Müller as the Austrian chief surveyor of mines in Transylvania was responsible for the analysis of ore samples. He analyzed gold ore from Kleinschlatten (today Zlatna, Romania). This ore was known as "Faczebajer weißes blättriges Golderz" (white leafy gold ore from Faczebaja) or antimonalischer Goldkies (antimonic gold pyrite), and, according to Anton von Rupprecht, was Spießglaskönig (argent molybdique), containing native antimony. Müller concluded that the ore did not contain antimony, but that it was bismuth sulfide. The following year, he reported that this was erroneous and that the ore contained mostly gold and an unknown metal very similar to antimony. After a thorough investigation which lasted for three years and consisted of more than fifty tests, Müller determined the specific gravity of the mineral and noted the radish-like odor of the white smoke which passed off when the new metal was heated, the red color which the metal imparts to sulfuric acid, and the black precipitate which this solution gives when diluted with water. Nevertheless, he was not able to identify this metal and gave it the names  and , as it did not show the properties predicted for the expected antimony.
In 1798, the German chemist Martin Heinrich Klaproth isolated the new element from a sample sent by Müller. After a thorough examination of the material he concluded that a new metal was present in the sample. He called it tellurium, but gave the credit of the discovery to Müller.