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Assuming that you are working in Bragg geometry you will see one peak corresponding to one angle, from which you can get the spacing between crystal planes from Bragg reflection condition. $$2d\sin\theta=n\lambda$$ and $$\lambda=\frac{h}{\sqrt{2mE}}$$ where $E$ is the energy of the electron. Now you should gather the information about different peaks ...


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The hamiltonian of a perfect crystal can be approximated at low temperature as the sum of harmonic oscillator hamiltonians. In 1D we have $$H = \sum_{i=1}^N \frac{p_i^2}{2 m} + \frac 1 2 m \omega^2 \sum_{ij} ( r_i- r_j)^2 $$ where the $ij$ sum is over nearest neighbors. It is possible to verify that the eigenvalues of this hamiltonian are $$ E_n = \left( ...


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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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