One milestone was the discovery of the geometrical law of crystallization by René Just Haüy, a further development of the work by Nicolas Steno and Jean-Baptiste L. Romé de l'Isle (the characterisation of a crystalline mineral needs knowledge on crystallography).
Important contributions came from some Saxon "Bergraths"/ Freiberg Mining Academy: Johann F. Henckel, Abraham Gottlob Werner and his students (August Breithaupt, Robert Jameson, José Bonifácio de Andrada and others).
The overview of the organic bonds by Kekulé was necessary to understand the silicates, first refinements described by Bragg and Machatschki; and it was only possibly to understand a crystal structure with Dalton's atomic theory, the notion of atomic orbital and Goldschmidt's explanations.
Nowadays, non-destructive electron microprobe analysis is used to get the empirical formula of a mineral.
[1] The mineral evolution in the geologic time context were discussed and summarised by Arkadii G. Zhabin (and subsequent Russian workers), Robert M. Hazen, William A.