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Journal Club Theme of 15 May 2008: Experimental Mechanics at Nano-scale

Julia R. Greer's picture

Based on much experimental and theoretical work in the last decade or so, mechanical properties of materials at nano-scale are proving to significantly deviate from their bulk counterparts. This is true not only for nano-structureD materials (i.e. composed of nano-scale components like nanocrystalline materials) but also for nano structureS (surface-dominated structures like carbon nanotubes (CNT’s), nanowires, etc.). Nanoindentation has been a very effective and well-characterized technique for determination of hardness, modulus, and stiffness, and for crystalline materials the indentation hardness has been widely shown to be significantly higher at shallower indentation depths (so-called indentation size effect, or ISE). However, inserting a sharp indenter tip into a material inevitably sets up strong strain gradients in the deforming volume, which is often linked to the origin of the ISE. Moreover, the infinitesimal volumes probed via this technique are coherent with the remaining matrix, rendering the effects of free surfaces on mechanical properties inaccessible.

To significantly reduce the effects of strain gradients and to investigate the effects of free surfaces on plasticity of nano-scale single crystals, metallic glasses, and polycrystals, an increasingly popular experimental technique involves uniaxial compression of nano-pillars made out of these materials. For example, with the help of this technique, it was shown that pure metals and metallic alloys exhibit strong size effects in plastic deformation manifested through “smaller is stronger” phenomenon. There are several theories (both computational and experimental) trying to explain the observed size effect, but at this point there is no unified phenomenological model fully explaining these size effects. One of these theories is coined as Dislocation Starvation, or a condition attained in fcc metals when most mobile dislocations annihilate at a free surface leaving the crystal effectively dislocation-free, and subsequent plasticity is dominated by nucleation events. This concept based on experimental work on nano-pillars was first introduced by Greer and Nix  [Phys Rev B 2007], and recent work of Shan, et al [Nature Materials 2008] on in-situ TEM deformation of Ni nano-pillars clearly shows a phenomenon the authors call “mechanical annealing,” which is very consistent with the dislocation starvation mechanism. A common technique for fabricating these nano-pillars involves the use of the FIB (Focused Ion Beam), which inevitably introduces some Ga+ damage into the surface. This damage layer certainly is expected to have some effect on the strength of these nano-crystals. Moreover, in the recent work of Bei, et al, it was shown that Mo micro-posts made without the use of the FIB all attain the theoretical strength of Mo and don’t  show any significant size effect.

In this Journal Club topic, I’d like to discuss the following 4 articles, which involve nano-pillar compression. The first one (Shan, et al) shows the results of in-situ TEM FIB-machined Ni (fcc) nano-pillar compression and postulates that mechanical annealing, or dislocation escape in response to mechanical deformation, is prevalent in fcc metals at these scales. The 2nd one (Bei, et al) – the only one where the compression specimens were not fabricated by using FIB – does not find any size effects in deformation of Mo posts made through selective etching of NiAl-Mo eutectic. And the final, 3rd one (Shan, et al) discusses enhanced ductility and lack of catastrophic failure in metallic glass nanopillars.

As a natural continuation of this discussion, a Journal Club topic on plasticity at sub-micron scale will be led by Professor Wei Cai of Stanford University on July 15th. 


Articles for Discussion:

1. Z. W. Shan, R. K. Mishra, S. A. Syed Asif, O. L. Warren, and A. M. Minor, ”Mechanical annealing and source-limited deformation in submicrometre-diameter Ni crystals” Nature Mater. 7, 115 (2008)

2. H. Bei, S. Shim,, E.P. George, M.K. Miller, E.G. Herbert, and G.M. Pharr, “Compressive strengths of molybdenum alloy micro-pillars
prepared using a new technique” Scripta Materialia 57 (2007) 397–400

3. Z. W. Shan, J. Li, Y. Q. Cheng, A. M. Minor, S. A. Syed Asif, O. L. Warren, E. Ma
“Plastic flow and failure resistance of metallic glass: Insight from in situ compression of nanopillars” Phys. Rev. B  77, 155419 (2008)

