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[Silvia Pomes](https://orcid.org/0000-0002-0536-9427), Nozomu Adachi, [Masato Wakeda](https://orcid.org/0000-0002-6377-1318), [Takahito Ohmura](https://orcid.org/0000-0001-7528-566X)

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[Temperature Dependence of Nanoindentation-Induced Deformation Dynamics in Zr-Based Bulk Metallic Glass](https://mdr.nims.go.jp/datasets/b4af622c-da28-4490-ba04-0655a40d57d8)

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Temperature Dependence of Nanoindentation-Induced Deformation Dynamics in Zr-Based Bulk Metallic GlassTemperature Dependence of Nanoindentation-Induced Deformation Dynamics in Zr-Based Bulk Metallic GlassSilvia Pomes1,2, Nozomu Adachi3, Masato Wakeda1 and Takahito Ohmura1,2,+1Research Center for Structural Materials, National Institute for Materials Science, Tsukuba 305-0047, Japan2Department of Materials Science and Engineering, Graduate School of Engineering, Kyushu University, Fukuoka 819-0395, Japan3Department of Mechanical Engineering, Toyohashi University of Technology, Toyohashi 441-8580, JapanNanoindentation-induced deformation in Zr-based bulk metallic glasses in distinct structural states was studied over a broad temperaturerange, both below and above the glass transition temperature. These findings emphasize the occurrence of a predominant deformationmechanism, identified as a percolation or diffusion process, triggered by exceeding a chemical and topological short-range order-insensitiveenergy barrier. [doi:10.2320/matertrans.MT-MBW2023002](Received November 22, 2023; Accepted January 31, 2024; Published February 16, 2024)Keywords: bulk metallic glass, nanoindentation, deformation, mechanical properties, glass transition temperature, percolation/diffusion1. IntroductionBulk metallic glasses (BMGs) have garnered attention aspromising materials for structural applications primarilybecause of their exceptional mechanical properties, includinghigh elastic limit, remarkable strength, and hardness.1,2) Inaddition, BMGs have a distinctive microstructure that lackslong-range order and exhibits regions with diverse geo-metrical constraints and degrees of frustration. Thesestructural characteristics contribute to their peculiar deforma-tion response, which is significantly influenced byenvironmental factors, particularly the temperature. Thestructure of BMGs constantly evolves through atomicrearrangements and free-volume redistribution3,4) duringdeformation, driven by the supplied mechanical and thermalenergy. Notably, the mechanical performance and inherentmicrostructure of BMGs are significantly influenced by theirglass transition temperature (Tg). Indeed, Tg exhibits a linearrelationship with the activation energy for β-relaxation.5)Moreover, at a specific temperature, denoted as Tx, aboveTg, BMGs undergo a crystallization process, leading tofurther alterations in the mechanical properties of the alloy.Furthermore, deformation in BMGs can manifest as eitherhomogeneous or inhomogeneous flow, contingent on bothtemperature range and strain rate. Homogeneous flow isexpected in the range 0.6 – 1 Tg.6–8) Nevertheless, thetemperature range for each type of flow is significantlyimpacted by the strain rate: a slower strain rate correspondsto a lower transition temperature from inhomogeneous tohomogeneous flow.9)Given the heterogeneous and unstable microstructure ofBMGs, nanoindentation testing is a robust approach forassessing the mechanical properties at a highly localizedscale, offering both time and cost efficiency.10) Furthermore,owing to the advancements in thermal managementtechniques, nanoindentation can be conducted at elevatedtemperatures,11) providing valuable insights into the under-lying deformation processes of BMGs. Recently, Ghodkiet al.12) employed high-temperature nanoindentation to studythe bulk deformation behavior of a Zr-based BMG anddiscussed it based on the shear transformation zone concept.In their study, testing was conducted below the Tg andfeatured indentation marks in the range of tens of micro-meters. However, it has been demonstrated that studying theeffects of more localized deformation, resulting in indentationmarks on the scale of hundreds of nanometers, can aid inidentifying elemental deformation dynamics.13) Additionally,expanding the temperature range of investigation to includetemperatures above Tg would serve the same purpose.The high-temperature deformation of Zr-based