Peer review of: Unique universal scaling in nanoindentation pop-ins (2020)

Reviewers' Comments: 
 
Reviewer #1: 
Remarks to the Author: 
In this manuscript, the authors investigated experimentally the statistical effects hidden in the 
noise of force-depth nanoindentation curves in BCC iron. The authors find that the distribution of 
the pop-in magnitudes transitions from Gaussian-like for the first pop-in to power-law-like for the 
second and subsequent pop-ins, and they demonstrated it by nanoindentation testing with 
measurements of the contact stress drop. The Gaussian-like distribution of the first pop-in appears 
consistent with the theoretical distribution based on the thermal activation theory of dislocation 
nucleation. Thus, the authors' data indicate that the first pop-in is dominated by a thermal 
activation process of dislocation nucleation, as reported in many past studies. Further, the authors 
conclude that more importantly, the second and subsequent pop-ins are dominated by dislocation 
avalanches, which follow power-law statistics. 
 
This is a well written manuscript with an important and novel conclusion that should become 
publishable in a high impact journal such as Nature Communications. However, there are several 
steps to be performed before recommending such a publication. My concerns and questions are 
posed below: 
 
1. The authors state that power-law exponents have not been identified in experimental testing of 
nanoindentation. This is not true since in: 
Crystals 2019, 9(12), 652; https://doi.org/10.3390/cryst9120652 
there is a clear study of various FCC metals in a very high-throughput study of nanoindentation 
force-depth curves. There, first pop-ins were not separated from second pop-ins, but other 
conditions (Berkovich tip, load-control) appear similar. There, it appears that the exponent the 
authors investigated is closer to 1.6-2.0 for FCC metals. This is a very interesting difference that 
not only should be mentioned by the authors in their manuscript, but also should be investigated if 
possible (by testing an FCC metal, such as Ni), in order to strengthen significantly their message. 
 
2. The authors display a Force-Depth curve in Fig.1 that suggests that their maximum depth is 
approximately 100nm. This statement is also supported by their description in Methods, where 
they emphasize that they set their max force to 1mN (as shown in Fig.1). However, the 
Supplementary Information contains a post-indent image (last page) that seems to suggest that 
the indents went much deeper than 100nm. Is it possible to include (possibly in the supplement) a 
figure with all indentation curves that were utilized for producing the distributions in Fig.2 ? 
 
3. The authors fit the statistical distribution of the first pop-ins to a rate nucleation model (Eq.2). 
While this is very interesting, there is a crucial dependence on temperature that needs to be 
confirmed in some way. To my understanding, no prior publication has explicitly demonstrated a 
statistical dependence of these events on temperature, and the authors' model is crucially 
dependent on it. It is imperative that the authors demonstrate in some way that the experimental 
data of the first pop-ins contain significant temperature dependence that could be modeled in such 
a simple manner. While performing an appropriate temperature-dependent experiment would be 
ideal, another possibility would be that the authors find data from other publications on the subject 
that confirm this model. 
 
4. The first pop-in distributions in Fig.2 appear skewed in log scale. Is it possible that the 
distributions are also shown in linear scale? 
 
5. The molecular dynamics simulations in Fig.3 are interesting. However, it is not clear to me why 
the authors chose to not show the event distributions from these simulations? Don't they have 
enough events? It would be important that the authors comment on this issue, since MD 
simulations can provide insights for such statistical effects, and especially the temperature 
dependence of the first pop-in events. 

6. Another issue with Fig.3 and the associated discussion in the main text is that the event 
definition is confusing. For a displacement-controlled simulation, one should define "equivalent" 
displacement bursts out of the force-drops, something that is discussed in detail in Ref.[19] for 
example. The definition of a displacement burst out of the displacements that are "recovering" the 
load, should be at least identified as a "specially" defined one, and should be mentioned as one. 
The issue with this definition is that the aforementioned displacements are force-balanced by the 
applied loads, so they are not formally avalanche events, which should be by definition out-of-
equilibrium. That said, the authors can only choose to focus on the force drops, which can be 
associated to displacements through appropriate unit change by using the elastic modulus. 
 
7. In the MD simulations, is there any significant difference between the statistical distributions of 
the first event, compared to the next ones? Can the authors comment on any evidence they may 
collect? 
 
 
 
Reviewer #2: 
Remarks to the Author: 
The manuscript presents an interesting study of the stress and strain burst statistics during nano-
indentation of iron single crystals. The authors present experimental results and MD simulations 
showing that pop-ins are power law distrubuted, apart from the first nucleation event that is 
approximately Gaussian distributed. While I judge that the work has merit and could be acceted in 
Nature Communications, the authors did not exploit fully the results they have at hand and some 
obvious questions remain unanswered. I suggest a series of additional analysis that should 
strengthen the conclusions of the paper. 
 
-The authors claim that displacement steps Dh are not power law distributed, while stress drops 
are. I can not see any convincing evidence for this. The "power laws" in Fig. S1 are as good (or as 
bad) as those in Fig. 2. I suggest to bin in logarithmic scale: this is conventionally done for power 
law distributions. Please also show bin-free distributions by reporting (in the supplement) the 
cumulative distribution by simply rank-ordering the recorded values of Δh (and Δσ). 
 
-The authors make a complicated argument with several assumptions to measure stress drops. 
While all this might be reasonable, I would like to see a demonstration. This could be obtained by 
MD simulations where it is possible to have at the same time access to stresses and 
displacements. The authors should verify that their relation between stress drops and 
displacement is correct. 
 
