Obtaining Structure from X-Ray Diffraction Data

As stated previously, the Laue conditions determine the circumstances under which reflections might occur, but the intensity of the reflections is determined by the content of the unit cell through the structure factor. Recall that in Equation 6.24 when we integrated the electron density function over the volume to get the E-vector amplitude of the spot pattern, we obtained 

It is easy to see by analogy that the integral over the electron density function times the phase shift is just a complex 3D Fourier transform that transforms a periodic function in direct lattice space to reciprocal lattice space. Therefore, one may think of the diffraction pattern as a Fourier transform of the direct lattice. In principal, one should then be able to measure the intensities and locations of the reflections in the diffraction pattern, take the inverse Fourier transform, and recover the electron density function. The inverse transform is obtained by 

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