# Structure factor

The **static structure factor**, , for a monatomic system composed of spherical scatterers is defined by (Eq. 1 in ^{[1]}):

where is the radial distribution function, and 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.

## Binary mixtures[edit]

^{[2]}^{[3]}^{[4]}

## References[edit]

- ↑ A. Filipponi, "The radial distribution function probed by X-ray absorption spectroscopy", Journal of Physics: Condensed Matter
**6**pp. 8415-8427 (1994) - ↑ T. E. Faber and J. M. Ziman "A theory of the electrical properties of liquid metals III. the resistivity of binary alloys", Philosophical Magazine
**11**pp. 153-173 (1965) - ↑ N. W. Ashcroft and David C. Langreth "Structure of Binary Liquid Mixtures. I", Physical Review
**156**pp. 685–692 (1967) - ↑ A. B. Bhatia and D. E. Thornton "Structural Aspects of the Electrical Resistivity of Binary Alloys", Physical Review B
**2**pp. 3004-3012 (1970)

- Related reading

- F. Zernike and J. A. Prins "Die Beugung von Röntgenstrahlen in Flüssigkeiten als Effekt der Molekülanordnung", Zeitschrift für Physik
**41**pp. 184-194 (1920) - P. Debye and H. Menke "", Physik. Zeits.
**31**pp. 348- (1930) - B. E. Warren "X-Ray Diffraction", Dover Publications (1969) ISBN 0486663175 § 10.4
- Jean-Pierre Hansen and I.R. McDonald "Theory of Simple Liquids" (Third Edition) Chapter 4: "Distribution-function Theories" § 4.1