Comments

Pradeep Sharma's picture

Julia,

Thanks for the interesting discussion. Although I don't personally work in this research topic I have sporadically followed, with fascination, some of the developments in this subject. Accordingly I have some "layperson" oriented questions: At the moment what is your own personal take on the differing experimental results (i.e. some exhibiting size-effects, some not)? If I  understand correctly, plasticity size-effects are also seen in specimens where there are minimal strain gradients; so obviously some other mechanisms are at play (e.g. you mentioned dislocation starvation as one possible cause). However, this probably does not mean that strain gradients do not lead to size effects. As you allude, perhaps there are multiple mechanisms operative in general (although the nanopillar experiments cleverly isolated away the strain gradients). Has there been any success in creating, in the style of now classic Ashby's deformation mechanism maps,  some sort of "size-effect mechanism" maps?---for example, a schematic that provides insights into the range of length scales or other enviornmental conditions under which perphaps strain gradients are a dominant mechanism versus dislocation starvation versus something else.....

Julia R. Greer's picture

Pradeep,

This is a very interesting observation. Strain gradient-based size effects certainly play a key role in the plasticity of single crystalline solids (regardless of the sample dimensions) - when the deformation is inhomogeneous. What the pillar experiments have revealed is that even in the absence of strain gradients  there are size effects in single crystals , which means that other  plasticity mechanisms must be operating at nano-scale - especially when there are free surfaces and/or interfaces in the deforming specimen. I don't believe a deformation map with various governing mechanisms for plasticity has been created - mainly due to the fact that this is still a topic of great controversy. For example, while it might be more or less agreed that in nano-scale single crystal fcc metals dislocation starvationis the prevalent plasticity mechanism, it is not the case for bcc metals (we have recently published a paper in PRL on it - Brinckmann, Kim, and Greer). Even more interesting is the size effect in metallic glasses where, of course, there are no dislocations, yet a size effect is observed. The computational community is very much engaged in investigating this topic, as well. For example, based on at least some preliminary first principles calculatios, once the size of the specimen becomes low enough, apparently softening is observed (reference, for example, Marian and Knap, 2008). The idea is that the surfaces themselves have a certain amount of pre-stress associated with them, which energetically affects the deformation behavior. 

So, the overall picture... there is still much work to be done on the origins of plasticity at nano-scale in different types of crystals, but what we already know is that it is different at nano-scale no matter what the material is.

Thank you,

Julia 

 

Julia Rosolovsky Greer

Amit Acharya's picture

Dear Julia,

1) In interpreting the pillar compression tests as has been conventionally done, how does one rationalize away the inhomogeneous deformations that should result from the base of the pillar being 'built-in' to the substrate?

2) From the purely mechanics viewpoint, it is in general very hard to induce homogeneous deformation in a nonlinear solid undergoing finite deformation, especially something as anisotropic as a single crystal - one typically would need very complicated boundary tractions to be applied to achieve homogeneous deformation, or else there would be boundary inhomogeneities. In this connection, it would be instructive to hear the experimentalist point of view on why these effects are not serious contenders for inducing deformation inhomogeneities in the pillar experiments.

3) Somewhat of an aside, but a related question to this thread (not necessarily for only you, but to other experimentalists too). The size effect in the presence of inhomogeneous plastic deformation - is it predominantly an internal stress effect or is it due to work-hardening? My feeling is that if it were a predominantly internal stress effect, the size effect would necessarily go both ways, harder and softer with decreasing specimen size, depending upon, roughly speaking, the sign of the plastic distortion gradient. On the other hand, if it was a predominantly work-hardening related effect, i.e. the GND/excess/polar dislocations set up by the inhomogeneous deformation act as obstacles to plastic flow via short-range interactions, then one would only see hardening with decreasing specimen size.

