharper, more horizontal discontinuities. This trend was also observed in the Pd- [6] and Ti-rich [11] MGs. At the same loading rate, the serration behavior is more pronounced for the ribbon sample than that for the bulk sample (see Fig. 3(c)). Similar phenomenon of the ribbon alloys displaying more conspicuous serrations has been detected for many other MGs, such as Zr-Cu-Ni-Al [10] and Ni-Nb-Zr [34] systems. From Fig. 3(a) and (b), the maximum depth (hmax ) at the end of the load holding segment is measured to be larger in the ribbon than that in the bulk. The hardness H is obtained from the corresponding P–h curves based upon the Oliver and Pharr method [35], and summarized in Table 2. The H value decreases from 4.90 GPa (bulk sample) to 4.58 GPa (ribbon sample), i.e. a 6.5% change.
Fig. 3. The load-displacement curves at different loading rates (0.025 mN s−1 to 0.25 mN s−1 ) for the bulk alloy (a), and the ribbon alloy (b), and enlarged P–h curves for the portions as rectangled in (a) and (b) highlighting typical pop-in evolution with different loading rates (c).
4. Discussion 4.1. Correlation between frozen-in excess volume and hardness Further insights into the effect of the frozen-in excess volume on the mechanical properties of the Al86 Ni6 Y4.5 Co2 La1.5 bulk and ribbon MGs can be obtained from numerical simulations of P–h curves. In the free volume theory [36,37], the shear strain rate ␥˙ of MGs is determined by a combination of applied stress , temperature T and free volume accumulation, as described in the following equation:
=f ˙ exp
−
˛*
f
2w sinh
V 2kT
Gm
exp −
kT
(1)
˙ where where the shear strain rate ␥˙ can be expressed as =0.16 ˙ ε, ε˙ is the strain rate [18]. f is the volume fraction of the flow units, and commonly used as 1 when material is applied at low strain rate loading, ˛ is a geometrical factor between 0.5 and 1, ∗ is the critical (hard-sphere) free volume required for an atomic jump, f is the free volume of an atom, w is the frequency of atomic vibration (∼Debye frequency). Further, in Eq. (1), is the applied shear stress, V is the atomic volume (∼1.25∗ ), k is the Boltzmann’s constant (1.38 × 10−23 J/K), T is the temperature and the activation energy for an atomic jump, Gm is roughly estimated to be 8/2 G␥2C s ( C ∼0.0267, ∼3, ˝s ∼ 2∗ here) [25,38].
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Table 3 The estimated STZ volumes of the Al86 Ni6 Y4.5 Co2 La1.5 bulk and ribbon metallic alloys based on three different methods: the cooperative shearing model (CSM) [25], the rate-jump method (RJM) [16] and the dynamic-mechanical response (DMR) [17]. For comparison, the volume of icosahedral supercluster medium-range order (MRO) [26] structure model is also listed.
Fig. 4. Correlation between the hardness H and the normalized free volume f /˛∗ as given by the numerical solution of Eq. (3).
Considering the√shear stress is relevant to indention hardness, described as H ≈ 3 3 [39], at a fixed shear strain rate, Eq. (1) can be rearranged as √ ˛∗ Gm ˙ 6 3kT −1 exp H= + (2) sinh V f 2wf kT −3 /s, ˙ In the case of the current Al-rich MG, ␥∼10 w ∼ 9.37 × 1012 /s, ∗ ∼0.02 nm3 , V ∼0.025 nm3 , G ∼30 GPa and Gm ∼2.08 × 10−21 J (T is taken to be 300 K). Considering the absolute value of free volume in MGs, f , is rather difficult to be obtained, herein, the normalized free volume is adopted from Spaepen [36] as f /˛∗ . Correspondingly, the quantitative relationship between the normalized free volume f /˛∗ and hardness H is established as
H = 1.72 sin h−1 8.74 × 10−17 exp
˛∗ f
(3)
The numerical solution of Eq. (3) is plotted in Fig. 4, in which the correlation between the hardness, H, and the normalized free volume, f /˛∗ is obtained. Interestingly, such a relationship could be effectively confirmed in the reported data of hardness (H = 3.89 GPa) and normalized free volume (˛∗ /f = 38.8) of Al86.8 Ni3.7 Y9.5 [3,40]. Further, from Fig. 4, it is noted that, within the region of f /˛∗ ≈ 2.4%–2.7%, the curve is approximately linear, i.e. the hardness linearly decreases with the increase of the normalized free volume. Correspondingly, the hardness change from the bulk to the ribbon samples can be expressed as |bulk -ribbon | |Hbulk − Hribbon | f ≈ f Hbulk bulk
(4)
f
At present, it is almost impossible to obtain the absolute value of free volume in MGs. Previous works suggested that the relative change of frozen-in excess volume could be approximately treated as that of free volume per atomic volume [32,41,42]. Thus, from Eq. (4), we might as well calculate the hardness change between the bulk and the ribbon from the angle of the change of their structural relaxation exothermic heat. The hardness change is estimated to be ∼7.5% in the two samples, which is close to the experimental one (∼6.5%). This reflects an interconnection between the frozen-in excess volume and hardness. 4.2. STZs for plastic flow of Al-rich MGs To reveal the characteristics of STZs in MGs, to date, several main methods have been proposed: the cooperative shearing model (CSM) [25], the rate-jump method (RJM) [16] and the dynamicmechanical response (DMR) [17]. The DMR method was probing a
STZ (nm3 )
Models
Eqs.
