The static structure factor, , for a monatomic system composed of spherical scatterers is defined by (Eq. 1 in ):
where is the radial distribution function, and is the scattering wave-vector modulus
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.
- 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