We report the design of an optical floating-zone furnace for single-crystal growth under ultra-high vacuum (UHV) compatible conditions. The system is based on a commercial image furnace, which has been refurbished to be all-metal sealed. Major changes concern the use of UHV rotary feedthroughs and bespoke quartz-metal seals with metal-O-rings at the lamp stage. As a consequence, the procedure of assembling the furnace for crystal growth is changed completely. Bespoke heating jackets permit to bake the system. For compounds with elevated vapor pressures, the ultra-high vacuum serves as a precondition for the use of a high-purity argon atmosphere up to 10 bar. In the ferromagnetic Heusler compound Cu

$_2$
2MnAl, the improvements of purity result in an improved stability of the molten zone, grain selection, and, hence, single-crystal growth. Similar improvements are observed in traveling-solvent floating-zone growth of the antiferromagnetic Heusler compound Mn
$_3$
3
Si. These improvements underscore the great potential of optical float-zoning for the growth of high-purity single crystals of intermetallic compounds.

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