The Correlation Factors and Mechanisms of Diffusion for P and S in the Cu Single Crystal

The full description of the mechanisms for the diffusion of substitutional impurities requires an account of the correlation of the atomic jumps. This study investigated the diffusion of phosphorus (P) and sulfur (S) in the fcc copper (Cu) single crystal using density functional theory (DFT). Vacancy formation energies and impurity–vacancy interactions were calculated, revealing attractive interactions of P and S with the vacancies. The attractive interactions between S and a vacancy were roughly twice as strong as those between P and a vacancy. The 5-frequency—or 5-jump—model was employed to describe the correlation effects during diffusion. The potential energy profiles and activation energies were determined for the different jump paths necessary for the model and to account for all the correlation effects in substitutional impurity diffusion in the single crystal. The results indicated that S diffuses significantly faster than P in Cu, primarily due to lower activation energies for certain jump paths and a more favorable vacancy–impurity interaction. This occurs because when bonding with the crystal, S tends to prefer atomic sites with larger volumes and more asymmetric geometric arrangements when compared to P. This favors the interactions between S and the vacancies, and reduces friction with the matrix during the diffusion of S. The effective diffusion coefficients were calculated and compared with experimental data. The findings provide insights into the diffusion mechanisms of P and S in Cu and how these can be affected by the presence of extended defects such as grain boundaries.