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# Difference between revisions of "Structure factor"

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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 molecular simulations one typically uses: | + | To calculate <math>S(k)</math> in [[Computer simulation techniques |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} \langle\exp(-i\mathbf{k}(\mathbf{r}_n-\mathbf{r}_m)) \rangle </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 | ||

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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} \langle \exp(-i\mathbf{k}(\mathbf{r}_n(t)-\mathbf{r}_m(0))) \rangle </math>, |

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

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==References== | ==References== | ||

− | + | <references/> | |

+ | ;Related reading | ||

+ | *[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 08:56, 16 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

- Related reading