Structure factor: Difference between revisions

From SklogWiki
Jump to navigation Jump to search
No edit summary
No edit summary
Line 29: Line 29:
:<math>S(k,t) = \frac{1}{N} \sum^{N}_{n,m=1} <\exp(-i\mathbf{k}(\mathbf{r}_n(t)-\mathbf{r}_m(0)))> </math>,
:<math>S(k,t) = \frac{1}{N} \sum^{N}_{n,m=1} <\exp(-i\mathbf{k}(\mathbf{r}_n(t)-\mathbf{r}_m(0)))> </math>,


The ratio between the static and the dynamic structure factor, <math>S(k,t)/S(k,0)</math>, is known as the collective or
The ratio between the dynamic and the static structure factor, <math>S(k,t)/S(k,0)</math>, is known as the collective (or
coherent intermediate scattering  
coherent) intermediate scattering  
function.   
function.   



Revision as of 17:46, 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 molecular simulations one typically uses:

,

where is the number of particles and and are the coordinates of particles and respectively.

The dynamic, time dependent structure factor is defined as follows:

,

The ratio between the dynamic and the static structure factor, , is known as the collective (or coherent) intermediate scattering function.


References

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