may I first ask what is the size of your nanoparticles, and what is the matrix?

then I would like to direct your attention to my RG page, where you can find that nanoparticles in a (polymer) matrix are by far not statistically evenly distributed, but arranged in a highly complex manner: dissipative structures (in the meantime, I am convinced this is more or less comparable in any matrix).

Here are some Links where you can find something which is not (directly) referring to a software but giving you the background:

experimental findings:

https://www.researchgate.net/publication/229816762_Electrical_conductivity_in_heterogeneous_polymer_systems._V_%281%29_Further_experimental_evidence_for_a_phase_transition_at_the_critical_volume_concentration

review including non-equilibrium thermodynamical explanation (theory):

https://www.researchgate.net/publication/253651172_Conductive_Polymers_as_Organic_Nanometals

Here is the link to a paper I have published showing how I used "cellular automata" (however, only in 2D, maybe now softare for 3D could also be available? but it should be able to reflect the non-equilibrium thermodynamics guiding these distribution mechanism, I believe it would be complicated ...)

https://www.researchgate.net/publication/45379665_Cellular_Automata_Simulation_of_Dissipative_Structure_Formation_in_Heterogeneous_Polymer_Systems_Formation_of_Networks_of_a_Dispersed_Phase_by_Flocculation?ev=srch_pub&_sg=Hz%2Bif8zK2dR94iZtkkMz7jHV7bZtu9NXdIMON35T6kGn8kAIdK0PpMPpYUY8pBi6_IiDHM46pF5SNlUzidkdcJF%2BGqOb6V4Ise48Io6QKVX6J7xRZf%2F8SsI30xpN1jeSt

Here is some further discussion about it:

https://www.researchgate.net/publication/234020633_Roselieb_Simulation_of_Wessling_Model_for_Network_Formation_in_Dispersed_Polymer_Phases?ev=srch_pub&_sg=YyEA5brheIh%2BRzlO0btpyZLvcdrnnNw0lQSvCRkrSMXXy1K5hbd3x%2FVCpE02xd35_kheLx3d5iRrambij1N0vbr%2Bzr%2BCkEddi%2FNsT8B83Z%2Fd28qWjcnGi%2BWwc6aS2mVmh

https://www.researchgate.net/publication/259062150_Comments_on_C._Roselieb%27s_simulation_of_Wessling_Model_for_Network_Formation_in_Dispersions?ev=srch_pub&_sg=FG9ypQtRpCWVwqwMRGXS9VhRBz46V71vuHkaYOjUv2%2BJF%2Ba6DkhQWF68giE4Vjs8_H2qwKdaZnA4iIoMHR%2BhNov5wRYWIF0%2Fb2SK1JCKXirfQLv3XU9T9cmkc59kY3E0N

Article Electrical conductivity in heterogeneous polymer systems. V ...

Chapter Conductive Polymers as Organic Nanometals

Article Cellular Automata Simulation of Dissipative Structure Format...

Data Roselieb Simulation of Wessling Model for Network Formation ...

Article Comments on C. Roselieb's "simulation of Wessling Model for ...

Dear Dr. Wessling,

Thanks for your response.

The particles size is in range of 20-80 nm and normally nonferrous alloys are as matrix. But we want to find a general and accurate method for metals with least limitation.

what is the type of nanoparticles you want to disperse in the nonferrous metal alloys? with 20 - 80 nm, I am sure, the principles which I have described in my papers for polymer and liquid systems are basically also applicable, because the non-equilibrium thermodynamical character of heterogeneous systems is similar, not in detail *identical*, but in principle *similar*.

In mentioned range different nanoparticles used such as SiC, Al2O3 and TiO2.

ok; you mentioned in your question "experimental samples" and that simulating software did not match what you found. May I ask - what did you find? can you show some results? how had the particles been distributed?

Do you disperse the particles in an alloy melt?

We disperse particles in solid-state form, Friction stir welding. Indeed I studied on experimental methods and for example we observed agglomeration of particles in some areas under special flow of materials but we couldn’t simulate it exactly. Please let me know what is your suggested software and solution as per our conditions?

