A brief encounter with notations in mineralogy

Overview

In June 2022, I was lucky to enjoy a tour of Vienna's Museum of Natural History and its Mineral Collection.

I encountered a variety of samples which happened to be tagged with unexpectedly sophisticated labels, employing standard mathematical syntax interleaved with common chemistry notation.

I lack knowledge of chemistry beyond the secondary education level, so chemical experts who happen to stumble on this post should expect the observations of someone well-versed in mathematical syntax, but a novice in other related sciences (materials science, crystallography, etc).

Observations

Here are 23 exhibits with some interesting use of notation.

Mineral	Image	Notes
Argentoliveingit		restricted variable "x"
Penroseite		mineral series notation, aka "continuous substitution", "or".
Skutterudite		"variable formula subscript", "3 or 2"
Rathite		division, subtraction, addition with "x"
Gearksutite		square brackets denote a coordination complex and not concentration
Thomsenolite		The dot indicates that these are two separate molecules, but they are rationally proportionate. see Hydrous Minerals
Ilsemannite		The letter "n" is used to describe a variable amount of water. see Hydrous Minerals
Connellit		non-standard use of vertical bar, maybe old-fashioned?
Sahlinite		same use of vertical bars
Creedite		maybe non-standard use of slash?
Arthurite		same use of slash?
Uranmicrolite		standard elision "…"
Aeschynite		standard elision "…"
Uranpyrochlore		some serious use of mineral series
Stetefeldtite		coordinated use of the hyphen as "1 or 2", "2 or 1"
Davidite		Lewis dot structure annotations for Fe?
Sarkolith		nested parenthetical
Tourmaline		symbolic variables A,B with substitution
Alluaudite		inequality restriction "<2"
Hollandite		inequality restriction "≤2"
Goethite		α-polymorph
Boracite		β-polymorph
Holmquistite		a vacancy denoted by ◻

Other syntax

While compiling this page, a couple of other pieces of related syntax came to my attention:

1. Variable Formulas, where an underscored chemical element, as in Ce "may be present in small amounts or may not be".
2. Use of @ for a small molecule trapped inside a shell, as in
   $M@C_{60}$.
3. Completely unrelated, but it looks like all common balanced fences, namely () [] {} <>, have specialized meanings in Crystallography.
4. It may be that some of the notations in the images here are specific to Materials science, as in Schottky notation vs Kröger-Vink notation.