In Situ Indentation of Nanoporous Gold Thin Films in the Transmission Electron Microscope

Transcription

1 MICROSCOPY RESEARCH AND TECHNIQUE 72: (2009) In Situ Indentation of Nanoporous Gold Thin Films in the Transmission Electron Microscope YE SUN, 1 JIA YE, 2 ANDREW M. MINOR, 2,3 AND T. JOHN BALK 1 * 1 Department of Chemical and Materials Engineering, University of Kentucky, Lexington, Kentucky National Center for Electron Microscopy, Lawrence Berkeley National Laboratory, Berkeley, California Department of Materials Science and Engineering, University of California, Berkeley, California KEY WORDS gold; dislocations; TEM; porous materials; mechanical behavior; loading rate ABSTRACT The mechanical behavior of nanoporous gold was investigated during in situ nanoindentation in the transmission electron microscope. Thin films of nanoporous gold, with ligaments and pores of the order of 10-nm diameter, offer a highly constrained geometry for deformation and thus provide an opportunity to study the role of defects such as dislocations in the plasticity of nanomaterials. Films ranging in thickness from 75 to 300 nm were indented, while the motion of dislocations and deformation of ligaments were observed in situ. Dislocations were generated and moved along ligament axes, after which they interacted with other dislocations in the nodes of the porous network. For thicker films, the load-displacement curves exhibited load drops at regular intervals. The question of whether the spacing of these load drops was related to the collapse of pores in the nanoporous films or due to bursts of plasticity within the ligaments was investigated. Additionally, the effect of the indenter displacement rate on the mechanical response of these gold films with nanoscale porosity was investigated. Indentation rates were varied from 1.5 to 30 nm/s. There appears to be a kinetic factor related to dislocation nucleation, where slower displacement rates cause load drops to occur at shorter distance intervals and over longer time intervals. Microsc. Res. Tech. 72: , VC 2009 Wiley-Liss, Inc. INTRODUCTION Recent and ongoing studies have focused on nanoporous gold (np-au) and other noble metals (e.g., np- Pt) to investigate the potential of nanoporous films for applications such as catalysis and gas sensing (Ding et al., 2004a,b; Dursun et al., 2003; Erlebacher et al., 2001; Pugh, 2003). However, most of this work focused on the electrochemical preparation or chemical properties of these films (Dursun et al., 2003; Huang and Sun, 2004; Ji and Searson, 2002; Sieradzki et al., 2002). Recently, the surface functionalization of np-au was explored in the context of chemical sensing (Huang and Sun, 2005). In addition to these important research areas, the mechanical properties of nanoporous metals have begun to attract increasing attention (Biener et al., 2005; Hodge et al., 2005; Li and Sieradzki, 1992). These studies suggest that np-au may exhibit brittle fracture due to the characteristic length scales of pore size and sample dimension (Li and Sieradzki, 1992), and that theoretical shear strengths may be achieved by Au ligaments during nanoindentation testing (Biener et al., 2005, 2006; Volkert et al., 2006). The mechanical behavior of nanoporous metals warrants attention for two reasons. First, the ligaments, which are of the order of 10-nm wide, impose a severe geometric constraint on dislocation motion and thereby offer an opportunity to investigate the deformation of nanoscale volumes of metal. Second, understanding the mechanical behavior of nanoporous noble metals will facilitate their use in applications that require mechanical integrity, for example, catalysis or actuation. Recently, Hodge et al. performed a systematic study involving nanoindentation of bulk np-au, where the ligament size was varied by annealing (Hodge et al., 2007). They proposed a modified form of the Gibson Ashby equation (Gibson and Ashby, 1997), introducing a Hall-Petch type factor that affected the strength of np-au. Based on their findings, Hodge et al. set a threshold ligament size of 500 nm, above which the Hall-Petch term becomes negligible. The np-au samples described in the current article were thin films with a maximum thickness of 300 nm, ligament widths of nm, and pore diameters of nm. Moreover, indentations were limited to 100 nm in depth. Thus, this study probes the mechanical behavior of nanoporous thin films at a much smaller length scale than previously reported in the literature. Although nanoindentation testing has been performed on np-au thin films (Lee et al., 2007), that work entailed traditional indentation, which does not permit simultaneous microstructural observation. In situ nanoindentation in the transmission electron microscope (TEM) enables the possibility of real-time observation of deformation and simultaneous measurement of load-displacement behavior (Minor et al., 2001; *Correspondence to: T. John Balk, Department of Chemical and Materials Engineering, University of Kentucky, 177 F. Paul Anderson Tower, Lexington, KY , USA. balk@engr.uky.edu Received 13 May 2008; accepted in revised form 1 October 2008 Contract grant sponsor: American Chemical Society Petroleum Research Fund; Contract grant number: G10; Contract grant sponsor: Scientific User Facilities Division of the Office of Basic Energy Sciences, U.S. Department of Energy; Contract grant number: DE-AC02-05CH11231; Contract grant sponsor: National Center for Electron Microscopy (NCEM Visiting Scientist Fellowship). DOI /jemt Published online 22 January 2009 in Wiley InterScience ( wiley.com). VC 2009 WILEY-LISS, INC.

