Interpretation of deformation electron density maps (for Al alloys)

[MaybeNextTime]

Brace yourselves for this is going to be a long post. Forgive me if this is not the right forum. I did not find a dedicated Materials Science or Solid State Physics forum.

 

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TLDR:

 

I am trying to figure out the reason for AlSi's lower than expected from atomic misfit solid solution hardening (compared to AlZn, AlMg and AlCu). After about two weeks of digging I couldn't come up with any other explanation than Si's different electronic structure/being a metalloid. This article (http://www.springerlink.com/content/80408u1202556086/?MUD=MP; for coloured images http://crm-eac.imr.a...98%E7%A3%8A.pdf) reinforced my assumptions. Fast forward several months, and I'm researching (together with Dr Banach) this subject at the Institute of Low Temperature and Structure Research of Polish Academy of Sciences during an internship. There I've found another interesting article (Science Magazine: Sign In) that hinted where to look, i.e. the tetrahedral interstices. Now we're done with most of the calculations for those alloys, particularly electron density maps, but can't seem to find any apparent tendency among those alloys (unlike the first article).

 

Does anyone know how to analyze deformation density maps (in metal alloys)? Is there any literature that could be helpful? I haven't found any, unfortunately. Maybe some researcher here is well versed in this sort of thing?

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Let me first introduce myself. I'm a student at the Mechanical Faculty of Wroclaw University of Technology (Poland) with a keen interest in materials science, metal alloys in particular, but also smart materials and metamaterials. During one of the Engineering Material Design lectures the professor asked us, without hinting anything, why solid solution hardening of Al alloys with Si is weaker than one would expect from the atomic misfit of the two elements, and showed us the table below (turned out I overlooked one word - "% składnika" = "% of ingredient", i.e. solute):

 

http://s7.postimage....ab1_2_kopia.jpg

 

Now, I'm not the kind of person who's satisfied with cop-out answers (which pretty much all other students turned out to be) and the question intrigued me, so I analyze the problem. After two weeks of digging and verifying various hypotheses, I concluded that there's no correlation between electronegativity of the solutes or the difference in electronegativity of Al and the solutes and solution hardening. Same goes for the the type of equilibrium crystal lattice of the solutes, i.e. elements crystalizing in BCC were not better at hardening Al's FCC or any such thing.

 

I noted that YS strengthening (at%) is proportional to the misfit factor, while TS strengthening (at%) is not, as well as the fact that TS increase is always bigger than that of YS. Because of that, I concluded that most likely the only factor in YS strengthening is the atomic misfit (because it's unlikely other strengthening mechanisms were correlated with the atom size), while TS strengthening is influenced by more factors.

 

Knowing that Si is a metalloid, this made me believe that maybe the atom size of Si in Al alloys is different from that assumed by the table above (regular atom radius). I hypothesized that maybe the bonding between Al and Si is more covalent than in case of the remaining solutes, and thus it's more adequate to compare their covalent radii instead. In that case, the atomic misfit would be roughly 8.3%, placing Si right below Zn, making solution hardening indeed proportional to the misfit factor:

 

http://s15.postimage...ab1_3_kopia.jpg

 

Al-Si bond's covalence would result in lowered free electron density e/a. The lower the e/a, the weaker is the Stacking Fault Energy decrease. If the SFE decrease is too weak, then cross slip of a screw dislocation is not counteracted enough, leading to easier deformation compared to higher e/a.

 

Furthermore, based on Quantitative prediction of solute strengthening in aluminium alloys (Nature Materials), I learned that Si (in Al alloys) exhibits unusually low solute-dislocation interaction and volume deformation, at least compared to the likes of Mg or Cu. The latter would further reinforce the hypothesis of different than expected atom size of Si in Al's FCC structure. The interaction energy gradient for Si is much weaker and smoother, which could mean that Si atoms are interacting with Al matrix stronger with dislocations.

