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Journal Club Theme of May 2007: Experimental Mechanics of Nanobuilding Blocks

Xiaodong Li's picture

Welcome to the May 2007 issue. This issue focuses on experimental nanomechanics of nanobuilding blocks. The extremely small dimensions of nanobuilding blocks (for instance, nanoparticles, nanotubes, and nanowires) have imposed great challenges to many existing instruments, methodologies, and even theories.  In this issue, we will discuss – (1) experimental techniques and (2) size-effects. 

The methods that have been developed and used for measuring the mechanical properties of isolated individual nanobuilding blocks include uniaxial tensile loading using a nanomanipulation stage, in-situ compression of nanoparticles and nanopillars, mechanical/electric-field induced resonance, AFM bending, and nanoindentation. The following is a brief summary of these methods for discussion.

Can one perform tensile tests on a nanowire as we normally do on a big dog-bone sample? Prof. Rod Ruoff’s group realized such challenging tests on individual multiwalled carbon nanotubes (MWCNTs) using a testing stage based on a nanomanipulation tool operating inside a SEM. The nanomanipulation stage makes 3-D manipulation possible – picking, positioning, and clamping of individual 1-D nannomaterials. The individual 1-D nanomaterials were attached and clamped to AFM probes by a localized electron beam induced deposition of carbonaceous materials inside the SEM. A single 1-D nanomaterial so clamped between two AFM probes was then tensile loaded by displacement of the rigid AFM probe and the applied force was measured at the other end by the AFM cantilever deflection of the other, compliant AFM probe. The measured force-elongation data were converted, by SEM measurement of the nanomaterial geometry, to obtain a stress-strain curve.  In addition to the Young’s modulus, breaking strength can be measured by this method.  Prof. Rod Ruoff’s paper is the first one under discussion in the present issue of journal club. 

Yu MF, Lourie O, Dyer MJ, Moloni K, Kelly TF, Ruoff RS, Strength and breaking mechanism of multiwalled carbon nanotubes under tensile load, Science, 287 (2000) 637-640.

Compression tests on small pillars inside a SEM provide a new way to study the sample size effects. To mimic the conventional compression tests, FIB was used to cut a bulk sample to a smaller size (top-down approach).  A flat nanoindenter was then used to perform uniaxial compression tests on the FIB cut sample in situ. Engineering stress-strain curves can be obtained. Sample’s morphology change such as slip bands can be studied by SEM.  The second paper selected for discussion is:

Uchic MD, Dimiduk DM, Florando JN, Nix WD, Sample dimensions influence strength and crystal plasticity, Science, 305 (2004) 986-989.

Prof. C. M. Lieber’s group used an AFM operating in lateral-force mode to bend cantilevered MWCNTs that were deposited on a low-friction MoS2 surface and pinned down at one end by overlaying SiO2 pads using lithography. The bending modulus of individual MWCNTs was calculated from deflection of a cantilevered MWCNT and the lateral force applied by the AFM probe. Another approach is to use AFM to perform indentation three point bending tests on the 1-D nanomaterials deposited on a membrane having nanopores. The suspended 1-D nanomaterial was considered as a double-clamped simple beam that was clamped to the membrane by its high surface energy at the ambient humidity condition. By positioning the AFM tip directly on the center of the 1-D nanomaterial spanning the pore and applying an indentation force, the Young’s modulus of individual 1-D nanomaterials can be obtained from the AFM tip force-deflection curve. Below please find Prof. C. M. Lieber’s paper:

Wong EW, Sheehan PE, and Lieber CM, Nanobeam mechanics: elasticity, strength, and toughness of nanorods and nanotubes, Science, 277 (1997) 1971-1975.

To study the size-effects of nanoparticles is extremely difficult.  Prof. Bill Gerberich’s group performed compression tests on individual silicon nanospheres using in situ nanoindentation techniques. In situ TEM provides insightful information such as dislocation initiation and motion, onset of plasticity, and fracture mechanisms. Here I would like to use one of Prof. Bill Gerberich’s papers for discussion:

Deneen J, Mook WM, Minor A, Gerberich WW, Carter CB, In situ deformation of silicon nanospheres, Journal of Materials Science, 41 (2006) 4477-4483.

In a cantilever vibration test, individual cantilevered 1-D nanomaterials are thermally oscillated using a variable-temperature sample holder in a TEM or oscillated by directly inducing the mechanical resonance using an electric field. Using continuum beam mechanics, the bending modulus of 1-D nanomaterials can be calculated from the measured resonance frequency and the selected nanomaterial geometry. Below, please find the two representative papers:  

Treacy MMJ, Ebbesen TW, and Gibson JM, Exceptionally high young's modulus observed for individual carbon nanotubes, Nature, 381 (1996) 678-680. 

Wang ZL, Poncharal P, and de Heer W A, Measuring physical and mechanical properties of individual carbon nanotubes by in situ TEM, Journal of Physics and Chemistry of Solids, 61 (2000) 1025-1030. 

Nanoindentation techniques and theories have been well established for the mechanical characterization of solid surfaces and thin films. The major challenge we are facing is: can we extend application of traditional nanoindentation approaches to 0-D (nanoparticles) and 1-D nanomaterials (nanowires/nanobelts) for directly measuring their mechanical properties? The early work includes: 

Mao SX, Zhao MH, and Wang ZL, Nanoscale mechanical behavior of individual semiconducting nanobelts, Applied Physics Letters, 83 (2003) 993-995. 

Li XD, Hao HS, Murphy CJ, and Caswell KK, Nanoindentation of silver nanowires, Nano Letters, 3 (2003) 1495-1498. 

The mechanisms (physics/science) of size-effects are still, to a large extent, unknown. One of the basic debates is size-dependency of Young’s modulus. The reported Young’s modulus of many nanobuilding blocks exhibits a large variation relative to the corresponding values of the bulk materials. For many metallic nanowires or small-scale samples, the strength was reported to increase as size decreases. The above selected papers cover the mechanisms of size-effects.  Insightful discussion on this topic is greatly needed.

Previous discussions and selected papers on experiemntal mechanics can be found in this forum and may help stimulate further discussions.

Please note that due to space restrictions, I am not able to include all the papers that I know of.  I sincerely apologize for any omission of papers that should be included in this post.  


I am running a TEM Lab. at the Center for Integrated Nanotechnologies (CINT), Sandia National Laborarories. Our Lab. has the capability of tensile loading or compression of individual nanotubes and nanowires. We have several unique platforms, called TEM-STM, TEM-AFM, TEM-Nanoindentor platforms (Nanofactory), which incorporate a full functional STM, AFM, and Nano Indentor into a HRTEM, enabling simultanuous atomic-scale microstructure and electrical, mechanical property measurements of the same nanotube/nanowire. The CINT TEM Lab. is open to external users for free (because we are a DOE user facility). You are welcome to come and use our facility. For detailed access procedure, please visit

Recent paper: Huang et al., PRL 98, 185501 (2007)

Watch movies at:


Henry Tan's picture

Dear Jianyu,

In your experiment the behaviors of carbon nanotubes were observed at temperatures above 2000 C. The temperatures were applied through high bias voltages.

My question is:how to understand that nanotubes may have no 'temperature' at all?


I noted Zhigang, you and others interesting argument regarding the temperature in a small system like a nanotube in the blog. From a theoretical point of view, the argument certainly stands, say what's the meaning of a temperature in a single atom? I am not in a position to comment on such challenging issues, since I am an experimentalist.

