On the Calculation of the Relative Amounts of Endmember Constituents For Garnet

It is commonly accepted that the calculation of the proportions of endmember constituents in garnet is dependent on the particular sequence of calculating the amounts of the endmembers, and this belief has been used to justify avoiding the use of endmembers in the definition of a mineral species. Calculating the amounts of endmember constituents to represent a specific mineral formula involves the solution of a set of simultaneous equations, and hence the idea that the solution is dependent on the order in which the amounts of endmember constituent are determined conflicts with the meaning of the term “simultaneous equations”. Here I examine the data on which these conclusions are based and show that these sequence-dependent results arise because of the use of non-stoichiometric formulae that are not electroneutral. If a garnet formula is adjusted slightly such that it exactly fits the general formula of a garnet, [8]X3[6]Y2[4]Z3O12, and is electroneutral, the simultaneous equations relating its chemical formula to a set of endmember constituents have a single unique solution. Thus, the argument that has been used to justify avoiding the use of endmembers in the definition of a mineral species is specious.