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Multinary Alloys (metallurgy)

 
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chiarizio
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PostPosted: Sun Jan 21, 2018 12:27 am    Post subject: Multinary Alloys (metallurgy) Reply with quote

Setup: Why am I asking about this?:
Certain sets of multi-component alloy-systems have gotten interest lately.
One of them is High-Entropy Alloys (HEAs).
Another is Bulk Metallic Glasses (BMGs).
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HEAs were originally defined (heuristically, IMO) as equiatomic (equimolar) or nearly-equiatomic alloys of five or more elements (at least one a metal, probably most or all metals).
"Equimolar" means there are just as many moles of each element in the alloy as there are of each other element in the alloy.
If the fraction of the atoms in a sample is expressed as a percent, the abbreviation "at%" is used. That's different from percent-by-mass and from percent-by-volume.
"Near-equiatomic" was originally defined (heuristically IMO) as between 5at% and 35at% for each element.
The HEAs that are studied in publications tend to be substitutional solid solutions, not interstitial solid solutions and not intermetallic compounds.
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"Metallic Glasses" are amorphous (i.e. non-crystalline) alloys.
For (probably all, maybe only) most alloys, to get them to solidify amorphously, they must be cooled too rapidly to crystallize.
This used to mean that the solid amorphous sample thus produced had to be no thicker than 1mm in at least one dimension.
Metallic glasses that could be solidified in samples thicker than 1mm in every dimension are called "Bulk Metallic Glasses".
Some of them can be produced in samples as thick as 15mm in every dimension.
Some of them can be cooled as slowly as 1-degree-Kelvin-per-second.
(Older MGs had to be cooled as rapidly as 1000-degrees-Kelvin-per-second, or even 1000-degrees-Kelvin-per-millisecond.)

BMGs are almost always "multinary" (more than two elements in the alloy); but they apparently don't need to be equimolar, and may be interstitial solid solutions or a mix of any two or all three of interstitial solutions, substitutional solutions, and/or intermetallic compounds.

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A guy named William Hume-Rothery came up with two sets of four rules in each set for when to expect two elements to form good solid solutions in one another.

For substitutional solutions:
1. The atomic radius of the larger of atoms shouldn't be more than 1.15 times the atomic radius of the smaller atoms.
(Otherwise substituting one kind of atom in a lattice made up of the other kind of atom would disturb its crystal structure too much to call it "a solution").

2. The two elements should have electronegativities differing by no more than 0.4 (Pauling scale or Allen scale? Maybe either is OK.)
(Otherwise the elements may be too likely to form an intermetallic compound rather than a solid solution.)

3. The two elements should have the same valency.
(Otherwise the elements may be too likely to form an intermetallic compound rather than a solid solution.)
(I just haven't worried about valency. Transition metals have so many different valencies that any two of them are quite likely IME to have at least one valency in common.)

4. The two elements should have the same crystal structure as each other, when solidified and crystallized as pure elements.

- - - - - -

Guys named L.S. Darken and R.W. Gurry came up with a refinement on rules 1 and 2 above.
If the electronegativities differ by no more than 0.2, and the larger atoms' radius is not more than 1.075 times the smaller atoms' radius, one should expect* each element to be soluble in the other at any concentration, or, at least, at a wide range of concentrations.
OTOH if the electronegativities differ by no more than 0.4, and the larger atoms' radius is not more than 1.15 times the smaller atoms' radius, one should expect each element to be soluble in the other in concentrations up to at least 5at%.
*(But that doesn't always happen.)

- - - - - - - - - -

For interstitial solutions:
1. The atomic radius of the smaller atoms shouldn't be more than sqrt(2)-1 = .4042 times the atomic radius of the larger atoms.
(Otherwise the smaller atoms won't fit into the interstices between the larger atoms well enough to not disturb their lattice enough to still be called "a solid solution").

2. The two elements should have electronegativities differing by no more than 0.4 (Pauling scale or Allen scale? Maybe either is OK.)
(Otherwise the elements may be too likely to form an intermetallic compound rather than a solid solution.)

3. The two elements should have the same valency.
(Otherwise the elements may be too likely to form an intermetallic compound rather than a solid solution.)
(I just haven't worried about valency. Transition metals have so many different valencies that any two of them are quite likely IME to have at least one valency in common.)

