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


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:
$$\begin{aligned} \log D_{\text{Zr}}= & {} (-0.40 \pm 0.47) + (-0.253 \pm {0.019}) \log \frac{f\text{O}_2}{10^{-7}} - \frac{414\pm 11\,\hbox {kJ/mol}}{\text{R}T \ln 10}\\ \log D_{\text{Hf}}= & {} (-0.08 \pm 0.63) + (-0.266 \pm 0.023) \log \frac{f\text{O}_2}{10^{-7}} - \frac{428\pm 15\,\hbox {kJ/mol}}{\text{R}T \ln 10}\\ \log D_{\text{Nb}}= & {} (-0.19 \pm 0.36) + (-0.294 \pm 0.014) \log \frac{f\text{O}_2}{10^{-7}} - \frac{421\pm 9 \,\hbox {kJ/mol}}{\text{R}T \ln 10}\\ \log D_{\text{Ta}}= & {} (0.45 \pm 0.73) + (-0.304 \pm 0.015) \log \frac{f\text{O}_2}{10^{-7}} - \frac{463\pm 18\,\hbox {kJ/mol}}{\text{R}T \ln 10} \end{aligned}$$


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



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.


  1. Akse J, Whitehurst H (1978) Diffusion of titanium in slightly reduced rutile. J Phys Chem Solids 39(5):457–465. CrossRefGoogle Scholar
  2. Alim MA, Bak T, Atanacio AJ, Du Plessis J, Zhou M, Davis J, Nowotny J (2017) Electrical conductivity and defect disorder of tantalum-doped TiO2. J Am Ceram Soc 100:4088–4100CrossRefGoogle Scholar
  3. Amano F, Nakata M, Yamamoto A, Tanaka T (2016) Effect of Ti3+ ions and conduction band electrons on photocatalytic and photoelectrochemical activity of rutile titania for water oxidation. J Phys Chem 120:6467–6474CrossRefGoogle Scholar
  4. Amano F, Tosaki R, Sato K, Higushi Y (2018) Effects of donor doping and acceptor doping on rutile TiO2 particles for photocatalytic O2 evolution by water oxidation. J Solid State Chem 258:79–85CrossRefGoogle Scholar
  5. Aulbach S, O’Reilly SY, Griffin WL, Pearson NJ (2008) Subcontinental lithospheric mantle origin of high niobium/tantalum ratios in eclogites. Nat Geosci 1:468–472CrossRefGoogle Scholar
  6. Bak T, Nowotny J, Rekas M, Sorrell CC (2003) Defect chemistry and semiconducting properties of titanium dioxide: II. Defect diagrams. J Phys Chem Solids 64:1057–1067CrossRefGoogle Scholar
  7. Bak T, Bogdanoff P, Fiechter S, Nowotny J (2012a) Defect engineering of titanium dioxide: full defect disorder. Adv Appl Ceram 111:62–71CrossRefGoogle Scholar
  8. Bak T, Nowotny J, Sucher NJ, Wachsman ED (2012b) Photocatalytic water disinfection on oxide semiconductors: part 1—basic concepts of TiO\(_2\) photocatalysis. Adv Appl Ceram 111:4–15CrossRefGoogle Scholar
  9. Bak T, Li W, Nowotny J, Atanacio AJ, Davis J (2015) Photocatalytik properties of TiO\(_2\): evidence of the key role of surface active sites in water oxidation. J Phys Chem 119:9465–9473CrossRefGoogle Scholar
  10. Bak T, Nowotny J, Nowotny MK (2006) Defect disorder of titanium dioxide. J Phys Chem B 110(43):21560–21567. CrossRefGoogle Scholar
  11. Blackburn T, Shimizu N, Bowring SA, Schoene B, Mahan KH (2012) Zirconium in rutile speedometry: new constraints on lower crustal cooling rates and residence temperatures. Earth Planet Sci Lett 317–318:231–240CrossRefGoogle Scholar
  12. Cherniak DJ, Manchester J, Watson EB (2007) Zr and Hf diffusion in rutile. Earth Planet Sci Lett 261:267–279CrossRefGoogle Scholar
  13. Clark JR, Williams-Jones AE (2004) Rutile as a potential indicator mineral for metamorphosed metallic ore deposits. DIVEX Rapport Final Sous-project SC 2:18Google Scholar
  14. Corfu F, Muir TL (1989) The Hemlo-Heron Bay greenstone belt and Hemlo Au–Mo deposit, Superior Province, Ontario, Canada 2. Timing of metamorphism, alteration and Au mineralization from titanite, rutile, and monazite U–Pb geochronology. Chem Geol 79:201–223Google Scholar
