X-ray diffraction helps to analyze crystalline structures, the quality and structural ordering of sample.
You can use XRD patterns of your sample to compare it with Standard pattern which helps you to find out your nano-material have been successfully synthesized or not.
You can use Scherrer equation to determine the size of particles of crystals in the form of powder.
You can also use Bragg eq. to calculate lattice space and then calculate crystal lattice parameter.