 

Solute-dislocation interaction energies and volume deformations of discussed solutes/alloys:

 

http://s10.postimage.org/civ91376x/nature.jpg

I concluded that in order to understand, why the way Si interacts with the dislocations/Al matrix so different compared to other solutes discussed here, I'd have to investigate its electronic structure. Based on this article (http://www.springerl...408u1202556086/) I decided that ELF (electron localization function) might be the right tool, as in this article the authors explained the opposite phenomenon - Y and Gd strengthening Mg more than expected due to increased bonding covalence. I gathered that the electronic structure (electron density or such) could potentially explain Si's comparativly weak solution hardening. I asked several researchers for help, but none of them could really help me. However, Dr Banach from the Institute of Low Temperature and Structure Research of Polish Academy of Sciences offered me an internship where we could try to solve this problem together.

 

Together with Dr Banach, I have calculated electron densities and deformation electron densities of pure Al and four other Al alloys (AlSi, AlZn, AlCu and AlMg), using 2x2x2 supercells (basically a unit cell copied x2 in each ortogonal direction, resulting in a structure made of 32 atoms, 31 Al and 1 solute) and substituted the central supercell atom - Si/Zn/Cu/Mg instead of Al. (We've also done some calculations of 3x3x3 structures but haven't got round to analyzing any of them.) For calculations we've used Density Functional Theory programme WIEN2k, and for visualization - VESTA (although this was the first time Dr Banach used it, normally he used to work with XCrysDen but VESTA boasts much more impressive functionality).

 

Our prime achievement, though, was repeating the results from Dr Nakashima's article (http://www.sciencema...583.full.pdf%29, both Fig. 3 and Fig. 4., although we're still struggling to properly visualize the latter. We're on our way of getting the equivalents of Fig. 4. for all the Al alloys I'm discussing here, however, due to being unfamiliar with VESTA, we're unable to extract the deformation density values in each direction. Once we manage to do that, we're going to compare those different alloys and see whether Si's weaker hardening is a result of lower Young modulus in certain (all?) directions. All in all, this article was a true revelation for us. It gave us a clear direction (analyzing tetrhedral interstices instead of the whole structure).

 

We have calculated not only deformation densities for each alloy, but also the diference bewteen AlX (X = Cu, Si, Mg or Zn) and pure Al in terms of total electron density and each structure's respective deformation density (in order to see how different those alloys are from pure Al in terms of electron gradient). The problem is we can't find the right scale for the gradient maps to contain all the details and nuances, because the difference between core and non-core areas is several orders of magnitude, ad the difference between positive and negative peaks of the non-core area is of at least one order of magnitude.

 

Here's the deformation electron density map for pure Aluminium (the core regions are slightly different due to differences in the method of obtaining deformation density data, ours was based purely on WIEN2k):

 

http://s18.postimage...37mx/Al_new.png

 

The next step will be integrating the charge density from the interstices in order to compare their strength and see whether AlSi structure is weaker in that regard. The problem is, we still haven't figured out how to do that.

 

It would be interesting to see how much weaker a metallic bond like that in Al is compared to a covalent bond, which according to this lecture from Yale (http://www.cosmolear...nsity-6652/%29/) is equivaent to 0.1 eV (single bond).

 

Here are the deformation electron density maps for each alloy. The color scale is different from used by Nakashima et al. In my notes I wrote down that the max value (red) is +0.006 and min value (blue) is -0.006, although I am not sure what the unit used by VESTA is. WIEN2k used Ry/bohr^3 for electron density by defualt, but VESTA has the option of converting it to eV/A^3. I'm gonna have to check that out next week, but it's not relevant to my questions, fortunately. The second picture of each alloy tries to imitate Nakashima's scale, although ignoring negative values.

 

 

For comparison, I recommend opening each alloys' map in a separate tab.

 

Al:

 

 

 

 

 

AlCu:

 

 

 

 

 

AlMg:

 

 

 

 

AlSi:

 

 

 

 

 

AlZn:

 

 

 

 

 

So my questions are:

 

Does anyone know how to properly interpret deformation density maps (or AlX - pure Al difference maps I haven't posted yet)? How can we integrate electron density in VESTA or some other software? The densities do change depending on the alloy, but do they tell us anything meaningful like with MgY and MgGd (Chinese article)? What are the aspects I should pay attention to? - electron gradient morphology? Peaks? Integrated charge of the intersticial areas?