BMG wasstudied through compression testing by Bletry et al.14) Thedeformation behavior was interpreted in terms of the free-volume model, which attributed plasticity to the cooperativemotion of a group of a few tens of atoms. Although it iswidely accepted that deformation in BMGs involves thereorganization of a chemical short-range order (CSRO) andtopological short-range order (TSRO), the underlyingdynamics and process variability concerning the testingenvironment temperature and structural state of the originalsamples remain unclear.In this study, we performed nanoindentation tests atelevated-temperature on a Zr-based BMG in two distinctstructural states. Our approach covers a wide range of testingtemperatures, from room temperature to the crystallizationtemperature, including Tg. We conducted numerous tests toensure the statistical significance of the overall temperaturedependence of the mechanical properties and provide insightsinto potential deformation mechanisms.2. Experimental ProcedureTwo samples of Zr50Cu40Al10 at% BMG were used in theas-cast and as-relaxed structural states. The BMG wasproduced in the form of rods with a diameter of 10mm byarc melting and tilt casting, as elaborately described inprevious studies.15,16) The as-cast sample was annealed for3 h at 40K below the Tg = 693K (420°C) to obtain the as-relaxed sample. Disks with a thickness of 2mm were+Corresponding author, E-mail: OHMURA.Takahito@nims.go.jpMaterials Transactions, Vol. 65, No. 5 (2024) pp. 481 to 486©2024 The Japan Institute of Metals and Materialshttps://doi.org/10.2320/matertrans.MT-MBW2023002obtained from the rod. The disk samples were mechanicallypolished using sandpaper and diamond suspension with aparticle size of up to 1 µm. Finally, a sol–gel Al2O3suspension with a particle size of 0.05 µm was used toremove the damaged surface layer resulting from mechanicalpolishing. The surface roughness (RMS) was 1 nm afterfinal polishing. The nanoindentation was conducted using aprototype high-temperature experimental setting in inertatmosphere. Details of the device are described elsewhere.17)A schematic diagram of the machine is shown in Fig. 1(a).A high-temperature-stage nanoindentation testing setup(Bruker Co.) was used, which was placed in a vacuumchamber on a vibration isolation stage (Minus K TechnologyInc.). The vacuum chamber was equipped with gas inletsthat allowed for the control and introduction of gases, alongwith an external cooling system. Prior to heating, the vacuumchamber undergoes cyclic evacuation to a pressure of1.33mPa (10¹5 Torr) and is subsequently backfilled with amixture of 98% argon gas and 2% H2 to minimize the oxygenlevels. In the experimental setup, the sample was positionedbetween two independently controlled heaters with heatingapplied simultaneously from the top and bottom. The dualheating configuration ensures uniform temperature distri-bution within the sample, with a slow heating rate(²10°C/min). The indenter tip was positioned 100 µm abovethe sample surface and passively heated. Both the tip andsample were maintained at the testing temperature for 1 hbefore the measurements began, to improve the thermalstability. Tests were performed in the load control mode witha peak load of 300 µN and a symmetrical loading andunloading rate of 10 µN/s and holding time of 10 s at thepeak load. The distance between the test locations was 5 µmto ensure no interaction between the induced strain fields.For statistical significance, 125 tests were performed at eachtemperature, resulting in 750 tests in total on one sample.18)Nanoindentation tests were performed with a sharpBerkovich tip, with tip radius Ri ³ 290 nm, at 25°C, 100°C,200°C, 300°C, 400°C, and 500°C. The collected data wereanalyzed using Python.19,20)3. Results and DiscussionsFigure 1(b) illustrates load P versus displacement h plots,with each curve representing an average of 125 tests. Theaveraging of the curves is performed as the measuredhardness values displayed no discernible trend with respect totesting time. This observation suggests that the technical timerequired to conduct the tests did not exert a substantialinfluence on the mechanical properties. The curves of as-relaxed sample were shifted horizontally to enhance theclarity of visualization. The inset in the upper-left cornershows the definitions of hload and hhold parameterscorresponding to the indentation depths recorded at the endof the loading and holding segments, respectively. In