2 IN SITU INDENTATION OF NANOPOROUS GOLD THIN FILMS 233 Warren et al., 2007). Only recently has this technique been applied to the study of np-au deformation. Using this technique, Sun et al. reported observations of the motion of dislocations through np-au ligaments and their interaction with each other (Sun et al., 2007). In the present study, np-au thin films with various thicknesses were tested by in situ TEM nanoindentation. In addition to measuring the load-displacement behavior of the films and observing dislocation motion within Au ligaments, the effect of indenter displacement rate on the mechanical response of these np-au films was investigated. The motivation for varying the indentation rate was provided by the fortuitous realization that two different tests, which exhibited noticeably different load drop intervals, had been conducted at different indentation rates. MATERIALS AND METHODS When alloyed with a sacrificial metal such as Ag, noble metals such as Au can be subjected to a selective dissolution process known as dealloying that dissolves the Ag atoms, producing a nanoporous noble metal nanostructure via surface diffusion (Newman et al., 1999; Sieradzki et al., 1989). The resultant structure consists of an interconnected network of ligaments and open porosity, with a high surface-to-volume ratio [other researchers report values of 4 7 m 2 /g (Ji and Searson, 2002)], which could make np-au a relevant material for applications that require large amounts of active surface area, such as catalysis. When Au-Ag alloys with at% Au are immersed in HNO 3,Ag is selectively dissolved, and np-au with pore diameters and ligament sizes of the order of 10 nm or larger is formed (Erlebacher et al., 2001; Ji and Searson, 2003). However, there is typically a finite amount of residual Ag that remains in the np-au. Following the dealloying process, energy dispersive X-ray spectroscopy revealed a residual Ag content of 10 at% in the 300 nm np-au films. Although most studies of np-au have focused on bulk or free-standing thin film samples, it has been shown that blanket thin films of np-au supported by Si substrates can be produced with uniform porosity and no cracking (Sun et al., 2008). This form is most relevant to the current study, as it readily allows for the in situ nanoindentation of np-au in the TEM. Au-Ag alloy films with 30 at% Au and thicknesses of 75, 150, and 300 nm were deposited onto wedgeshaped Si substrates by cosputtering from Au and Ag targets (ORION system, AJA International, base pressure Pa, 99.99% Au and Ag target purity). Sputtering power and argon pressure were set during film deposition to produce films with a Au content of 30.5 at%. Before sputtering the Au-Ag alloy layer, a 10-nm Ta interlayer and a 10-nm Au interlayer were sputtered. This combination of interlayers produced excellent adhesion of the final np-au film to the Si substrate. As-sputtered specimens were dealloyed by immersion in concentrated HNO 3 (70% stock concentration) for 30 min, followed by rinsing in ethanol and slow drying in air. Some specimens were annealed in air at 2008C for 10 min, to coarsen the porous structure. In situ nanoindentation of dealloyed np-au on Si wedges was performed with a Hysitron Picoindenter TM inside a JEOL 3010 TEM (operated at 300 kv). A cube corner indenter with radius of curvature 100 nm was used. All indentations were performed under displacement control and the indenter displacement rate was varied from 1.5 to 30 nm/s (constant for a given test). Ligament size was measured from scanning electron microscopy (SEM) plan-view images of samples. Based on measurements per film thickness, it was determined that the average ligament width was 15 nm for as-dealloyed films (ligament width ranged from 7 to 23 nm). Films that had been annealed at 2008C exhibited an average ligament width of 30 nm (with a range of nm). Pore size could not be reliably measured from the micrographs, and instead was calculated from the ligament width and relative density. According to Gibson and Ashby s book on porous materials (Gibson and Ashby, 1997), the relative density (ratio of porous film density to the density of solid Au) is equal to (d/l) 2, where d is ligament width and l is cell size (ligament width plus pore diameter). For the asdealloyed np-au films studied here, relative density was calculated to be 35%. This was determined by taking the volume percentage of Au in the precursor alloy (the same as the atomic percentage of 30.5%, due to the nearly identical lattice parameters of Au and Ag) and accounting for the measured decrease in thickness of 13% that occurred during dealloying of np-au on Si wedge samples. Because of this contraction, the film had only 87% of the original thickness, so the nominal density of 30.5% was divided by 87% to achieve a corrected relative density of 35%. From this density, the pore size was calculated to be 10 nm. For the annealed np-au films, the calculated pore size was 20 nm. Figure 1 illustrates the sample geometry used for in situ TEM nanoindentation. Here, a focused ion beam (FIB) image has been stretched into a perspective view and further altered to show the wedge shape of the specimen. The electron beam direction is oriented vertically downward in Figure 1, and the diamond tip moves to the left, contacting the ridge of the wedge during indentation of the film. Depth of indentation was limited to approximately half the film thickness, and no noticeable effect of the Si substrate on the load-displacement curves was observed. This statement is based on the comparison to separate in situ indents that were observed to contact the Si wedge and which were accompanied by loading slopes one order of magnitude higher than those in the load-displacement curves for np-au presented below. RESULTS Thin films of np-au consisted of an open network of interconnected pores and ligaments. This is seen in the TEM image shown in Figure 2, where a 75-nm (nominal thickness) film is shown in the as-dealloyed and annealed states. Figure 2a reveals the numerous pores that existed in the as-dealloyed film, which had an average ligament width of 15 nm (measured from TEM and SEM images of multiple np-au films) and an average pore size of 10 nm (calculated from the average measured ligament width and relative density of the films). In the annealed state (Fig. 2b), the np-au film appeared denser, yet still exhibited an open nanoporous structure. The denser appearance, however, was due to the wider ligaments and not due to true

3 234 Y. SUN ET AL. densification of the np-au. In both cases, the actual film thickness (measured from the Au interlayer to the average film surface) was 65 nm. This is indicated by the longer white arrows in Figures 2a and 2b. Dealloying thus caused a contraction of 13% in film thickness, consistent with other results for film-on-wedge samples (Sun et al., 2007). Annealing caused the porous structure to coarsen (average measured ligament width 30 nm and calculated pore size 20 nm), but did not lead to further densification or reductions in film thickness. Fig. 1. FIB image of np-au on Si wedge sample, stretched into perspective view to provide a schematic illustration of the sample/indenter geometry for in situ TEM nanoindentation. The electron beam direction is vertical, oriented perpendicular to the ridge of the Si wedge, and the direction of indentation is into the wedge. After deposition onto the Si wedge, this 300 nm np-au film was dealloyed for 30 min. Still images taken from in situ TEM nanoindentation of a 75 nm np-au film are presented in Figure 3. These images were obtained by averaging three successive frames from the in situ indentation movie, in order to average out background noise and improve the quality of these micrographs. In this experiment, the indenter tip was moved forward manually, by sending commands from the control software to indent in small, independent steps (as opposed to the programmed load unload ramp functions used to generate the loaddisplacement curves presented below in Figs. 6 10). Dislocations were nucleated under the indenter tip and moved easily along the axes of ligaments. An example is shown in Figure 3a, which shows the microstructure after a brief period of indentation, where three dislocations (indicated by white arrows) span the diameter of a ligament just beneath the center of the image. These dislocations were not present prior to indentation of the np-au film, but instead were created during the initial period of indentation that preceded the recording of the TEM image in Figure 3a. As indentation proceeded, these dislocations moved up and toward the node. An example of this behavior is shown in Figure 3b, where one dislocation moved into the node, but the other two dislocations (indicated by white arrows) moved only slightly. Further indentation caused these two dislocations to also move into the node. Figure 4 presents frame-averaged TEM images from a second in situ nanoindentation experiment on the same 75 nm np-au film that was shown in Figure 3. Before deformation (Fig. 4a), the ligaments were nearly free of dislocations. During initial indentation (performed manually, in small steps, as was done for the images in Fig. 3), there was a significant amount of dislocation activity within the wider ligament, marked by white arrows in Figures 4a and 4b. Dislocations in this ligament were oriented roughly perpendicular to the film surface, that is, parallel to the loading direction. Additionally, the thin ligament (marked by black arrows in Figs. 4a and 4b) has been sheared nearly to Fig. 2. (a) TEM image of an as-dealloyed 75 nm np-au film, showing an open nanoporous structure with interconnected ligaments. (b) After annealing at 2008C, the 75 nm np-au film exhibited thicker ligaments but experienced no contraction in film thickness. The long arrows in each image indicate the average thickness of the np-au film, which is seen to be nearly the same before and after annealing. The small white arrow in (b) points to the interface between the Ta and Au interlayers, and helps identify the fully dense 10 nm Au interlayer that supports the np-au film.

