Crystal Imperfection of the First Kind

This shows that w(b) is actually the autocorrelation function of p(a). 

In Equation (3.35) for the autocorrelation function Tz(r), there are many terms under the double summation that correspond to the same value of r k but with different extent of deviation. The function Tz(r) around each lattice points therefore consists 

The second term in the last member of (3.43) gives the Bragg diffraction peaks. The fact that Zo(s) is simply multiplied by P (s) 2 means that the widths of the diffraction peaks are not broadened, and only their heights are modified. A good approximation to p(r) is a Gaussian function, given in (1.102), with a representing the root-mean-square displacement of atoms about their mean positions. In such a case, P (s) 2 can be represented by 

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