Revision as of 15:40, 24 November 2009 edit Marie Poise (talk \| contribs) 1,723 edits corr. statement on calculation, link to Ornstein-Zernike equation ← Previous edit		Revision as of 20:00, 24 November 2009 edit undo Marie Poise (talk \| contribs) 1,723 edits Definition: more precise and concise. Experimental: description of scattering was at best half true; better rely on link. Next edit →
Line 3: In [[statistical mechanics]], a '''radial distribution function''' (RDF), ''g''(''r''), describes how the atomic density varies as a function of the distance from one particular atom. More precisely, if there is an atom at the origin 0, and if ''n''=''N''/''V'' is the average number density, then the local density at distance ''r'' from O is ''ng''(''r''). Suppose, for example, that we choose an atom at some point O in the volume. What is then the average density at some point P at a distance r away from O? If <math>\rho=N/V</math> is the average density, then the mean density at P ''given'' that there is an atom at O would differ from ρ by some factor g(r). One could say that the radial distribution function takes into account the correlations in the distribution of atoms arising from the forces they exert on each other: ~~<center>~~ ~~(mean local density at distance r from O) = <math>\rho</math>g(r)~~ ~~</center>~~ [[File:Lennard-Jones Radial Distribution Function.svg\|thumb\|300px\|Radial distribution function for the [[Lennard–Jones potential\|Lennard-Jones model fluid]] at <math>T^* = 0.71, \; n^* = 0.844</math>.]] Line 45 ⟶ 41: ==Experimental== It is possible to measure g(r) experimentally with [[neutron scattering]] or [[x-ray scattering]] diffraction data. In such an experiment, a sample is bombarded with neutrons or x-rays which then diffract in all directions. The average atomic density at each distance can be extracted according to [[Snells law]]: r=wavelength/sin(scattered angle), where r is the distance the neutron traveled during diffraction.<br /> It is possible to measure g(r) experimentally with [[neutron scattering]] or [[x-ray scattering]] diffraction data. For an example of an RDF experiment see [http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JCPSA6000125000001014508000001&idtype=cvips&gifs=yes Eigen vs. Zundel structures in HCl solution, 2006] ==Formal derivation==

Radial distribution function: Difference between revisions