Why the first peak in the X-ray diffraction of an amorphous solid has significantly high, in terms of intensity than the second peak? In the XRD pattern of an amorphous solid we do not observe sharp peaks. Instead we see only diffused peaks. Why these peaks are diffused and more importantly why the first peak is significantly high in intensity than the other?  What is the physical significant of this?
 A: In a perfectly crystalline solid the distances between the scattering planes are precisely defined so the scattering angles are precisely defined. In principle the XRD spectrum would show an infinitely narrow peak at the scattering angles. In practice the limited resolution of the equipment broadens the peak as do imperfections in the crystal and for powder XRD the grain size in the powder. However while the peak may be broadened the integrated intensity, i.e. area under the peak, remains constant and is proportional to the form factor for the scattering.
In an amorphous solid there is no long range order so there are no well defined scattering planes and therefore no sharp peaks. However there is usually short range order. For example silica glass may be amorphous, but we still expect to see four oxygen atoms arranged in a tetrahedron around the silicon atoms just as in quartz. It's only when we look farther away, at the 2nd, 3rd nearest neighbours and so on, that we see deviations from the expected atomic positions in a crystal.
The first peak in the spectrum corresponds to the scattering from the nearest neighbour lattice points, so in our example of glass this would be the closest shell of silicon atoms (not the oxygen atoms as they aren't lattice points) which is the second nearest neighbour shell. The second nearest neighbour shell will be significantly disordered compared to the crystal, but not completely disordered. So we get a peak that is substantially broadened compared to the crystal, and because the area is constant it is also substantially reduced in intensity. Nevertheless it remains a distinct peak.
But the second peak corresponds to a shell farther away - something like the fourth nearest neighbour shell or maybe even farther depending on the exact material you're looking at. This is highly disordered compared to the crystal so the peak is much broader, and as with the first peak the area is constant so the peak intensity is much lower.
As a general rule in the usual lab XRD setups the higher order peaks are so broad they are impossible to see. When you're trying to do structure determinations on amorphous solids you usually have to resort to neutron scattering to get a spectrum that is good enough to extract the radial distribution function.