bothsamples, hload and hhold increased with temperature, peakingat 400°C (red curves) and showing a decreased value at500°C (blue curves). Figure 2(a) shows the hardness valuesof the as-cast and as-relaxed samples at different testingtemperatures. Compared to previous studies, the hardnessvalues obtained were higher, which might be due to the sharptip or strain-rate sensitivity at low peak loads.21) Moreover, aspreviously reported,22) structures such as oxides may haveformed in conjunction with zirconium, potentially impactingthe calculated hardness at the tested locations. Due to thisinfluence, the detailed discussion of the computed hardnessvalues is omitted, in favor of a more in-depth discussion ontheir trend.The light-blue hatched area indicates the temperaturerange of 200°C to 400°C where softening is observed. Itis noted that this area is included in the 0.8 Tg (³ 336°C) toTg temperature range, previously reported as range forhomogeneous flow in bulk metallic glasses.6) Furthermore,the range where softening is observed also falls in the0.6 Tg (³ 142°C) to Tg temperature span, reported by Argonas domain for homogeneous flow in metallic glasses.7)However, it may be possible that, even at the sametemperature, deformation may exhibit flows with varyingdegrees of uniformity, due to the complexity introduced bythe amorphous samples. In fact, highly localized deformationprocesses might not be exclusively dictated by temperatureand loading rate but could also be contingent on specificFig. 1 (a) Schematic of high-temperature nanoindentation testing in aninert-atmosphere machine.15) (b) Load versus displacement plot ofaveraged nanoindentation curves for as-cast (continuous line) and as-relaxed samples (dashed line). Tests are performed at 25°C, 100°C,200°C, 300°C, 400°C, and 500°C. As-relaxed sample curves arehorizontally shifted. The inset shows the definition of hload and hholdparameters as the indentation depth recorded at the end of loading andholding segments, respectively.S. Pomes, N. Adachi, M. Wakeda and T. Ohmura482testing location. In this work, the temperature range reportedby Schuh et al.6) and Argon7) is regarded as potential rangefor homogeneous flow based on the absence of any detectableserrated flow in our tests. Furthermore, the local variationscan be averaged due to the collection of a large dataset.The overall trend of hardness confirms the observationsmade for the averaged curves in Fig. 1(b), i.e., the meanvalues of hardness exhibited a decreasing trend, reaching aminimum at 400°C, near Tg, followed by higher values at500°C. At 25°C, the wider standard deviation can beattributed to the microstructural heterogeneity, resulting inregions with different degrees of atomic mobility. Conversely,at 500°C, the increased hardness value, compared to 400°C,could be attributed to microstructural changes occurringwithin the supercooled region, encompassing the temperaturerange between Tg and Tx. The supercooled region ischaracteristic of each alloy and typically spans the temper-ature range of 40K–90K.23) Considering the Tg of the presentalloy as 420°C, it can be reasonably assumed that the Txmay fall within the range of 460°C to 510°C. This estimate isconsistent with previous experimental evaluations of alloyswith the same composition, with Tg = 706K (433°C) andTx = 792K (519°C).24–26) Hence, crystallization processesmight affect the hardness values measured at 500°C.Overall, the as-relaxed sample exhibited a higher hardnessthan its as-cast counterpart, which can be attributed to theincreased energetic stability of the microstructure and thelower volume fraction of free-volume within the sample.The softening observed at temperatures below the Tg canbe attributed to a deformation process activated uponreaching a certain activation energy threshold. Figure 2(b)shows the estimation of the activation energy for softeningusing the method adopted by Wesseling et al.:8)Hn / expðQ=RT Þ: ð1ÞThe activation energy coincides with the slope of the dashedlines in Fig. 2(b) under a condition of n = 1.As proposed in the previous work,8) n is considered equalto 1 because the temperature range in this work is consistentwith the range for homogeneous flow6,7) and homogenousflow usually corresponds to a Newtonian flow in metallicglasses.7) Typically, as commonly done in uniaxialcompression testing, Newtonian flow is assessed byevaluating the induced strain rate dependency. However, innanoindentation, the indenter induces a complex