Moreover we want to know is there any machine that cans analyses a real sample and create a virtual 3D model of it?

I am not familiar with metal based composited, especially not nano-composites where a metal alloy is the continuous matrix. But from my basic understanding of heterogeneous systems with one dispersed being nanoparticles, I would conclude that also in a metal nanocomposite the continuous phase must adsorb on the nanoparticles surface.

I would think that also in such a case you need to work at higher temperature (maybe not necessarily above melting temperature), but the metal must be a least somehow liquid, otherwise no adsorption can happen.

I don't know what temperatures you get to under "friction stir welding conditions, how liquid the metal phase is then, but when you describe that you observed agglomerates = undispersed nanoparticles, I conclude that the metal was not liquid enough, could not well enough disperse the particles and not adsorb on the nanoparticles surfaces.

I have no software for simulating this ...

Dear Dr. Wessling,

Thank you very much for your time and consideration.

I am not aware of any mechanism for getting a true 3-D image of structure at this scale, although I'll be interested to hear if someone has a good suggestion of which I am unaware. You are easily beyond what I understand to be the present range for X-ray tomography. If 2-D is actually sufficient, then clearly TEM would do the trick. Are you interested primarily in measuring how far away from homogeneous your distribution is? .Or, are you interested in running virtual experiments of some properties (mechanical or thermal?) on you give nano-structures? If the latter, you might check out a free software called OOF on the NIST web site. Very nice program for running virtual experiments (modulus, etc.) on various true input structures, and I think they now have a 3-D component, although again I don't know of a way for you to get true 3-D structures at this scale. Additionally, One would need to cover enough volume so that you had a good overall view of the structures involved in your MMCs.

Dear Dr. Koopman,

Thank you very much for your nice advice.

Software, now matter how sophisticated, is only a simulation of reality. It is better when it takes into account more mechanisms present (acting) in a simulated composite object. Thus you may not expect to obtain correct nanoparticle size distribution if you don't know how those nanoparticles are formed. Ok, this is usually guessed parameter (or just taken for granted from real measurements). How about inhomogeneities? One may safely assume that the software (if there is any) uses some kind of random number generator to find the initial positions of individual nanoparticles and then tries to relocate them to remove overlaps. No physics, no interactions are taken into account, be it turbulent flow, viscosity, electrostatic interactions, or anything like this. Accuracy of such simulations? Only by accident, if you're lucky or if you accept the "accuracy" (what's that?) so obtained.

Dear prof. Gutowski,

Thanks a lot for your answer. But please let me know do you consider any special software or machine for such simulation?

As I wrote: "if there is any". For the simulations exploiting random number generation any ordinary PC should suffice. The harder part is writing your own code ...

Dear prof. Gutowski,

Yes of course, you’re right.

I would be very surprised (but I am open to any surprise) if in any system, a *dispersion* of nanoparticles is statistically even, homogeneous, and can be simulated by the use of "random number generations".

In fact, a dispersion ALWAYS involves the interaction of surface to form interfaces, and is ALWAYS a non-equilibrum process (thermodynamically spoken). Therefore, as a consequence, the resulting distribution will be non-random, but (in case you achieve a good dispersion), very fine detailed structures will be generated.

Whether or not these are similar to the structures I have found in the polymer matrix based systems or in liquid colloidal systems which I have studied, I don't know, but I would gues so to begin with.

(you can see such structures in my papers).

Also, I would like to refer again to the "cellular automata" program which I had used for simulating these structures in 2D - this program uses "interactions", it does not generate random numbers!

I think you can use elemental map, I have published similar results for nano-Ni-nano-TiO2 at 63rd Annual Meeting of the International Society of Electrochemistry in Prague, Czech Republic; 08/2012

Dear Dr. Negem,

Would you please send the link or source of the mentioned publication?

sorry, this is modelling the distribution of macro/micoscopic particles, submicron particles behave totally different! I have shown this in many publications

You can find the below article which is considered one of the recent during 2017.

"A Modified Ant Colony Optimization algorithm for the Distributed Job shop Scheduling Problem*

http://www.sciencedirect.com/science/article/pii/S1877050917316769

Best regards