Exact value of the correlation factor for the divacancy mechanism in FCC crystals: the end of a long quest

Abstract

The correlation factor for diffusion by the divacancy mechanism in an FCC lattice has been the target of a long quest. Amounting to 0.54 at the beginning, its value was progressively decreased down to 0.4582 with a confidence interval of 0.0005. The limitations of previous studies came from the matrix method at work which confined the defect trajectories to a volume of finite extension around the tracer atom, or, more basically, from the availability of computing time for the numerical simulations. The present study determines the exact value thanks to a double Laplace-Fourier transform of the transport equation, which takes into account all the divacancy trajectories without any limitation of their lengths. The exact value is lower than all the preceding evaluations, but falls within the confidence interval which was estimated from the best evaluations based on simulations. One interesting byproduct of our analytical approach is the proof of the equality t11=t22.