However, from experimental point of view, carbon nanotube certainly has temperature. I list a few convincing evidence:

1. Graphitization. Just like a steel worker can judge the temperature of the steel from its color, we can get temperature information from the graphitization of graphite or nanotube. Perfect graphitization (the basal planes are well aligned) requires temperatures close to 3000C. When I increase a current through a CNT coated with amorphous carbon, I found the amorphous graphitize to turbostratic stacking (c-plane randomly aligned), and then to well aligned nanotube walls, indicating the temperature is rising with increasing current.

2. Phase transformation. We deposited diamond or Al2O3 on the nanotube surface, and found that these particles are melted and evaporated with increasing current in the CNT.

3. Black body radiation. Experiments showed that the raddiation spectrum fitted excellently with a temperature of ~2000C before the nanotube breaks.

For more information, you can read the following papers:

J. Y. Huang et al., Phys. Rev. Lett. 94, 236802 (2005).

J. Y. Huang et al., Nano. Lett. 6, 1699 (2006).

S. Chen et al., Appl. Phys. Lett. 87, 263107 (2005).

Cai, X. Y., Akita, S. & Nakayama, Y. Current induced light emission from a multiwall carbon nanotube. Thin Solid Films 464-465, 364-367 (2004). 

Xiaodong Li's picture

We know that for bulk metallic materials plastic deformation is associated with dislocation nucleation and propagation. What are the plastic deformation mechanisms for metallic nanowires? For example, if we have a single-crystal metallic nanowire with a diameter of 1 nm, how surface atoms (high surface to volume ratio) play roles in its plastic deformation. Can we use the conventional dislocation theories based slip systems?  

Ying Li's picture

From many papers I have seen, there is no or less dislocation in the nano crystal metal. Both from the experiments and MD simulation, when the grain size decrease to less than 30-60nm, the dislocation based theory would not effect the yield strength and the grain boundaries sliding mechanism will take the role.  

While both theoretical considerations and experimental observations support the absence of dislocations within such small dimensions, where proximate free surfaces would impose strong image forces, the concept of dislocation plasticity may still play a role.  Perhaps this becomes a question of semantics, but it is likely that dislocation nucleation will still be a relevant mechanism for deformation in nano wires.  If one were to consider an embryonic dislocation in a 20 nm diameter wire, the critical nucleation radius is likely larger than the wire diameter. In this case the dislocation is both nucleated and fully propagated through the wire at the same time. One would find a slip step at the perimeter of the wire and no dislocation would be observed. We believe that this nucleation-without-much-propagation is a likely deformation mechanism in nanoporous Au (C.A. Volkert,, APL 89 (2006)). I believe similar arguments hold for nanocrystalline materials, supported experimentally and with MD simulations by the van Swygenhoven group (PSI, Switzerland); no observation of dislocations after deformation does not preclude that dislocations carried the plasticity.

Kaushik Dayal's picture


I remember reading (a long time ago, probably in Dieter), that the surface oxide layer is usually stiffer than the metal. This causes the image forces to change sign and the dislocations are repelled from the free surface. This discussion was in the context of bulk specimens.

I wondered if oxide layers have any role in the nano/micro scale specimens that you work with? Does FIB or other machining process cause surface properties to change significantly?



Ying Li's picture

Yeah, I’d like to say that the dislocation mechanism may also affect the strength of materials in nanometer. But, the grain boundary slipping mechanism/ grain boundary creep mechanism and the dislocation mechanism, which is the in the first role? I have found many papers in these fields and find that almost all of the works prove that in the nanometers the grain boundary slipping mechanism/ grain boundary creep mechanism will take the first role and the dislocation mechanism will show less effect in such nanometers. So, we conclude that the strength of materials is controlled by two mechanisms: the dislocation mechanism and the grain boundary slipping mechanism, which play against each other in the deformation. So, when the scale goes to the critical parameter, the effect of the grain boundary slipping mechanism and the dislocation mechanism will give the largest yield strength of the material. If the scale of grain size go beyond the critical parameter, then the dislocation mechanism take the first role, so we can see the Hall-Petch relationship. But, when the scale of the grain size below he critical parameter, the grain boundary slipping mechanism would take the dominate role and the inverse Hall-Petch relationship show. It do exist in the nano crystal Cu experiments and both the experimental result and the MD result agree well at about 20 nm. By the way, the instinct scale in the plastic gradient theory will also change as the grain size changing. Some theories give the relationship between the grain size vs the instinct scale. When the grain size is quit small (nearly 20nm), the instinct scale is about 0.5 micrometer and as the grain size increasing, the instinct scale increase rapidly, when the grain size increase to some scale large enough, the instinct scale will arrive its limitation as about 18 micrometer( I am sorry that I can’t remember the exact number) . Lee              

Henry Tan's picture

As pointed out in the third paper “Nanobeam Mechanics: Elasticity, Strength, and Toughness of Nanorods and Nanotubes” by Wong et al.,

“The ability of carbon nanotubes to elastically sustain loads at large deflection angles enables them to store or absorb considerable energy. One obvious application of this unique energy-absorbing capability of carbon nanotubes would be in armor, although a suitable matrix must be chosen to exploit these properties in a macroscopic article.”

Carbon nanotubes (CNTs) have great potential applications in making ballistic-resistance materials.(

What we need now is a suitable matrix and a good understanding of the nanotube-matrix bonding.

Henry Tan's picture

Also in the above apper, Huang et al. ( discovered super stretchy carbon nanotubes at high temperatures; this could lead to the finding of super energy absorbing material.

Xiaodong Li's picture

Thanks! I agree that there are still a lot we can learn from CNTs. I hope to see more experimental results/findings on the new functionalities of CNTs.


I totally agree with Prof. Li for a lot we mechanicians may contribute on experiments and/or computational modeling on CNTs. For my case, not only the experimental works (tension test, bending test, etc) on CNTs but also applications of CNTs to NEMS device are intriguing to me. If you are also interested in applications of CNTs to NEMS device, the following papers may be interesting:

V. Sazonova, Y. Yaish, H. Ustunel, D. Roundy, T.A. Arias, P.L. McEuen, Nature, 431, p284 (2004)

The above paper suggests that CNTs may be utilized as NEMS resonators for further various applications. There are still many rooms to characterize the nanomechanical behaviors of CNTs and/or graphene sheets for gaining insight into the design concept of NEMS device for many applications including electromechanical force sensor application, biosensor application, chemical sensor application, etc.

Xiaodong Li's picture

I have just checked the ISI web site and found out that there are thousands of papers about synthesis of nanobuilding blocks. Surprisingly, there are only less than a hundred papers on the mechanical property measurements of nanobuilding blocks. We know if we construct nanodevices with nanobuilding blocks, we need to know the mechanical properties of every block. Mechanical properties of materials are size-dependent. If we want to use a steel bar, for instance, we can easily find a handbook to get its mechanical properties. People have already synthesized thousands of different nanomaterials with various shapes. Unfortunately, we do not know their mechanical properties. How can we use these nanobuilding blocks in practical applications? I have a dream that one day if we want to use a nanomaterial, we can find its mechanical properties from a nanomechanical property handbook (we badly need this handbook). I think that our community plays a very important role in nanotechnology.  

That's true, there is still so much to discover about nanotubes. Hopefully computational modeling will help us improve what we know about the CNT. The Lieber group is doing amazing and i really hope things will work out well.

