Natural Science Forum / Chemistry / General Chemistry / July 2009

Now what happens if given a specific cube or square where
the staggered packing in hex or hexagonal-close-packing
ends up with the top layer as being filled such as in the below
illustration:

OOOOOOOOOO
OOOOOOOOO
OOOOOOOOOO
OOOOOOOOO
OOOOOOOOOO
OOOOOOOOO
OOOOOOOOOO
OOOOOOOOO
OOOOOOOOOO

Where you cannot scoot over to the rightmost and have
an empty space on the leftmost.

Well the solution is really simple as shown by the X.

OOOOOOOOOO
XOOOOOOOOO
OOOOOOOOOO
OOOOOOOOO
OOOOOOOOOO
OOOOOOOOO
OOOOOOOOOO
OOOOOOOOO
OOOOOOOOOO

In that situation we scoot over to the rightmost corner the
2nd layer before the topmost layer and then fill that X mark
with another circle or in the case of 3D, fill an entire row of
more spheres.

So we have two cases of scooting over. We have this situation

OOOO
OOOOO

or we have this situation

OOOOO
OOOO

In the first case we scoot over the topmost layer and add one
more circle in the second case we scoot over the second to
topmost layer and thus provide the empty room for a added
circle, or for a entire row of spheres in 3D.

Now the above maximum density by Corner-Edge-HCP is
larger in density than the HCP-alone.

Now I know of examples in Nature of packing oranges or
golf balls or tennis balls in boxes wherein Corner-Edge-HCP
is applied. We can do it any day of the year if we have the
materials.

But I wonder if Nature has Corner-Edge-HCP within the fundamental
particles of physics and chemistry, in atoms and in molecules.

Do we see any signs of Corner-Edge-HCP versus HCP-alone
in physics or chemistry?

How would we recognize it?

Well one way is to see signs that a object is more dense at
one end of the object than anyplace else and has an overall
HCP packing.

I remember a box of oranges that was packed full and nested
in hollows and was more dense at the top, but did not inspect
why it was such.

In chemistry the most dense element is osmium or iridium. A toss
up between the two. Now I wonder if both are HCP packed?
And I wonder if one of them maybe Corner-Edge-HCP whereas
the other is not and thus the one more dense than the other
only slightly so.

Now I wonder in physics of its particles whether there are two
particles one of which seems to be slightly more dense than the
other? Yet both are known to be HCP packed?

So I wonder if Nature in physics or chemistry has some examples
of the HCP-alone packed and another that is slightly more dense
in a corner as Corner-Edge-HCP.

I rather doubt that packing of oranges or tennis balls is the only
places in Nature where a packing can occur of this maximum packing.
If something exists as a maximum it is likely to show up not just
in humanmade conditions but rather shows up in chemistry and
physics also.

Archimedes Plutonium
www.iw.net/~a_plutonium
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies