Specht was invited to join the National Geographic Society and Smithsonian Institution sponsored Arnhem Land Scientific Expedition in 1946. After completing his Honours project he and the 15 other members of the group set out from Adelaide in March 1948. As the botanist for the group, Specht would spend 8 months with the team, collecting 25 tonnes of specimens. After the expedition ended, Specht and his specimens flew to Brisbane in 1949 where the collected materials were identified and prepared for distribution around the world. Materials were sent to six herbaria within Australia, to Kew in England, the Rijksmuseum in Leiden, the Smithsonian Institution and Arnold Arboretum in the U.S.