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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 Ge 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 Ge with an average yield of 99.85%. Subsequently, the Ge was purified to intrinsic purity by zone-refining and an overall Ge 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.