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513.001 Molecular and Solid State Physics | |
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Structure factorA simple approximation for the electron density of an atom is the atomic number times a delta function $Z\delta (\vec{r})$. The atomic number $Z$ is the number of electrons that an atom has. In this approximation, the electron density of a crystal is, $\large n(\vec{r}) = \sum \limits_{i,l,m,n}Z_i\delta(\vec{r}_i+l\vec{a}_1+m\vec{a}_2+n\vec{a}_3)$, where $i$ sums over the atoms in the unit cell and the translation vector $\vec{T}_{lmn}=l\vec{a}_1+m\vec{a}_2+n\vec{a}_3$ repeats the unit cell everywhere in the crystal. (a) Write down the general expression for a 3-D periodic function in terms of a Fourier series. (b) CsCl has a simple cubic Bravais lattice. $Z_{Cs} = 55$, $Z_{Cl} = 17$. What are the structure factors $G_{000}$ and $G_{100}$? |