4 IN SITU INDENTATION OF NANOPOROUS GOLD THIN FILMS 235 Fig. 3. Still images from video sequence acquired during in situ TEM nanoindentation of an as-dealloyed 75 nm np-au film. Dislocations, for example the series of three dislocations indicated by white arrows in image (a), were readily created during indentation, undergoing glide along the axes of the Au ligaments and interacting with other defects in the nodes of the nanoporous structure. (b) After further indentation, one of the dislocations moved up and into the node, leaving two dislocations in the ligament. Fig. 4. (a) TEM image of a second location in the 75 nm np-au film, prior to in situ nanoindentation. (b) Microstructure after a brief period of manual, that is, nonautomated, indentation. A wider ligament, on the right side of these images and marked by a white arrow, experienced more dislocation activity than shown in Figure 3. Also note the thin ligament at the film surface (marked by a black arrow), which was nearly sheared apart in (b). the point of rupture in Figure 4b. It should also be noted that, in the video sequences that yielded Figures 3 and 4, the motion of the indenter was observed to be jerky (as opposed to the smooth motion that would be expected from the continuous load unload ramps that had been programmed for the indenter). This jerky motion was observed in the majority of indentation tests. Other in situ TEM video sequences (not presented in this article) suggest that the jerky motion may be due to bursts of dislocation motion or due to pore collapse during the deformation of np-au. The collapse of a pore during indentation of annealed np-au is shown in Figure 5, which presents still images from a video sequence acquired during in situ TEM nanoindentation. This experiment was run with a continuous, programmed indenter displacement rate of 6 nm/s. The 75-nm thick, annealed film contains wider ligaments (30 nm) and larger pores (20 nm) than the as-dealloyed films. A pore can be seen slightly to the left of center in Figure 5a, marked by white arrows in the middle of the np-au film. The pore overlapped with a ligament, lowering the contrast at the edges, although the pore was still identifiable. During indentation, numerous dislocations moved through the ligaments surrounding the pore. At the same time, the pore was gradually compressed to a flattened, oval shape in Figure 5b. The change in pore shape was not sudden, but instead continuous and smooth, as was also observed for other pores during subsequent indentation tests. The np-au films with 75-nm film thickness (Figs. 2 5) were ideal for obtaining micrographs of the porous structure and in situ videos of indentation, due to their electron transparency and minimal overlap of ligaments in the two-dimensional projected TEM images. However, the 75-nm films did not provide sufficient indentation depth to obtain meaningful load-displacement curves, that is, the load data were not significantly greater than the background noise of the measurement system. This is likely due to the limited total contact area for indentation of the 75-nm films, which were not subjected to indentations as deep as those in the thicker films. On the other hand, the 150 and 300 nm np-au films, although not ideal for observation of microstructure and dislocations, yielded interpretable and repeatable indentation curves for the measurement of mechanical behavior.