CSM RJM DMR MRO
Eq. (6) Eq. (8) Eq. (11) V ≈ 2.1817a3
STZ (atoms)
Bulk
Ribbon
Bulk
Ribbon
5.00 2.77 0.27 2.60
5.05 3.59 0.29
250 218 13 216
252 282 14 216
subset of STZs activated during their pre-straining. Unlike the DMR method derived from the homogeneous deformation mode of MGs, the CSM and RJM methods are both based upon inhomogeneous flow mode of MGs. The CSM method based on the concept of the potential energy landscape was proposed to effectively interpret the plastic deformation of MGs well below Tg . RJM method also indicates its flow localization tendency while undergoing plastic deformation. And the RJM method is the further development of the CSM method by considering strain-rate sensitivity measurements in nanoindentation. Though it has been widely applied, RJM method has its limitations since the STZ volume can only be calculated from this method if strain rate sensitivity is greater than zero. It has not been confirmed that the STZ size of one certain composition might be changed under different experiment methods. Now one question arises very naturally: does the STZ size intrinsically exist or depend on the calculation method? Next, from the above methods, we begin to analyze the characteristics of STZs in Al-rich MGs. 4.2.1. CSM Normally, the formation of STZ is associated with the shear-flow energy barrier W. For an STZ at finite stress 0 < CT < C0, W can be defined as [25]:
W = 4RG0 C2 1 −
CT C0
3/2 ˝
(5)
where ˝ is the STZ volume, C is the average elastic limit (∼0.0267), is a correction factor arising from the matrix confinement (∼3). CT and C 0 are the threshold shear resistances at temperature T and 0 K. G0 is the shear modulus at 0 K. R actually varies from 1/4 to 2 /32 as CT decreases from C 0 to 0. For the cooperative shearing model (CSM) of Johnson and Samwer [25] from Eq. (5), the barrier W can be obtained: W = 8/2 C2 G˝ while T = Tg and CT = 0. Considering the glasstransition temperature of the amorphous material is recognized to be a good measure of the shear-flow barrier, W ≈ 37kTg [43], thus, the STZ volume can be determined by: ˝=
2 W 8 C2 G
≈ 9.8 × 10−3
Tg G
(6)
From Table 1, Tg values are taken as 510.1 K and 515.3 K, respectively. According to Eq. (6), the STZ volumes are estimated to be 5.00 nm3 (bulk sample) and 5.05 nm3 (ribbon sample), respectively, as listed in Table 3. By comparison, it can be noted that the STZ volume of the Al86 Ni6 Y4.5 Co2 La1.5 bulk sample is very close to that of the ribbon sample. The average atomic volume (= Mi /( i NA )) was calculated based on the molar atomic weight (Mi ) and density ( i ) of the i-th component element, where NA is Avogadro’s number. Due to the average atomic volume of 0.02 nm3 in Al-rich MGs, we obtained their effective numbers of atoms participating in a STZ as 250 atoms for the bulk sample and 252 atoms for the ribbon sample.
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4.2.3. DMR The first quantitative model of STZ behavior was developed by Argon, in which the free energy F for STZ activation was calculated in terms of the elastic constants of the MGs as [12,17,44]
F =
1 0 2 (1+ ) 2 7 − 5 + ˇ + 30 (1 − ) 9 (1 − ) 2␥0 G
× G02 ˝
(10)
where is the Poisson’s ratio, 0 is the resistance of the STZ itself to shear, G is the shear modulus, 0 /G = 0.027 [44]. ˇ2 relates the hydrostatic stress to shear strain and is approximately equal to 1. The characteristic strain, 0 ≈ 0.2 [17]. The characteristic activation energy F would be equal to EC (=ATC , where the A ≈ 3.13 × 10−3 eV/K, TC is the value of the crystallization onset temperature)[45,46]. Thus, the volume of the STZ is changed as: Fig. 5. Logarithmic hardness vs logarithmic equivalent strain rates, are determined for the strain rate sensitivity, where in identification of STZ volumes of plastic flow of bulk and ribbon MGs.