Edited September 23, 2012 by MaybeNextTime

[Enthalpy]

Hi, and welcome here!

 

These are some places where I imagine you could inject some theoretical lubricant in the reasoning...

 

Do the alloys keep a uniform composition when you deform them to measure the properties? Al-Zn, -Cu, -MgSi... are metastable when solution treated, with Al-Zn and Al-Cu transforming even at room temperature. I expect intermetallic phases to precipitate, even if more locally than through ageing, when these alloys are measured.

 

Silicon is a near-metal. Anyway, "metalloid" looks more like a collective property than an atomic one, and pressure can change it. For being a "smaller aluminium" with one proton more, I'd expect silicon to integrate the aluminium matrix smoothly, let the excess electron go away, and leave just one positive charge - just like phosphorus does as a dopant in silicon. Or does it?

 

Typical Al-Si alloys have 7 to 13% Si, which means one Si atom every 2 atoms in each direction (I mean, 1 atom of 8 in volume) so Si atoms aren't really independant. Maybe the effect of Si should be measured at low concentration.

 

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If you like metallurgy, I have a personal wish...

 

Galling is not understood up to now. All books and courses allege dissimilar materials cure it, but that's brutally false. Too little experimental data exists and, consequently, theories are bad. Worse: we have no empirical rule neither to predict if an alloys galls easily.

 

From trials published by Allegheny and my limited user's experience:

- Hardness improves a bit

- Lubricant it very doubtful.

 

But I've found no relationship with:

- Material pairing. They're individually good or bad. Ti-Al6V galls horribly against hard Cr layer.

- Static, dynamic friction coefficient, ratio of them

- Elongation at break, hardening by cold work, breaking energy, UTS to YTS ratio...

- Heat conductivity, heat capacity, short-time heat capacity, fusion temperature, annealing temperature, change of YTS with heat, thermal expansion, ratios of them

- Precipitates and heterogeneous phases, Bcc-Fcc-Hex, crystal size

 

Maybe a relationship with:

- Individual alloying elements! C, P would improve, Cr being very bad, and Mn being a better replacement for Ni.

 

So if some day you choose a research topic:

- We know how to make aluminium alloys. A theoretical explanation is intellectually interesting but unlikely to result in better materials.

- We ignore how to improve anti-galling alloys because we have no theory, no empirical knowledge, too few experiments.

You're more likely to improve knowledge in this less known field, and as an alloy user, I'd badly need it.

[MaybeNextTime]

Thank you for your reply. To clarify, we're talking about really low concentration of the solute - the table assumes 1% concentration of the solute. In my research I assumed simple substitution (all those alloys are substitutional) as considering the effect of intermetallic phases or any substructures is out of my scope - too complex for an undergraduate student like myself.

 

As for galling, I think the problem is it's such a broad term. It's similar to cancer - there are many kinds of cancer, with different etiology etc., so lumping them all together is fallacious. The same for applies for galling. I think it'd be more sensible to focus on a specific form of galling and come up with a model explaining it, instead of trying to create a general model for galling in general.

 

But this is just an opinion of a first degree student, keep in mind.

[MaybeNextTime]

Going back to galling, by saying that "they're individually good or bad" did you mean that certain pairings are either good or bad, or that individual materials are? "No relationship with material pairing" suggests the latter, but "Ti-Al6V galls horribly against hard Cr layer" suggests the former (otherwise it would've simply been "Ti-Al6V galls horribly").

 

Did you consider:

 

1) (Vickers) microhardness at the surface, microhardness gradient from surface towards the core of the material, tangent of the microhardness distribution curve (see below)?

