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As far as I understand a new pattern of crystal growth has been found experimentally. How does it relate to the known 2D and 3D nucleation and growth of crystals? The dominating theory of crystal growth nowadays is that initiated by Cabrera and Frank. How is the new finding related to what we know so far or is it at odds with what we know and how?

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""As far as I understand a new pattern of crystal growth has been found experimentally."" No, what he found were new patterns of crystal structure! Laws for seed and growth are the same as for a classic crystals, because that is plain thermdynamics and kinetics. –  Georg Oct 6 '11 at 11:36
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The Cabrera-Frank theory is strictly speaking valid for crystals only. Quasicrystals – which were awarded by the Nobel prize – are strictly speaking not crystals. Crystals, by definition, have to be periodic while quasicrystals are not. So details of the theory for crystals of course don't have to hold for quasicrystals. But there are still many similarities in their growth and structure.

Indeed, Shechtman's 1982 discovery falsified some assumptions that people used to believe, e.g. that non-periodic quasicrystals with five-fold symmetries (otherwise behaving just like crystals for which five-fold symmetries are forbidden) were impossible. He was being humiliated by many people before he was admitted to be clearly right.

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thanks for the link where the new definition of a crystal goes as "any solid having an essentially discrete diffraction diagram." I wonder how the discovery at hand relates to superstructures found in amorphous materials and even in water. –  ganzewoort Oct 6 '11 at 15:10
    
With your definition, amorphous materials are not crystals (these "superstructures" make the diffraction diagram essentially continuous) but quasicrystals are crystals. Concerning the latter point, quasicrystals show that the assumption/proposition that "discrete diffraction diagrams imply periodic arrangement of atoms" was a widely believed myth. –  Luboš Motl Oct 7 '11 at 4:31
    
I am not sure about this. Any structure, if there is such, should give discontinuous diffraction. Otherwise it would go against the essence of waves. –  ganzewoort Oct 7 '11 at 17:19
    
I think that the adjective "essentially discrete" doesn't mean just "discontinuous". It means a more constraining thing, maybe even a sum of a countable number of delta functions. –  Luboš Motl Oct 9 '11 at 5:30
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