In nanoscale contact experiments, it is generally believed

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1 A new view of the onset of plasticity during the nanoindentation of aluminium ANDREW M. MINOR 1,S.A.SYEDASIF 2, ZHIWEI SHAN 1,ERICA.STACH 3, EDWARD CYRANKOWSKI 2, THOMAS J. WYROBEK 2 AND ODEN L. WARREN 2 * 1 National Center for Electron Microscopy, Lawrence Berkeley National Laboratory, Berkeley, California 9472, USA 2 Hysitron Incorporated, 125 Valley View Road, Minneapolis, Minnesota 55344, USA 3 School of Materials Engineering, Purdue University, West Lafayette, Indiana 4797, USA * owarren@hysitron.com Published online: 13 August 26; doi:1.138/nmat1714 In nanoscale contact experiments, it is generally believed that the shear stress at the onset of plasticity can approach the theoretical shear strength of an ideal, defect-free lattice 1 4, a trend also observed in idealized molecular dynamics simulations 5 9. Here we report direct evidence that plasticity in a dislocation-free volume of polycrystalline aluminium can begin at very small forces, remarkably, even before the first sustained rise in repulsive force. However, the shear stresses associated with these very small forces do approach the theoretical shear strength of aluminium ( 2.2 GPa). Our observations entail correlating quantitative load displacement measurements with individual video frames acquired during in situ nanoindentation experiments in a transmission electron microscope. We also report direct evidence that a submicrometre grain of aluminium plastically deformed by nanoindentation to a dislocation density of 1 14 m 2 is also capable of supporting shear stresses close to the theoretical shear strength. This result is contrary to earlier assumptions that a dislocation-free volume is necessary to achieve shear stresses near the theoretical shear strength of the material 5 9. Moreover, our results in entirety are at odds with the prevalent notion that the first obvious displacement excursion in a nanoindentation test is indicative of the onset of plastic deformation. The yield strength of a material is one of the most fundamental concepts in materials science, and is frequently used in designing materials for engineering applications. However, yield strength is not an inherent material property, and depends on the internal structure of the material and the loading conditions. Conventionally, this strength is defined by the point at which the material response deviates significantly from elastic deformation under applied load 1. In bulk materials, because of their high concentration of defects, a simple numerical value for yield strength often suffices. However, matters are greatly complicated in nanoscale materials, as differences in specific defect distribution or even the complete lack of pre-existing dislocations can greatly alter the point at which the material yields. As a result, nanoscale material volumes can sustain stresses significantly higher than can be sustained by their bulk analogues 11. In a small, confined volume, dislocations can pack close together under applied stress, thereby increasing the internal stress 11. However, direct evidence correlating dislocation activity in a confined volume with applied stress has not been achieved to date. Consequently, our understanding of how a reduction in the dimensions of a material affects its strength remains limited. Another important descriptor of the mechanical response of a material is its theoretical or ideal strength, the strength which an ideal, defect-free crystal can sustain. There is substantial interest in understanding the ideal strength of materials, as this provides an upper bound on achievable mechanical behaviour However, owing to the difficulty in obtaining perfect crystalline materials, much of our understanding of ideal strength behaviour has been derived from computational studies exploiting electronicstructure-based total-energy methods to determine the onset of permanent deformation for a given material under a given loading condition 5,13,16,17. Attempts 13,18,19 have been made to correlate calculated ideal strengths with data from nanoindentation, a standard method for determining the hardness of nanoscale volumes of material 2. Because of the high stresses induced and the small, potentially dislocation-free volumes probed, it has been inferred that nanoindentation can experimentally interrogate how a perfect material responds at its point of elastic instability 3,21,22. The depth of material over which this high stress is imposed is of the order of the indenter radius (usually 5 1 nm) and thus may very well be free of initial dislocations, thereby providing an ideal crystal for comparison. During nanoindentation, wellannealed and electropolished metals typically show an initial elastic response followed by a large displacement excursion at constant load, generally referred to as a pop-in event 2 4. A number of experiments 3 and simulations 5 9 have inferred that the first displacement burst results from nucleation and glide of large numbers of dislocations into a previously dislocation-free material, and thus corresponds to the onset of plasticity at the ideal strength. There have been reports of dislocation generation prior to nature materials VOL 5 SEPTEMBER Nature Publishing Group

