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Molecular Dynamics Simulation of Small Metallic Nanowires

Adrian S. J. Koh's picture

Attached is a post-print of one of my journal papers submitted in 2005.  A brief description of my paper is as follows:

This paper looks at the unique and interesting behavior of a particular metallic nanowire - a single crystalline, fcc platinum nanowire, when it was subjected to uniaxial strain under two different temperatures (50K & 300K) and three strain rates with increasing orders of magnitude.  This was done using molecular dynamics simulation, using the fundamentally-sound, theoretically-accurate and experimentally-verified many-body Sutton-Chen potential.

The metallic nanowire displayed three different deformation characteristics under three strain rates of 1.2 m/s, 12 m/s and 120 m/s.  The slowest one resulted in a crystalline-ordered deformation where a single (111) dislocation plane was formed at the onset of yielding.  Subsequent straining resulted in the repeated formation of minor dislocation planes leading to a periodic stress-strain response.  The moderate strain rate causes a mixed-mode deformation characteristic where multiple twinning planes were formed almost simultaneously at yield, resulting a the attainment of a maximum stress, followed by an abrupt drop in stress and subsequent mini periodic stress-strain cycles.  The fastest strain rate led to a break-down of the ordered crystalline structure, resulting in glass-like amorphous deformation.  Similar amorphization response characteristics of other nanowires were previously reported in the works of Ikeda et. al. (1999) and Branicio & Rino (2000).

This autonomous strain-induced melting of a nanowire was an interesting observation; but the mechanism behind this phenomenon, and the properties resulting from it was not discussed in detail in the preceding works.  The paper I've attached have attempted to address the latter issue, with a collation of interesting material properties of the ultra-small platinum nanowire.  The former issue was addressed in a separate paper, which I'll place a post-print here in due time.  So watch this space!

Enjoy your read Smile

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PDF icon Small_Pt_NW.pdf1.47 MB

Comments

Hi Adrian,


0. Let me say right at the outset that I am new to MD simulations. So, my comments might seem naive to you (and to any other MD researchers).


1. First of all, I wanted to convey that I really enjoyed going through your paper. It's written to be understood. 

Yet, I would also like to see a more detailed description of the transition of deformation mode to the amorphous deformation... Precisely how it is that the timing issues in the atomic level interactions together give rise to a change in the deformation modes at the more gross scale. You have given some description in this paper, of course, but I was wondering if there could be some specialized discussion of these aspects in reference to a more simplified model... It would be great if someone (you) could essentialize it to a problem from numerical analysis, say, in reference to a problem in plain 1D and then 2D. ... May be things as in this para are common knowledge to the MD specialists... I don't know...


2. Also, I wanted to know a little about the computational complexity of your reported simulations--things such as the following... Back of the envelope calculations/estimates will do perfectly:

(i) How many atoms/ionic cores can your current system/implementation handle? On what kind of hardware? How many nodes are there in the parallel system? What kind of system is it--what kind of architecture?

(ii) What is the typical time taken for a simulation run? Say, for the case of the slowest strain rate, all the way through fracture? (Only the basic simulation time, not the visualization with VMD).

(iii) Are there any special considerations involved in applying boundary conditions? (Just asking--nothing specific in mind).

If your institute/employer policy goes against disclosing some of the above kind of details, that's fine... I was just being curious, that's all...


3. When I used to be an undergraduate (in early 80s), all that was available in those times was those static diagrams of collections of atoms and dislocations etc. (say, as in introductory books of materials science like the series by MIT's Wolf et al or van Vlack of Michigan...) But even these static pictures were far better as compared to the plain circles that stood for atoms in the even earlier texts... The atoms had acquired shading, making them 3D spheres (not circles), thereby making it easier for 3D visualization...

Against that background, now, it's so nice to see *dynamic* simulations like these... The very idea of a strain-rate dependent amorphous deformation is now that much more convincing!!

That brings me to my final point: Have you thought of making a movie out of your simulations?

(BTW, is Adrian your first name? Is it OK to address you by that name?)