stress state,encompassing both compression and shear componentswith corresponding compression and shear strain rates.Furthermore, in the context of nanoindentation testing, adirect observation of Newtonian viscous flow in the volumebeneath the indenter presents technological challenges. Forthese reasons, the method proposed by Wesseling et al.8) isconsidered. They performed microhardness Vickers tests atelevated temperature and directly evaluated the activationenergy for softening from the indentation data under theassumption of a Newtonian flow. This approach can beapplied to our nanoindentation study offering a valuableperspective on the material behavior under the complex stressconditions induced by the indenter.The estimated activation energies of the as-cast and as-relaxed samples were 126 and 128 kJ/mol, respectively.These results suggest that the initial structural state doesnot influence deformation dynamics at elevated temperatures.The obtained values were compared with an estimate ofthe activation energy for β-relaxation, obtained as E¢ =26(«2)RTg, where R is the gas constant.5) Hence, in thecase of the studied alloy, E¢ falls within the range of 138–161 kJ/mol. Although slightly lower, the estimated activationenergies for softening were comparable to the potentialrange of activation energies for β-relaxation. Generally,β-relaxation is regarded as a local atomic rearrangementachieved through short-range diffusion.27) However, Gaoet al.28) recently questioned the local nature of β-relaxationdynamics and explored this phenomenon in various BMGs.They emphasized that β-relaxation corresponds to thepercolation of mobile atomic clusters and revealed auniversal activation volume, expressed as a percentage ofactivated atoms. Considering both interpretations, it isreasonable to expect that the structural states of a sampledo not influence the energy barrier of such dynamics. For thesame alloy composition, the distinction between the as-castand as-relaxed states lies in their CSRO and TSRO, implyingthat the enthalpy barrier for mobilizing atoms in unstableregions would likely be the same. Eventually, the weakestatomic arrangements, identified as non-pentagon configu-rations in the TSRO,29) would be activated and constitute themobile clusters.Fig. 2 (a) Estimated hardness for as-cast and as-relaxed samples atdifferent testing temperatures and (b) estimation of activation energy forsoftening in the homogeneous flow range.Temperature Dependence of Nanoindentation-Induced Deformation Dynamics in Zr-Based Bulk Metallic Glass 483To further examine the effects of temperature on thedeformation processes specific to the loading and holdingstages, the trends of hload and length of the holding segment,hcreep = hhold ¹ hload, are analyzed in Fig. 3(a) and 3(b),respectively. In Fig. 3(a), the maximum indentation depth atloading increases in both samples with respect to temperatureand exhibits a peak at 400°C. Similarly, in Fig. 3(b), hcreepincreases with the temperature until its peak at 400°C. At500°C, both samples exhibited a lower, comparable value.Notably, the observable trends exhibited similarities betweenthe samples and the two plots, as shown in Fig. 3. Theobserved consistent patterns suggested a common dominantdeformation dynamic, possibly identifiable as either apercolation or a diffusion process. Indeed, the overshadowingof load effects by diffusion processes has also been reportedthrough creep strain rate sensitivity analysis of a Zr-basedBMG tested below its Tg.12)However, Fig. 3(a) displays a less smooth distributioncompared to Fig. 3(b), which can be attributed to thepresence of multiple mechanisms in the loading process,including displacive ones, acting synergistically during theloading stage of nanoindentation. As the applied loadincreases, the volume influenced by the applied stress alsoincreases, leading to the involvement of more defects andfree-volume regions in the energy dissipation process.Figure 3(c) provides a qualitative schematic of the atomisticstructure of as-cast (top) and as-relaxed (bottom) sampleswith unstable regions represented in yellow. However, duringthe holding time, the deformation volume is predominantlyestablished, and the eventual activation and percolation ofatomic clusters are facilitated by high-temperature-inducedstructural vibrations under a constant applied load.This rationale is applicable to both samples. However,as shown in Fig. 3(a) and 3(b), it translates into largerdisplacements