 

In katana the sharp edge quality is determined (among other factors) by the tangent of the microhardness distribution curve:

 

 

 

 

 

The hardness gradient is important to countermeasure things like peeling, the steeper the curve, the easier it is for the surface layer to detach from the material's body. Maybe microhardness gradient has a similar effect on galling.

 

2) Different methods of machining, forging, etc.?

 

E.g. different machning tools may result in the same surface roughness, but their respective surface pattern may be totally different, leading to different abrasion resistance.Here's an example (same roughness, different surface profile):

 

 

 

 

 

3) Residual stress at the surface?

 

Compressive residual stress hinders crack occurence. I would assume galling may be caused by bits of material detaching from the main body due to microcracks. (To be perfectly honest, I can't even find a Polish term for galling. I'm currently reading the wiki article on it to see how different it is from regular abrasion.) Machining typically leads to compressive residual stress, while heat (e.g. during the machining) leads to tensile residual stress. Which one you end up with depends on the process, I believe.

 

 

I'm pretty sure there's a number of factors involved here and the electronic structure may be one of them. My internship's supervisor said that one of his friends is researching the topic (or at least something related). Namely, he's doing a theoretical experiment at the atomic scale, where two cones of atoms move past each other. The atoms of one of them have to detach (and usually attach to the other cone). He's studying the topic from the electronic structure/element type point of view. I don't know more than that, though.

 

 

4) Oxide layer depth and its regeneration rate?

Edited October 1, 2012 by MaybeNextTime

[Enthalpy]

Alloys good or bad individually. When two parts rub, both can use the same good material. But if one part is of bad material (chromium layer) the other must be good (bronze), probably hence the false belief. This original opinion is what an alloy producer saw and showed in a report.

 

The chromium and titanium example is one I experimented. They galled horribly. Though, both materials are as different as they could be, with the hard chromium layer free of any titanium, and the Ti-Al6V4 part free of any significant chromium. The chromium layer was hard as desired, and the titanium alloy not really weak. I like this example because it proves that pairing different materials is not the solution.

 

I didn't spend weeks and months on that topic, which popped up as an annoyance to be solved. I designed mechanical functions at that time (for crash-test, fun) so in that occasion, the game was not to understand everything and produce nothing, but rather to achieve something without understanding how. It was enough to see that the doxa in books and courses (pair different materials) is grossly false and that I saw no relationship with documented macroscopic properties.

 

So, no, I didn't investigate the microhardness.

 

I suppose lapping was circumferential at my chromium layer, and I just turned the titanium part, so all grooves were perpendicular to the axial movement I had. But hydraulic pistons are leaped in the axial direction (to reduce wear at polymer sealing rings) and their chromium layer galls against badly chosen materials.

[Chromium layer on hydraulic parts has virtually no alternative, to preserve seals and withstand sand dirt, but it galls badly]

 

Corrosion resistance by a spontaneous oxide layer of proper quality is often linked with galling. For instance, Al-Mg galls but Al-Zn doesn't. Though, there are exception again, like Al-Si and Al-MgSi being rather good, or aluminium bronze Cu-Al as well. An other exception is Fe-Mn-C construction steel which galls. And the oxide layer alone won't explain why hardness improves a bit against galling, including through cold work which doesn't need to precipitate any phase.

 

Frankly, this must be re-thought from the beginning, starting from new experience, and with a fresh mind. Useful research topic.

 

This is just an opinion of a first degree student, keep in mind.

Not the worst first degree student, if my intuition works.

 

We meet funny people on Internet forums. One chemist entered University last year, as he had already synthesized all known secondary explosives in his garage. You know, the nitramines, and constrained polycycles of nitrogen with multiple bonds.

[Ronald Hyde]

I'm way out of my league on this one but consider that holes as well as electrons may be involved. We know that metals get a lot of their strength

and toughness from being squeezed by the 'electron gas' which has a kind of surface tension, i.e. surface potential. So holes being present may

change things.

[Enthalpy]

An electron gas is an extremely primitive model of a metal. MaybeNextTime conducts more subtle modelling than an electron gas.