Karen, rpg games.. in tubes

First, let me offer congratulations for the Lieber group for undertaking such challenging experiments. It is very beautiful experimental work.

Second, let me point to a recent article, a collaborative effort between Weiqiang Ding, then a student in my group and now an assistant professor at Clarkson, Zaoyang Guo, then a postdoctoral fellow with Brian Moran at Northwestern, and now an assistant professor at the University of Glasgow, and myself, that addresses what we believe could be a weakness in terms of the analysis in the aforementioned work on nanobeam mechanics by the Lieber group. This article is:

Ding, Weiqiang; Guo, Zaoyang; Ruoff, Rodney S.. Effect of cantilever nonlinearity in nanoscale tensile testing. Journal of Applied Physics (2007), 101(3), 034316/1-034316/10.


Xiaodong Li's picture

Thanks a lot! Excellent! This is a very systematic study of the nonlinearity in the AFM cantilever-based nanomechanical testing. I like this paper a lot! I think that the results are also applicable to the AFM three-point bending tests, in particular, when an applied load is high.

Yong Zhu's picture

Thank you very much, Prof. Li, for the nice overview. In terms of experimental techniques, I would like to add one more: microelectromechanical system (MEMS) based testing technique. As we know, tensile test is the preferred mechanical testing method for large-scale specimens. However, it encounters great challenges when coming down to nanostructures. Recently several groups have developed MEMS-based instrumentations and successfully performed tensile tests for various one-dimensional nanostructures. Here I pick up a few references.

Y. Zhu and H. D. Espinosa, An electro-mechanical material testing system for in situ electron microscopy and applications, Proc. Natl. Acad. Sci. USA 102, 14503-14508 (2005)

S. Lu, D. A. Dikin, S. Zhang, F. T. Fisher, J. Lee, and R. S. Ruoff, Realization of nanoscale resolution with a micromachined thermally actuated testing stage, Rev. Sci. Instrum. 75, 2154 (2004).

M.A. Haque and M.T.A. Saif, Deformation mechanisms in free-standing nanoscale thin films: A quantitative in situ transmission electron microscope study, Proc. Natl. Acad. Sci. USA 101, 6335-6340, (2004).

MEMS-based instrumentation is effective in bridging the size scales and conducting experiments in a well-controlled fashion. In addition, it offers a unique advantage for quantitative in-situ testing, such as inside SEM and TEM. In spite of tremendous potential, at present this technique is somewhat limited by nanomanipulation, which is quite time-consuming. Manipulating nanostructures at will and integrating with MEMS devices is not only a challenge for experimental nanomechanics but also, in a sense, for the entire nanotechnology including nanomanufacturing and nanoelectronics. A large number of methods including top-down (e.g., using a nanomanipulator or electric field alignment) and bottom-up (e.g., direct growth) approaches have been demonstrated. This will facilitate the advance of MEMS-based nanomechanics testing. Please see the link to a recent review paper addressing some of the techniques for experimental nanomechanics as well as nanomanipulation.

Y. Zhu, C-H. Ke and H.D. Espinosa, Experimental Techniques for the Mechanical Characterization of Thin Films and One-Dimensional Nanostructures, Experimental Mechanics 47, 7-24, (2007).

Xiaodong Li's picture

Thanks a lot, Yong. Development of nanomechanical testing instruments advances the field. I hope that modeling groups follow up the new experimental results/findings, and/or predict the new properties/phenomena (which in turn drive experimental work as well). A lot of experimental work was based on early theoretical predictions.

Henry Tan's picture

Can people move atoms with today’s nano-technology?

Hi Henry,

Search Don Eigler, and then forward search papers citing his work.

As you probably know, he is at IBM Almaden.

But...beyond rather specialized situations, it is hardly as if the community has garnered the level of control that is touted in...books by Drexler and others.  As I always say to interested students (after first letting them think for awhile on how they would characterize this problem), that "Anything not violating the laws of physics or the constraints of chemistry will probably be, by some more technologically advanced societies, done with atoms and molecules."

Henry Tan's picture

Thanks, Rod.

I recall that exciting news in 1989 when I was a college freshman.

I searched the internet and got Dr. Don Eigler's lecture delivered at the Kavli Institute for Theoretical Physics (, UCSB.

Building Things with Atoms: A Report from the Small Frontier

Julia R. Greer's picture

IF we are discussing size effects in NANO-sized structures, perhaps a more appropriate "microcompression" paper would be Greer, et. al.'s Acta Materialia (53) one where NANOMETER-sized gold pillars are homogeneously compressed. The paper by Uchic, et al, discusses MICRON-sized samples, which also exhibit a size effect, but with a different scaling law and at a much larger scale.

Julia Rosolovsky Greer

Dear Greer

    It is really an excellent paper, it has been cited 53 times from ISI yesterday. In this article, the "dislocation starvation" model attributed to size effect of nanopillar was presented, it is convincing that dislocations escape or annihilate from the pillar surface as the size decreasing to hundreds of nanometers, my question is "Is there any change of deformation mechanism which dominates the deformation process at this scale?(such as from dislocation to other defects)". In addition, your SEM images show that the nanopillar has a taper along the gauge,  is there a strain gradient comparing to the standard homogeneous comprssion in the deformation?  thanks a lot!


It is critically important to note that there is an erratum (Greer, et. al. Acta Mater. 54 (2006) p.1705) published in regard to Greer´s Acta Materialia paper cited in
this discussion. This erratum points out that the highest strength data points
in the plot of flow stress versus pillar diameter were in error. Yet it is
specifically these data points which are needed to demonstrate a scaling
exponent different from the exponent Dimiduk and others have observed almost
universally (it holds for a variety of metal systems as well as LiF, and
continues to the sub-micron length scale). The submission of errata
is one route to rectify the publication of erroneous data, but published errata
are not easily found (to my knowledge INSPEC does not recognize them during a
standard author search) and they typically follow some time after the general
acceptance of the erroneous publication. I
n regard to
a second publication with the same data (Greer et. al, Applied Physics A vol 80 (2005)
p.1625-29), no erratum appears to have been published.
Given the uncertainty surrounding the
data from Greer, et. al., the papers from the Dimiduk and Uchic group are the
most appropriate suggested reading regarding this important technique.


Xiaodong Li's picture

Thanks a lot, Julia. This is the paper that addresses the nanoscale effects. Can you please write more about the mechanisms that govern the effects. Hope this helps further discussions

Weixu Zhang's picture

There is a interesting paper in Script Materialia 56 (2007) 313–316 "Contribution to size effect of yield strength from the stochastics of dislocation source lengths in finite samples" This means the properties of small structures may be controlled by its defects distribution.

Before this paper appeared, I also discuss the same topic with Zhengya Song and Zaiwang Huang (They are both in Jun Sun's group). Zhengya once reminded me the properties of small structures perhaps are descrete intrinsicly for their different defect distribution. It well known that there is a lot of defects in macroscopic solids. When the material is large enough, the defects are statisticly uniform in different structures. So the large material has uniform property. However, when the material is small enough which size can compare with the defect size, the statisticly uniform distribution does no long exist. In this case, the small structures still have uniform properties?? We think they are not.

Besides, in my own opinion, the continuun mechanics will continue to be valid for very small structures even in the atomic level when it be added more necessary parameters.

Julia R. Greer's picture

The Acta paper is more of a demonstration of a first-of-a-kind experiment with some early data when no other data on microcompression at that scale has been published.

