Title: Parts-per-billion Trace Element Detection in Anhydrous Minerals by Micro-scale Quantitative NMR

Abstract: Nominally anhydrous minerals (NAMs) composing Earth's and planetary rocks incorporate microscopic amounts of volatiles. However, volatile distribution in NAMs and their effect on physical properties of rocks remain controversial. Thus, constraining trace volatile concentrations in NAMs is tantamount to our understanding of the evolution of rocky planets and planetesimals. Here, we present a novel approach of trace-element quantification using micro-scale Nuclear Magnetic Resonance (NMR) spectroscopy. This approach employs the principle of enhanced mass-sensitivity in NMR microcoils formerly used in \textit{in-situ} high pressure experiments. We were able to demonstrate that this method is in excellent agreement with standard methods across their respective detection capabilities. We show that by simultaneous detection of internal reference nuclei, the quantification sensitivity can be substantially increased, leading to quantifiable trace volatile element amounts of about $50$ wt-ppb measured in a micro-meter sized single anorthitic mineral grain, greatly enhancing detection capabilities of volatiles in geologically important systems.