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Fragmented thoughts on Molecular Packing in miniature devices

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RJSV:
   If you could take a few seconds to view the enclosed photo,  a casual gaze shows some important aspects, of modern molecular physics, in miniature electronic devices.
It's only a tiny bit of curiosity, sorry about that part...But, as with many folks, I don't have the luxury to engage in only one subject, as pure academia.

   In the photo, you can realize, for building a 3-D enclosure, the side walls are almost pure OVALS,  but the bottom 'plate' must then accommodate the round shapes, by having a very 'pointy' characteristic.
   While many folks, in electronics technology,  choose some obvious path, like circuit design, many are involved on a more basic molecular physics level.

   Considering the designs, of a cube-like box,  I mused that there likely could be a numerical gauge, of the type.   Oval type with no sharp points, and accommodating bottom having a shape that's really quite 'pointy'.

   Circles can get packing, by offsetting each row.   A couple of EEVBLOG members refer to the molecular packing geometry, and it's not trivial:
Nominal Animal, and Rick Law have this expertise, mentioning 'Face centered' lattice constant (0.543 nm) with molecular details of only 25 or so atoms.
   I'm thinking; by use of square shaped, you can pack things (atoms in this discussion), pack things perfectly.   But atoms, modeled in other shapes, don't have the luxury.

   As just maybe a fragment of an idea, I realized that my photo shape, of a common laundry bag, has round oval shaped, that need some pointy members for completion of a whole cube like object.   Squares and rectangles get a perfect match, in efficiency of packing.   That's of the 2-D shape needed, for building the overall 3D box

   Too bad we can't at present, do things to manipulate the basic shapes being packed.
And I'd like to know if there are numbers of classification rather than using the crude term 'pointy'.

RJSV:
   My first point being:
   The close packing, using OVALS or circles goes too far.   The ovals then require some less-smooth member (the bottom plate in photo).
   So, maybe using squares;  the squares are moderately smooth, and moderately not (thus the word pointy).   Using all squares, or rectangles puts the ultimate 3D shape into a sort of moderate or median amount of faster changing shapes.
   That's topology, but I can only express some armchair thoughts.

   Has anyone read this month edition of SCIENCE Magazine?   One article deals with molecular layers, and chemistry-looking words that have, like, 32 letters in them.  Very dense reading, but I like to challenge myself.

   DI-methyl-2378-latetal-chlorophosphate- tri423-w axis.  VS.
   Oxy-chromo+made-thisup-inol-6

....yeah, THAT.

RJSV:
   Part of the thoughts here involve a sphere, which can be viewed as occupying each of the 3 axis equally, just as a cube can.
So the topology of a cube could be said as having 8 'points' in the object.

   You can notice, the photo shows a fairly 'sharp' set of points.   Going to a cube model, those 8 protruding points involve 90 degree angles, that being more than shown in photo object.   Going with this idea, it's clear that a pyramid solid, again in 3D, has sharper points than a cube.   That example has 6 points.

   Going the way, towards more edges, say, 5-sided 'panels, as the 2D elements in a 3D solid enclosure.   That solid has more degrees in angles (around the points), and thus somewhat softened 'points'.   Thus nearer to sphere (no protruding points).
That solid has interesting quality that the upper and bottom panels aren't aligned.

   This sort of gaming has been explored in much more detail bulk than I can discuss.
But it seems much of the tiling discussion tends towards 2D surfaces.
So, I'm not prepared to get too much into the territory of tiling a 3D object, tending towards a sphere, but, obviously the sphere example is for the case when the number of sides and points is infinite (at the limit).

But, at the same time those tiles are growing in count that character number changes.   From pyramid, with large 'pointy' character, up through the shapes to a perfect sphere, where it's clear that elusive number is zero.
Maybe only elusive because I don't have a huge expertise in topology.

   That article in SCIENCE, has a lot of topology involved, being involved with a solar cell construction, for changing light energy into voltage.   They discuss things on a molecular level, with, like I said, very complex chemical labels used.
   It's a union of chemistry, physics, and electric focus.   Surface layers of only a couple of atoms in thickness.

Nominal Animal:

--- Quote from: RJSV on June 28, 2024, 09:21:56 pm ---I'm thinking; by use of square shaped, you can pack things (atoms in this discussion), pack things perfectly.
--- End quote ---
Face-centered cubic lattice and hexagonal close packed lattice are the densest possible packings of equal-sized spheres in 3D.  The fraction of the volume occupied by the spheres is \$\pi/\sqrt{18} \approx 0.74048\$, i.e. the "spiky" shapes between the spheres only occupy about 26% of the total volume.

Atoms are not exactly spheres, though: they don't have a well defined "surface" or "radius", because it's the electrons bound to the nucleus that defines the atom size and "shape", and in lattices and molecules some of the outermost ones are shared with other atoms.  (If we ignore the outermost electrons, the inner electrons tend to be rather spherically symmetric, so using a sphere as a representation is better than any other shape.)

So, it is not really about packing cubes or squares; it's more about packing equal-sized spheres, really.

RJSV:
   The word term I was (fumbling) seeking is 'SOLID', a seemingly trivial term.
   My opinion, this topic, on atomic scale construction, is at the top, or belongs so.   Readers;  you see a smattering of topics as I post, but the TOPOLOGY science is really deserving of attention.

My 'excuse' being resource issues, so I don't expect somebody to extract clarity....
Next;  planning to get back to local library, searching on Topology subjects, in pure mathematics section.

   The term;  'Solid' by the way, is for objects like beverage cans, in terms of 3-axis expression.  Some responders here mentioned a bit of what I'm thinking, for very small and deliberately built materials (the promise of nano-materials).
   It's a really wide open field.

   'Solids', that's the term I was seeking.

Thanks for reading!

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