In order to better observe the rearrangements that occur in association with avalanche
scaling, an experiment similar to those discussed previously was performed in situ under
the beam of a TEM. Two frames from a video of these experiments are shown in Figure 5.8, along with the force curve before and after a load drop occurs. A rearrangement about 60 nm across is visible in the center of the image. This rearrangement corresponds with the
load drop of 2.3 µN, which is visible in the inset in Figure 5.8b. The slight recoil toward
the bottom of the load drop occurs because the experiment is performed in displacement control, but the controller does not respond quickly enough to prevent overshoot when
(a) (b)
Figure 5.8: Two frames of a video from an indentation experiment performedin situ under
the beam of a transmission electron microscope, viewed from the side, (a) before and (b) after a load drop occurs. In the inset force curve of (b), the load drop is visible at right. The silicon substrate is in the top right behind the inset, the diamond indenter is in the bottom left, and the nanoparticle film is in the center. The arrows point to locations where rearrangements, corresponding with the load drop, are visible.
micrograph, indicates that it more closely matches the STZ picture of rearrangements than the T1 process; it may even be large enough to constitute a system-spanning rearrangement of multiple particles.
Due to the larger contact area, the magnitude of this load drop is much greater than the maximum load ever applied in AFM-based nanoindentation experiments in this study. The ranges of load drop magnitudes that can be explored by the type of experiments do
not substantially overlap. Nevertheless, these in situ experiments exhibit an exponential
distribution, as shown in Figure 5.9, which is similar to the high-magnitude cutoff observed in the AFM-based experiments. The exponential distribution is consistent for rearrange- ments that occur in dynamic contact, in which the indenter continues to vibrate but is in contact for the majority of an oscillation cycle, and the distribution is also consistent for rearrangements that occur in rigid contact where vibration has ceased. The oscillations out of contact do not feature the same scaling. Unlike in Figure 5.2, these data are not normal- ized by the total number of load drops. These experiments were performed in displacement control with a maximum depth specified, so the maximum force varies between indentations
0 0.5 1 1.5 Load drop magnitude [nN]
100 101 102 103
Number of load drops
Rigid contact, N = 612 Dynamic contact, N = 5583 Out of contact, N = 6151
Figure 5.9: The distribution of load drop magnitudes for experiments performed in situ in the TEM. The blue curve represents load drops that occurred before the indenter made contact, which are part of the overall noise floor of the instrument. The root mean square of this noise is approximately 200 nN. The orange curve represents load drops that occurred after the indenter first made contact, but where mechanical oscillations caused the indenter to vibrate out of contact. The yellow curve represents load drops that occurred after the indenter made rigid contact, and was no longer vibrating.
and normalizing the data by the number of indentations would be nonsensical.
Because many of the load drops occurring in dynamic or rigid contact are smaller in magnitude than the amplitude of free oscillation out of contact, it must be demonstrated that the load drops in contact are not artifacts of the instrument’s background noise. The similarity between the distributions corresponding to dynamic and rigid contact strongly
suggests that these distributions represent the same mode of deformation. Conversely,
the distribution due to the noise floor of the instrument is distinct from the other two distributions. This parallel between the dynamic and rigid contact data, and distinction from the out of contact data, confirms that white noise can be distinguished from authentic rearrangements, and that the exponential distributions observed here are reflective of the response of the material.
The exponential distributions observed in the in situ TEM nanoindentation experi-
ments are consistent with the distribution shape observed in avalanche scaling above the upper-magnitude cutoff. Rearrangement events whose magnitudes are near or above this cutoff may be interpreted to be system-spanning, which is consistent with the large-scale
rearrangement appearing visibly in multiple locations in Figure 5.8b. However, the decay lengths of the exponential distributions are on the order of 140-180 nN, which is not only larger than the cutoffs or decay lengths observed in the AFM-based experiments but also larger than all but the largest load drops ever observed in AFM. This larger decay length may be due to the larger contact area, or to the increased mechanical noise present in this
system. In the in situ TEM-based system, the root mean square of the mechanical noise
out of contact is approximately 200 nN, whereas for the AFM, it is only 0.5 nN. The vi- bration of the apparatus also serves to nucleate plastic rearrangements, and this dynamic effect combined with the larger contact area are likely responsible for the greater decay length. No power law scaling is observed, potentially because the TEM apparatus does not have adequate resolution to observe load drops less than 100 nN in magnitude, which
a typical range for the cutoff as discussed previously in Section 5.2. Nonetheless, the in
situ experiments demonstrate visually that load drops correspond with small particle-level
rearrangements rather than any other mechanism of plasticity such as fracture or plowing. It is worth mentioning that the TEM-based experiments are performed under high vacuum conditions, in which capillaries would not form. This stands in contrast with the AFM experiments, which were all performed at ambient pressure with relative humidity between 18% and 100%. However, as discussed in Section 5.2, the strength of bonds appears to have no effect on avalanche scaling except to change the number of events that occur. Therefore, it is reasonable to assume that the physical mechanisms that are at work in the AFM-based experiments are at work in the TEM-based experiments as well.