  15. Crank J (1975) The mathematics of diffusion, 2nd edn. Oxford University Press, OxfordGoogle Scholar
  16. Cruz-Uribe AM, Zack T, Feineman MD, Barth MG (2014) Metamorphic reaction rates at 650–800\(\,{}^{\circ}\text{C}\) from diffusion of niobium in rutile. Geochim Cosmochim Acta 130:63–77CrossRefGoogle Scholar
  17. Dodson MH (1973) Closure temperature in cooling geochronological and petrological systems. Contrib Miner Petrol 40:259–274CrossRefGoogle Scholar
  18. Dohmen R, Chakraborty S (2007) Fe-Mg diffusion in olivine II: point defect chemistry, change of diffusion mechanisms and a model for calculation of diffusion coefficients in natural olivine. Phys Chem Miner 34(6):409–430. CrossRefGoogle Scholar
  19. Dohmen R, Becker HW, Meissner E, Etzel T, Chakraborty S (2002a) Production of silicate thin films using pulsed laser deposition (PLD) and applications to studies in mineral kinetics. Eur J Miner 14:1155–1168CrossRefGoogle Scholar
  20. Dohmen R, Chakraborty S, Becker HW (2002b) Si and O diffusion in olivine and implications for characterizing plastic flow in the mantle. Geophys Res Lett 29(21):26CrossRefGoogle Scholar
  21. Ewing TA, Rubatto D, Hermann J (2014) Hafnium isotopes and Zr/Hf of rutile and zircon from lower crustal metapelites (Ivrea-Verbano Zone, Italy): implications for chemical differntiation of the crust. Earth Planet Sci Lett 389:106–118CrossRefGoogle Scholar
  22. Ganguly J, Cheng W, Chakraborty S (1998) Cation diffusion in aluminosilicate garnet: experimental determination in pyrope-almandine diffusion couples. Contrib Miner Petrol 126:137–151CrossRefGoogle Scholar
  23. Ghate PB (1964) Screened interaction model for impurity diffusion in zinc. Phys Rev 133:A1167CrossRefGoogle Scholar
  24. Hofmann S (1993) Approaching the limit of high resolution depth profiling. Appl Surface Sci 70(71):9–19CrossRefGoogle Scholar
  25. Hoshino K, Peterson NL, Wiley CL (1985) Diffusion and point defects in \(\text{TiO}_{2-\text{x}}\). J Phys Chem Solids 46:1397–1411CrossRefGoogle Scholar
  26. Hu W, Lau K, Liu Y, Withers RL, Chen H, Fu L, Gong B, Hutchison W (2015) Colossal dielectric permittivity in (Nb+Al) codoped rutile \(\text{TiO}_2\) ceramics: compositional gradient and local structure. Chemis Mater 27:4934–4942CrossRefGoogle Scholar
  27. King JR, Sharp TE, Tuck B, Rogers TG (1995) Mathematical modelling of the interstitialcy diffusion mechanism. Proc R Soc Lond A 450(1940):623–649CrossRefGoogle Scholar
  28. Kofstad P (1972) Nonstoichiometry, diffusion and electrical conductivity in binary metal oxides. Wiley, New YorkGoogle Scholar
  29. Kohn MJ, Penniston-Dorland SC, Ferreira JCS (2016) Implications of near-rim compositional zoning in rutile for geothermometry, geospeedometry, and trace-element equilibration. Contrib Miner Petrol 171:78CrossRefGoogle Scholar
  30. Kooijman E, Mezger K, Berndt J (2010) Constraints on the U–Pb systematics of metamorphic rutile from in situ LA-ICP-MS analysis. Earth Planet Sci Lett 293:321–330CrossRefGoogle Scholar
  31. Lasaga A (1979) Multicomponent exchange and diffusion in silicates. Geochim Cosmochim Acta 43(4):455–469. CrossRefGoogle Scholar
  32. LeClaire AD, Lidiard AB (1956) Correlation effects in diffusion in crystals. Philos Mag 47:518–527CrossRefGoogle Scholar
  33. Lee D, Jeon J, Kim M, Choi W, Yoo H (2005) Oxygen nonstoichiometry (delta) of TiO\(_2\)-\(\delta \)-revisited. J Solid State Chem 178(1):185–193. CrossRefGoogle Scholar
  34. Li QL, Lin W, Su W, Li XH, Shi YH, Tang GQ (2011) SIMS U-Pb rutile age of low-temperature eclogites from southwestern Chinese Tianshan, NW China. Lithos 122:76–86CrossRefGoogle Scholar
