Hydrogen reduction of enriched germanium dioxide and zone-refining for the LEGEND experiment

The LEGEND experiment, now under construction, will operate a large array of germanium detectors for the search of neutrinoless double-beta decay of ${}^{76}$Ge. In this paper we report on the process development for the hydrogen reduction of germanium dioxide enriched in ${}^{76}$Ge as part of the effort to manufacture detectors for the LEGEND experiment. The process was optimized via a kinetic un-reacted shrinking model and tested with a batch of natural GeO${}_2$. We completed the reduction of a batch of 23 kg isotopically enriched germanium with an average yield of 99.85%. Subsequently, the germanium was purified to intrinsic purity by zone-refining and an overall germanium yield of 99.05% was achieved. Using an intermediate underground storage, an average cosmogenic exposure of 156 h was accumulated. Special care was taken to avoid and recycle losses during the process.