in the as-cast sample, due to its higher volumefraction of unstable regions, as depicted in Fig. 3(c).The smaller displacements recorded at 500°C in bothsamples may be attributed to the proximity of the testingtemperature to the Tx range; the indenter motion may behindered by newly formed structures.To gain an additional understanding of the underlyingmechanisms governing deformation in the holding stage, theevolution of displacement was analyzed with respect totime, as shown in Fig. 4(a). The averaged experimental datareplotted from Fig. 1(b) are indicated by circular anddiamond markers for the as-cast and as-relaxed samples,respectively. The fitting curves were obtained from thefollowing empirical equation:30,31)hðtÞ ¼ h0 þ atþ bðt� t0Þc ð2Þconsidering a, b, and c as the fitting parameters, and h0 andt0 as the origin of the plot, marked with solid and dashed linesfor the as-cast and as-relaxed samples, respectively. Thecoefficient of determination value was higher than 0.97 for allcurves except for the tests performed on the as-relaxedsample at 25°C (0.929) and 100°C (0.964). Figure 4(b)Fig. 3 Analysis of indentation depths, (a) hload and (b) hcreep (P = constant), reveal deformation is favored in the as-cast sample.(c) Qualitative schematics of the atomistic structure of as-cast (top) and as-relaxed (bottom) samples. Unstable regions are represented inyellow and they are more abundant in the as-cast sample.S. Pomes, N. Adachi, M. Wakeda and T. Ohmura484illustrates the estimated fitting parameters for each test(depicted in black) along with the average values (presentedin green). Overall, a steady-state stage with parameter a forcreep was not clearly detectable. This suggests the occurrenceof an unstable deformation behavior in the early stage ofdeformation under constant applied load. While the overalldeformation and energy dissipation may demonstrate a cleartemperature dependence, as shown in Fig. 3(b), the specificlocal dynamics underlying these processes might still exhibitless predictable and less stable behavior at each testinglocation.The fitting parameters exhibited significant variability,primarily attributed to structural fluctuations within thesamples. Specifically, the parameter a governing the linearterm in eq. (2) exhibited values close to zero, as shown inFig. 4(b). However, the power-law term in eq. (2) becomeslinear when the exponent, which is the fitting parameter c,is approximately unity. This applies to tests conducted at400°C, where the estimated fitting parameters show higherand less sparse values, overall. This phenomenon may beattributed to the proximity of the testing temperature to Tg,leading to increased atomic mobility and potential enhance-ment of the diffusive processes.4. ConclusionIn summary, we investigated the deformation behaviorof Zr50Cu40Al10 bulk metallic glass (Tg = 420°C) in acomprehensive temperature range, encompassing 25°C,100°C, 200°C, 300°C, 400°C, and 500°C, via nano-indentation testing in an inert atmosphere. The followingkey conclusions were drawn:(1) The estimated hardness decreases with increasingtesting temperature and reaches a minimum inproximity of Tg at 400°C.(2) The estimated activation energies for softening werenearly identical for both samples, suggesting that theunderlying physical dynamics were not affected by theinitial structural state of the bulk samples.(3) At 500°C, the hardness value increases compared withthat at 400°C. This may be attributed to the higherresistance to atomic motion caused by crystallization.(4) hload and hcreep revealed similar temperature-dependenttrends, which suggest that the same diffusive deforma-tion mechanism may be predominant during bothtesting stages.(5) Larger hcreep values were recorded in the as-cast sampledue to the higher volume fraction of unstable regions.AcknowledgmentsS.P. is thankful for experimental support by Nakagawa Eri.REFERENCES1) W. Klement, R.H. Willens and P. Duwez: Nature 187 (1960) 869–870.2) M.F. Ashby and A.L. Greer: Scr. Mater. 54 (2006) 321–326.3) A.L. Greer and F. Spaepen: Ann. N. Y. Acad. Sci. 371 (1981) 218–237.4) F. Spaepen: Scr. Mater. 54 (2006) 363–367.5) L. Hu and Y. Yue: J. Phys. Chem. C 113 (2009) 15001–15006.6) C.A. Schuh, A.C. Lund and T.G. Nieh: Acta Mater. 52 (2004) 5879–5891.7) A.S. Argon: Acta Metall. 27 (1979) 47–58.8) P. Wesseling, T.G. Nieh, W.H. Wang and J.J. Lewandowski: Scr. Mater.51 (2004) 151–154.9) B. Yang, J. 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