Adrian S. J. Koh's picture

Dear Ajit,

Thank you very much for your kind comments and for showing interest in my work.  I'll tackle your questions one-by-one.  Your questions will be reproduced in red, and my answers will be in blue:

I would also like to see a more detailed description of the transition of deformation mode to the amorphous deformation... Precisely how it is that the timing issues in the atomic level interactions together give rise to a change in the deformation modes at the more gross scale

This would require a zoom-in study of the deformation response of the nanowires, using a series of closely-spaced strain rate magnitudes.  The evolution of the deformation mode from crystalline-to-amorphous could then be observed against the spectrum of varying strain rates.  I've presented this study in a separate paper, published in Nano Letters.  This paper cannot be posted here either in pre- or post-print at the moment as Nano Letters is considered a "gray publisher".  I'll try and get permission from them and post it here in due time.

if there could be some specialized discussion of these aspects in reference to a more simplified model... It would be great if someone (you) could essentialize it to a problem from numerical analysis, say, in reference to a problem in plain 1D and then 2D

There is one available.  I've suggested an explanation in my other paper published in Nanotechnology.  The premise is simple - amorphization occurs when the kinetic energy from the rate of change of strain overcomes the cohesive energy that binds the fcc crystalline structure of the nanowire (otherwise known as the fusion of enthalpy).  In your language, this is basically an explanation from the atomistic 0D level, which could be easily extended to 1D, 2D or even bulk 3D systems.

(i) How many atoms/ionic cores can your current system/implementation handle? On what kind of hardware? How many nodes are there in the parallel system? What kind of system is it--what kind of architecture?

(ii) What is the typical time taken for a simulation run? Say, for the case of the slowest strain rate, all the way through fracture? (Only the basic simulation time, not the visualization with VMD).

At the time of writing of this manuscript, the program I used was an in-house MD program.  This program was then at a crude stage of development and could only run in serial, up to only 2,000 atoms efficiently.  Nevertheless, essential benchmarking and verification works were done prior to running my simulations.  I've since switched to another program - DL_POLY, which is an excellent MD program available open-source from the Daresbury Labs (UK).  Two versions were available - DL_POLY_2 & DL_POLY_3.  The only difference between these two versions is the parallelization strategy.  The former uses the replicated data (RD) strategy, and the latter uses the domain decomposition (DD) strategy (these strategies were specialized techniques developed for atomistic simulations, you may click on the hyperlinks to know more about them).  DL_POLY was programmed using MPI, and assumes a hypercube computational architecture.  DL_POLY_2 could run up to 30,000 atoms efficiently, and DL_POLY_3 could theoretically handle up to 1 billion atoms.  DL_POLY could handle equilibrium MD (EMD) with its original source code.  I've since modified it to perform non-equilibrium MD (NEMD) for mechanical and thermal instabilities.  My program run took about 4 hours to run for the slowest strain rate for this work, but took only 30 mins in DL_POLY_2 on 4 CPUs.

(iii) Are there any special considerations involved in applying boundary conditions? (Just asking--nothing specific in mind).

If there are any at all, they are purely physical considerations.  I usually ask the question, " What physical sense does imposing a say, PBC, or no BC make?"  The answer would naturally lead me to choosing an appropriate BC. 

Have you thought of making a movie out of your simulations?

I've thought of making one and I did!  I am not so sure if the ones I did was in accordance to what you have in mind but I've presented my works in various conferences (NSTI Nanotech 2005, IEEE-NANO 2005, 7th WCCM), and showed movies displaying simultaneous progression of nanowire deformation against the stress-strain response.

And yes, Adrian is my first name, you may call me that Smile  And I hope I've addressed you correctly too Undecided

 

Cheerios,

Adrian KSJ

 

Adrian,

Thank you so much for addressing all my concerns in a nice, point-by-point manner. Here are a few comments, roughly in the same order as our discussion above.

-- "This would require a zoom-in study of the deformation response..." A great way to put it! That's precisely what I had in mind.

If you can't post your other paper, you could perhaps think of posting your conference presentation slides... Also, may be, computer simulation movies. (like .AVI).

-- The Doppler red-shift effect you reported in IOP Nanotechnology journal paper would be interesting to see further... Does it get captured in a visually noticeable way in the simulation movies you have made? Is the simulation accurate enough to show such a wave effect? Are 360 atoms enough? I am not doubting, just being curious.

-- If your "crude" code itself took only 4 hours for 360 atoms on a single PC in the year 2005, then that itself is a pretty neat result! Let me tell you why I think so...

In 2005, a commercially well-known CFD solver routinely took overnight runs for simulating simple external flows on a single Intel PC (the then latest machine). I know because I wanted to see exactly how poorly my own toy FEM solver ran, and so, I went out and enquired around a bit... The engineers (actually, end-users of the product) informally told me, strictly off the record, that for simulating aerodynamic drag over automobiles (external smooth incompressible flow over about 1000 tetrahedral elements in a nonuniform mesh) took them about 18 hours over a single PC...

