For the same reason, g(r) is often obtained by Fourier transformation of the total structure factor that is measured in neutron, X-ray and electron scattering experiments, and thus analysis of liquid and amorphous structures is usually based on g(r).įigure 3097b shows the schematic illustration of pair distribution functions of crystal, amorphous, liquid, and gas states. Similar to radial distribution function ( RDF), PDF is also related to the Fourier transform of the measured scattering intensity S(Q), also called structure function, as indicated in Equation 3097e. Then, PDF can be obtained through direct Fourier transform, The measured scattering intensity can be given by, The average scattering length over all atoms. Therefore, we can have PDF given by,ī i and b j - The scattering lengths for atom i and j, respectively. Schematic illustration of g(r) dependence on r.įor PDF, each peak is assigned to every atom j at the position corresponding to the interatomic distance r ij between atoms i and j. The magnitude of the oscillations directly reflects the lower or higher density at r.įigure 3097a. The function may oscillate about 1 until gradually approaching 1. Figure 3097a shows the schematic illustration of g(r) dependence on r. The probability is then given by ρ 0g(r)dr. PDF analysis describes a probability of finding any two atoms at given inter-atomic distances r, also called a distance map inside a solid. PDF is radially averaged and thus is an one-dimensional (1-D) function. Here, g(r) is called pair distribution function (PDF), which in fact is a probability density function. Then, the number density of atoms at a distance r from an origin atom will be given by ρ 0g(r). In a gas, liquid, or solid, the average number density of atoms can be given by, Practical Electron Microscopy and Database. Pair Distribution Function (PDF) Analysis
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