Pair Distribution Function Cases with a Single Atomic Species

1 Pair Distribution Function Cases with a Single Atomic Species 

The method of studying the short-range structure in an amorphous polymer, as long as the polymer is isotropic, is essentially the same as that used for the study of an ordinary liquid. In crystal structure analysis the aim is to determine the positions of all the atoms in a unit cell as well as to find the lattice structure by which the unit cell is repeated in the crystal. In an amorphous substance, the environment surrounding 

To see how the pair distribution function can be determined from the scattering data, we start from Equation (1.70) for the amplitude A(q) of scattering, which on squaring gives the intensity 

The last term in (4.5) represents the unobservable null scattering or the scattering from the sample as a whole (see Section 1.6), and it will be ignored in the discussion from now on. At this point we define the interference function (or reduced intensity function) i(q) by 

Equation (4.7) shows that g r) — 1 can be evaluated by taking the inverse Fourier transform of the interference function i(q) derived from the observed intensity I(q) in accordance with (4.6). 

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