Editing Structure factor
Jump to navigation
Jump to search
The edit can be undone. Please check the comparison below to verify that this is what you want to do, and then publish the changes below to finish undoing the edit.
Latest revision | Your text | ||
Line 1: | Line 1: | ||
The ''' | The '''structure factor''', <math>S(k)</math>, for a monatomic system is defined by: | ||
:<math>S(k) = 1 + \frac{4 \pi \rho}{k} \int_0^{\infty} ( g_2(r) -1 ) r \sin (kr) ~dr</math> | |||
:<math>k= |\mathbf{k}|= \frac{4 \pi }{\lambda | where <math>k</math> is the scattering wave-vector modulus | ||
:<math>k= |\mathbf{k}|= \frac{4 \pi }{\lambda \sin \left( \frac{\theta}{2}\right)}</math> | |||
The structure factor is basically a [[Fourier analysis | Fourier transform]] of the [[pair distribution function]] <math>{\rm g}(r)</math>, | The structure factor is basically a [[Fourier analysis | Fourier transform]] of the [[pair distribution function]] <math>{\rm g}(r)</math>, | ||
Line 17: | Line 18: | ||
from which one can calculate the [[Compressibility | isothermal compressibility]]. | from which one can calculate the [[Compressibility | isothermal compressibility]]. | ||
To calculate <math>S(k)</math> in | To calculate <math>S(k)</math> in molecular simulations one typically uses: | ||
:<math>S(k) = \frac{1}{N} \sum^{N}_{n,m=1} | :<math>S(k) = \frac{1}{N} \sum^{N}_{n,m=1} <\exp(-i\mathbf{k}(\mathbf{r}_n-\mathbf{r}_m))> </math>, | ||
where <math>N</math> is the number of particles and <math>\mathbf{r}_n</math> and | where <math>N</math> is the number of particles and <math>\mathbf{r}_n</math> and | ||
Line 26: | Line 27: | ||
The dynamic, time dependent structure factor is defined as follows: | The dynamic, time dependent structure factor is defined as follows: | ||
:<math>S(k,t) = \frac{1}{N} \sum^{N}_{n,m=1} | :<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 dynamic and the static structure factor, <math>S(k,t)/S(k,0)</math>, is known as the collective (or | |||
coherent) intermediate scattering | |||
function. | |||
==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)] | |||
[[category: Statistical mechanics]] | [[category: Statistical mechanics]] |