Atomic disorder in irradiated materials is investigated by means of X-ray diffraction (XRD), using cubic SiC single crystals as a model material. It is shown that, besides the determination of depth-resolved strain and damage profiles, XRD can be efficiently used to determine the probability density function (pdf) of the atomic displacements within the crystal. This task is achieved by analyzing the diffraction-order dependence of the damage profiles. We thereby demonstrate that atomic displacements undergo Lévy flights, with a displacement pdf exhibiting heavy tails (with a tail index in the γ = 0.73-0.37 range, i.e. far from the commonly assumed Gaussian case (γ = 2)). It is further demonstrated that these heavy tails are crucial to account for the amorphization kinetics in SiC. From the retrieved displacement pdfs we introduce a dimensionless parameter, f D XRD , to quantify the disordering. f D XRD is found to be consistent with both independent measurements using ion channeling and with molecular dynamics calculations.