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Even for interacting particles, at high scattering vector the structure factor goes to 1. This result follows from Equation , since () is the Fourier transform of the "regular" function () and thus goes to zero for high values of the argument . This reasoning does not hold for a perfect crystal, where the distribution function exhibits ...
In statistical mechanics the Ornstein–Zernike (OZ) equation is an integral equation introduced [1] by Leonard Ornstein and Frits Zernike that relates different correlation functions with each other. Together with a closure relation, it is used to compute the structure factor and thermodynamic state functions of amorphous matter like liquids ...
2.1 Structure factor for a set of N equally spaced planes 2.2 Determination of the profile near the peak, and hence the peak width 3 Peak broadening due to disorder of the second kind
The structure factor is a complex number containing information relating to both the amplitude and phase of a wave. In order to obtain an interpretable electron density map , both amplitude and phase must be known (an electron density map allows a crystallographer to build a starting model of the molecule).
The structure function, like the fragmentation function, is a probability density function in physics. It is somewhat analogous to the structure factor in solid-state physics , and the form factor (quantum field theory) .
In condensed matter physics, the dynamic structure factor (or dynamical structure factor) is a mathematical function that contains information about inter-particle correlations and their time evolution. It is a generalization of the structure factor that considers correlations in both space and time.
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One can determine () indirectly (via its relation with the structure factor ()) using neutron scattering or x-ray scattering data. The technique can be used at very short length scales (down to the atomic level [ 10 ] ) but involves significant space and time averaging (over the sample size and the acquisition time, respectively).
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