So, we need wisdom from the experimentalists - what mechanism 'actually' dominates when we see predominantly  harder response with decreasing size?

thank you,

Amit

 

Julia R. Greer's picture

 Dear Amit, 

Thank you for the comment! 

I am addressing your points in order:

 1) Sure, there are some inhomogeneities in the base of the pillar, however even when the pillars are fabricated from a thin film on a substrate, significant size effects are observed. Moreover, the base deformation happens relatively late in the test, as we are observing in our in-situ SEMentor system, so most of the data corresponds to the more-or-less homogeneous compression. The effects of the pillar itself acting as a rigid flat punch indenter are incorporated into the stiffness calculations (or they should be).


2) At the scale that these experiments are performed, the "inhomogeneities" are significantly smaller than the overall pillar size (on the order of the Burgers vector/diameter). Sure, the surfaces are not atomically smooth, and from that viewpoint, no deformation can be homogeneous. In the pillar experiments, "homogeneous" really means "symmetrical" - as in, throughout the deformation the pillar gradually becomes smaller and fatter, without generating any instabilities as would be the case with the single-slip orientation.

3) I think the size effect is dependent on what kind of inhomogeneity is involved in the deformation. For those experiments where strong strain gradients exists, such as bending, nanoindentation, torsion, etc. - the GNDs would account for the additional dislocation density and the associated increase in the stress through hardening. However, in pillar deformation experiments, the inhomogeneity might arise, for example, from the low-symmetry orientation of the pillar, in which case the dislocations are still able to escape at the free surfaces, thereby enabling dislocation starvation. The strain gradients are minimal in this situation, but the severe surface steps most likely serve as the dislocation nucleation sites. Therefore, this situation would still result in a nucleation-controlled plasticity.

 I hope this at least somewhat addresses your concerns!

 Thank you,

Julia Rosolovsky Greer

Joost Vlassak's picture

Dear Amit,

Regarding your last point - the following experimental observation may help: We have measured the stress-strain curves of thin polycrystalline copper films where we have either free or passivated surfaces. If the surface is free, there is only a small size effect with decreasing film thickness that may well be explained by the decreasing grain size (at least over the thickness range we considered). If the surface is passivated, there is a strong size effect in addition to a strong Bauschinger effect on unloading. The latter would imply that internal stresses do play a role. More details can be found in papers 49 and 50 on my group's website http://www.seas.harvard.edu/vlassak_group/.

Best regards,

Joost J. Vlassak

Xiaodong Li's picture

Thanks Julia for hosting the discussion. I hope this helps our further understanding of experimental nanomechanics which we had a good theme last May (2007). Tons of papers have been published on synthesis or fabreication of nanostructures/nanomaterials, only few papers about mechanical properties are avaliable in literature. For practical applications of nanostructures/nanomaterials, mechanics plays an important role. I think that experimental data/results are critical for advancing this area, of course modeling and simulation provide predictive capability and insightful physics that governs the size effect.

Again, thank you and hope to see more colleagues and friends join this discussion.

Julia R. Greer's picture

Thank you, Xiaodong. Yes, it would be great to have a variety of fabrication and testing methods for these nano-scale materials as they are proving to be not only different from their bulk counterparts byt also from one type of material to another. 

 We are currently working on FIB-less fabrication methods and on tension experiments during in-situ deformation. We hope to be able to share these results soon!

Julia Rosolovsky Greer

Xiaodong Li's picture

Thanks so much for the discussion here. Our recent paper in Nano Letters shows that the twinned Mg2B2O5 nanowires achieve a slight increase in hardness but 19% decrease in elastic modulus compared to their bulk counterpart. It will be nice to see modeling work on this. Another thought is if some one can make a pillar with twin structure to do compression or tensile tests.

Xinyong Tao and Xiaodong Li, "Catalyst-free Synthesis, Structural and Mechanical Characterization of Twinned Mg2B2O5 Nanowires," Nano Letters, 8 (2008) 505-510.