  35. Li X, Hu R, Rusk B, Xiao R, Wang C, Yang F (2013) U–Pb and Ar–Ar geochronology of the Fujiawu porphyry Cu–Mo deposit, Dexing district, Southeast China: implications for magmatism, hydrothermal alteration, and mineralization. J Asian Earth Sci 74:330–342CrossRefGoogle Scholar
  36. Lidiard AB (1955) CXXXIII. Impurity diffusion in crystals (mainly ionic crystals with the sodium chloride structure). London Edinburgh Dublin Philos Mag J Sci 46(382):1218–1237CrossRefGoogle Scholar
  37. Lucassen F, Dulski P, Abart R, Franz G, Rhede D, Romer RL (2010) Redistribution of HFSE elements during rutile replacement by titanite. Contrib Miner Petrol 160:279–295CrossRefGoogle Scholar
  38. Luvizotto GL, Zack T, Meyer H, Ludwig T, Triebold S, Kronz A, Münker C, Stockli DF, Prowatke S, Klemme S, Jacob DE, von Eynatten H (2009) Rutile crystals as potential trace element and isotope mineral standards for microanalysis. Chem Geol 261:346–369CrossRefGoogle Scholar
  39. Marschall HR, Dohmen R, Ludwig T (2013) Diffusion-induced fractionation of niobium and tantalum during continental crust formation. Earth Planet Sci Lett 375:361–371CrossRefGoogle Scholar
  40. Mantina M, Wang Y, Chen LQ, Liu ZK, Wolverton C (2009) First principles impurity diffusion coefficients. Acta Mater 57(14):4102–4108CrossRefGoogle Scholar
  41. Meinhold G (2010) Rutile and its applications in earth sciences. Earth-Sci Rev 102:1–28CrossRefGoogle Scholar
  42. Mezger K, Hanson GN, Bohlen SR (1989) High-precision U–Pb ages of metamorphic rutile—application to the cooling history of high-grade terranes. Earth Planet Sci Lett 96:106–118CrossRefGoogle Scholar
  43. Molinari R, Palmisano L, Drioli E, Schiavello M (2002) Studies on various reactor configurations for coupling photocatalysis and membrane processes in water purification. J Membr Sci 206:399–415CrossRefGoogle Scholar
  44. Myers J, Eugster H (1983) The system Fe–Si–O: oxygen buffer calibrations to 1,500 K. Contrib Miner Petrol 82(1):75–90. CrossRefGoogle Scholar
  45. Nowotny J, Bak T, Nowotny MK, Sheppard LR (2007) Titanium dioxide for solar-hydrogen I. Functional properties. Int J Hydrog Energy 32:2609–2629CrossRefGoogle Scholar
  46. Nowotny J, Bak T, Alim MA (2015) Semiconducting properties and defect disorder of titanium dioxide. Electrochem Soc Trans 64:11–28Google Scholar
  47. Nowotny J, Bak T, Dickey EC, Sigmund W, Alim MA (2016a) Electrical conductivity, thermoelectric power, and equilibration kinetics of Nb-doped \(\text{TiO}_{2}\). J Phys Chem 120:6822–6837CrossRefGoogle Scholar
  48. Nowotny J, Macyk W, Wachsman E, Rahman KA (2016b) Effect of oxygen activity on the n–p transition for pure and cr-doped \(\text{TiO}_{2}\). J Phys Chem 120:3221–3228CrossRefGoogle Scholar
  49. Nowotny J, Bak T, Burg T (2007a) Electrical properties of polycrystalline TiO\(_{2}\) at elevated temperatures. Electrical conductivity. Phys Status Solidi B 244(6):2037–2054. CrossRefGoogle Scholar
  50. Nowotny J, Bak T, Burg T (2007b) Electrical properties of polycrystalline TiO\(_{2}\). Prolonged oxidation kinetics. Ionics 13(2):79–82. CrossRefGoogle Scholar
  51. Nowotny J, Bak T, Burg T (2007c) Electrical properties of polycrystalline TiO\(_{2}\). Thermoelectric power. Ionics 13(3):155–162. CrossRefGoogle Scholar
  52. Nowotny J, Bak T, Nowotny MK, Sheppard LR (2007d) Titanium dioxide for solar-hydrogen II. Defect chemistry. Int J Hydrog Energy 32(14):2630–2643. International conference on materials for hydrogen energy, Univ New S Wales, Sydney, Australia, Aug 27, 2004.