5 236 Y. SUN ET AL. Fig. 5. Still images from in situ TEM nanoindentation of a 75 nm np-au film that had been annealed at 2008C. (a) Before indentation begins. (b) Near the end of indentation. During indentation (displacement rate of 6 nm/s), the pore in the center of the film collapsed continuously (not abruptly). Before and during pore collapse, there was significant dislocation activity within the ligaments surrounding the pore. Load drops were observed during indentation of the thicker np-au films. This is apparent in the load-displacement plots of Figure 6, each with a consistent spacing between load drops. These load drops have not been observed by other groups performing indentation testing of np-au, perhaps due to the much smaller length scale of the tests in the current study; indentation depths ranged from 60 to 120 nm in this study, as opposed to depths of 600 nm in the literature (Biener et al., 2005). The curves in Figure 6 were obtained from an annealed 300 nm np-au film that was indented at various displacement rates, decreasing from 30 nm/s in Figure 6a to 7.5 nm/s in Figure 6d. This was done to investigate the effect of loading rate on deformation behavior. Overall, the distance interval between load drops decreased with decreasing displacement rate. At the highest rate (Fig. 6a), the most obvious load drops were spaced 20 nm apart. However, closer inspection (by magnifying the horizontal axis) of Figure 6a revealed smaller, more closely spaced load drops, and the average measured spacing of all load drops was 11 nm. It is noted that Figure 6b, which was obtained at a displacement rate very similar to that for Figure 6a, exhibited load drops that were more uniform in magnitude and appeared to be more regularly spaced than those in Figure 6a. However, the average measured interval spacing was 11 nm, the same as that in Figure 6a. When analyzing these load-displacement curves, care should be taken to identify all load drops, not just those that are most prominent. Similar tests were performed on an as-dealloyed 300 nm np-au film, but over a broader range of indenter displacement rates. Figure 7 presents load-displacement data from five indentation experiments. As was the case in Figure 6, a decreasing rate of indenter displacement caused a decrease in the spacing of load drops. For the slowest loading rate (1.5 nm/s, Fig. 7e), the load drop interval was so short that the load data may appear to be noisy, and casual observation of this plot may result in the false conclusion that it exhibits a large amount of scatter. As shown in Figure 7f, however, this variation in load during indentation was still due to discrete load drops. Without knowledge of the dependence of load drop interval on loading rate, one could mistakenly attribute the load variations in Figure 7e to scatter. DISCUSSION Significant numbers of dislocations were nucleated and underwent glide during the indentation of np-au. This was observed during all indentation tests, as shown for example in Figures 3 5. Plasticity in this material is carried by dislocations, and np-au thin films exhibit ductile behavior, as would be expected based on the behavior of bulk Au. This is in contrast to the brittle behavior of bulk np-au, which typically cracks when subjected to tension or bending during handling. However, this apparent discrepancy is in agreement with the findings of Li and Sieradzki, who performed threepoint bend tests on bulk np-au samples of varying pore/ ligament size and found that samples significantly larger than their intrinsic pore size were more brittle (Li and Sieradzki, 1992). In the case of the thin films examined in the current study, film thickness was only 3 12 times the cell size (ligament width plus pore diameter) of the np-au, and thus the films would be expected to behave in a more ductile fashion. The decrease in the spacing of load drops at slower indentation rates could be due to a kinetic effect. A slower loading rate should allow more time for dislocation nucleation to occur, improving the ability of dislocation production to keep pace with the imposed deformation, and thereby leading to more closely spaced load drops (in agreement with Figs. 6 and 7). During analysis of the data, the question arose of whether the load drops occurred at a constant time interval (as opposed to a distance interval), which would strongly suggest a kinetic (or statistical) effect in the plastic deformation of np-au films. To explore this idea, the indentation data from Figures 6 and 7 were also plotted as load-time curves. These are presented in Figures 8 and 9, and the curves exhibited load drops with distinctly different shapes than in the load-displacement plots. Indeed, the load drops were more easily identified in Figures 8 and 9 (e.g., compare Figs. 6a and 8a; Figs. 7c and 9c). In several cases, the load-time plots revealed load drops that had not been recognized in the corresponding load-displacement curves (e.g., Figs. 8a vs. 6a). Once the load-time curves have been inspected

6 Fig. 6. Load-displacement curves for an annealed 300 nm np-au film indented at various displacement rates v:(a) 30 nm/s; (b) 28 nm/s; (c) 15 nm/s; (d) 7.5 nm/s. As displacement rate v decreased, the average distance interval between load drops decreased. Fig. 7. Load-displacement curves for an as-dealloyed 300 nm np- Au film indented over a broad range of displacement rates v. (a) 30 nm/s; (b) 15 nm/s; (c) 7.5 nm/s; (d) 3 nm/s; (e) 1.5 nm/s. (f) Detailed view of the loading curve from (e), indented at 1.5 nm/s. As the displacement rate v decreased, the average distance interval between load drops decreased so much that the data may appear to suffer from a high amount of scatter. Figure (f), however, shows that this actually is not the case: the loading curve exhibited very closely spaced drops.

