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Any tip functionalization of carbon nanotubes, for which the relative orientation between their (metallic) catalyst particle and the nanotube axis is essential, requires a detailed knowledge of the nature of the internal interface between the particle and the outgrown tube. In the present work, this interface is characterized with atomic precision using state-of-the-art low-voltage aberration-corrected transmission electron microscopy in combination with molecular dynamics simulations for the case of hard-magnetically terminated carbon nanotubes. Our results indicate that the physical principle based upon which the interfacial metal facet is chosen is a reduction of the desorption energy for carbon. [ABSTRACT FROM AUTHOR]