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\begin{document}

\title{An experimental study to explore hydrogen diffusion in clinopyroxene at
low temperatures (195 - 400 \selectlanguage{ngerman}°C) and consequences for re-equilibration at
near surface conditions\selectlanguage{english}}



\author[1,1]{Thilo Bissbort}%
\author[2,2]{Kendra Lynn}%
\author[3,3]{Hans-Werner Becker}%
\author[4,4]{Sumit Chakraborty}%
\affil[1]{Institut für Geologie, Mineralogie und Geophysik, Ruhr-Universität Bochum}%
\affil[2]{U.S. Geological Survey,University of Delaware}%
\affil[3]{Ruhr-Universität Bochum,Ruhr-Universität Bochum}%
\affil[4]{Ruhr-Universitat Bochum}%


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  \date{May 27, 2024}


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\begin{abstract}
Studying diffusion of hydrogen in nominally anhydrous minerals (NAMs),
like clinopyroxene, at low temperatures is a challenging task due to
experimental and analytical difficulties. We applied a combination of
hydrogen implantation to produce concentration gradients in natural
diopside crystals with Nuclear Resonance Reaction Analysis (NRRA)
measurements of nanoscale diffusion profiles. Thereby, we were able to
conduct experiments at temperatures between 195 -- 400 \selectlanguage{ngerman}°C. Obtained
diffusion rates show a consistent Arrhenius relation \selectlanguage{english}D\selectlanguage{russian}н = 5.47 (\selectlanguage{ngerman}±
13.98) ·10\selectlanguage{english}-8 \selectlanguage{ngerman}· exp (-115.64 (±11.5) kJ mol\selectlanguage{english}-\selectlanguage{ngerman}¹/RT) m²s\selectlanguage{english}-\selectlanguage{ngerman}¹. Notably, our
results lie well within the range of extrapolations from high
temperature experiments (\selectlanguage{english}[?] 600 degC) of previous studies. This implies
that fast diffusion of hydrogen (compared to other elements) extends to
low temperatures. We used these results in a non-isothermal diffusion
model that simulates the ascent of crystals (0.5, 1.0, and 2.0 mm) along
two representative geotherms (oceanic and continental) from 600 to 100
degC, to assess potential re-equilibration of H contents in clinopyroxene
at low temperatures. Our model highlights the need to carefully consider
boundary conditions, which are a function of P-T-\selectlanguage{english}?O\selectlanguage{english}2, that control the
concentration gradient at the crystal's rim. The results from this model
allow an assessment when re-equilibration in dependence of crystal size
and cooling rate must be considered. Fast ascent (e.g., kimberlitic
melt) preserves initial hydrogen contents even in 0.5 mm size
clinopyroxene crystals. However, dwelling at low temperatures (e.g., 300
\selectlanguage{ngerman}°C) for several thousands of years (e.g., serpentinization) leads to
extensive re-equilibration in 2 mm crystals.%
\end{abstract}\selectlanguage{ngerman}%



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\textbf{Hosted file}

\verb`h_diffusion_cpx_supplementary.docx`  available at \url{https://authorea.com/users/560750/articles/608609-an-experimental-study-to-explore-hydrogen-diffusion-in-clinopyroxene-at-low-temperatures-195-400-c-and-consequences-for-re-equilibration-at-near-surface-conditions}

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