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\mathbf{k}(\mathbf{r}_i-\mathbf{r}_j))> </math>
:<math>S(k) = \frac{1}{N} \sum^{N}_{i,j=1} \left<\exp(-i\mathbf{k}(\mathbf{r}_i-\mathbf{r}_j))\right> </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 17:29, 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 (syntax error): {\displaystyle S(k) = \frac{1}{N} \sum^{N}_{i,j=1} \left<\exp(-i\mathbf{k}(\mathbf{r}_i-\mathbf{r}_j))\right> }
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>}


References

  1. A. Filipponi, "The radial distribution function probed by X-ray absorption spectroscopy", J. Phys.: Condens. Matter, 6 pp. 8415-8427 (1994)