Sphere Packing {was: Re: [Rockhounds] Another extinction impact-13
KYA}
Kreigh Tomaszewski
Kreigh at Tomaszewski.net
Fri Jan 2 18:43:49 PST 2009
Pete,
To answer your first question, I think the binding energy barrier is at
a minimum when the layers are arranged in the right order. The surface
is affected by the layer(s) below it, and the new layer of atoms goes
into position easier when the atoms are in the right orientation.
In the two examples given the layers are staggered
o o o o o
o o o o
o o o o o
There is another alternative where the layers are aligned
o o o o o
o o o o o
o o o o o
In this case the second layer can either stack on top of the existing
layer (AAAAAA), or it can fill the gaps between the spheres (ABABABA).
Admittedly, it is not as closely packed as the staggered layers, but it
is a third alternative to sphere packing.
Kreigh
On Friday, Jan 2, 2009, at 19:40 America/Detroit, R. Peter Richards
wrote:
> Dihexagonal dipyramidal is the name of the symmetry class within the
> hexagonal symmetry system. It simply defines all the symmetry
> elements (axes of rotation, planes of mirror symmetry, etc) possessed
> by minerals with structures that fall within that symmetry class (of
> which there are 32, and only 32). I cannot comment authoratitively on
> the claim in wikipedia that lonsdaleite forms by a distortion of a
> graphite structure, but I have my doubts. Graphite has carbon bonds
> only in the planes parallel to its sheets, and much weaker bonds in
> between; diamond and lonsdaleite have carbon-carbon bonds in three
> dimensions. Something profound would have to be undone and done up
> again to turn graphite into lonsdaleite (maybe that's what Superman
> really did...) This is analogous (though maybe somewhat crudely) to
> the difference between mica, with sheets of linked silicate
> tetrahedra, and quartz, with a 3-D network of linked silicate
> tetrahedra. The similarity in properties is not coincidental.
>
> The structure shown in the Wiki article does not look close-packed
> because the atoms are shown essentially as points, not at their
> effective sizes in the structure.
>
> To get really technical, the difference between the cubic and
> hexagonal closest packed structures is that, if you form layers of
> spheres (pennies work OK for this analogy), once you lay our the first
> layer, with all the spheres (pennies) touching each other, the place
> for the next layer to go (to be closest-packed) is over the triangular
> holes between the first-layer spheres or pennies. There are two
> choices; you can choose one or the other. Which ever one you choose,
> it's called choice B. B because the orientation of the first layer is
> called A; this does not matter now but it will later. So now we get
> to build the third layer. We can either choose the holes in the
> second layer (B) that are right under the centers of the atoms in
> layer A, or we can choose the as-yet unused position C. Then we
> repeat this layering gazillions of times to build a crystal. The
> first alternative has the layer sequence ABABABABAB... The second has
> the sequence ABCABCABCABCABC... The first creates a hexagonal
> closest-packed structure, the second creates a cubic closest-packed
> structure. These layers are laid up perpendicular to the c-axis of a
> hexagonal mineral, or parallel to the body diagonal, the [111] axis,
> of an isometric mineral. See
> http://en.wikipedia.org/wiki/Close-packing_of_spheres.
>
> Several interesting points arise from this...
>
> 1. How does a growing crystal "remember" what sequence it is using to
> build itself? A closest-packed structure cannot repeat a particular
> layer twice in a row, i.e. AAABBBABBAA is not closest-packed, but why
> don't we get ABABCBCABCBACABABCA or other comparable garbage?
>
> 2. It must be really destructive (in terms of disturbing strong
> chemical bonds) to try to change an ABABABAB layering sequence into an
> ABCABCABC layering sequence. How can this happen? Does it ever
> happen? Is this part of the reason that diamond can get shot up from
> the depths of the earth and not get changed in to graphite?
>
> There's even more, but by now most everybody is looking at another
> message or something....
>
> Happy New Year,
> Pete Richards
>
>
> On Jan 2, 2009, at 6:16 PM, J Bryan Kramer wrote:
>
>> That's interesting, wiki has a page on it:
>>
>> <http://en.wikipedia.org/wiki/Lonsdaleite>
>>
>> But that drawing of the crystal structure does not look like
>> hexagonal close
>> packing to me. It looks more like some deformed cubic structure.
>> Mindat
>> calls it Dihexagonal Dipyramidal, which as a chemist is greek to me.
>>
>> BK
>>
>> On Fri, Jan 2, 2009 at 18:03, R. Peter Richards <rpr at heidelberg.edu>
>> wrote:
>>
>>> I think the reference is to a diamond-like mineral with a hexagonal
>>> atomic
>>> structure, not a hexagon-shaped diamond. Normal diamond
>>> crystallizes in the
>>> isometric (cubic) symmetry system. Look up lonsdaleite in a mineral
>>> reference book; it's the analog for diamond in the hexagonal symmetry
>>> system.
>>>
>>> Since graphite, diamond, and lonsdaleite are pure carbon, they can be
>>> considered structures formed from spheres (atoms) of one size only.
>>> There
>>> are two different ways to put together spheres as densely as
>>> possible (i.e.
>>> with as little open space among the atoms as possible); these are
>>> referred
>>> to as "closest packing" structures. Diamond structure has one form
>>> - cubic
>>> closest packing - and lonsdaleite has the other - hexagonal closest
>>> packing.
>>> Graphite has a lot of open space - it is not a close-packed
>>> structure.
>>>
>>> Dana's System Volume 8 mentions that lonsdaleite is often associated
>>> with
>>> diamonds and with meteorites or impact sites, and is generally
>>> microscopic.
>>>
>>> I think this is what is being referred to as "hexagonal diamonds".
>>>
>>> Pete Richards
>>>
>>>
>>> On Jan 2, 2009, at 4:05 PM, donhalterman at verizon.net wrote:
>>>
>>>
>>>>
>>>>
>>>>
>>>>
>>>> > The abstract mentions two
>>>> > kinds of diamond particles found, and I think the terminology
>>>> is a
>>>> little
>>>> > more technical than six-sided diamonds.
>>>>
>>>>
>>>> Hi,
>>>>
>>>> Unfortunately
>>>> I don't have time to read these linked articles, but I've seen some
>>>> posted references to "hexagonal diamonds," and I'm thinking the
>>>> following might help (or maybe not...)
>>>>
>>>> A hexagon is a
>>>> 2-dimensional figure, which is Greek for "six sides." On the other
>>>> hand, a six-faced, equilateral, 3-dimensional solid is--a cube!
>>>> Take a
>>>> look at a cube and count the faces. The crystallographic name for a
>>>> cube is a hexahedron. There are cubic diamonds; in fact, former list
>>>> member John Betts sells cubic diamond crystals on his website. These
>>>> form on earth as well.
>>>>
>>>> I don't know if that helps with the discussion here, but at least it
>>>> should be a fun fact.
>>>>
>>>> Best,
>>>> Don
>>>>
>>>>
>>>>
>>>>
>>>>
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>>>
>>> ___________________________________
>>> R. Peter Richards
>>> rpr at heidelberg.edu
>>> Morphological crystallographer
>>>
>>>
>>>
>>>
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>>
>>
>>
>> --
>>
>> ""It often seems to me that the night is much more alive and richly
>> colored
>> than the day."
>>
>> Vincent van Gogh
>> J Bryan Krämer
>> North Florida, USA
>> photos at:
>> http://pbase.com/photoburner
>>
>>
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>
> ___________________________________
> R. Peter Richards
> rpr at heidelberg.edu
> Morphological crystallographer
>
>
>
>
>
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