Over the last 50 years many definitions of element substitution series have been proposed for describing natural Fe-Li micas with complex chemical compositions. In order to compare these definitions and ascertain their reliability, a new geometric frame composed of ideal mica points, mica joins (segments), substitution vectors and substitution planes is constructed to express the entire substitution system of ideal Fe-Al-Li micas. The frame is built in composition space with the coordinate system (0; Si, Al VI , Al IV , Fe (super 2+) , Li, [] VI , K), but has a 3-dimensional analogue, i.e. a visual image. Using this frame, it has been proved that there are only five possible types of replacement for definitions of Fe-Li micas, and that all possible types have been suggested except the Al IV -constant. Furthermore, it has been proved that the main point in different definitions is that the replacement of Li by Fe (super 2+) needs to be balanced with Al IV , Al VI , or [] VI . In order to solve this problem, a set of formulae determining spatial relations between geometric elements in the frame is suggested. With these formulae, the abstract frame is suggested to be a datum system used to ascertain quantitatively the reliability of definition of natural Fe-Li micas.

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