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}_{n,m=1} <\exp(-i\mathbf{k}(\mathbf{r}_i-\mathbf{r}_j))> </math>
:<math>S(k) = \frac{1}{N} \sum^{N}_{n,m=1} <\exp(-i\mathbf{k}(\mathbf{r}_n-\mathbf{r}_m))> </math>,
 


where <math>\mathbf{r}_n</math> and <math>\mathbf{r}_m</math> are the coordinates of particles
<math>n</math> and <math>m</math> respectively.


==References==
==References==
#[http://dx.doi.org/10.1088/0953-8984/6/41/006 A. Filipponi, "The radial distribution function probed by X-ray absorption spectroscopy", J. Phys.: Condens. Matter, '''6''' pp.  8415-8427 (1994)]
#[http://dx.doi.org/10.1088/0953-8984/6/41/006 A. Filipponi, "The radial distribution function probed by X-ray absorption spectroscopy", J. Phys.: Condens. Matter, '''6''' pp.  8415-8427 (1994)]
[[category: Statistical mechanics]]
[[category: Statistical mechanics]]

Revision as of 17:33, 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:

,

where and are the coordinates of particles and respectively.

References

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