Using β-radiation-detected nuclear magnetic resonance (β-NMR) in the special form of cross-relaxation spectroscopy we studied the diffusional behavior of implanted ${}^{12}\mathrm{B}$ nuclei in Cu single crystals at temperatures $T=115\mathrm{}–750\mathrm{K}.$ An extended and completely revised dynamic theory of nuclear cross relaxation is developed to analyze the experimental data. Especially the incorporation of (hitherto neglected) spin-lattice relaxation effects turned out to be an important improvement. Applying this formalism we obtain activation energies of $E_a=0.57\mathrm{}\left(5\right)\mathrm{}\mathrm{eV}$ for the migration of interstitial B, the dominating fraction for $T\lesssim 400\mathrm{K},$ and of $E_a=1.15\mathrm{}\left(10\right)\mathrm{}\mathrm{eV}$ for substitutional B formed at higher temperatures. The previously found direct-exchange mechanism for the diffusion of substitutional B in Cu is confirmed by our analysis.

• Received 27 June 2001

DOI:https://doi.org/10.1103/PhysRevB.64.224302