7 Fig. 8. Load-time curves of the annealed 300 nm np-au film deformed at various displacement rates. These plots were constructed from the same data used for Figure 6, but exhibit load drops with clearly different shapes. (a) 30 nm/s; (b) 28 nm/s; (c) 15 nm/s; (d) 7.5 nm/s. Load drops were more easily recognized in these load-time plots, which in some cases revealed additional load drops that were not apparent in the load-displacement curves. Fig. 9. Load-time curves of the as-dealloyed 300 nm np-au film deformed at various displacement rates. These plots are from the same tests portrayed in Figure 7. (a) 30 nm/s; (b) 15 nm/s; (c) 7.5 nm/ s; (d) 3 nm/s; (e) 1.5 nm/s; (f) Detailed view of the plot from (e), showing the smooth distribution of data along the time axis (as compared to Fig. 7f, where the load drops led to multiple data points at certain displacements).

8 IN SITU INDENTATION OF NANOPOROUS GOLD THIN FILMS 239 Displacement rate (nm/s) TABLE 1. Average spacing between load drops measured during indentation of 300 nm np-au films at various displacement rates Load drop interval (nm) Load drop interval (s) [Calculated] Load drop interval (s) [Measured] As-dealloyed Annealed As-dealloyed Annealed As-dealloyed Annealed The temporal spacing of load drops was obtained in two ways: dividing the interval distance by loading rate, and measuring from load-time curves such as those in Figures 8 and 9. and these additional load drops identified, the careful observer can perhaps notice these drops in the original load-displacement curves. Table 1 summarizes the average load drop intervals, as a function of loading rate, obtained from multiple tests on as-dealloyed and annealed 300 nm np-au films. The spacing of load drops was first measured from the load-displacement curves (Figs. 6 and 7) using the bottom edges of load dips. Average load drop spacing was determined from the steeper portion of each curve, and only over the region where load drops actually occurred (i.e., not across the entire load-displacement curve). As a first estimate of the equivalent load drop interval in time, these average distances were divided by the indenter displacement rate for a given test. Finally, the intervals were measured from the load-time curves in Figures 8 and 9. Comparison of the two sets of time interval data indicates that the values are generally consistent, although certain disparities exist. These are due to the inability of load-displacement curves to reveal all load drops, as opposed to the load-time curves, which clearly reveal certain load drops not seen in the load-displacement curves. This is more of an issue at faster displacement rates. Overall, the data in Table 1 show that, as the indentation rate decreased, load drops occurred at shorter distance intervals and were separated by longer time intervals. Initially, it was believed that the spacing of load drops corresponded to the average pore size in the np- Au films (Sun et al., 2007). The load-displacement curves from indentation of as-dealloyed 150 and 300 nm np-au films exhibited load drops at regular intervals of 10 nm. This interval spacing was equal to the average pore size calculated from measured ligament width and relative density, and the load drops were interpreted as resulting from the collective collapse of successive layers of pores during film compaction. To test this hypothesis, annealed np-au was also indented, since it was known that annealing at 2008C causes the ligament width to double but does not cause further contraction in the thickness of np-au films on Si (Sun et al., 2008). In light of the newer data presented in this article, however, the spacing of load drops does not appear to be determined by pore size. Indeed, the annealed 300 nm np-au film contained larger pores than the as-dealloyed film, yet exhibited load drops at shorter distance intervals (compare Figs. 6a and 7a; compare Figs. 6c and 7b). Additionally, the collapse of pores during slower loading experiments (e.g., 6 nm/s, as shown in Fig. 5) was gradual, not abrupt, and thus would not explain the load drops. During indentation of thicker films at faster loading rates, however, the indenter motion was jerky and suggested that collective displacement, perhaps due to dislocation motion or pore collapse, was occurring. A possible explanation for this observation is that at faster loading rates, the threshold stress required for dislocation nucleation was achieved simultaneously in multiple areas of the np-au film, leading to collective displacement of the film and jerky motion of the indenter tip. Systematic testing of thinner films at varying loading rates, to observe the behavior of dislocations as well as changes in the shapes of ligaments and pores during indentation, would be helpful in clarifying this phenomenon. In Figure 10, indenter load and displacement are plotted simultaneously versus time. It is seen that the load drops were accompanied by changes in the displacement rate, that is, the rate of indenter displacement varied due to the load drops. These small displacement excursions (forward surges) occurred because the feedback algorithm was not able to restore the position of the tip to its proper position in time. This was most noticeable at higher loading rates (Fig. 10a). For slow loading (Fig. 10c), the indenter displacement rate appeared constant, because the control system had more time to counter the sudden decrease in contact stiffness as the load dropped rapidly. The intervals between load drops (in distance and in time) were plotted as a function of indenter displacement rate, on a log log scale, to determine if there was a functional dependence. No clear functionality was seen. The data are therefore plotted on a normal scale in Figure 11, which presents the average interval spacings for as-dealloyed and annealed 300 nm np-au films (data taken from Table 1). Data for both specimens exhibited similar trends. In Figure 11a, it is seen that the distance interval increased with increasing displacement rate, and it appears that the distance interval may plateau at nm. However, additional testing would be required in order to determine this conclusively. In Figure 11b, the time interval between load drops decreased with increasing displacement rate, but did not exhibit a plateau. This suggests that further increases in loading rate (above 30 nm/s) would reduce the time interval to the point where the load drops could not be identified as individual events, but instead would be of the order of the data sampling rate.

