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Mathematical fractals do not exist in nature. There is however a huge amount of phenomena that behave 'fractally' within a finite range of scales. Take the typical example of the coast of Britain that can be arbitrarily long depending on how finely you are willing to measure it. The link goes to a map where only a portion of the coast is visible. If you use ...


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For any crystal, the First Brillouin Zone is found using the Wigner-Seitz construction for the reciprocal lattice. The high-symmetry points are labeled by certain letters mainly as a convention--like you said Gamma for (0,0,0) etc. The important thing to realize as far as the group theory, is that the group of the wavevector at the Gamma point has the full ...


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The summation given in the OP includes all points within a single unit cell; in this case there are $N$ such points. This looks like the expression for the structure factor, but the weighting for each point is unity, which implies that the crystal is made up of a single type of atom. Lattice sum, as given here, means the sum over all lattice points in the ...


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Both descriptions are correct; some people prefer the geometric description: the lattice of atoms is replace by a collection of planes, with different orientations. This corresponds to the Bragg model of partially reflective mirrors, and the K-vectors give the directions for the reflections which form the diffraction pattern. The description given by ...



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