 A much more detailed explanation of dislocation starvation with significantly more data is presented in Greer and Nix PRB paper (Phys Rev. B 73 (2006)).

Julia Rosolovsky Greer

Saurabh Puri's picture

Hi all, I have a question regarding the reference mentioned by Weixu. In that paper, it is mentioned that in smaller size specimens, the concept of dislocation starvation is dominant due to the conversison of majority of Frank Reed sources into single ended ones on interaction with the free surface.

But if we have a poly crystal, i suppose the operation of a Frank Reed source will result in accumulation of higher density of dislocations along the grain boundaries in smaller sample as compared to large ones, which in turn will result in more work hardening. isn't this contrary to the concept of dislocation starvation. Please correct me if i am wrong??

Most of the work regarding dislocation starvation is for single crystals, as
much of the published microcompression experiments are as well.  If there
are grain boundaries, then clearly the “easy” loss of dislocations is greatly
inhibited. Hardening in polycrystalline columns will be observed due to a higher
multiplication rate relative to the loss rate, rather than the loss of “easy” sources
and the increased stress to activate the next source, as is associated with source
starvation hardening. To address the question of whether dislocation starvation
occurs, and the question of what governs size effects more generally, I think
that it is best to consider the relative length-scales involved in the
experiment; specifically, what is the relative deformation length-scale (e.g.,
diameter or volume of the column) relative to the microstructural length-scale
(e.g., grain size, dislocation spacing)?  When these two scales are
comparable, I have observed large statistical variations in the data.  In the
case of a large deformation length-scale relative to the microstructural length
scale, such as with micron-scale columns from nanocrystalline and nanoporous
samples, I have not observed a dependence on the column diameter, but rather very
reproducible, column-size-independent behavior. When the deformation scale is
much smaller than the microstructural length-scale (e.g., well annealed,
single-crystalline columns) , then appreciable size effects occur (the strength
increases with decreasing deformation volume).  This size effect could be
explained by dislocation starvation, or by the finite size effect on self
organized critical (SOC) behavior, or potentially other effects.  Dimiduk
and coworkers have done a great deal in investigating SOC for microcompression
experiments.  With careful TEM analysis, they observe a scale-free
dislocation structure with a characteristic spacing on the order of 2 micron
(independent of column diameters, where the smallest diameters were a few
microns, if I recall correctly).  Thus,
it seems reasonable that at deformation length scales (specifically microcolumn
diameters) smaller than the scale-free dislocation structure size (2 micron for
Ni), that a source starvation mechanism may dominate. This is consistent with other
nanometer-length scale experiments. Andy Minor and coworkers have observed loss
of dislocation structure during compression of Ni using in situ TEM microcompression
testing (presented at Fall MRS Meeting 2006), and Arief Budiman and coworkers
have observed no characteristic Laue reflection broadening (associated with
dislocation structure) from x-ray microdiffraction investigations of sub-micron
scale compression experiments in Au (also presented at the Fall MRS Meeting


Rashid K. Abu Al-Rub's picture

Erica, I completely agree with your comments. In several of my papers, I have shown based on dislocation mechanics interpretations that the material length scale in metals, which controls the size effect, is indeed the mean spacing between dislocations or the distance traveled by a dislocation. Moreover, I have been working on formulating strain gradient plasticity theories that can be used successfully to explain the observed size effect at the micron and submicron length scales. However, recently, based on these experiments that you have mentioned in your comments, several have questioned the ability of strain gradient plasticity theory to explain the observed size effect in nano/micro pillars or columns when subjected to macroscopically homogenous deformation.  My question is: when you apply uniform strain (tension or compression), is the resulting stress uniform too??? Can you measure the stress distribution across the specimen deformation length scale (e.g. across the diameter of the pillar)? I expect that, particularly for single crystals, that the surfaces are softer than the core of the crystal such that the internal stress distribution (due to uniform straining) is non-uniform across the specimen characteristic size. If this is the case, then I can certainly predict the observed size effect in the experiments of Uchic et al. and Greer et al. using the strain gradient plasticity theory. Will you please comment.

Thank you


Rashid K. Abu Al-Rub, Ph.D.
Catholic University of America

Hi Rashid,

I have enjoyed the discussions that have followed your comment, and I hope I can add something of relevance as well.  Of course the microcompression test is not a perfectly uniaxial stress state, for a few reasons.  As deformation proceeds, especially in the case of single slip, an s-shape can form which clearly disrupts the state of stress.  On a more microstructural level (rather than geometric) any dislocation introduces a gradient in strain.  At large scales, a relatively uniform dislocation density may allow a "uniform" stress distribution assumption.  As the deformation length-scale decreases, such an assumption begins to fail.  However, whether a strain gradient plasticity law is required to physically describe the deformation is up for debate (as strain gradient plasticity seems always to be!). The microcompression test was a very elegant method to remove the extrinsic strain gradient inherent in traditional sharp-tip nanoidnentaiton studies, where the indentaiton size effect has been most commonly modeled by the Nix-Gao model.  The observation of a size effect in the microcompression test has persuaded some researchers to drop the SGP model for size effects. Others support the argument that while the extrinsic applied stresses are relatively uniform during microcompression, the internal strain gradients are still controlling the size effected response.  As for the effect of free surfaces, one should consider how "free" the surface is. In the case of metals, an oxide can be stiffer of more compliant, softer or harder, than the bulk material.  Even in the case of  noble (oxide-free) Au, the presence of hydrocarbons or Ga-embedded surface layers can effect the ability for dislocations to escape. The jury is still out on how this will effect the understanding of size effects. In any case, it is great that so many ideas are being pursued, and that the modeling and experimental communities seem to have found a problem (microcompression) which both groups can really investigate.

Rohit Khanna's picture

Hi all,

I wish to discuss on interpreting the nanoindentation data for viscoelastic-plastic composite materials say polymer based composites. I have experienced that if the microsructure is not homogeneous, it is very difficult to meangingful data and normally, spread in elastic modulus is very large depending on the load.

Second point for discussion is that does modulus mapping technique holds good for viscoelastic-elastic composites?

Can anybody comment on this?


Rohit Khanna 

Hi Rohit,One of the great things about nanoindentation is that it is site specific, so you can obtain mechanical properties for each component in your composite.  The spread in elastic modulus that you see will be due to the heterogeneity of the material that you are testing, which with regard to composites will be very large. 

Modulus mapping was a technique developed specifically for heterogeneous materials such as composites where the individual location of each measurement is mapped in addition to the mechanical properties at that location.  This will allow the visualization of both the topography and hence the identification of the particle or the matrix as well as the modulus measured at that point.  As the measurements include storage and loss modulus, in addition to others it is ideal for visco-elastic materials.

If you take a look at the following links it will show you the technique used in heterogeneous material applications:


Michelle Dickinson 


Rohit Khanna's picture

Hi ! Michelle. Thank you for your response. Your interpretation sounds convincing to me. I have a question about the resolution. The resolution of the AFM image and that modulus map image is different. You can not tell about the shape/morphology of the particles by looking at modulus map image, or if you try to compare AFM and modulus map image?

Rohit Khanna

Hi Rohit,

The resolution of all of the images produced by modulus mapping are carried out using the same nanoindentation probe, and hence there is no AFM image as such.  The nanoindentation tip raster scans the surface of the sample similar to an AFM tapping mode technique, however the force, displacement, frequency and phase shift are measured simultaneously generation both topographical and mechanical data.