9 240 Y. SUN ET AL. Fig. 11. Plots of the average interval between load drops as a function of indenter displacement rate (data taken from Table 1). For both the as-dealloyed and annealed 300 nm np-au films, higher displacement rates led to (a) increases in the distance between load drops and (b) decreases in the time between load drops. [Color figure can be viewed in the online issue which is available at wiley.com.] Fig. 10. Overlaid plots of load and displacement versus time, for indents of the as-dealloyed 300 nm np-au film from Figures 7 and 9. (a) 30 nm/s; (b) 7.5 nm/s; (c) 1.5 nm/s. At faster loading rates, for example, 30 nm/s in (a), the clearly separated load drops led to noticeable nonlinearities in the displacement ramp, despite these tests being run in nominally displacement-controlled mode. [Color figure can be viewed in the online issue which is available at www. interscience.wiley.com.] The spacing of load drops is clearly not governed solely by the pore size of np-au, and these drops do not occur at a fixed interval of time/distance for all film thicknesses and all indentation rates. For a given film indented at a certain displacement rate, the load drops do occur at regular intervals (values for each test condition are listed in Table 1). Although the distance interval between load drops is not simply equal to the average pore size of the np-au film, the porous structure may still play a role in the occurrence of load drops during in situ TEM nanoindentation. It is postulated that the interval spacing is related to the collective deformation of ligaments and mediation of plasticity by dislocations in np-au. At the lowest loading rates, dislocations have ample time to nucleate and carry the imposed deformation. As the indenter displacement rate is increased, the material must respond by deforming more quickly, and the time interval between load drops decreases. At the same time, dislocation nucleation, which is kinetically limited, may not be able to supply adequate numbers of dislocations to accommodate smooth and continuous plastic deformation. Strain energy accumulates within the np-au ligaments and, when it is released, causes load drops that represent a burst of dislocation motion. It is not yet clear how the nucleation and motion of dislocations affect the relationship between loading rate and load drop intervals. Further studies will be performed to investigate this in more detail.

10 IN SITU INDENTATION OF NANOPOROUS GOLD THIN FILMS 241 SUMMARY Thin films of np-au, ranging in thickness from 75 to 300 nm, were deposited on Si wedge samples and subjected to in situ nanoindentation in the TEM. The narrow Au ligaments (15 30 nm wide) provided a nanoscale constraint on dislocation motion. Dislocations were generated during indentation and moved along ligament axes, interacting with other dislocations in the nodes that connect ligaments. Motion of the indenter tip was observed to be jerky (as opposed to smooth and continuous), possibly due to collective displacement within the nanoporous film structure. This collective motion could be due to a burst of dislocation motion in multiple ligaments at once, or it could be due to the simultaneous collapse of multiple pores. Indeed, these two possible scenarios may be related and both could occur. Load drops were observed in the load-displacement curves measured during in situ TEM nanoindentation of thicker ( nm) np-au films. Observation of these load drops, which have not been reported by other research groups, was enabled by the smaller length scale of the indentations (typically limited to 100 nm or less), as compared to other studies in the literature. Initially, it was believed that these load drops corresponded to collective collapse of a layer of pores in the nanoporous structure, because the load drop interval of 10 nm measured in an as-dealloyed film was the same as the pore size calculated for that film. However, indentation testing of annealed films (with larger pores) and systematic variation of the indenter displacement rate revealed that the relationship between load drop interval and pore size is not that simple. In annealed films with larger pores, load drops generally occurred at similar or slightly shorter distance intervals than in as-dealloyed films. 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