The reason is simрle. X-ray peak is derived from the lattice sum over the entire crystal atoms. In ideal crystals, the sum is over infinite number which generate delta function on coherent spectral wavelength. Nano particles have much less atoms hence the lattice sum is not able to converge to a diffraction line but
bronden out. The smaller the particle the broad the diffraction peak. Therefore the brodening can be used to measure the particle size.
However, in calculating the particle size, intrisic instrumental width must be deducted from the measurements by root square difference.