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October 9

Sphere packing and alloy densities

I believe I am correct in asserting that sphere packing of unequal spheres can sometimes result in higher packing efficiency than equal sphere packing. If spheres are atoms, it seems plausible that alloys can be denser than either constituent metal. My question: does this ever happen?--Leon (talk) 17:12, 9 October 2016 (UTC)[reply]

Interesting discussion on this: http://forums.xkcd.com/viewtopic.php?t=106760 --Guy Macon (talk) 17:37, 9 October 2016 (UTC)[reply]

Yes, it can happen. See interstitial element. Note that the density differences are rather minor, but the real significance is in how the other properties of the material change. StuRat (talk) 17:48, 9 October 2016 (UTC)[reply]

See Sphere packing#Unequal sphere packing. It seems fairly obvious that after the closest possible packing of equal spheres has filled 74% of the volume, it must then be possible to add smaller spheres in the empty 26% volume. A demonstration of infinite accumulation in two dimensions of successively smaller circles is Ford circles. AllBestFaith (talk) 19:23, 9 October 2016 (UTC)[reply]

It would be interesting to see if StuRat's scenario actually occurs; in reality the addition of interstitials can cause expansion. Spot checking palladium hydride up to PdH.02 (where a phase change occurs), using a unit cell density calculation, I find that the addition of hydrogen actually reduces the density from 12.0179g/cc (Pd alone) to 11.9647g/cc (PdH.02). The expansion of the lattice parameter from 3.889 to 3.895 (from the palladium hydride article) overwhelms the additional mass of the hydrogen. Additional inputs: 4 atoms/cell and 106.42g/mol Pd, 0.08atoms/cell and 1.0079g/mol H, 6.022*10^23 atoms/mol.

Not sphere packing, but water-ethanol mixtures are somewhat well known for having a lower volume than the sum of their constituents, see Ethanol#Solvent_properties.--Wikimedes (talk) 21:24, 9 October 2016 (UTC)[reply]

The volume of mixing is rarely x+y gives (x+y). That and apparent molar property hint that the ideas are not specific to liquid solvent, but don't comment speciically on solids like alloys. DMacks (talk) 14:09, 10 October 2016 (UTC)[reply]

There is a long list of alloys that have densities greater than the mean density of the constituents, including some rather common ones such as brass and bronze. But I don't know if there are any with a density greater than either constituent. SpinningSpark 23:14, 9 October 2016 (UTC)[reply]

What about for compounds? I need examples for which the unequal sphere packing results in a higher density.--Leon (talk) 06:57, 10 October 2016 (UTC)[reply]

I haven't been able to find any examples for alloys. However, if we make the question more general, I think many ionic compounds qualify. For example, NaCl is significantly denser than either sodium metal or chlorine liquid. In this case though the change in density is because the exchange of electrons changes the size of the respective atoms. Whether or not that counts probably depends on why you are asking. Dragons flight (talk) 07:09, 10 October 2016 (UTC)[reply]

I'm giving a lesson on sphere packing to a non-technical class, essentially to illustrate how, in most cases, volume cannot be used with 100% efficiency. I was hoping to include a tangible example of how different sorts of packing are relevant to understanding common experience.--Leon (talk) 07:42, 10 October 2016 (UTC)[reply]

The common example I use for close-packing of equal spheres in that context is stacking fruit at the supermarket. Everyone can see that there are spaces among the apples or oranges. And one can carefully build a primitive cubic stack that is more "see-through" (lay language for "less dense", but technically also relates to the alignment of the spaces). But if one pulls out a mid-layer fruit, the local area collapses to face-centered cubic. It's still close-packed, but the layers become more compact vertically, suggesting more complete use of space. DMacks (talk) 14:19, 10 October 2016 (UTC)[reply]

Air pressure / volume graph

Hi, can anyone locate a graph of air pressure versus volume (at room temperature) that clearly shows the situation at extreme pressures when the air becomes no longer compressible? 109.148.99.203 (talk) 17:48, 9 October 2016 (UTC)[reply]