2 a 14 6 b 6, Load Displacement , 2, , 1 2 4, Load (μn) , Time (s) Time (s) d 2 (load)/dt 2 (μn s 2 ) c 6 d Repulsive contact Load (μn) Load (μn) Figure 1 Quantitative data from an in situ TEM nanoindentation of an Al grain using a Berkovich diamond indenter. a, Load and displacement as a function of time of the test. b, Second derivative of load as a function of time. c, Load as a function of displacement note that because the test was run in displacement control, this curve differs in appearance from load displacement curves obtained in load-control experiments. d, Load as a function of displacement for the leading portion of the loading curve. pop-in events 4 ; however, typically these observations are indirect or after-the-fact. Stress-reduction nanoindentation experiments 2 on electropolished single-crystal tungsten are consistent with the absence of mobile dislocations before pop-in and the presence of mobile dislocations after pop-in, suggesting that a pop-in event corresponds to the sudden multiplication of mobile dislocations. However, conclusions such as this do not diminish the fact that the currently held views on the onset of plasticity during nanoindentation are based solely on indirect evidence and idealized computational simulations. Here we investigate the onset of plasticity using quantitative in situ nanoindentation in a JEOL 31 transmission electron microscope (TEM) to directly correlate the onset of plasticity with dislocation activity. In previous work, in situ nanoindentation has been used to explore initial deformation modes in aluminium thin films 22 24, and attempts have been made to correlate load displacement behaviour with real-time images of the deformation response 23. However, these attempts have relied on ex post facto determination of indenter displacement from sequential TEM images and qualitative, indirect force measurements, and are thus inherently inaccurate. To enable the present work, we have developed a miniature capacitive load displacement transducer integrated into the TEM holder, thereby permitting high-resolution measurements of the load displacement response (resolution of <.5 μn in load, <1nm in displacement), to be directly correlated with real-time diffraction contrast images obtained during indentation. The experiments are run in displacement control, a mode shown to give greater sensitivity to transient phenomena, and which can be directly correlated with molecular dynamics simulations of the same processes 25. To be clear from the outset, a discrete yielding event in displacement control will be reflected by a sudden relaxation of load rather than by a displacement burst as is seen in load-control experiments. The polycrystalline aluminium films used in this study are prepared by evaporating pure Al (99.99%) onto silicon wedge substrates at 3 C (refs 22 24). Figure 1 shows quantitative data taken from one of the in situ nanoindentation experiments, with corresponding TEM images of the deformation responses shown in Fig. 2. A video of the indentation can be found in the Supplementary Information, Fig. S1. Similar to conventional 698 nature materials VOL 5 SEPTEMBER Nature Publishing Group

3 a 1 nm Al grain Diamond indenter b 1 nm c 1 nm 1 d 1 nm e 1 nm 2 f 1 nm g 1 nm 3 Figure 2 Video montage taken from the in situ TEM nanoindentation of an Al grain using a Berkovich diamond indenter. a, Initial bright-field (g = 22) TEM image taken prior to the indentation experiment note that the indented grain is initially free of dislocations. b,c, Extracted video frames corresponding to the transient arrowed as 1 in Fig. 1. d,e, Extracted video frames corresponding to the transient arrowed as 2 in Fig. 1. f,g, Extracted video frames corresponding to the transient arrowed as 3 in Fig. 1. nanoindentation experiments 26, the diamond indenter used here had a Berkovich geometry, with a radius of curvature of 1 nm. Load and displacement versus time are shown in Fig. 1a, the second derivative of load versus time is shown in Fig. 1b, load versus displacement is shown in Fig. 1c and load versus displacement for the leading portion of the loading curve is shown in Fig. 1d. Figure 2a shows the initial configuration of the indenter and the submicrometre Al grain to be indented. As is common in thin metallic films, the grain is not perfectly flat due to grain boundary cusps 27, and in this experiment the indentation was carried out at the apex of the grain. Two small transients are observed in the load response during the initial 3 nm of indenter sample interaction, indicated by arrows 1 and 2 in Fig. 1a d. These transients occur as a result of load build-up just above the force noise floor followed by complete load relaxation (most evident in Fig. 1d). The corresponding images associated with these transients are shown in Fig. 2b,c and d,e, respectively. It is apparent from the images that these small load nature materials VOL 5 SEPTEMBER Nature Publishing Group