- It is argued that MD simulations can not be compared with experiments because of the different 
loading mode. The argument is not very convincing. I do not understand the claim that 
displacement control was needed "to mantain stability". One can certainly apply a force to the 
indenter and slowly increase it and I can not see how this will affect the stability of the simulation. 
But even if there is a practical reason for which force driven simlations are unfeasible (and the 
authors should explain it with much more care), the authors should still do more to compare 
experiments and simulations: for instance they should measure the pop-in stress drop distribution 
from MD simulations. It is really a pity that almost non information is extracted from the MD 
simulations. 
 
- Are the dh steps statistically independent on time? Clearly the first step is larger but are all the 
other steps statistically equivalent? To test this the authors could plot 
<Δh| h> vs h (i.e. average step size at given displacement level) and/or <Δh| k> with k being the 
pop-in number (first, second, etc). Since N=1000 indentations are performed this should not be a 
problem. The same analysis should be performed for the stress drop. Doing this is extremely 
important to understand the universality class of the distribution. If the Δh (or Δσ) signal is not 
stationary then the high exponent of the distribution (i.e. β=2.8) can be explained as a result of 
the integration of a non-stationary signal. This is discussed in previous papers on crackling noise, 
see for instance Durin, G., & Zapperi, S. (2006). The role of stationarity in magnetic crackling 
noise. Journal of Statistical Mechanics: Theory and Experiment, 2006(01), P01002. 
 
- minor point: I do not understand the role of c in the x-axis of Fig. 2. The c constant is not 
discussed anywhere and looks completely useless (since of course c cancels out!). 
 
 
 
Reviewer #3: 
Remarks to the Author: 
 
This manuscript describes a series of nanoindentation experiments performed on iron single 
crystals, and preliminary analysis of molecular dynamics simulations of the same process. The 
central claim is that the contact stress drop of the initial pop-in roughly follows a Gaussian 
distribution, whereas the contact stress drop of the subsequent pop-ins roughly follows a power 
law distribution. The exponent of the power law is empirically measured to be higher than those 
generally observed in micro-pillar plasticity. This is suggested as evidence that the phenomena 
belong to different universal scaling classes. 
 
Before continuing with the techniques and analysis, I would like to discuss the significance of the 
claims. Whether or not the manuscript provides sufficient support for the claim that the physical 
process underlying the second and subsequent pop-ins belongs to a different universality class 
than that behind micro-pillar plasticity, it is unclear why this would be a result of general interest. 
I would certainly be interested in a precise explanation of the differences between these processes, 
particularly with regard to dislocation interaction and multiplication. That said, just reporting that 
they occur with different probability distributions of contact stresses does not substantially 
increase my understanding. As for the question of universality class, the knowledge that two 
processes belong to the same universality class (in principle) allows the transfer of some 
understanding about one process to the other. That is not done here, with the claim of differing 
universality classes amounting to the tautological statement "different processes are different". 
 
I do wish to acknowledge that the experiments are not trivial to perform, and that the authors 
have collected a substantial quantity of data about a question that could be of general interest. 
The analysis and conclusions feel incomplete though, and partly for that reason I do not believe 
that this manuscript would substantially change thinking in the field. 
 
I have several concerns with the techniques and analysis. These are enumerated below: 
 
1. The definition of a second pop-in is not precise. The authors set an arbitrary velocity threshold 
above which the event is identified as a pop-in, but this is unsatisfactory for several reasons. First, 
have the authors verified that the events they sample are not simply electrical and mechanical 
noise? The noise in electrical instruments is often pink noise, which could explain the observed 
power law probability distribution they observe in Figure 2. One natural resolution would be to 
consider all events after the first pop-in, and to see whether there is a natural decomposition of 
the resulting probability distribution into a noise contribution for the smallest events and 
everything else. Second, the main characteristic of the first pop-in is that there is irreversible 
plastic deformation during the event, but not before. The unloading curves in Figure 1 indicate that 
there is irreversible plastic deformation all along the loading curve after the first pop-in. Then are 
the points identified as subsequent pop-ins at all distinguishable from the rest of the loading curve 
on physical grounds? 
2. Perhaps the difficulty with identifying discrete subsequent pop-ins is that there is effectively 
continuous thermal activation of dislocation-related events. This could be suppressed by increasing 
the indentation rate and decreasing the temperature, thereby strengthening the claim that the 
subsequent pop-ins really are significant events. This could also have the effect of allowing the 
subsequent pop-ins to be more directly related to the athermal activation energies, allowing a 
more fundamental characterization of the phenomenon. Where is the temperature reported? 
 
3. Given the importance of the contact area to the calculation of the stress drop magnitudes, it is 
surprising and concerning that the authors did not verify the assumption that the contact area is 
proportional to the square of the indentation depth. Such verification would be relatively 
straightforward, involving a sequence of interrupted tests and subsequent investigation of the 
surface profile. 
 
4. The authors do not appear to address the possible formation of an oxide layer on the surface of 
the Fe. Such an oxide layer could form very quickly indeed, and be related to the difference 
between the first pop-in (film rupture) and subsequent pop-ins (dislocation multiplication). What 
assurance can the authors provide that such an oxide layer is not present? 
 
5. Have the authors considered fitting the probability distribution of initial pop-ins using the well-
established model of Schuh and Lund (DOI: 10.1557/JMR.2004.0276)? What is the advantage of 
the model derived in the supplementary material over that one? 
 
6. The simulations do not provide any atomistic insight into the processes occurring during the so-
called subsequent pop-ins, and have been performed many times before in the literature. It is 
unclear what value the simulations add to the manuscript. 
 
7. Why does the power-law exponent reported here differ so substantially from that reported in 
Ref. 19? That the power-law exponent in Ref. 19 is entirely consistent with the exponent for micro-
pillar plasticity suggests that this manuscript is the outlier. 
 
8. What is the algorithm that the authors use for the fitting of the models? I don't see any mention 
of this, or the resulting uncertainties in the fitting parameters.