4.2.2. RJM Based on Eq. (5), Pan et al. [16] proposed that the activation volume V* can be obtained by direct differentiation of the activation energy W, V* = −(∂W/∂ CT ). Thus, the volume of the STZ can be expressed as ˝=−
C0
6RG0 ␥2C
1−
CT C0
1/2 V
∗
(7)
Here the constant R is approximately equal to 1/4. Both CT and C 0 can be obtained from the related relation [25]: CT /GT = C 0 C 1 (T/Tg )2/3 , where C 0 = 0.036, C 1 = 0.016, G0 = 1.1GT , GT is the threshold shear resistance at temperature T (unit: K). In Eq. (7), V* can be derived from the strain rate sensitivity, V* =kT/(m), under nanoindentation tests. Thus, the volume of the STZ is changed as ˝=
kT 2 2R G0 ␥ mH √ C C0 3
1−
CT C0
(8)
1/2
˙ where m is the strain rate sensitivity (m = ∂ log H/∂ log , H P/A(hc )) and is the critical shear stress upon the traditional ten√ sile or compressive tests, ≈ H/(3 3) (H was detected in Table 2). The equivalent strain rate is from: 1 dh h˙ 1 ˙ ε= = = h dt h 2
P˙ h˙ − P H
≈
1 P˙ 2P
(9)
The corresponding strain rate sensitivity m is derived by lining up the hardness vs equivalent strain rate in a log-log scale and measuring the slope of the straight line (Fig. 5). In Fig. 5, the error bars represent the statistical variations of the hardness from the 16 indents at each loading rate. The hardness increases linearly with the increase in loading rate, consistent with the results in Fig. 3 and Table 2. The values of m are from 0.029 in the bulk sample to 0.024 in the ribbon sample. Combining Eq. (8) with (9), we have calculated the STZ volume in Al-rich MGs, as listed in Table 3. The STZ volumes of the Al86 Ni6 Y4.5 Co2 La1.5 MG vary from 2.77 nm3 (for the bulk sample) to 3.59 nm3 (for the ribbon sample). According to the dense-packing hard-sphere model of MGs, an average atomic radius statistically
1/3
can be estimated as R = Ai ri3 = 1.447 Å, in which Ai and ri are the atomic fraction and the atomic radius of each element, respectively. Correspondingly, we get the STZ sizes of about 218 atoms (for the bulk sample) and 282 atoms (for the ribbon sample).
˝=
3.13 × 10-3 × TC 41+5 +0.0675 90(1− )
×0.04G
(11)
In Eq. (11), generally, for Al-rich MGs, = 0.34, G = 30 GPa. From Table 1, the first crystallization onset temperatures of Al-rich bulk and ribbons MGs under investigation are about 515.6 K and 522.9 K, respectively. Thus, the STZ volumes ˝ of the Al86 Ni6 Y4.5 Co2 La1.5 MG are estimated to be 0.27–0.29 nm3 for the two samples. Considering the average atomic volume of 0.02 nm3 in Al-rich MGs, we obtained the effective numbers of atoms participating in an STZ of the bulk and ribbon as 13–14 atoms, as listed in Table 3. Recently, Atzmon and Ju [40] studied an elastic relaxation in a bent Al86.8 Ni3.7 Y9.5 MG, and modeled the relaxation time to estimate the value of STZ volume to be about 0.28–0.42 nm3 . They further quantized the sizes of STZs in the range of 14–21 atoms. These values are a little higher than those of the Al86 Ni6 Y4.5 Co2 La1.5 MGs estimated by DMR. From Table 3, it is clear that, the values of STZ volume calculated are much sensitive to the flow model used, i.e. 5.00–5.05 nm3 (CSM method), 2.77–3.59 nm3 (RJM method) and 0.27–0.29 nm3 (DMR method). The number of atoms n has a wide range for the bulk and ribbon MGs, i.e. 250–252 atoms (CSM method), 218–282 atoms (RJM method) and 13–14 atoms (DMR method). The obtained STZ size in turn explains the more conspicuous serrations in ribbon with large-sized STZ. Obviously, 30% enlargement on the STZ volume relying on the RJM method, from 2.77 to 3.59 nm3 , could explain the significant improvement of ductility in the ribbon one [47,48]. Frozen-in excess volume plays an important role in the evolution of STZs by providing fertile regions. Annealing effect was continuously imposed on the bulk, eliminating frozen-in volume. However, it does not reach an agreement on the correlation between the frozen-in excess volume content and STZ volume [48–50]. Pan et al. [48] found that as annealing embrittles the sample, the derived STZ size decreases. Recently, Jiang et al. [49] also demonstrated that there was a positive interplay between shear transformations and frozen-in excess volume. The development of amorphous plasticity was dominated by STZs, and the frozen-in excess volume fertilized shear transformations that further contribute to plasticity. While Choi et