I wouldn't think you would call it air then, as at those pressures the constituents would become solid and/or liquid, unless very hot, then it would be a plasma. StuRat (talk) 17:55, 9 October 2016 (UTC)[reply]

Oh really, surely it is clear enough what I mean. 109.148.99.203 (talk) 18:59, 9 October 2016 (UTC)[reply]

What the OP seeks is a Phase diagram for air. Here is its phase diagram. Dry air is mainly (78%) Nitrogen and here is its phase diagram too. These diagrams have temperature and pressure as variables. AllBestFaith (talk) 19:06, 9 October 2016 (UTC)[reply]

Thanks but no, what I seek is, funnily enough, exactly what I asked for, which is a graph of pressure versus volume. 109.148.99.203 (talk) 19:10, 9 October 2016 (UTC)[reply]

You will see only a graph of Boyle's law that turns into a straight horizontal line at high pressure. AllBestFaith (talk) 19:30, 9 October 2016 (UTC)[reply]

It is that region that I want to see. I doubt it is exactly Boyle's law instantly turning exactly into a straight line. Also, I want to know at what pressure these effects occur at room temperature. 109.148.99.203 (talk) 19:43, 9 October 2016 (UTC)[reply]

Another thing I don't understand that someone can hopefully explain. Here it says "oxygen cannot be liquified above a temperature of -119 degrees Celsius (-182 degrees Fahrenheit), no matter how much you compress it". So what happens when you compress oxygen at room temperature until the molecules are as close together as they are in liquid oxygen? What is the essential difference between the resulting substance and actual liquid oxygen? 109.148.99.203 (talk) 00:20, 10 October 2016 (UTC)[reply]

See here and here. Neither has the exact graph you're looking for, but they do discuss non-ideal gas behavior. You may also be interested looking into the Van der Waals equation. --Jayron 32 00:28, 10 October 2016 (UTC)[reply]

The reason oxygen can't be compressed to a liquid above -119C (154K) is that this is oxygen's critical temperature. Above this temperature, and above the critical pressure of 5MPa (50 atmospheres) oxygen is not a liquid, but is instead a supercritical fluid.--Wikimedes (talk) 07:28, 11 October 2016 (UTC)[reply]

Thanks for your reply. Despite the references, I still cannot visualise the key physical distinction between liquid oxygen below -119C and oxygen above -119C that is compressed to the point where the molecules are as close together as they are in liquid oxygen. On a molecular level, what is different? Also, here it says "For the cold liquids, adding more pressure would not increase the density very much because liquids are nearly incompressible. But the supercritical fluid in the cylinder is very compressible - to a first approximation you would get ten times as much gas in the cylinder at 3000 psi as you would at 300 psi". I don't understand this at all. Why would liquid oxygen below -119C be "nearly incompressible", and yet supercritical fluid oxygen above -119C compressed to the point at which the molecules are the same distance apart as in liquid oxygen still be "very compressible"? On a molecular level it seems not to make any sense. 86.129.206.211 (talk) 17:11, 11 October 2016 (UTC)[reply]

We're getting beyond what I really know, but I don't think that supercritical fluids are infinitely compressible, there's just no sudden change in volume with a small change in pressure as would happen between a gas and a liquid. I expect that the maximum density of a supercritical fluid would be close to that of the liquid. Supercritical liquid-gas boundaries and supercritical fluid extraction discuss some properties of supercritcical fluids. Some of the references appear to discuss the thermodynamic properties in some detail, but look fairly technical.--Wikimedes (talk) 21:21, 11 October 2016 (UTC)[reply]

This might be helpful: there is a stepwise change in density going the small distance from the gas to the liquid side of the line separating the gas and the liquid in the phase diagram. As temperature and pressure increase along the line, the gas gets denser (I don't think the liquid density changes much) so the change in density gets smaller, until at the critical point the gas and the liquid have the same density.--Wikimedes (talk) 21:37, 11 October 2016 (UTC)[reply]