Radioactive $^{67}$Cu atoms were accelerated to 60 keV at the online isotope separator ISOLDE at CERN, and implanted into a type IIa natural diamond sample to a dose of 2 $\times 10^{12}$ cm$^{-2}$. The channeling of $\beta^{-}$-particles and conversion electrons emitted in the decay of $^{67}$Cu and $^{67}$Zn*, respectively, were monitored about the three major axial directions with a two dimensional position-sensitive detector. The electron emission channeling data were collected from the room temperature implanted sample and after annealing at 1200$^\circ$ K. The observed channeling patterns were fitted with simulations based on the many beam formalism of electron motion through a crystal lattice. In the as-implanted sample, 25% of the Cu atoms were located a mean, isotropic displacement of 0.25(5) from substitutional sites, and the remainder, fR=75%, at sites that gave an isotropic emission yield. Annealing at 1200$^\circ$ K results in enhanced axial and planar channeling effects. The fits to the data yield either a fraction f1=43(5)% of Cu atoms located 0.22(4) from substitutional sites and fR=57%, or a fraction f1=10(2)% at substitutional sites, a fraction f2=50(5) % at mean isotropic displacement of 0.5 from substitutional sites, and a 'random' fraction fR=40%.
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