Structure factor: Difference between revisions
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To calculate <math>S(k)</math> in computer simulations one typically uses: | To calculate <math>S(k)</math> in computer simulations one typically uses: | ||
:<math>S(k) = \frac{1}{N} \sum^{N}_{i,j=1} <\exp(-i( | :<math>S(k) = \frac{1}{N} \sum^{N}_{i,j=1} <\exp(-i\mathbf{k}(\mathbf{r}_i-\mathbf{r}_j))> </math> | ||
:<math>S(k) = \frac{1}{N} \sum^{N}_{i,j=1} \left< \exp(-i(r_i-r_j)) \right></math> | :<math>S(k) = \frac{1}{N} \sum^{N}_{i,j=1} \left< \exp(-i(r_i-r_j)) \right></math> |
Revision as of 17:28, 15 September 2011
The structure factor, , for a monatomic system is defined by:
where is the scattering wave-vector modulus
The structure factor is basically a Fourier transform of the pair distribution function ,
At zero wavenumber, i.e. ,
from which one can calculate the isothermal compressibility.
To calculate in computer simulations one typically uses:
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle S(k) = \frac{1}{N} \sum^{N}_{i,j=1} \left< \exp(-i(r_i-r_j)) \right>}