Diffusion of Zr, Hf, Nb and Ta in rutile: effects of temperature, oxygen fugacity, and doping level, and relation to rutile point defect chemistry - Dohmen, Ralf; Marschall, Horst; Ludwig, Thomas; Polednia, Joana (Physics and chemistry of minerals, 2019)
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∘C1100∘C1100\,^{\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 (∼1000μg/g∼1000μg/g\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 DZr∼DNb>DHf>>DTaDZr∼DNb>DHf>>DTaD_{\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 fO2fO2f\hbox {O}_2 conditions. At 1000∘C1000∘C1000\,^{\circ }\hbox {C} for log fO2<fO2<f\hbox {O}_2 < FMQ+1, the diffusion coefficients decrease with increasing oxygen fugacity where D is proportional to fOn2fO2nf\hbox {O}_2^n with exponents n≈−0.25n≈−0.25n \approx -0.25 for Zr and Hf and n≈−0.30n≈−0.30n \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 Ti3+Ti3+\hbox {Ti}^{3+} on interstitial sites, which is dominant at approximately log fO2<fO2<f\hbox {O}_2 < FMQ+2; (ii) a vacancy mechanism involving Ti vacancies, which is dominant at approximately log fO2>fO2>f\hbox {O}_2> FMQ+2. The point defect calculations also explain the observed effects of heterovalent substitutions, such as Nb5+Nb5+\hbox {Nb}^{5+} for Ti4+Ti4+\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 m2/sm2/s\hbox {m}^2/\hbox {s}, fO2fO2f\hbox {O}_2 in Pascal and T in Kelvin), which are only applicable for log fO2<fO2<f\hbox {O}_2 < FMQ+2: logDZr=logDHf=logDNb=logDTa=(−0.40±0.47)+(−0.253±0.019)logfO210−7−414±11kJ/molRTln10(−0.08±0.63)+(−0.266±0.023)logfO210−7−428±15kJ/molRTln10(−0.19±0.36)+(−0.294±0.014)logfO210−7−421±9kJ/molRTln10(0.45±0.73)+(−0.304±0.015)logfO210−7−463±18kJ/molRTln10log⁡DZr=(−0.40±0.47)+(−0.253±0.019)log⁡fO210−7−414±11kJ/molRTln⁡10log⁡DHf=(−0.08±0.63)+(−0.266±0.023)log⁡fO210−7−428±15kJ/molRTln⁡10log⁡DNb=(−0.19±0.36)+(−0.294±0.014)log⁡fO210−7−421±9kJ/molRTln⁡10log⁡DTa=(0.45±0.73)+(−0.304±0.015)log⁡fO210−7−463±18kJ/molRTln⁡10\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}
First online: 01 October 2018
Gesehen am 18.07.2019