TY - JOUR

T1 - Calculating amphibole formula from electron microprobe analysis data using a machine learning method based on principal components regression

AU - Li, Xiaoyan

AU - Zhang, Chao

AU - Behrens, Harald

AU - Holtz, Francois

N1 - Funding Information: This study was supported by German Research Foundation (DFG) (BE 1720/40) and National Natural Science Foundation of China (NSFC) (41902052). We thank He Huang and an anonymous reviewer for their insightful comments and Michael Roden for efficient editorial handling. The Microsoft Excel spreadsheet for calculating amphibole formula from EMPA data is provided as supplementary file online.

PY - 2020/6

Y1 - 2020/6

N2 - 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.

AB - 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.

KW - Amphibole formula

KW - Amphibole nomenclature

KW - Electron microprobe analysis

KW - Machine learning

KW - Principal components regression

UR - http://www.scopus.com/inward/record.url?scp=85081245898&partnerID=8YFLogxK

U2 - 10.1016/j.lithos.2020.105469

DO - 10.1016/j.lithos.2020.105469

M3 - Article

AN - SCOPUS:85081245898

VL - 362-363

JO - LITHOS

JF - LITHOS

SN - 0024-4937

M1 - 105469

ER -