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Diamond is a material with multiple promising color centers for quantum technologies. In this work, emission channeling (EC) measurements and ab initio calculations were performed to study Ca defects in this material. The present work forms part of a more systematic study into the properties of group II elements in diamond, with EC experiments performed for the $^{27}$Mg, $^{45}$Ca, and $^{89}$Sr, experiment IS668. Density functional theory (DFT) was used to optimize the structure of 165 Ca defects, including multiple high symmetry sites of the diamond lattice, varying number of vacancies and five charge states, and a select few, based on EC input, were studied at the hybrid level. Formation, adiabatic charge transition and binding energies were calculated for all configurations. From them, it was possible to conclude that the bond-center (BC) configuration with two vacancies had the smallest formation energy, 13.36 eV for its neutral charge state. Shifting the formation energies by the difference between hybrid and generalized gradient approximation calculations for BC configuration, allowed vacancy formation energies within 0.5 eV from hybrid calculations in literature. A similar deviation is expected for the remaining results using this approach. The BC defect was studied for several charge states (-2 to +2). It shows $D_{3d}$ symmetry and introduces five defect-localized levels in diamond's energy gap, with two exceptions. For the positive charge states, +1 and +2, the lowest lying localized level is below the valence band maximum. No defect levels were found sufficiently close to the band edges for thermal ionization at room temperature. Results from $\beta^-$ EC measurements following low fluence implantation of $^{45}$Ca ($3×10^{12}$ ions/cm$^2$, 30 keV) performed at ISOLDE were analysed. To do so, a data driven approach was followed, performing many fits which were filtered and scored. Such scores were used to decide the sites to include in multi-site fits (up to three sites). This approach provided good results, guiding the analysis of the current work, however, a significant fraction of patterns was discarded, as such, the criteria used might be too strict. From the collected patterns, a Gaussian distribution around the BC site was found in the as implanted state, which is consistent with DFT results, and, after annealing, such contribution was reduced in favor of other sites, but no concrete assignment was possible as multiple configurations lead to similar quality fits. Such new sites have been formed during annealing, however, the BC is the minimum energy configuration from DFT, which is inconsistent with the creation of a significant fraction of other sites. Two hypotheses were presented to explain such inconsistency. One could consider the migration of vacancies away from Ca and towards other defects, mainly C interstitials. This would in turn make other sites more energetically favorable consistent with some of the models from the EC fits. Another option is that the lowest energy calcium defect was not found in the simulations performed. Due to the large number of vacancies after implantation, determined from the SRIM calculations, and the positive binding energies obtained, one could consider complexes with more vacancies. Starting from the BC site, from symmetry considerations, one would expect that Ca would be close to the <100>-split site, which is also observed in some of the best EC fits for the after annealing patterns. DFT calculations with more vacancies are thus a logical next step for correlation with EC measurements.
