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Physics and Chemistry of Minerals

, Volume 46, Issue 3, pp 311–332 | Cite as

Diffusion of Zr, Hf, Nb and Ta in rutile: effects of temperature, oxygen fugacity, and doping level, and relation to rutile point defect chemistry

  • Ralf DohmenEmail author
  • Horst R. Marschall
  • Thomas Ludwig
  • Joana Polednia
Original Paper
  • 296 Downloads

Abstract

We performed experiments with thin film diffusion couples to simultaneously measure diffusion coefficients of Zr, Hf, Nb and Ta parallel to the a- and c-axes of synthetic rutile in a gas mixing furnace at controlled oxygen fugacity at temperatures between 800 and \(1100\,^{\circ }\hbox {C}\). Depth profiles of the diffusion couples were measured using secondary-ion mass spectrometry. Some of the diffusion profiles show a concentration dependence, which indicates different diffusion mechanisms above and below a particular trace-element concentration level (\(\sim \,1000\,\upmu \hbox {g}/\hbox {g}\)). The diffusion coefficients for the mechanism dominant at high-concentration levels are approximately two orders of magnitude smaller than for the low-concentration mechanism. Below the critical concentration the diffusion coefficient is constant, as consistently shown in all of the experiments. For this diffusion coefficient we have found that \(D_{\text{Zr}} \sim D_{\text{Nb}}> D_{\text{Hf}}>> D_{\text{Ta}}\), and diffusion is isotropic for the four elements at all investigated T and \(f\hbox {O}_2\) conditions. At \(1000\,^{\circ }\hbox {C}\) for log \(f\hbox {O}_2 < \) FMQ+1, the diffusion coefficients decrease with increasing oxygen fugacity where D is proportional to \(f\hbox {O}_2^n\) with exponents \(n \approx -0.25\) for Zr and Hf and \(n \approx -0.30\) for Nb and Ta. Diffusivites of Nb and Ta strongly differ from each other at all investigated conditions, thus providing the potential to fractionate these geochemical twins, as suggested earlier. The present data and literature data for Zr and Ti self diffusion are interpreted and predicted based on published quantitative point defect models. Two end-member diffusion mechanisms were identified for impurity diffusion of Zr: (i) an interstitialcy mechanism involving \(\hbox {Ti}^{3+}\) on interstitial sites, which is dominant at approximately log \(f\hbox {O}_2 < \) FMQ+2; (ii) a vacancy mechanism involving Ti vacancies, which is dominant at approximately log \(f\hbox {O}_2> \) FMQ+2. The point defect calculations also explain the observed effects of heterovalent substitutions, such as \(\hbox {Nb}^{5+}\) for \(\hbox {Ti}^{4+}\) at high concentration levels for changes in the diffusion mechanism and hence diffusion rates. In the case of rutile, this concentration effect becomes much more sensitive to the substitution level at lower temperature. In natural rutile penta- and hexavalent cations may largely be charge balanced by mono-, di- and trivalent cations, such that the doping effect on diffusion may be reduced or may even be reversed. The Arrhenius relationships established here may therefore not be directly applicable to natural rutile. We obtained the following Arrhenius relationships (with diffusion coefficients D in \(\hbox {m}^2/\hbox {s}\), \(f\hbox {O}_2\) in Pascal and T in Kelvin), which are only applicable for log \(f\hbox {O}_2 < \) FMQ+2:
$$\begin{aligned} \log D_{\text{Zr}}= & {} (-0.40 \pm 0.47) + (-0.253 \pm {0.019}) \log \frac{f\text{O}_2}{10^{-7}} - \frac{414\pm 11\,\hbox {kJ/mol}}{\text{R}T \ln 10}\\ \log D_{\text{Hf}}= & {} (-0.08 \pm 0.63) + (-0.266 \pm 0.023) \log \frac{f\text{O}_2}{10^{-7}} - \frac{428\pm 15\,\hbox {kJ/mol}}{\text{R}T \ln 10}\\ \log D_{\text{Nb}}= & {} (-0.19 \pm 0.36) + (-0.294 \pm 0.014) \log \frac{f\text{O}_2}{10^{-7}} - \frac{421\pm 9 \,\hbox {kJ/mol}}{\text{R}T \ln 10}\\ \log D_{\text{Ta}}= & {} (0.45 \pm 0.73) + (-0.304 \pm 0.015) \log \frac{f\text{O}_2}{10^{-7}} - \frac{463\pm 18\,\hbox {kJ/mol}}{\text{R}T \ln 10} \end{aligned}$$

Keywords

\({\text {TiO}}_2\) Diffusion HFSE Impurities Experiments 

Notes

Acknowledgements

Financial support from NSF (EAR Grant #1220533) to HRM is acknowledged. HRM acknowledges support from the Wilhelm and Else Heraeus Foundation. We thank one anonymous reviewer for helpful comments and Jim van Orman for his very useful and constructive review, as well as Larissa Dobrzhynetskaya for editorial handling. We are grateful to Daniele Cherniak for providing sample HfSi-14 and for discussion at an early stage of this project.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institut für Geologie, Mineralogie und GeophysikRuhr-Universität BochumBochumGermany
  2. 2.Institut für GeowissenschaftenGoethe Universität FrankfurtFrankfurtGermany
  3. 3.Department of Geology and GeophysicsWoods Hole Oceanographic InstitutionWoods HoleUSA
  4. 4.Institut für GeowissenschaftenUniversität HeidelbergHeidelbergGermany
  5. 5.Bayerisches GeoinstitutUniversität BayreuthBayreuthGermany

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