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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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If I'm understanding your question correctly, then the answer is that you actually can't justify the connection of your equations along the quantized direction. In fact, the "bands" in the direction perpendicular to your slab are going to be completely flat, which corresponds to an infinite effective mass in that direction. (The infinity comes from the ...

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The answer to nearly everything is: yes :) your intuition about it is quite right, and your picture is good, too. You have two different kinds of points, and any pair with one point from each kind would be a suitable basis. You will of course take adjacent ones in practice. You could also take more than two points as primitive cell, but it will not be a good ...

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If we vary conditions (temperature/pressure), such that an FCC-BCC phase transition occurred, how would we know the BCC lattice formed? In this paper Zhang & Chen used Möbius pair-potentials to model NaCl phase transitions in an MD simulation, so I am not sure how relevant it is to your question, but they use several indicators of the FCC-BCC ...

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When we say that a lattice has a particular symmetry we mean that the lattice is mapped onto itself by the symmetry. So if I have a (2d) material which has inversion symmetry in the bulk and which has an atom at a point $(x,y)$ then inversion symmetry tells me that there is another, identical atom at $(-x, -y)$. At the surface, however, this is no longer ...

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Please keep in mind lemon's observation as to the correct nature of Block waves. This being said, the Hartree-Fock Hamiltonian is a general ansatz for localized orbitals, it applies equally well to periodic lattices and to non-periodic molecular systems. For a periodic lattice however, translation symmetry imposes that localized HF orbitals are (ideally) ...

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If they could not free it from the ice by hacking with saws, ice and ship had become one. An explosive charge would have as high a probability of breaking the ship as of breaking the ice. ( assuming it was a wooden boat). Now there are icebreaking ships to free trapped ships. It is not simple, though brute power is used to break the ice.

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