What are the definations of pair correlation function (PCF) and Radial distribution function (RDF)? In some sources I read that RDF is also called as PCF, and in some other sources I read that both are different.
There are four functions defined in the book of T. Egami and S.J.L. Billinge "Underneath the Bragg Peaks". In the first edition of this book (the second edition has just come out) that I have these are defined in Chapter in sections 3.1.3.1, 3.1.3.2, and 3.1.3.3 p. 58-62. These are g(r) = Pair Distribution Function, \rho(r) = Pair Density Function, G(r) = Reduced Pair Distribution Function and R(r) = Radial Distribution Function. They are related to the Fourier transform of the measured scattering intensity S(Q) by the relation
G(r) - 4\pi r \rho_0(g(r)-1)= 2/\pi Int_0^\infity Q[S(Q)-1]\sin{qr}dQ (1)
to yield g(r), the pair distribution function. g(r) is like a distance map of the inside of the solid. The function gives the probability of finding two atoms separated by the distance r.
The inverse transformation of the above equation and it yields the structure function S(Q) in terms of G(r),
S(Q)= 1 + 1/Q Int_0^\infityG(r)sin(Qr)dr. (2)
The pdf g(r) is related to the radial distribution function R(r) by
R(r)= 4\pi r^2 \rho_0g(r) (3)
The radial distribution function has the useful property that the quantity R(r)dr gives the number of atoms in the annulus of thickness dr at distance r from another atom.
Now Nazya please read the book of Egami and Billinge because I am tried of typing all these equations.
I have written the equations in latex symbols. So if you do not use latex then you will not not understand these equations. You have read the books. But learning latex is very useful.
Thank u Sir for ur kind concern.
Sir, above u have explained about pair distribution function,, Are pair distribution function and pair correlation function same???
Sir plz go through the following link and refer page no. 11.
http://people.virginia.edu/~lz2n/mse627/notes/Correlations.pdf
In this article, what definition u have given for radial distribution function, the same is for pair correlation function,, how far it is true???? plz explain.
The nomenclature in the total scattering field is notoriously perplexing, there being many definitions of functions in real and reciprocal space which only differ slightly, and many more names (such as PDF, PCF, RDF..) besides.
Unfortunately different authors use different names and definitions. A useful article which goes some way towards removing ambiguity is that of D. A. Keen:
D. A. Keen
A comparison of various commonly used correlation functions for describing total scattering
Journal of Applied Crystallography
34
2001
172-177
Thank u Dr. Oliver Alderman, I got the article u suggested and it is very useful..
Hi, The pair correlation estimate the distance between the centers btw two particles (random distribution) in other words it measures how they are closely packed. Radial distribution functions measure the same distribution however the range measurement is indicated through directional vectors.
Please Follow this link :
http://www.soft-matter.uni-tuebingen.de/teaching/vorlesung_condensed_matter_ws2017/Summary-g-of-r-2017-11-20-short.pdf
Hope this helps
Thanks
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