So, now it seems to me that the bad name that Molecular Dynamics has got for being computationally very expensive is not really all that justified. The computational costs of classical MD seem to be not very different from those of the commercial (ordinary) CFD solvers anyways!

BTW, for a *potential* flow problem over about 10,000 *triangles* (not tetrahedrons), my toy FEM solver also happened to take about the same time, i.e. 18 hours, on a comparable machine: Intel PIII, 933 MHz, 512 MB RAM, in the year 2005. (That was on Win2K; no symmetric multi-processing. BTW, I will have to check if it was 10,000 or 30,000 triangles--here, in this reply, just minutes earlier, I had first reported 3000 triangles for 18 hours, but that was wrong. 3000 triangles is almost lighteningly fast: about 1.5 minutes. Even if we take the conservative 10,000 triangles, that too is a good speed for a toy solver. I will look up in the old files and come back later...)

So, apparently, toy solvers also fare pretty well, whether in MD or in Solid/Fluid Mechanics applications. (Reliability, accuracy, stability, errors, etc. are different issues though!)

-- I am not challenging the appeal you make to using the de Broglie thermal wavelength as a criterion validating the choice of classical MD in your above paper. Yet, as a novice to this field, I was wondering if there won't be some applications in other domains (esp. outside of solid mechanics) where this de Broglie wavelenth argument doesn't really hold... After all, I am sure we all are familiar with the physics experiments reported in the more recent times wherein light was shown to have been "slowed down" to the speeds of the order of only ~10 km/hr.... Just an idle thought, this is...

-- Overall, yours was a great reply. Thanks for all the information. And yes, continue calling me by my first name, i.e. Ajit. 

Adrian S. J. Koh's picture

Hi Ajit,

De Broglie wavelength is often used only as an approximate guide for justification of the validity of MD.  It's definitely not the ultimate justification.  MD validity all depends on the context of the simulation.  MD could be valid for the simulation of mechanical response of a nanowire at a size scale of 1 nm, but could be invalid for the same size scale if the photonic or electronic property is of concern.

It all depends on context, proper validation of the model is always required.

Cheerios,

Adrian KSJ

One thing remained to be answered, about dimensionality of the essentialized problem.

Speaking of the terms I use: IMO, there is no such thing as a physical entity with zero dimensions.

Accordingly, if a statement is to be made about an atom, say, as a (hard or non-hard) sphere, then that's what it would be: a sphere. But a sphere is not a zero-dimensional entity. This remains so even if you take the sequence: 3D lattice (say FCC), 2D plane of spheres (say, close-packed), 1D line of spheres. This sequence cannot be further extended. All that you get then is: a single sphere. You could associate infinite dimensions with a sphere sitting all by itself, if you wanted to... Physically, it would be as meaningless as a zero dimensional thing.

Further, talking of this application, I suppose the idea of spherical symmetry won't apply for an atom/core in an FCC lattice, because any *regular* lattice is inherently anisotropic. If the energetics is such that cohesive energy is the lowest while in an FCC configuration, then, an atom thereof remains anisotropic even if considered singly.

Of course, this is a very minor point.

Adrian S. J. Koh's picture

Hi Ajit,

You're right.  In an absolute geometrical sense, nothing in this universe is 0D, or even 1D or 2D, everything is 3D.  0D is mentioned in the relative modeling sense where vanishing BCs are applied in all three cartesian directions.

Which this, I think, you are aware and yes, it's a minor point Smile

 

Cheerios,

Adrian KSJ

The issue, the way I saw it, was not so much as absolute vs. relative, primarily. The issue, primarily, was: meaning (of abstract terms).

In contrast to what you indicate above, I believe that it *is* meaningful to speak of 1D and 2D--even if lines and surfaces cannot physially exist separately from the objects of which they are features. And yet, qua features, they do exist. Therefore, unlike you, I do believe that it's OK to say that 1D and 2D exist. Essentially, one *can* ascribe a definite process of abstraction to these terms. One can tell in a definite way how 1D and 2D were abstracted from reality--from the actually perceived things in reality.