Thanks Julia for this blog, where so many interesting topics can be discussed informally. As a modeler I just wanted to bring up an issue that is very important to us, and that is the pre-characterization of these nanostructures. Some of our theories hinge on the pre-existence (or not) of two types of inhomogeneities, namely intrinsic defects such as surface steps or kinked cylinder walls -intrinsic to these nano-geometries-, and fabrication-induced defects such as vacancies, voids, SFTs and dislocation structures derived from the extremely high specific stresses that develop during FIBing or nanomachining. For example, a couple of years ago Chris Schuh at MIT showed the drastic effect that sub-surface vacancies can have in nanoindentation experiments, to reconcile the (much lower) measured hardenesses with those expected from Hertzian or other continuum-type contact laws.

I haven't seen much in the way of these pre-characterization in the literature (although I may have missed it) but I wascurious about the thoughts in the experimental community about this issue.

Thanks!

Jaime Marian, LLNL 

Xiaodong Li's picture

Thanks. This is a very good point. The effects of pre-existing defects and the defects generated during manufacturing or practical applications are still, to a large extent, unknown. Experimental studies are very challenging. Careful calibrations are needed (critical) for such experiments.  Hope that modeling can provide some predictive results. I would like to see if any colleagues or friends happen to know such papers.

Again, thanks a lot.

Julia R. Greer's picture

Jaime, that is a very good point, thank you so much for bringing it up! YES, the types, the amount, and the "signature" of pre-existing defects is very important in mechanical properties, **especially** at the scales where the presence of surfaces plays an increasingly important role. 

Unfortunately, it is extremely difficult to precisely measure and assess the defect density and distribution in these nano-structures. One of the reasons why Nanoindentation is such a powerful technique is that you can start with a bulk material where such distributions are much  more easily controlled and measured - and then probe the small volume inside. However, in the SURFACE-dominated strutures - just like you said - the FIB machining, the pre-existing defects, and the atomic roughness will all add to the stress-strain response, but the precise measurements are yet to be reportd. We actually just recently submitted a paper on the effects of the FIB damage layer in gold nanopillars to Acta MAterialia (hopefully it will get accepted ;-) )  - including some analytical modeling.

Thank you very much! 

Julia Rosolovsky Greer

Zaoyang Guo's picture

 Dear Julia,

 

A few years ago, we exploered the size effect from strain gradient plasticity: 

http://www.mech.gla.ac.uk/~zguo/Publications/J003.pdf

 

 I don't know if it works or not when the size of the structure is under 200 nm.

 

Hope this helps,

 

Zaoyang 

Julia R. Greer's picture

Thank you Zaoyang, I will definitely check it out! 

 

Julia Rosolovsky Greer

Cai Wei's picture

Thanks, Julia, for this timely discussion.  This is one of the interesting cases where experimentalists and theoriests need to work closely together to solve the puzzle.  I will try to highlight the insight gained from and current limitations of computer simulations of nano-scale mechanics in the forthcoming Journal Club discussion on July 15.

Wei Cai

Julia R. Greer's picture

 

THank you, Wei, I am very much looking forward to the Journal Club that you are going to lead very soon! 

Julia Rosolovsky Greer

Xiaodong Li's picture

Thanks a lot Julia and Wei. I agree. Your upcoming July theme will be of great interest. From experimental side, now we pretty much focus on elastic modulus and strength. How about other mechanical properties? For example, fatigue properties of nanostructures? We did some tests before and found some interesting phenomena (see below). I seek help from theoriests/modelers to get in-depth understanding.

Again, thanks for the help.

X. D. Li and B. Bhushan, "Fatigue Studies of Nanoscale Structures for MEMS/NEMS Applications Using Nanoindentation Techniques," Surface and Coatings Technology, 163 (2003) 521-526.

X. D. Li and B. Bhushan, "Development of a Nanoscale Fatigue Measurement Technique and Its Application to Ultrathin Amorphous Carbon Coatings," Scripta Materialia, 47 (2002) 473-479.

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