Mathematician Theorizes a Crystal As Beautiful As A Diamond

Roland Piquepaille writes "Why are diamonds so shiny and beautiful? A Japanese mathematician says it's because of their unique crystal structure and two key properties, called 'maximal symmetry' and 'strong isotropic property.' According to the American Mathematical Society (AMS), he found that out of all the crystals that are possible to construct mathematically, just one shares these two properties with the diamond. So far, his K4 crystal exists only as a mathematical object. And nobody knows if it exists — or if it can be synthesized."

Comments

4 points, in which any two vertices are connected

[Animats]

"4 points, in which any two vertices are connected by an edge." Isn't that a tetrahedron?

There are tetrahedral crystals. The last picture on that page is an unusually nice one.

The possible crystal forms for an element depend on the bond angles, and I don't think carbon will hold a stable tetrahedral lattice. Not sure, though.

Article is complete hogwash

[Anonymous Coward]

To get things out of the way: Yes, I am structural chemist, I did RTFA and I am not a native english speaker, so please bear with my broken english.

I don't want to comment so much on the mathematical part of the paper, which might be interesting, but on the chemistry, which is non-sensical.

First of all the style of the article is very un-scientific. Note how often he mentions how pretty this crystal structure is. This is completely subjective and I don't see how this structure is prettier than many others. There is many fascinating structures and I don't think this or the diamond lattice are the most fascinating ones.

Then the assumption that the prettyness of diamond is a direct result from the crystal structure is silly. Someone else noticed that Silicium (and also Germanium and Tin) have exactly the same crystal structure - and they are not "pretty".

He doesn't mention space group nor atomic positions, which are absolutely fundamental when talking about a crystal structure.

Now even if the crystal would form like he describes (with 1/3rd double bonds), there is just no way this would ever look anything like a diamond. The electronic structure is completely different - diamond is an insulator, a classic dielectric material, whereas this, due to its double bonds and it's extendef pi-electron system, would be a classical conductor. It would probably look like graphite.

But, and this is the worst point, which even someone who only did very basic (highschool?) chemistry should immediately note, the compound can never form in this way. That's the first thing you learn about double bonds: they're flat or nearly flat. Admittedly, in fullerene and carbon nano-tubes, there is a certain curvation (making them not as stable as graphite), but if you look at this crystal structure, the double bonds have a dihedral angle of about 90 degrees. It's totally impossible to obtain this compound and everybody with scientific education should know this. The molecular orbitals can't form this way.

All in all I have no idea how it comes that this non-scientific non-sensical article is published by the AMS. Maybe you could make something out of the math part, but all the babble about prettiness and chemistry has to go.

What about other single element crystals in A4 ?

[MrMr]

If the symmetry and isotropy give diamonds their shine, why are crystals of
for instance Si, Ge, Sn not as beautiful? They have the same isotropy and crystal structure.
And why is a low-symmetry sapphire prettier than high-symmetry table salt?
I would guess high index of refraction, and the lack of absorption of optical wavelengths are the more relevant properties.

(see any textbook on crystallography, or for instance http://cst-www.nrl.navy.mil/lattice/ )

Demand was inflated through marketing

[aepervius]

It is well known that before the ad-campaign of mid 20th diamonds were not that much in "demand". Heck, it is well known that before the oversupply of the 19th century diamond were relatively rare. Look at wiki for more detail.

quote The De Beers diamond advertising campaign is acknowledged as one of the most successful and innovative campaigns in history. N. W. Ayer & Son, the advertising firm retained by De Beers in the mid-20th century, succeeded in reviving the American diamond market and opened up new markets, even in countries where no diamond tradition had existed before. N.W. Ayer's multifaceted marketing campaign included product placement, advertising the diamond itself rather than the De Beers brand, and building associations with celebrities and royalty. This coordinated campaign has lasted decades and continues today; it is perhaps best captured by the slogan "a diamond is forever". End Quote


Source wiki

Despite being in over surplus from mid 19th to mid 20th, diamond were not that popular and high in demand.
in such context "And diamonds have always been in demand." the always is too much. If you change that to mid 20th century onward, you will be right.