4 a b Before indent 5 nm 1 nm c 1. d.5 Approach Retraction After indent Interaction force (μn) nm Figure 3 A shallow in situ TEM nanoindentation of an Al grain using a FIB-sculpted diamond indenter. a, Low-magnification TEM image of the FIB-sculpted diamond indenter approaching the polycrystalline Al sample from the top right. b, Bright-field (g = 111 for the largest grain) TEM image taken before contact. c, Load versus displacement curve for the indentation seen in Supplementary Information, Fig. S3, with the data from the indenter approach and retraction regimes plotted in different colours. d, Bright-field (g = 111) TEM image of the same area shown in b taken directly after the contact shown in c. transients are a result of nucleation and glide of many dislocations into the material. Assuming zero force corresponding to the outof-contact force noise evenly distributed between attractive and repulsive force regimes, the measured load just before the first transient is 1.5 μn. The maximum shear stress in a repulsive elastic contact can be calculated from the following expression originating from the Hertz contact model 28 : ( ( ).56 E 2/3 τ max = )F 1/3, (1) π R where F is the load, E is the reduced modulus and R is the effective radius of curvature of the indenter and the sample 28. The calculated shear stress at point 1 is 1.95 ±.4 GPa with a measured load of 1.5 μn, a reduced modulus of 7 GPa and an effective radius of curvature of 75 nm (radii of 1 nm for the indenter and 3 nm for the apex of the grain). This high shear stress is of the same order as the stress required to initiate plasticity in presumably dislocationfree Al grains in conventional nanoindentation experiments 3,4. The initial plasticity caused by the 1.95 GPa shear stress achieved at point 1 seems to blunt the apex of the grain at the contact point, with most dislocations escaping to the surface and creating surface steps. In addition, the lack of forces above the force noise floor for the first 5 nm of displacement following 7 nature materials VOL 5 SEPTEMBER Nature Publishing Group

5 the load relaxation at point 1 (best seen in Fig. 1d) indicates that a gap between the indenter and the sample has been created on account of the sample surface receding faster than the rate of indenter approach. The experiment is done in displacement control; therefore, the indenter is suppressed from jumping into the sample by way of feedback enforcing the indenter to follow the programmed displacement rate, which permits a gap to be detected if formed. A gap between the indenter and the surface would not have been detected if the experiment had been carried out in load control; then feedback would have immediately closed the gap to maintain the programmed loading rate. The propensity for gap formation during the earliest stages of plasticity is evident by the surprisingly extended displacement range from the point of initial dislocation nucleation and multiplication (arrow 1 in Fig. 1a d), through the point of a subsequent dislocation burst (arrow 2 in Fig. 1a d), to the point of finally achieving sustainable repulsive contact (the start of the sharp increase in load as indicated in Fig. 1d). The reduced constraint associated with the wedge-shaped geometry of the samples might have contributed to this phenomenon. Once sustained repulsive contact is established, the submicrometre Al grain supports increasing loads and contact size until 2 μn, where small load transients immediately precede a large load-drop indicated by arrow 3 in Fig. 1a c. On the basis of the TEM images, the contact at the onset of sustained repulsive interaction can be modelled as a sphere on a flat surface, as the radius of curvature of the apex of the grain is now very large due to the initial plasticity. TEM images show that the microstructure does not change between the onset of sustained repulsive contact and the small load transients just before the first major load-drop at point 3, which indicates elastic loading over this portion of the data. The penetration depth from the onset of sustained repulsive contact to these small load transients (which cause only minor changes to the microstructure, Fig. 2e versus Fig. 2f) is 15 nm. Recasting equation (1) to the following expression allows the maximum shear stress at point 3 to be calculated 28 : )( F τ max =.31 ( 3 2π where a is the contact radius. Assuming a circular contact area estimated directly from the images (see Supplementary Information, Fig. S2), this load value corresponds to a maximum shear stress of 2.3 ± 1. GPa (calculated from the combination of the load displacement curve and the TEM image), which is also of the order of shear stresses sustained before the first pop-in event in previous conventional nanoindentation experiments 3,4. On the basis of our previous research on comparing nanoindentation control modes 25, points 1 and 2 and possibly the small load transients just before point 3 would not have been detected if the load displacement curve had been acquired in load control, the most commonly used nanoindentation control mode on account of its ease of implementation. Therefore, relating these experiments to previous work, point 3 would correspond to the initial pop-in event that has been expressed in numerous publications on nanoindentation of metals 2 4. The deformation occurring during the sharp load increase preceding the small load transients just before point 3 is indeed an elastic response with invariant microstructure, but obviously not that of a dislocationfree volume (a dislocation density of 1 14 m 2 is estimated from Fig. 2e). Apparently the dislocations present at the start of this elastic response are immobile up to high shear stresses. Our results reveal that the high stresses achieved prior to the first major pop-in/load-drop event in nanoindentation tests are not necessarily due to elastic instability in a dislocation-free a 2 ), volume. Rather, high stresses are achievable even in a dislocated grain. The origin of this small-volume strengthening behaviour at stresses close to the theoretical strength is not entirely clear. Mechanisms