[Ugly_Bird]

Hi,

Last days I was reading a lot about magic numbers of various clusters.
People say that magic numbers correspond to the most stable species relative their neighbours (for example on a mass-spec).
If we consider laser ablation of solids and look at the mass spec of, say, carbon, we observe a strong peak of C60, which has much larger intensity in comparison with C58 and C62. I cannot understand really what kind of stabilty people mean here? The laser ablation is terribly non-equilibrium process. How come people talk about thermodynamical stability relative to those? I am really confused. If someone could explane me the stuff it would be great. Thanks!

[gregpawin]

Hmm... I would think that when they talk about magic number clusters they usually are talking about unreactive atoms that form stable clusters due to geometrical formations of a stable sphere.  Carbon on the other hand, likes to from structures and I would guess forms a fullerene at C60.  From the point of view of fullerenes versus different kinds of similar structures, I would have to guess that the fullerene puts the least amount of stress on the bonds evenly over the entire structure compared to the other structures, though I'm not sure what this has to do with magic numbers.

[gregpawin]

After asking my physics lab mate, who's PHD was about clusters, let me regurgitate some of what he said.  For every kind of cluster there's their own magic numbers.  Its very similar to chemistry in that all we're doing is filling up empty valence shells.  So with the simplest case, as in alkali metals, we get one electron for every atom.  So, for the first magic number we'd get 2 because two free electrons can fill up the 1s orbital.  The next would be 4 because two more electrons would fill up the 2s orbital.  Then we'd get 8 because it takes 6 more electrons to fill up the 2p orbital... and so on.  You'd get the mass spec of this stuff and get spikes at these numbers of atoms: 2,4,8...etc.

With other metals, they have different amounts of free electrons, so its a bit harder to say which are their magic numbers.  I'm not sure what the rule is if the number of electrons don't exactly fall into a stable valence shell.

[Ugly_Bird]

Gregpawin, thank's a lot for taking time and answering my question.
Yes, I know about electron shells in alkali metal clusters. That's pretty well described in Jellium Model. The magic numbers there correspond to closed shells (analog of closed shells in noble gases from the Periodic Table). BTW, talking about noble gas cluster formed in supersonic jet, those also form magic number clusters but those are explained from geometrical point of view. The noble gas magic number clusters correspond to polyhedra formed by closely packed atoms, for example 55 (cuboicosohedron if I'm not wrong).
Thus, there are two reasons for magic numbers: electronic closed shells and geometrical closed shells. Both exhibit great energetical stability.
OK, now back to my question.  
Along with others, magic number clusters are formed in various strongly nonequlibrium processes (laser ablation, supersonic jet expansion, arcing etc.). It means that thermodynamical control is unlikely. If we do not have thermodynamical control how can we talk about magic number clusters, which have higher stability in terms of energy?
Uf...that rather puzzling...

Thanks again!


 
 

[gregpawin]

Ok... after a quick discussion with my clusters guy, he drew upon a elementary principal of thermodynamics... he just said that the only thing that matters are the clusters' stability in relation to one another (one magic number configuration or the next).  They don't have any "memory" of being anything else and have stability independant of the processes that created them.  Stability is a state function.