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The article concludes by suggesting that people will create more quasicrystals in labs, with various desired properties. That seems reasonable. What I didn’t un
by throwawaysea 5y ago
The article concludes by suggesting that people will create more quasicrystals in labs, with various desired properties. That seems reasonable. What I didn’t understand is this line:
> And the more mathematically perfect they are, the less electrically conductive.
Anyone understand what “mathematically perfect” means here, or why that implies reduced conductivity?
- mastazi 5y agoI'm not sure if my guess is right but my understanding is that "mathematically perfect" is related to how close to actual crystals they are. For example the Penrose tiling in the picture is made of tiles of 2 different types, so it's more "perfect" than another pattern that would use 3 different types of tiles, etc.
- nleconte 5y agoI would have imagined it is used in the same way it is used for crystals. Mono-crystals are considered mathematically perfect, while poly-crystals (with their grain-boundaries separating different cyrstal orientations) are less perfect. So, for quasi-crystal, the patterning which follows a set of mathematical rules (although lacking translational invariance), can be interrupted, thus being "mathematically less perfect". Now as to why that implied reduced conductivity... thinking in terms of Bloch waves, they require periodicity. In absence of Bloch waves that describe the electron density probability, the electrons are considered to be localized (e.g. as in the Landau level description of electrons implying localization of electrons in a perfect crystal). So for perfect quasi-crystals, this periodicity is fully absent, thus they are localized too. The latter hand-wavy argument is just speculation of mine...