Statistical Nature of Atomic Disorder in Irradiated Crystals

Atomic disorder in irradiated materials is investigated by means of x-ray diffraction, using cubic SiC single crystals as a model material. It is shown that, besides the determination of depth-resolved strain and damage profiles, x-ray diffraction 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 diffractionorder dependence of the damage profiles. We thereby demonstrate that atomic displacements undergo Levy flights, with a displacement PDF exhibiting heavy tails [ with a tail index in the. gamma = 0.73-0.37 range, i.e., far from the commonly assumed Gaussian case (gamma = 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.