al. [50] reported a negative effect of frozen-in excess volume on STZ volume. Here, an enhancement of frozen-in excess volume on the STZ volume is reported, more investigations still need to be carried out to look insights into the frozen-in excess volume effect on STZ volume. What’s more, the STZ volumes obtained from CSM method are about 1.5 times and 15 times of those from the RJM method and DMR method, respectively. This difference could be attributed to the characteristics of the calculation methods. The RJM method is based on plastic flow, which according to the CSM method, corresponds to percolations of the meta-basin. Therefore, it is not surprising to obtain a very large number of atoms for the estimated STZ size. While the DMR method focuses on the ‘pop-in’ phenomena
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prior to the steady plastic flow, a much smaller number of 10–20 atoms is obtained. In this section, we will provide a comparison about the effectiveness of these flow models for Al-rich MGs. Note that, in essence, the origin of STZs is related to the closely packed atomic cluster. For comparison, it becomes important to provide the possible eigenvalue about the STZs size in Al-rich MGs from the angle of topological glassy structure. Icosahedral cluster structure is regarded as one of the most recognized frame structure. And the local icosahedral order was observed in metallic glasses by means of Angstrom-beam electron diffraction of a single icosahedron [51]. For the Al-transition metal (TM)-rare earth (RE) glassy alloys, it has been recognized that there is the icosahedral supercluster medium-range order (MRO) structure based upon RE- or TM-centered clusters with the icosahedral fivefold packing [26,52]. In the icosahedral supercluster, there are 12 RE(TM)-centered clusters on the vertex of the icosahedral supercluster, one RE(TM)-centered clusters in the center, TM(RE) atoms located at RE(TM)-centered cluster tetrahedral interstices in the icosahedral supercluster [26]. Here, we set the edge length of an icosahedral supercluster MRO as a (the distance between the RE(TM)-centered clusters on the vertex and the RE(TM)-centered can be calculated by a clusters in the center), and then the cluster √ cubic box with minimum edge length L=(1+ 5)a/2. The volume is √ 3L2 − a2 /12 ≈ 2.1817a3 for V=20 × (1/3) × (1/2) × ( 3/2)a2 × an icosahedral supercluster MRO. Thus, for a given a ∼1.06 nm, the volume V of the Al86 Ni6 Y4.5 Co2 La1.5 MG is determined to be 2.60 nm3 and the number of atoms in the MRO is ∼216. In contrast, only the range of 2.77–3.59 nm3 values is very close to the volume value of 2.60 nm3 obtained by MRO. The type of MRO clusters could have a potential association with the STZ size. More experimental work and computational simulation need to be carried out to further gain insight into the intrinsic correlation between the structure unit and deformation unit. 5. Conclusion The deformation behavior of the Al86 Ni6 Y4.5 Co2 La1.5 bulk and ribbon MGs have been investigated under nanoindentation. It was indicated that from ribbon to bulk sample, with the decrease of frozen-in volume, the serration behavior becomes inconspicuous together with the increase of hardness. We have estimated the STZ sizes based on three different models: CSM, RJM and DMR. It was found that the STZ volumes, calculated by the RJM, increase from 2.77 nm3 in the bulk to 3.59 nm3 in the ribbon. However, the STZ volumes are calculated to be close for the two samples as 5.00–5.05 nm3 using CSM method and 0.27–0.29 nm3 using DMR method. On the whole, the STZ volumes from RJM method is in agreement with 2.60 nm3 obtained from the icosahedral supercluster MRO structure model in Al-rich MGs. Moreover, an increase in the STZ volumes from the bulk to the ribbon was analyzed in terms of the frozen-in excess volume content. We believe that these results may improve the understanding of the plasticity mechanism of MGs.
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This work was supported by the National Natural Science Foundation of China (Nos. 51131006 and 51471166) and the National Key Research and Development Program of China (No. 2016YFB1100204). Special thanks are indebted to Prof. J. Xu and Dr. Z.Q. Song for helpful discussion, Prof. H.W. Yang and Dr. F.X. Bai
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