Feature Gems & Gemology, Spring 2019, Vol. 55, No. 1

# Appendix 3: Calculation Method for Tourmaline Species Classification Used Here

The simplified procedure of the method can be described as follows:

1. Use 29Si as internal standard to calculate raw ppmw.
2. Convert raw ppmw to atoms per formula or moles.
3. Calculate Li and B atoms per formula based on stoichiometric chemical formulae.
4. Convert this formula from atoms to wt.% oxides and ppmw.

The exact procedure of the method is given below:

There are three variables used in this method: Limole, Bmole, and A.

Limole is the Li (in moles) before normalization.

Bmole is the B (in moles) before normalization.

A is the normalization factor, which converts moles of each element into atoms per tourmaline formula unit.

To calculate values of the three unknown variables, three independent equations are required.

Function 1: The numbers of ions in the formula are based on 31 (O, H) per chemical formula. Assuming stoichiometric amounts, there are three atoms of B per formula unit . This reduces the number of independent variables to two: Y is the total of ppm (mole) oxygen to charge balance cations except for Li and B before normalization. Y is measured by LA-ICP-MS. All element (Rppmw) symbols used below represent ppmw of the elements before normalization (this statement holds for all other uses). Function 2: The summation of cations in Y-, Z-, and T-sites equals 15. X is the summation of cations per formula in Y-, Z-, and T-sites before normalization. X can be measured by LA-ICP-MS. All element (Rppmw) symbols used below represent ppmw of the elements before normalization. By solving the following equation set, normalization factor A and values for tourmaline species classification are obtained. Finally, using A, the raw data for the major elements in ppmw is converted to atoms per formula unit. This is done by dividing the ppmw concentration of each element by its atomic mass and then multiplying by A. The concentration of each element in atoms per formula unit is used for the tourmaline species classification.