The resolution of the mapping technique itself is limited by the sharpness of the tip you are using, a sharp cube cornered diamond probe will result in a much higher resolution image than a more rounded Berkovich tip.


Rohit Khanna's picture

Hi Michelle, i agree with your information about the modulus mapping. Actually, my question is "can we compare an AFM image to modulus map image taken for same area?"

I have experience with such a issue. I very well understand that in modulus mapping, we get pixel by pixel data for E. But still one can not make out the shape of the particle from modulus map image whereas AFM tapping mode technique gives a very clear picture of a particle morphology etc.



Hi Rohit,

It is possible to create a topographical image using AFM after a modulus map scan.  I suggest creating large marker indents to enable easy identification of the same location when moving from one scanning technique to another.  The resolution of the modulus map will not be as high as the AFM image, as already mentioned due to the size of the nanoindentation tip, however use of a very sharp diamond tip such as a Northstar cube corner tip would give you the highest modulus mapping resolution and hopefully allow direct comparison from one scan to the other.

The 256x256 pixel acquisition will be your limiting factor for the resolution of large scans, so by keeping the scan size small you can obtain more information about your sample.


PJ Guruprasad's picture

In general a uniform loading applied in the form of  homogeneous deformation should be accomodated by a uniform stress distribution. But the presence of a dislocation structure or the heterogeneity due to dislocation mediated slip can lead to an inhomogeneous stress distribution. And as mentioned by Rashid above this can present in the form of a soft surface and a hard core (mainly due to an evolving dislocation structure). This fact has been well appreciated since the publication on this subject by Fourie.J.T, 1968. "The flowstress gradient between the surface and centre of deformed copper single crystals" Phil Mag 17, 735-756. Our own studies (see the link below)  on homogeneous deformation of sub-micron specimens based on "mechanism based discrete dislocation" simulations reveals this observation in a qualitative way. It should be noted that in these cases the initial dislocation source density is quite high (alomst 2 orders more than that considered by Volkert et al (2006) and Greer et al (2005)). Hence, when the initial dislocation density is low one may not observe a nonuniform stress distribution. As there too few sources to result in dislocation structures. 

Our paper is titled,  Size effects under homogeneous deformation of single crystals : A discrete dislocation analysis

 (accepted for publication in J Mech and Phy of Solids, 2007)

Rohit Khanna's picture



Your paper is on single crystals and the same type of response can not be expected from a polycrystalline materials and that too from composites. Regarding the nanoindentation response about which i am discussing, the microstructural distribution plays a big role in influencing the mechanical response. Then, depending on the choice of load, the mechanical response (measured elastic modulus) can be different becoz bulk response can be expected at higher loads.

I am not very sure about the dislocation density theory and its applicability to composites.  


PJ Guruprasad's picture

Dear Rohit,

Yes, you are right. The results discussed in the paper is not applicable to polycrystals and  composites. Also, it cannot be used in anway to either interpret or gain insight into any nanoindentation data. Our work is more in line with one of the papers related to strength in micon/nano crystals subjected to uniform loading currently being discussed in this J-club.

I do not have sufficient background to throw some light on nano-indentation of composites. But I believe one can draw some analogy between dislocation structure (after sufficient deformation) and interconnected chains in polymers used as composite matrix. The unfolding or folding of these chains could lead to differences in strength observed. In reality I'm sure the governing mechanism or phenomenon is more complicated than the layman interpretation that I have provided here for composites.


Rashid K. Abu Al-Rub's picture


 Thank you for making this comment. Your paper with Benzerga is very interesting. I am glade that you have concluded that local geometrically necessary dislocations do exist under uniform straining of single crystals. This agrees very well with my expectation that dislocation nucleation and motion will cause non-uniform distribution of internal stress across the specimen width even under macroscopically uniform deformation and with the surface being softer than the core of the crystal. However, in your paper it is mentioned that the length scale parameter in nonlocal gradient plasticity theory has no physical interpretation and it is assumed constant. I have published several papers emphasizing the physical nature of the length scale in gradient plasticity and its relationship with the microscopic features of the material, particularly, the spacing between dislocations. You can check: Abu Al-Rub, R.K., Voyiadjis, G.Z. “Analytical and experimental determination of the material intrinsic length scale of strain gradient plasticity theory from micro- and nano-indentation experiments,” International Journal of Plasticity, Vol. 20, No. 6, pp. 1139-1182, 2004.  Moreover, I have argued and showed that the length scale is not fixed but evolves with deformation and several evolution equations are proposed. You can check: Voyiadjis, G.Z., Abu Al-Rub, R.K. “Gradient plasticity theory with a variable length scale parameter,” International Journal of Solids and Structures, Vol. 42, No. 14, pp. 3998-4029, 2005. Finally, I have noticed that you are a student of Benzerga at Texas A&M University. This is very interesting. I am actually moving from Catholic University of America and joining the Department of Civil Engineering at Texas A&M University this coming June. I have not noticed the work of your advisor until now and I don’t think that I have met him before. But I believe that we will have many discussions and perhaps collaboration in the near future. I am very glade that I have found some people at TAMU are working on research topics that are of great interest to me. Please say Hi to your advisor and hopefully I will be able to meet you and your advisor in the coming month.


Rashid K. Abu Al-Rub, Ph.D.
Catholic University of America

PJ Guruprasad's picture

Dear Rashid,

Congratulations and welcome to Aggieland! I'm sure you will find this quite college town conducive for your academic and research pursuits. Looking forward to having you in our campus and hopefully we can continue our healthy academic interactions in future also.

Thanks for the relevant references. I will go through the same and hopefully they will help me to gain more insight into modelling aspects of GNDs.  

Xiaodong Li's picture

This paper may be of interest to you. The paper reports the nanoindentation data for SWCNT-reinforced epoxy composites. You can see storage and loss moduli for various percent SWCNT composites

Xiaodong Li, Hongsheng Gao, Wally A. Scrivens, Dongling Fei, Xiaoyou Xu, Michael A. Sutton, Anthony P. Reynolds and Michael L. Myrick, "Nanomechanical Characterization of Single-Walled Carbon Nanotube-Reinforced Epoxy Composites," Nanotechnology,15 (2004) 1416-1423.

Rohit Khanna's picture

Thank you Prof. Li for addressing my concerned problem. The paper is very interesting and i have some useful points to discuss. In your paper, it was mentioned that homogeneous dispersion of SWCNT is not obtained ( as also appears from bundles of SWCNT in TEM image).

In the results part, it was mentioned that hardness and elastic modulus remain constant with increasing indentation depth (p1420),  on this statement it was said that good dispersion was achieved for SWCNT-reinforced samples.  I think it may happen that there is a critical depth beyond which microstructure/distribution does not interfere with the indentation response. We can not truely say that 'good dispersion was achieved'.

i am also curious to know the loads used for the nanoindentation experiments for which the contact depth range was varied between 200-1000 nm.

 Also, may i know if it meaningful to carry out modulus mapping on such a class of composites.

thank you.


Xiaodong Li's picture

Yes. From the TEM image, you can tell that SWCNTs agglomerated to form bundles. So the homogeneous dispersion of SWCNTs was not obtained. Then the bundles were well dispersed in the epoxy matrix. Here the good dispersion of bundles (not individual nanotubes) was achieved. The nanoindentation load ranged roughly from 100 uN to 5000 uN.  I would like to encourage you to do modulus mapping. The modulus mapping on such a polymer composite sample needs careful calibration. Hope you can get some exciting results.


