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Mathematician Theorizes a Crystal As Beautiful As A Diamond

Posted by Zonk on from the i-prefer-my-stones-blood-free-thanks dept.

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."

1 of 302 comments (clear)

  1. Article is complete hogwash by Anonymous Coward · · Score: 5, Informative

    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.