In collaboration with Theodore H. Geballe, Matthias broke the record in 1954, with the discovery of superconductivity in niobium–tin (Nb 3 Sn) which had the highest known transition temperature of about 18 K. Later Matthias would try to come up with general empirical properties to find superconducting alloys. In the same year he published a first version of his famous guidelines which came to be known, as the "Mathias rules". Matthias was able to show in 1962 that some deviations from his rules where due to impurities or defects in the materials. Using his rules, Matthias and collaborators found in 1965 that niobium–germanium (Nb 3 Sn) with a record critical temperature above 20 K.