Rohit Khanna's picture

Thank you Prof. Li for the encouraging response. I wish to know that did you want to form agglomerates/dispersion of individual SWCNTs? Although, i don't work with SWCNTs, do you think you can avoid agglomeration.

Since your load was varied from 100-5000 uN, i expect the response from the individual constituents of the microstructure(bundles or single tube) at low load (100uN),and expectedly, higher values of E can be obtained. In your paper, i could not see any high values. 

At high loads, the bulk response is expected from a composite sample, which is obtained in your paper.  i hope i get some meaningful results from modulus mapping.

Rohit Khanna 

Rohit Khanna's picture

Dear All,

 I wish to discuss about the suitability of nanoidentation tests for different class of materials:polymer, ceramic or metal.

For nanoindentation, we normally do two types of tests: load controlled or displacement controlled? Both of these kind of tests are used for evaluating the nanomechanical properties of different materials (metals/ceramic/polymers and their composites).

The argument is "if we want to compare the nanomechanical properties of a ceramic, metal and a polymer, which kind of test is most suitable?" (load or displacement controlled).

Knowing that these materials have very different elastic modulus and under a given applied load, they tend to show different contact depths. For comparing their nanomechanical  response we should choose the separate load for each material so as to displace them to approx same depth? or else, use displacement controlled tests.

and then, which of the tests is more reliable for comparison of nanomechanical properties  of these materials?

I know this is very generic issue, may i know your comments/suggestions on this?

Rohit Khanna 


Both load control and displacement control were created for different reasons, and they are used accordingly.

The advantage of load control is the ability to apply the same load to different samples and study the behaviour under the same conditions, however as you mentioned the contact depths will differ for different materials, and hence comparison of a 1000uN indent on a ceramic will result in a much lower displacement than 1000uN in a polymer.


As there are many materials that have displacement dependent properties, metals with an oxide coating for example will have different mechanical properties at the surface than in the bulk when the film has been penetrated.  Displacement control allows the user to keep the indentation depth constant which is important in layered materials or for thin samples when minimization of substrate effects are needed.


The calculation of hardness and modulus are the same whichever method is used.  Load control and displacement control are also used to measure properties such as creep and stress relaxation during the peak hold period.


I can not give you a black and white answer, but the majority of our users tend to use load control when comparing samples.  Each person’s reasons for choosing a method is very application specific and so there is no real hard and fast rule as for which one to choose.

Rohit Khanna's picture

Hi Michelle, thank you very much for a quick response. I agree with your suggestion that for such a comparison, load controlled tests can be the suitable ones. 

More specifically, if i attempt to compare a polymer, ceramic and polymer-ceramic composite using load controlled nanoindentation, and knowing that Elastic modulus is strongly dependent  on contact depth. How can one chose the same load for these three different materials? For example, for 1000 uN load, contact depths are as follows:

polymer: 2000nm

ceramic: 500 nm

polymer/ceramic composite (50:50): 1000 nm

Having such a great difference in depths, one can not say anything conclusively. From this example, i infer that for relatively softer sample like polymer one should chose a lower load. 

may i know your suggestions?

MichelleLOyen's picture

These comments are primarily focused not on load- or depth- control of indentation experiments but really on whether comparisons are made based on a load- or depth-limit (maximum value).  I suspect the simple response to these questions would include the idea that no good comparison would involve only a single data point for comparison of widely different materials; the data from different materials should (with modern automation of nanoindenters) be compared over a range of values in terms of the load- or depth-limits.  If I did have to choose one single comparison to make, it would be for different loads and comparable depths.

A separate issue entirely is the control mode of the experiment itself, in terms of load- or displacement-control or even hybrid conditions (spring loading).  For polymers and PMCs, of course, this matters a great deal as the data analysis is wholly dependent on the control mode in terms of the viscoelastic responses, and it goes without saying that an Oliver-Pharr approach for making hardness and modulus measurements is insufficient for any control mode! 

MichelleLOyen's picture

There are two separate issues in the discussion above, one related to the intrinsically viscoelastic response of composite materials with one polymer phase, and one related to the composite materials.  The viscoelastic indentation topic has been discussed elsewhere on this website in great detail and also on my website , and I will not add much more to that subject here.  More interesting is the problem of indentation of composites in which there are two or more phases with a large elastic modulus mismatch, as in a carbon nanotube-reinforced polymer or a natural mineralized biological tissue such as bone.  The indentation results are (a) not directly the modulus of either phase, (b) strongly dependent on the indenter location relative to the phases, and (c) for stiff reinforcement in a compliant matrix, largely reflecting the compliant phase modulus due to the "springs in series" sort of argument where the deformation is largely accommodated by the most compliant link in the chain.    We addressed this problem with both modeling and experiments in the following proceedings article:

Oyen ML and Ko C-C, Variability of Nanoindentation Responses of Bone and Artificial Bone-like Composites, Advances in Bioengineering, BED, (Proceedings of the ASME-IMECE, 2004) 391-2.

and I can provide a pdf copy if you're interested (drop me an email). 

Rohit Khanna's picture

Dear All,

 I wish to discuss a very important topic about calibrating the nanoindentation tip. We normally use

fused silica sample (known elastic modulus and hardness) for calibration. and then  area function is calculated. The concerned issue is what if one want to indent a softer sample (say polymer),

in this case, area function needs to be re-calculated because the range of contact depths obtained for a polymer sample will be far different (of the order of several hundred nanometers) from that obtained with fused silica. Simply, extrapolating the calibration curve obtained for silica to larger contact depth range for softer polymers may have no relevance to 

the actual tip shape function at such greater depths.

We should use the standard polymer sample with known elastic modulus for the calibration...

The relevant papers for discussion are:

 C. Klapperich et al, Nanomechanical properties of polymers determined from nanoindentation experiments. , 123, 624-31, 2001.

L. Pruitt and D. Rondinone, The effect of specimen thickness and stress ratio on the fatigue behavior of polycarbonate, Polym Eng. Sci. 36, 1300-1305, 1996.



MichelleLOyen's picture

Rohit:  Interesting point and one that seems to come up a lot.  To a first approximation, the issues with nanoindenter calibration for polymers are unrelated to those seen in stiffer and harder materials.  Imperfections in the tip shape at nm-depths are just not as important with polymers, even for relatively thin polymer films because normal nanoindenter loads result in larger contact depths in compliant materials.   Assuming the tip is  a perfect cone with a fixed included angle does not result in large errors in polymers, as long as the  cone angle selected is the right one (and in this point I am suggesting a 24.5 C0 term is not always the right answer!)  For spherical indentation on polymers an assumption of a single-valued radius has been shown to be effective. 

The key problem that arises with identifying good calibration standards for compliant materials is the intrinsic time-dependence of response.  We have tried over the years polymers, compliant metals (single-crystal indium) and compliant crystals (NaCl).  The best materials I have come across are photoelastic coating sheets from Vishay, as described and evaluated in this recent publication:

Sensitivity of polymer nanoindentation creep measurements to experimental variables
by Oyen ML, Acta Materialia 2007, 55(11):3633-9.

These materials were also used in comparing Berkovich and spherical indentation of polymers:

Analytical techniques for indentation of viscoelastic materials  by Oyen ML, Philosophical Magazine 2006, 86(33-35):5625-41.