But the terms "0D" and "infinite-D" are in a special category altogether. One cannot at all describe any definite abstraction process of whatever nature (of geometric or other kind, in an extended geometric or physical sense) for either "0D" or for "infinite-D". Accordingly, these terms are completely meaningless--and so are any statements using them. That is what I meant.

The context, of course, had made it clear that you meant isotropy (or the equality of values along all the independent axes) for the BCs. Whether the values are vanishing or not (esp. of the derivatives), so long as their *isotropy* is maintained, one could loosely call it the "0D" situation. But only loosely so.

Anyways, let me not distract the discussion away from the central theme of this thread here. I think the main work done by you is wonderful and that the discussion here should rather focus on it... After all, peole have debated dimensionality for more than a century!... So, let me raise another question; see another comment below.

Hi Adrian,

              I have read your post and came to know that you are using DL_POLY for nano simulation. I am beginners in the field of MD. I am using DL_POLY_3. Can you please tell me that is it possible to simulate the GROWTH of NANOTUBE using DL_POLY?

I  am waiting for your reply

thanks and regards

utpal 

Adrian S. J. Koh's picture

Hi Utpal,

This is a new problem.  I have not given serious thought to it but I hazard that it would be very difficult to do so.  Let me explain.

First, growth requires the program to have an effective energy minimization algorithm in order to find the stable growth direction and configuration.  DL_POLY currently do not have a good one, just a conjugate-gradient algorithm in its latest version (3.08).  If you wish to do growth, it isn't impossible but I'm afraid you have to go into the program and add a new subroutine on your own.

Second, growth requires introduction of new atoms during the simulation.  I am not sure how you can do this but I think this is another variant of non-equilibrium MD (which I've made some modifications to DL_POLY).  By non-equilibrium MD, I mean the usual statistical ensembles were not preserved.  Usual statistical ensembles refer to NVE, NVT, NPT, NsT etc.  You would require a changing N, probably coupled with a changing E and therefore, changing V in your simulations.  Which would lead to a highly non-equilibrium type of simulation.  This is certainly challenging.

So my simple answer to you is:  No, DL_POLY is not able to simulation crystal growth in its original version.  But you may take the challenge to make the necessary modifications to it to enable this functionality.

Good luck! 

 

Cheerios,

Adrian KSJ

If you wanted to model a solid solution instead of the pure metal, how easy or difficult would the task be, starting from the effort you have described here? Please assume that there is enough computing power to model a micro-wire or even a 1 millimeter dia wire. How accurate would this technique be for a solid solution?

How about the extension to a "mixture" of a nano-sized second-phase in a pure metal matrix?

How about the extension to the case of micro-sized second-phase in a pure metal matrix? Would the simulation methodology be accurate or suitable enough that it could show the stress-induced nucleation and growth of voids during ductile deformation?

Please note, I am just looking for some general knowledge-like, or the back-of-the-envelope kind of answers here, that's all.

Adrian S. J. Koh's picture

Hi Ajit, 

MD simulation is centered on the interatomic potential that is assigned to model the atomic interactions.  Hence, the simulation is only as accurate as the assigned interatomic potential.  Although the accuracy could be improved by fitting the potential parameters to a few specific material or system properties, the formulation and selection of the potential form remains most crucial.  This is usually achieved via approximation from first-principles theory, using approximation techniques like the Hartree-Fock or tight-binding approach.  The ease of modeling any physical system thus lies in the initial potential formulation, and therein, lies the challenge.  There are potentials that describe the physical system very accurately but would incur a huge amount of computational resources.  A balance has to be struck between accuracy and computational resources but very frequently, it would depend on the problem that you intend to simulate.

I am not sure if a good potential exists for the simulation of a solid-liquid mixture.  My knowledge tells me that the conventional LJ pairwise-additive potential (or known as the 6-12 potential) models the weak van der Waals forces reasonably well for fluids.  Appropriate external pressure conditions could then be imposed between the solid-liquid interface to model the suspension behavior.  Stress-induced nucleation could be modeled similarly and dislocation path, growth and nucleation could be simulated beginning with an equilibrated poly-crystalline model.  The randomly-orientated, granular structure of such models are usually fashioned from Voronoi construction, in order to achieve an isotropic material.

Hope this provides some insights to your queries.

 

Cheerios,

Adrian KSJ

Adrian,

Actually, what I had in mind was not a mixture of different states of matter (like liquid/amorphous "droplets" distributed randomly inside an otherwise fully solid state matrix), but something else: e.g. carbon forming an interstitial solid solution in iron, or copper atoms forming a substitutional solid solution in nickel. 