 

You can forget the hope of getting sensible strength figures of a metal from the electron gas model. Movement of dislocations reduce the strength by a huge factor, like 10 or 10,000 (pure gold, aluminium...).

 

Holes mean only the curvature of bands where some electrons reside. This curvature changes the movement behaviour of these electrons. What relation with the movement of dislocations?

[Enthalpy]

Found again some material about galling.

 

http://www.nickelins...Steel_9006_.pdf

a foundation paper by Schumacher. Before, Harry Tanczyn wrote "Stainless Steel Galling Caracteristics Checked" which is too old to find on the Internet.

 

Some explanation attempts in the "prior art" section of the US Patent 4,039,356 for instance at FreePatentsOnline or where you prefer.

I'm not fully convinced that harder precipitates improve, because 17-4 PH has such precipitates and galls horribly.

Nor am I convinced by the high work hardening rate, as for instance Al-Mg5 hardens quickly and galls.

As for the oxide layer favoured by Si... Cr and Ti make an oxide layer and gall, even as an alloying element, so Si would be different.

 

Additional experimental results in the datasheet of Nitronic 60:

http://www.hpalloy.com/alloys/brochures/Nitronic60book.pdf

 

Please remember these papers are old, like 1977. Imaging and analysis weren't as detailed as presently.

 

Galling probably designates several different processes, yes. Refine that as you want... But to be useful, a theory must be applicable by mechanical designers! That is, the recommandations should fit in few lines.

Edited October 4, 2012 by Enthalpy

[Ronald Hyde]

An electron gas is an extremely primitive model of a metal. MaybeNextTime conducts more subtle modelling than an electron gas.

 

You can forget the hope of getting sensible strength figures of a metal from the electron gas model. Movement of dislocations reduce the strength by a huge factor, like 10 or 10,000 (pure gold, aluminium...).

 

Holes mean only the curvature of bands where some electrons reside. This curvature changes the movement behaviour of these electrons. What relation with the movement of dislocations?

I actually know about some of the things of which you wrote. Since his question was about less than expected hardening, and work hardening in

metals is due to dislocations 'piling up' and further refusing to move, I just thought that the presence of holes might be relevant in some way.

Seems not, now that you mention it.

[MaybeNextTime]

My post was about solution hardening, though, not work hardening.

[Ronald Hyde]

My post was about solution hardening, though, not work hardening.

Do you mean through heat treatment or just as cast hardness?

[MaybeNextTime]

I mean this:

 

http://en.wikipedia....n_strengthening

http://books.google....epage&q&f=false

 

When you substitute the matrix atoms in a pure metal with "foreign" atoms (or add interstitial atoms, depends on the type of the alloys), various effects increase the crystal structure's strength (sorry for using the confusing, yet popular, term "solution hardening" - it's not related to HB or HRC hardness).

Edited October 6, 2012 by MaybeNextTime

[Enthalpy]

More thoughts about galling and protective oxide layer.

The efficient oxide layer correlates suspiciously with the tendency to gall. It may be the property best correlated to galling. For instance tantalum and titanium are horrible, chromium and stainless steel too, Al-Mg alloys are bad but Al-Cu decent, while most Ni and Cu alloys are decent to good.

But there are strong exceptions. Silicon bronze Cu-Si4 is known to gall badly and makes no protective oxide. And among the austenitic stainless steel, much-demanded improvement results from keeping the oxide-forming Cr and replacing most Ni with Mn, which changes very little in the corrosion behaviour. Further improvement, at the Nitronic alloys, results from adding 4% Si to the kept Ni, Mn and barely reduced Cr, which also keeps a very protective layer.

So this seems a wrong direction too.

[Enthalpy]

One sensible candidate criterion to determine if a material is prone to galling is if heat increases its coefficient of friction. This increase would let the temperature and friction power diverge locally if the pressure and speed suffice.

Or if heat increases the friction too steeply, possibly in comparison with the heat capacity. And the increase may apply to the already hot material.

I have no data about this, which is the main difference with the previous rejected criteria.

Marc Schaefer, aka Enthalpy