Xiaodong Li's picture

I think we need input from the modeling side. What are the most important parameters or boundary conditions needed for modeling or simulation? What kind of experiments are the best or the easiest for the modeling side to follow up? What intriguing properties have been predicted by modeling work?  We need insightful discussions and I hope this J club issue will serve as a bridge to promote both experimental and modeling work. Your suggestions and comments are greatly appreciated.

Fred Sansoz's picture

Dear Xiaodong,

Thanks to broaden the scope of this J club and engage the members of by calling for an integrated research forum between experimentalists and modelers in the field of mechanics of nanoscale materials, as this rapidly growing field will play an increasingly important role in materials research.

 To put my two cents in, I would like to comment on two timely problems:

 (1) Nanomechanics of nanopillars.

To my knowledge, the recent experimental development in plasticity size-effects under uniaxial compression has only been achieved with sub-micron scale pillars obtained via FIB-machining or electrodeposition.  In their PRB paper (Phys Rev. B 73 (2006)), Greer and Nix have tested 200 nm-diameter gold pillars machined in the FIB. From a fully atomistic modeling standpoint, it would help if the nanopillars could be decreased to 50 nm and below in diameter. What are the limits in the use of FIB machining and nanoindentation for such small pillar diameters?

 (2) Size-dependent strengthening effects in nanowires

As nicely pointed out by Erica Lilleodden in one of the above comments, there can be two types of size-dependent plasticity effects in nanowires: geometric size effects and microstructure size effects (I recommend, for example, to read the Letter by Wu et al. "Mechanical properties of ultrahigh-strength gold nanowires", Nature Materials (2005) 4, 525). A vast majority of the simulation literature on this topic is focused on the former type. It seems however that microstructure size effects in nanowires are less documented. For the modelers, it would help if experimentalists could better document the pre-existing microstructure of nanowires in terms of dislocation densities, grain boundary structure, grain size, etc.  For example, is the microstructure of nanowires truly "size-independent"?  Or how does the microstructure evolve during testing?  An intriguing aspect of the mechanical properties of nanobuilding blocks is related to the role of interfacial plasticity (Note: I will have a forthcoming article published in Nano Letters related to this topic).


 To conclude, I would like to propose that more conference symposiums focusing on "connecting simulation and experiment in nanomechanics" be organized.  The simulation and experiment communities would gain from debating on challenges, opportunities and breakthrough in this area.


Fred Sansoz

yfzhang's picture

Dear  Fred Sansoz

I fully agree with your comments about microstructure size effects in nanowires.The mechanics propertie of one dimensional nanomaterials  may be closely related to the microstructre, such as stacking faults, dislocations, and twins. The anisotropic performance  of mechanical properties  is also very strong in nanowires and tubes. So, the experimental datum is scattered.  Obviously, experimental studies are required to clarify the true deformation features and mechanisms of the nanowires. Researchers have investigated the mechanical properties of various nanowire systems using different techniques, such as nanoindentation, atomic force microscopy (AFM) and transmission electron microscopy . In situ experiments provide direct visualization and description of the events as they happen and give qualitative information about the structure of deformation.  It is  need develop some new   in situ experimental technology in nano and atomic scale to clear some basic deformation mechanism. Recent some paper   show   a good development in this fields. The paper list is following:

 1.Y. Huang, S. Chen, S. H. Jo, Z. Wang, D. X. Han, G. Chen, M. S. Dresselhaus, and Z. F.Ren, Phys. Rev. Lett. 94, 236802 (2005).2.Y. Huang, S. Chen, S. H. Jo, Z. Wang, D. X. Han, G. Chen, M. S. Dresselhaus, and Z. F.Ren,Nature, 439,281(2006).3. F. Yu, O. Lourie, M. J. Dyer, K. Moloni, T. F. Kelly and R. S. Ruoff, Science, 287, 637-640 (2000).4. Ding, L. Calabri, X. Chen, K. M. Kohlhaas, and R. S. Ruoff, Composites Science and Technology, 66, 1109-1121 (2006).5. C-H. Ke and H.D. Espinosa. Small, 2, 1484(2006).

6. Zhu, A. Corigliano and H.D. Espinosa. Journal of Micromechanics and Microengineering, 16, 242(2006).

7.D.Han, Y.F. Zhang, K. Zheng, Z. Zhang, Y.J. Hao, X.Y. Guo, J. Yuan and Z.L. Wang, Nano letter. 7, 452 (2007).

Yuefei zhang

Xiaodong Li's picture

Thanks a lot, Fred for your following up message. I agree. I think that experiemntal results also need modeling validation. Another thing that has been largely ignored is the development of nanomechanical testing instruments and calibration procedures. I hope to see more research in nanoinstrumentation and calibration procedure methodologies. Like nanoindentation, a new nanomechanical testing instrument may open up a new research area and lead to more findings.

benzerga's picture

There are fascinating issues in the field of small-scale plasticity and the recent pillar experiments have created momentum in that regard. More than ever the interaction between physics and mechanics is intense, sometimes exacerbating misunderstandings between the two communities.

For mechanicians, one fundamental premise in developing constitutive descriptions is that the mechanical response of a given material sample can be identified with the constitutive relation for that material. Two conditions are commonly observed for this identification to be valid (i) the sample needs to be statistically homogeneous (with respect to the type of behavior of interest); (ii) the sample is subject to uniform boundary conditions (in the sense of Hill, Mandel, ...).

Speaking of micropillar deformation, and from a theoretical point of view, I think it is healthy to distinguish low dislocation density from high dislocation density scenarios for it is evident that sufficiently small samples are not statistically homogeneous.

There is reason to believe that the bulk of the pillar data accumulated so far corresponds to low (initial) dislocation densities (where by low it is meant that the actual number of potential active sources is small) although some bigger samples could store dislocations in the course of deformation. The (purist) mechanician would probably find the problem ill-posed and leave it there! "The mechanical response of any given pillar represents that pillar and nothing else" would he shout! Indeed, there is no deterministric response if there is no statistical homogeneity.

Yet, small-scale structures and devices are being designed and sought for numerous applications and there definitely is interest in understanding what goes on in the pillars, accepting (at least some level) of stochasticity, uncertainty and so on.

Our own work has been directed at exploring the two extreme scenarios of low and high dislocation source density. The framework of analysis is discrete dislocation modeling (or a variant of it that is enriched with some physics; let us call it M-DDP). Two advantages of the framework are (i) the ability, in principle, to predict stochasticity and therefore quantify uncertainties; (ii) the ability to predict size dependency (in an ensemble-average sense) with conventional boundary conditions. One drawback is that our analyses are two-dimensional. We believe that many of the conclusions would remain valid and there certainly is room to (in)-validate our conclusions as more powerful 3D analyses become accessible.

I would summarize our current findings as follows:

(i) in the low density case, the dislocation starvation hypothesis is supported. But sustainable starvation requires that exhaustion hardening mechanisms dominate. In terms of scaling, this is a regime where the flow stress roughly varies as 1 over the sample diameter (up to deviations caused by an exhaustion hardening rate that varies itself with size and up to internal stress effects, albeit to a lesser extent).

