from the diffraction patterns you can say something about the shape of a nanoparticle(s) and their preferential growth/crystallization. If they are round in shape, ratios between intensities of reflexes (rings) should be the same as in powder XRD patterns (e.g. taken from crystallographic database) for every crystallographic direction. If there are differences between directions, it mens that you have elongated structures (one of directions is present more in the area of which diffraction pastern was taken). And there is also possibility to estimate the size of particles by measuring broadening of the reflexes, but in this case I can not help you much, because I did not calculated with the use of this method.