such as confined-volume dislocation hardening 11 or source-limited deformation 29 are possible sources of the observed stress enhancement, and future work will attempt to answer this question directly. The first major load-drop at point 3 correlates with a large burst of dislocation activity and results in further flattening of the apex of the grain (Fig. 2f,g). This load-drop is presumably due to rearrangement of the dislocation structure releasing some of the stored energy and/or activation of a less favourable slip system at high stresses within the grain. Although far larger in magnitude than the earlier transients, the load relaxation at point 3 and subsequent load relaxations are less than 1%; therefore, the indenter does not lose contact with the sample in these instances. To better focus on the nature of the response seen during the initial indenter sample interaction, we used a FEI Strata 235 focused ion beam (FIB) to machine a diamond indenter that would be transparent to the electron beam to enable more accurate positioning. Figure 3a shows the FIB-sculpted indenter approaching the Al film, where the indenter apex is approximately hemispherical. The effective radius of curvature for this experiment is 6 nm, with radii of 85 nm for the indenter and 175 nm for the apex of the grain. A considerably shallower indentation test was programmed with an indenter velocity of 5 nm s 1, more than twice slower than the first indent. Figure 3b shows the submicrometre Al grain prior to indentation. Clearly, dislocations are not present in the grain at this stage; however, once the indenter starts to interact with the sample, dislocations are observed to emit from the contact area almost immediately (a video of this indentation can be found in Supplementary Information, Fig. S3). The corresponding load displacement curve is shown in Fig. 3c, in which approach and retraction traces are plotted as separate colours. As can be seen in Fig. 3c, the interaction starts at 26 nm of indenter displacement, and continues for another 24 nm of indenter sample approach. Dislocation loops were punched into the grain during this interval, remnants of which can be seen in Fig. 3d. This indentation, also run in displacement control, demonstrates a series of alternating positive and negative force spikes during approach, but only negative long-range adhesive forces during retraction. Two smaller positive force spikes of unknown cause are seen prior to 26 nm of indenter displacement; however, it is the subsequent.6 μn positive force spike plus its associated load relaxation that best correlates to the first appearance of dislocations. Inserting this force and the other appropriate values into equation (1) yields a maximum shear stress of 1.7 ±.5GPa. The force swinging into the attractive force regime after many of the load relaxation occurrences is not entirely understood at this time, but it might be related to progressive rupture of the thin native oxide accompanying the plasticity events, providing freshly exposed Al to interact attractively with the indenter through a momentary gap (a similar mechanism has been proposed for indium and its thick native oxide 25 ). Although negative force swings are not evident in the vicinity of points 1 and 2 of the load displacement curve in Fig. 1, oxide rupture must have occurred at some point of that indentation test as well, because a large adhesive pull-off force is clearly evident. As in Fig. 1, the indentation response in Fig. 3 confirms that plasticity can commence prior to a sustained rise in repulsive force. Our observations of the onset of plasticity (via nucleation and propagation of many dislocations) occurring even before a sustained rise in repulsive force challenge many previous conclusions regarding nanoindentation pop-in/load-drop behaviour. In addition, it is apparent that in the case of indentation nature materials VOL 5 SEPTEMBER Nature Publishing Group

6 experiments, pop-in yielding events involving near-theoretical shear stresses may occur after initial plastic deformation, and that mechanisms such as dislocation strengthening caused by dimensional confinement or source limitation may play a larger role than predicted by idealized simulations. Thus, the initial displacement excursions seen in conventional nanoindentation tests may not always indicate the onset of plastic deformation in a material. Received 6 February 26; accepted 15 June 26; published 13 August 26. References 1. Gane, N. & Bowden, F. P. Microdeformation of solids. J. Appl. Phys. 39, (1968). 2. Asif, S. A. S. & Pethica, J. B. Nanoindentation creep of single-crystal tungsten and gallium arsenide. Phil. Mag. A 76, (1997). 3. Gouldstone, A., Koh, H. J., Zeng, K. Y., Giannakopoulos, A. E. & Suresh, S. Discrete and continuous deformation during nanoindentation of thin films. Acta Mater. 48, (2). 4. Kramer, D. E., Yoder, K. B. & Gerberich, W. W. 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This work was also supported by the Director, Office of Science, Office of Basic Energy Sciences, of the US Department of Energy under Contract No. DE-AC2-5CH Correspondence and requests for materials should be addressed to O.L.W. Supplementary Information accompanies this paper on Competing financial interests The authors declare that they have no competing financial interests. Reprints and permission information is available online at 72 nature materials VOL 5 SEPTEMBER Nature Publishing Group