(ii) in the high density case, the usual mechanisms of athermal hardening  (by an evolving forest) operate effectively, dislocation storage occurs and, most importantly, the dislocation structure is found to evolve so as to lead to a build-up of polar or GND density in local domains (that can be thought of as being statistically homogeneous). In turn, the rise of local GND density raises the local flow stress (perhaps in the very same ways debated in SGP theories). By way of consequence, the overall flow stress is also raised while the net GND density in the deformed sample remains essentially zero. The M-DDP calculations reveal very clearly that the integral measure of local GND density increases with decreasing specimen size, and this is the key to the size effect.

Scenario (i) may be more relevant to explain currently available data but (ii) is interesting from a purely mechanics viewpoint. In my opinion, the alternative interpretations rooted in percolation theory (as recently attempted by Dimiduk and co-workers) are questionable. It would definitely help us make progress if the elegant pillar experiments could be performed on samples FIB'd out of pre-deformed bulk samples to investigate the effect of initial density on the type of size effect.

Regarding Fred's question about how small the pillars can be made, my understanding is that below 1 micron or so, tapering is difficult to avoid. Also, for diameters about 30nm and below there may be some buckling issues to worry about unless the aspect ratio could be kept small. Julia and Erica are best positioned to comment on that.

Xiaodong Li's picture

Thanks a lot, Fred and Amine for your posts. I agree! We need to have more symposiums on connecting nanomechanics simulation and experiment. There will be a symposium on Mechanics of Nanomaterials and Micro/Nanodevices - Experiemntal and Modeling at MS&T07, September 16-20, 2007, Detroit, Michigan. Another related symposium is Emerging Methods To Understand Mechanical Behavior at 2008 TMS annual meeting, March 9-13, 2008, New Orleans, LA. There will be several sympsoiums at . I think that this J-Club is an excellent platform for connecting nanomechanics simulation and experiment. I would like to see a following up J-Club theme on computational nanomechanics in the near future.  

MichelleLOyen's picture

The upcoming "Fundamentals of Nanoindentation and Nanotribology IV" symposium to be held at the MRS Fall meeting 2007 (details here ) will also include focus on nanomechanics simulation and the linkage with experiments.   Abstracts are due 20 June.

Xiaodong Li's picture

Thanks. This symposium - Fundamentals of Nanoindentation and Nanotribology IV is timely and of great interest. Hope we can have sessions on bridging simulation and experiments. We may have another Imechanica get-together meeting.

MichelleLOyen's picture

Thanks.  Let's have a best-ever showing in this symposium and a comprehensive proceedings volume to document the current state-of-the-art!

In conjunction with this symposium, we will definitely be planning an iMech get-together for the MRS Fall 2007 meeting!  Details to come closer to the time.

Rohit Khanna's picture


May i know if you have any plans to organize imechanica get-together during MRS Fall 2007 meeting.

Best wishes,


MichelleLOyen's picture

I would very much like to have an iMechanica get-together at the MRS fall meeting in Boston (26-30 Nov. 2007).  I am seeking at least a few volunteers to help with organization and running of such an event; please reply here or email me if you are willing to get involved! 



Rohit Khanna's picture

Prof. Oyen,

Regarding imechanica get-together at MRS Fall meeting, i will be happy to volunteer.

Sorry, i checked your post on imechaica today only. let me know if i can help you.

Best Regards,


Xiaodong Li's picture

One more. Dr. Jun Lou and Dr. Junlan Wang are co-editing a special issue on Nanomechanics and Nanostructured Multifunctional Materials: Experiments, Theories, and Simulations for Journal of Nanomaterials. This will be a good opportunity to promote bridging nanomechanics simulation and experiments.

Fred Sansoz's picture

Food for (experimental) thought:  A new size effect in metallic nanowires due to interfacial plasticity predicted by molecular dynamics simulation.

To learn more, read the following article:

 K. A. Afanasyev and F. Sansoz, Strengthening in gold nanopillars with nanoscale twins, Nano Letters, 2007 (ASAP article)


Xiaodong Li's picture

Thanks, Fred. I just read this paper and found that this is paper of great interest to experimental community. I like the paper a lot. Excellent! I believe that you will see a lot of follow up papers soon.

gurpreet's picture

Great website. Great to see all the biggies!!

I was curious if there any group who has done 3-d manipulation of individual SWNTs? is it possible at all? Also is it possible (or how difficult) to see defects in an individual SWNT using 200 kV TEM (F-20)? Please note that I am not talking about a SWNT Rope. Thank You.

Gurpreet Singh

Manipulation of individual SWCNT has not been possible. Using 200 kV TEM, the SWCNT is likely to be burned rapidly by e-beam irradiation. 80 kV or 120 kV is ideal. At such low kV, your resolution is not that great, hopeless to image point defects. However, if you have a Cs-corrector, it is possible to image point defects, such as 5/7, or individual vacancies.  Iiijima's group published some papers in this regard recently.

Caizhi Zhou's picture

Experimental micro-compression studies showed the staircase stress–strain behavior. However this behavior is not obvious in larger samples and the polycrystals. ‘Dislocation starvation’ mechanism often used to describe this behavior. However, in-situ TEM experiment just could verify this mechanism in small samples with diameter smaller then 200nm (Z.W. Shan on Nature Mater., 2008). In larger samples, dislocations could not be fully eliminated. And the measured flow stresses of micropillars are much lower than those of nanowires. That means the plastic deformation of micropillars not nucleation controlled.Currently, there are several explanations on staircase stress–strain behavior as following:One is that the moving dislocations was trapped by the junction and caused the intermittency of plastic deformation (S.I. Rao on Acta Mater., 2008). So the applied stress must be increased to sustain the applied strain rate. Actually, how often of the moving dislocations could be trapped by the junctions and whether the junctions are strong enough to cause such high stress jump in the stress–strain curves are two major questions on this explanation.The second explanation is the cross-slip of the moving dislocations divided them into several shorter segments, and then the stress need to be increased to bow out the shorter dislocation segment (J.A. El-Awad on JMPS, 2008). But this explanation could not be verified by atomistic simulation at this time. The above two explanations are both based on 3D dislocation dynamics simulation.The third explanation based on FEM simulation is that the rotation of sample after yielding could change the Schmid factor on slip planes and then cause the change of flow stress (Y.S. Choi on Scripta Mater, 2007). Actually, the rotated sample under bending may also trap moving dislocations at the neutral plane where there isn’t share stress and the applied stress need to be increased to bow out new dislocations. In addition, even the rotation of sample is not obvious, there must be some surface steps caused by the slip out of upper part of the sample. This surface steps decreased the original area of the slip planes on which active dislocations are moving, and then shortened the effective length of dislocation arms. This also might case the increase of applied stress. However, the underlying mechanisms are still under debate. More sophisticated modeling and simulations are still needed to determine which conjecture would take the dominate role on the stress jump in compression of single crystals.

Xiaodong Li's picture

Thanks a lot Caizhi for your message. Yes, it will be of great interest to see large samples. I think that in addition to dislocation, surface also plays a very important role. Recent publications on the surface effects on the mechanical properties of nanosized samples give an in-depth underdtanding of the mechanisms that work at the samll scale. Below may you please see the papers that may be of interest to you.

Guofeng Wang and Xiaodong Li, "Predicting the Elastic Modulus of
Nanowires from First-principles Calculations on Their Surface and Bulk
Materials," Journal of Applied Physics (in press).

Guofeng Wang and Xiaodong Li, "Size Dependency of the Elastic Modulus
of ZnO Nanowires: Surface Stress Effect," Applied Physics Letters, 9
(2007) 231912.

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