  53. Nowotny MK, Sheppard LR, Bak T, Nowotny J (2008) Defect chemistry of titanium dioxide. Application of defect engineering in processing \(\text{TiO}_2\)-based photocatalysts. J Phys Chem C 112:5275–5300CrossRefGoogle Scholar
  54. Nowotny MK, Bak T, Nowotny J (2006a) Electrical properties and defect chemistry of TiO2 single crystal. I. Electrical conductivity. J Physl Chem B 110(33):16270–16282. CrossRefGoogle Scholar
  55. Nowotny MK, Bak T, Nowotny J (2006b) Electrical properties and defect chemistry of TiO\(_{2}\) single crystal. II. Thermoelectric power. J Phys Chem B 110(33):16283–16291. CrossRefGoogle Scholar
  56. Nowotny MK, Bak T, Nowotny J (2006c) Electrical properties and defect chemistry of TiO\(_{2}\) single crystal. IV. Prolonged oxidation kinetics and chemical diffusion. J Phys Chem B 110(33):16302–16308. CrossRefGoogle Scholar
  57. Sahasrabudhe G, Krizan J, Bergman SL, Cava RJ, Schwartz J (2016) Million-fold increase of the conductivity in \(\text{TiO}_{2}\) rutile through 3% niobium incorporation. Chem Mater 28:3630–3633CrossRefGoogle Scholar
  58. Sasaki J, Peterson NL, Hoshino K (1985) Tracer impurity diffusion in single-crystal rutile (\(\text{TiO}_{2-\text{x}}\)). J Phys Chem Solids 46:1267–1283CrossRefGoogle Scholar
  59. Schmidt MW, Dardon A, Chazot G, Vannucci R (2004) The dependence of Nb and Ta rutile-melt partitioning on melt composition and Nb/Ta fractionation during subduction processes. Earth Planet Sci Lett 226:415–432CrossRefGoogle Scholar
  60. Sheppard LR, Bak T, Nowotny J, Nowotny MK (2007) Titanium dioxide for solar-hydrogen V. Metallic-type conduction of Nb-doped titanium dioxide. Int J Hydrog Energy 32:2660–2663CrossRefGoogle Scholar
  61. Sheppard LR, Lamo MB, Dietrich T, Wuhrer R (2014) Development of novel photoelectrode materials with improved charge separation properties. Adv Mater Res 975:224–229CrossRefGoogle Scholar
  62. Tomkins HS, Powell R, Ellis DJ (2007) The pressure dependence of the zirconium-in-rutile thermometer. J Metamorph Geol 25:703–713CrossRefGoogle Scholar
  63. Triebold S, von Eynatten H, Zack T (2012) A recipe for the use of rutile in sedimentary provenance analysis. Sediment Geol 282:268–275CrossRefGoogle Scholar
  64. Usui H, Yoshioka S, Wasada K, Shimizu M, Sakagushi H (2015) Nb-doped rutile TiO\(_2\): a potential anode material for Na–ion battery. Appl Mater Interfaces 7:6567–6573CrossRefGoogle Scholar
  65. Vineyard GH (1957) Frequency factors and isotope effects in solid state rate processes. J Phys Chem Solids 3(1–2):121–127CrossRefGoogle Scholar
  66. Vry JK, Baker JA (2006) LA-MC-ICPMS Pb–Pb dating of rutile from slowly cooled granulites: confirmation of the high closure temperature for Pb diffusion in rutile. Geochim Cosmochim Acta 70:1807–1820CrossRefGoogle Scholar
  67. Watson EB, Dohmen R (2010) Non-traditional and emerging methods for characterizing diffusion in minerals and mineral aggregates. In: Zhang YX, Cherniak DJ (eds) Diffusion in minerals and melts. Reviews in mineralogy and geochemistry, vol 72. Mineralogical Society of America, Chantilly, pp 61–105. CrossRefGoogle Scholar
  68. Watson EB, Harrison TM (2005) Zircon thermometer reveals minimum melting conditions on earliest Earth. Science 308:841–844CrossRefGoogle Scholar
  69. Zack T, von Eynatten H, Kronz A (2004a) Rutile geochemistry and its potential use in quantitative provenance studies. Sediment Geol 171:37–58CrossRefGoogle Scholar
  70. Zack T, Moraes R, Kronz A (2004b) Temperature dependence of Zr in rutile: empirical calibration of a rutile thermometer. Contrib Miner Petrol 148(4):471–488CrossRefGoogle Scholar

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

Personalised recommendations