Let us consider the simpler case of the substitutional solid solution. It is obvious that in an all-nickel crystal, the inter-atomic potential would be of the same form throughout the crystal.

But what if copper atoms are distributed inside a nickel crystal, occupying the same lattice positions as what nickel atoms otherwise would have?

Here, I was guessing, there would be these considerations: (i) The inter-atomic potential between nickel-copper would be different from those between nickel-nickel and copper-copper. (ii) There would be a longer range, perhaps a globally significant component which depends on precisely how the copper impurity is distributed. For example, if 3-4 copper atoms are losely seggregated together, this would locally alter the nature of electron gas (or the bond or the potential) as compared to what a uniform distribution of impurity atoms would lead to. (This point need not be overstressed: I suppose it was Pradeep Sharma's group whose simulation showed development of strain inside a qubit following the entrapped of a photon.) 

Given this background, I was wondering what methodology or technique would be employed within the classical MD fold, to effectively deal with this kind complexity. Or is it that classical MD falls short here and so, either ab initio or some other approaches might be pursued? I have no idea, and was simply wondering what people do for this kind of problems.

As you can see, most of the rest of my question was simply based on altering the degree and morphology of clustering for the impurity (or solute) atoms within the regular "solvent" lattice in which they are embedded.

Adrian S. J. Koh's picture

Dear Ajit,

As an extension of the many-body simple SC potential, Rafii-Tabar & Sutton formulated an atomistic description for binary metallic alloys.  The formulation was based on the density-dependent many-body formulation (similar to the embedded-atom model & Finnis-Sinclair model), and correlates well with experimental studies on mechanical and thermal properties, with an excellent description on the FCC metal surface reconstruction.  I am not sure how the description for the interface between a metallic atom and a non-metallic atom could be formulated, this problem is more complex and (I guess) would require either a tabular interpolation between the disimilar potentials, or a constant pressure simulation within a very weakly bonded fluid solvent.  Just an off-the-cuff thought...

 

Cheerios,

Adrian KSJ

Hi Adrian,

I just started Molecular Dynamics and want to do something in Fracture Mechanics. I wanted to know if you have used any package or wrote code for your work. Better if you provide some resource to start the subject. 

Sandip Haldar

Ashfaq Adnan's picture

Hi Adrian,

In your work, you loaded your nanowires with three different degree of strain rates, the lowest being ~10^8/s which is essentially several order of magnitude higher than any mechanical tests that we do in experiments. I extensively employ MD in my resarch and am still looking for answers whether MD at this high level of strain rate can be contrasted with real mechanical tests. What is the physical implication of your chosen strain rate effects when all are way higher than quasistatic tests. It is  even higher than highest achievable high-velocity tests. Is it possible to extrapolate our understanding from the trends we see at MD to quasistatic type tests results.  In other words, can the physics of MD be contrasted to experiments?

Sincerely,

-Adnan

Adrian S. J. Koh's picture

Dear Ashfaq,

Good question.  You're perfectly right that, at present, common experimental techniques only allow very slow strain rates of up to 10^3/s to be performed.  Although some previous works stated that the seemingly polar discrepancy between the tenable strain rates that computational simulation can handle, versus the realistic strain rates in experimental setups can be reconciled with the steepest descent method during energy minimization for quasi-static simulations, I am not so sure about accepting the proposition wholesale, for obvious reasons.

The motivation for me to perform these studies were based on pure curiosity on how metallic nanowire systems behave under extreme physical conditions.  The virtual experiment would be sufficiently realistic as long as the atomistic mechanical and thermal properties were well within the tolerable limits when compared with experimental results.  The main concern would be the description of surface reconstruction in FCC metallic atoms.  This was beautifully described with the simple SC model.  Hence, at this stage, I would safely use this model to "recce" into the unknown field of metallic nanowires subjected to very high strain rates.

However, there still lies some promise for experimental verification.  As you would note that, although the strain rates I've used was in the order of 10^8/s, the linear velocity worked out to be about 1.2m/s, which could be easily realized in atomic tip retraction experiments (I can only think of this at the moment as I am not really well-verse in nanomaterials experiment, maybe you could share some of your knowledge).  Recent developments in laser-induced shock in laser-powered facilities showed some promise in inducing extremely high strain rates.

 

Cheerios,

Adrian KSJ

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