Bragg diffraction for X-rays by a crystal structure is governed by
$$ n\lambda=2dsin\theta ,$$
where $n$ is an integer and the diffraction order, $\lambda$ is the x-ray wavelength, $d$ the lattice spacing and $\theta$ the angle of incidence, taken from the horizontal.
I obtained the x-ray diffraction spectrum of NaCl, clearly showing all expected features, namely the first, second and third orders of the characteristic $K_{\alpha,\beta}$ peaks, enveloped by the bremsstrahlung spectrum.
The repeated peaks decrease in height and increase in spacing, with order – but why? I can explain the increase in spacing, but why do fewer x-rays interfere constructively at higher (steeper) angles of incidence? My suggestion is that this has something to do with the scattering mechanism (Thomson scattering) but works I have looked at are highly theoretical, and beyond my current scope. Is there a simple or heuristic way of looking at this?
Best Answer
The diffraction pattern is essentially a Fourier transform of the product of the illumination beam and the diffractive structure. The envelope of the power spectrum of the far-field diffraction pattern is determined by the width of the illumination beam. See Fraunhofer diffraction.