4. The two elements should be soluble in each other at a wide range of concentrations.
[edit]The above wording of rule 4 for interstitials, must be wrong; because it explains that things will be soluble if they are soluble. Wikipedia's actual wording is
Wikipedia wrote:
They should show a wide range of composition.
The only other way to interpret that I've thought of is "they should form a lot of different compounds";
but that defeats the purpose of the rules about electronegativity and valence, which is to guarantee that they won't form any intermetallic compounds. I am trying to find out what the real rule is.[/edit]


- - - - - - - - - - - - - -

If the smallest atomic radius isn't smaller than cuberoot(1/2) of the largest radius; i.e. the largest atomic radius isn't bigger than cuberoot(2) times the smallest radius; that has an effect on the glass-forming ability of the alloy. (I'm not quite sure what it is.) OTOH if that ratio is more aggressive -- the big atoms are bigger than 1.26 times the smaller atoms or the small atoms are smaller than 0.79 times the big atoms (my numbers may be off a bit), adding a third alloyant with an intermediate atomic radius sometimes greatly increases the glass-forming abiltiy of the alloy.

[/end of setup]

_____________________________________________________________


Questions:

Here's the thing.
I've found it very difficult to find a system of more than four metals that satisfy Hume-Rothery's rules for substitutional solid solutions.

For instance: Copper is face-centered cubic-close-packed as a crystal of a pure metal.
So are nickel and lead and silver, among many other metals.
Copper's electronegativity and atomic radius are close enough to each of nickel's and lead's, to make copper and nickel soluble in each other at a wide range of concentrations (maybe all of them), and also to make copper and lead soluble in each other at a wide range of concentrations.
Nickel and lead are likewise close.
Silver's electronegativity and atomic radius are close enough to copper's to make silver and copper soluble in each other at concentrations at least as high as 5 at% (maybe higher); and the same is true of silver and nickel, and/or silver and lead.
So I would expect there might be a good substitutional solid-solution alloy of 25at% Cu, 25at% Ni, 25at% Pb, and 25at% Ag.
But I can't find anything out about such a quaternary alloy.
Also I can't find out anything about a quinary equimolar alloy involving copper.

Gold, rhodium, platinum, palladium, and iridium, are pairwise within 0.4 of each other in electronegativity and within 7.5% of each other in atomic radius. In fact, four of those metals -- Rh, Pt, Pd, and Ir -- are with 0.2 of each other in electronegativity. So we'd expect there to be a pretty good substitutional solid solution of 20at% Rh, 20at% Pt, 20at% Pd, 20at% Ir, and 20at% Au. But I can't find anything about such a quinary alloy.


-- -- -- -- --

Iron crystallizes in the BCC (Body-Centered Cubic) structure as a pure metal.
(Note: BCC is not a close-packed structure.)
So do chromium, vanadium, manganese, and many other metals.
Iron and chromium are close enough in electronegativity and atomic radius that according to Hume-Rothery's rules they should be soluble in each other at a wide range of concentrations; perhaps at any concentration.
Each of chromium, vanadium, and manganese are also that close to each other.
Each of vanadium and manganese is close enough to iron in electronegativity and atomic radius to expect each pair of elemnts (both the iron-vanadium pair and the iron-manganese pair) to be soluble in each other at ratios at least as high as 5%; maybe more.
So perhaps we ought to expect an alloy of 45at% Fe, 45at% Cr, 5at% V, and 5at% Mn to form a good substitutional solution.
I expect (justly or not) that we could get an alloy of 35at% Fe, 35at% Cr, 10at% V, and 10at% Mn, to form a solid solution.
That would be (probably, I'm guessing) as close to the first definition of an HEA as one could get with only four elements instead of five or more.
OTOH maybe 25at% Fe, 25at% Cr, 25at% V, and 25at% Mn, is also possible and also makes a solid solution. Or 30at% iron, 30at% chromium, 20at% vanadium, and 20at% manganese. Or something.

However, I am unable to find any information on a quaternary alloy of iron, chromium, vanadium, and manganese.
I am unable to find any five-element set of BCC elements all of which are pairwise mutually inter-soluble in each other according to Hume-Rothery's rules for substitutional solutions.
I haven't (yet?) found any other foursome of BCC elements that are all intersoluble in each other. (According to Hume-Rothery's rules for substitutional solutions.)

-- -- -- -- --

I have found one set of six lanthanides that should be pairwise highly intersoluble in each other at a wide range of concentrations.
They are gadolinium, terbium, dysprosium, erbium, thulium, and lutetium.
But I haven't found anything about an alloy of five or all six of Gd, Tb, Dy, Er, Tm, and Lu.
I haven't even found out anything about quaternary alloys of any four of these.
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chiarizio
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Posts: 1789
Location: Bungula Qintaurion, Toliman

PostPosted: Thu Mar 08, 2018 9:35 pm    Post subject: Reply with quote

I just realized: I never actually asked a question!
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Can anyone tell me anything else about good rules for which sets of elements will form good high-mixing-entropy >=5-ary crystalline solid solutions?

How about >=4-ary amorphous bulk metallic glasses?
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