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There may be a few options for describing the crystalline order. Personally, I love the one used by Anderson in his book 'Basic Notions of Condensed Matter Physics'. Following him, one writes the atomic density as $\rho(\vec{r}) = \sum_{\vec{G}}\rho_{\vec{G}}e^{i\vec{G}\vec{r}}$. The appearance of Crystalline order is signified by a set of finite ...


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You need to define an appropriate "order parameter" for your system, one that takes into account the symmetries in the configuration as well (rotational, transnational, etc). There are many ways you could define such "correlator" as you call it, it depends on the system. For example the nematic order parameter in liquid crystals is taken with respect to a ...


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In the image above, you can see a series of Bragg planes drawn in the crystal. This is called one "set of planes". Another "set of planes" would be if one would just draw a series of horizontal lines through the atoms. (Of course by lines I mean planes, but they are projected here onto a 2D image). The planes are those formed by the atoms, so in that ...


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and 2. Crystal planes contain sets of atoms, which occupy identical positions in the primitive cell. So to say, the planes are made out of atoms (and nothing in between). Or if you want a more quantum mechanical picture, you would have electron orbitals in between, which are responsible for the chemical bonding. X-rays get scattered by individual atoms. If ...


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(1) Since $u(\textbf{r}) = u(\textbf{r}+\textbf{R})$, we can expand this part in terms of reciprocal lattice vectors, $u_k(\textbf{r}) = \sum_\textbf{G}{e^{i\textbf{G}\cdot \textbf{r}}u_\textbf{k-G}}$. We can therefore write: \begin{equation} \psi_{\textbf k+\textbf K} = e^{i(\textbf k + \textbf K)\cdot \textbf r}\sum_\textbf{G'}{e^{i\textbf{G'}\cdot ...


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This looks like a combination of capillary action and evaporation. When the container starts out clean, moisture evaporates from the edge of the miniscus, thereby leaving crystals. These crystals form capillary pathways for more fluid to climb just above the crystal, where it evaporates and forms more crystal. This process repeats so that the crystal ...



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