Calculating amphibole formula from electron microprobe analysis data using a machine learning method based on principal components regression

Abstract

We present a new method for calculating amphibole formula from routine electron microprobe analysis (EMPA) data by applying a principal components regression (PCR)-based machine learning algorithm on reference amphibole data. The reference amphibole data collected from literature are grouped in two datasets, for Li-free and Li-bearing amphiboles respectively, which include Fe2+, Fe3+, OH contents and the ion site assignments determined by single crystal structure refinement. We established two PCR models, for Li-free and Li-bearing amphiboles respectively, by the 10-fold cross validation of training datasets and evaluated by independent test datasets. The results show that our models can successfully reproduce the reference data for most ions with an error less than ±0.01 atom per formula unit (apfu), for Fe3+ within an error less than ±0.2 apfu and for WOH and WO2− with errors less than ±0.3 apfu. The error in estimated Fe3+/ΣFe ratio shows a rough negative dependence on FeOT content (total iron expressed as FeO), ranging within ±0.3 for amphiboles with FeOT ≥ 5 wt% and within ±0.2 for amphiboles with FeOT ≥ 10 wt%. Our models are applicable to both W(OH, F, Cl)-dominant and WO-dominant amphiboles. It is notable that this method is not suitable for calculating mineral formula of amphiboles that have been affected by deprotonation as a result of secondary oxidation, but it could offer an estimation of initial WOH prior to the post-formation oxidation. A user-friendly Excel worksheet is provided with two independent PCR models for calculating the formula of Li-free amphibole and Li-bearing amphibole, respectively. An automatic nomenclature function is also provided according to the nomenclature criteria of the 2012 International Mineralogical Association (IMA) report.