Abstract
Diffusion of Al and Si has been measured in synthetic and natural rutile under anhydrous conditions. Experiments used Al2O3 or Al2O3-TiO2 powder mixtures for Al diffusant sources, and SiO2-TiO2 powder mixtures or quartz-rutile diffusion couples for Si. Experiments were run in air in crimped Pt capsules, or in sealed silica glass ampoules with solid buffers (to buffer at NNO or IW). Al profiles were measured with Nuclear Reaction Analysis (NRA) using the reaction 27Al(p,g)28Si. Rutherford Backscattering spectrometry (RBS) was used to measure Si diffusion profiles, with RBS also used in measurements of Al to complement NRA profiles. We determine the following Arrhenius relations from these measurements: For Al diffusion parallel to c, for experiments buffered at NNO, over the temperature range 1100–1400 °C:
DAl = 1.21 × 10–2 exp(–531 ± 27 kJ/mol-1/RT) m2s-1.
For Si diffusion parallel to c, for both unbuffered and NNO-buffered experiments, over the temperature range 1100–1450 °C:
DSi = 8.53 × 10–13 exp(–254 ± 31 kJ/mol-1/RT) m2s-1.
Diffusion normal to (100) is similar to diffusion normal to (001) for both Al and Si, indicating little diffusional anisotropy for these elements. Diffusivities measured for synthetic and natural rutile are in good agreement, indicating that these diffusion parameters can be applied in evaluating diffusivities in rutile in natural systems Diffusivities of Al and Si for experiments buffered at IW are faster (by a half to three-quarters of a log unit) than those buffered at NNO.
Si and Al are among the slowest-diffusing species in rutile measured thus far. Diffusivities of Al and Si are significantly slower than the diffusion of Pb and slower than the diffusion of tetravalent Zr and Hf and pentavalent Nb and Ta. These data indicate that Al compositional information will be strongly retained in rutile, providing evidence for the robustness of the recently developed Al in rutile thermobarometer. For example, at 900 °C, Al compositional information would be preserved over ~3 Gyr in the center of 250 mm radius rutile grains, but Zr compositional information would be preserved for only about 300 000 yr at this temperature. Al-in-rutile compositions will also be much better preserved during subsolidus thermal events subsequent to crystallization than those for Ti-in-quartz and Zr-in-titanite crystallization thermometers.
Acknowledgments and Funding
This work was supported by NSF grant no. 1551381 to E.B.W. We thank Christopher Hoff for helpful discussions about Al and Si uptake in rutile. Constructive comments by reviewers Ralf Dohmen and Elias Bloch and Associate Editor Antonio Acosta-Vigil helped in improving the final version of the manuscript.
References cited
Akse, J.R., and Whitehurst, H.B. (1978) Diffusion of titanium in slightly reduced rutile. Journal of Physics and Chemistry of Solids, 39, 457–465.10.1016/0022-3697(78)90022-7Search in Google Scholar
Bak, T., Nowotny, J., Rekas, M., and Sorrell, C. (2003) Defect chemistry and semiconducting properties of titanium dioxide. Journal of Physics and Chemistry of Solids, 64, 1057–1067.10.1016/S0022-3697(02)00480-8Search in Google Scholar
Bak, T., Bogdanoff, P., Fiechter, S., and Nowotny, J. (2012) Defect engineering of titanium dioxide: full defect disorder. Advances in Applied Ceramics, 111, 62–71.10.1179/1743676111Y.0000000027Search in Google Scholar
Béjina, F., and Jaoul, O. (1996) Silicon self-diffusion in quartz and diopside measured by nuclear micro-analysis methods. Physics of Earth and Planetary Interiors, 97, 145–162.10.1016/0031-9201(96)03137-8Search in Google Scholar
Béjina, F., and Jaoul, O. (1997) Silicon diffusion in silicate minerals. Earth and Planetary Science Letters, 153, 229–238.10.1016/S0012-821X(97)00190-8Search in Google Scholar
Boisvert, G., Lewis, L.J., and Yelon, A. (1995) Many-body nature of the Meyer-Neldel compensation law for diffusion. Physical Review Letters, 75, 469–472.10.1103/PhysRevLett.75.469Search in Google Scholar
Brenan, J.M., Shaw, H.F., Phinney, D.L., and Ryerson, F.J. (1994) Rutile-aqueous fluid partitioning of Nb, Ta, Hf, Zr, U and Th; implications for high field strength element depletions in island-arc basalts. Earth and Planetary Science Letters, 128, 327–339.10.1016/0012-821X(94)90154-6Search in Google Scholar
Cherniak, D.J. (1993) Lead diffusion in titanite and preliminary results on the effects of radiation damage on Pb transport. Chemical Geology, 110, 177–194.10.1016/0009-2541(93)90253-FSearch in Google Scholar
Cherniak, D.J. (1995) Diffusion of Pb in plagioclase and K-feldspar measured by Rutherford Backscattering spectroscopy and resonant nuclear reaction analysis. Contributions to Mineralogy and Petrology, 120, 358–371.10.1007/BF00306513Search in Google Scholar
Cherniak, D.J. (2000) Pb diffusion in rutile. Contributions to Mineralogy and Petrology, 139, 198–207.10.1007/PL00007671Search in Google Scholar
Cherniak, D.J. (2003) Silicon self-diffusion in single crystal natural quartz and feldspar. Earth Earth and Planetary Science Letters, 214, 655–668.10.1016/S0012-821X(03)00394-7Search in Google Scholar
Cherniak, D.J. (2006) Zr diffusion in titanite. Contributions to Mineralogy and Petrology, 152, 639–647.10.1007/s00410-006-0133-0Search in Google Scholar
Cherniak, D.J. (2008) Si diffusion in zircon. Physics and Chemistry of Minerals, 35, 179–187.10.1007/s00269-007-0210-6Search in Google Scholar
Cherniak, D.J., and Watson, E.B. (1992) A study of strontium diffusion in K-feldspar, Na-K feldspar and anorthite using Rutherford Backscattering Spectroscopy. Earth and Planetary Science Letters, 411–425.10.1016/0012-821X(92)90142-ISearch in Google Scholar
Cherniak, D.J., and Watson, E.B. (2007) Ti diffusion in zircon. Chemical Geology, 242, 473–486.10.1016/j.chemgeo.2007.05.005Search in Google Scholar
Cherniak, D.J. Manchester, J., and Watson, E.B. (2007a) Zr and Hf diffusion in rutile. Earth and Planetary Science Letters, 261, 267–279.10.1016/j.epsl.2007.06.027Search in Google Scholar
Cherniak, D.J., Watson, E.B., and Wark, D.A. (2007b) Ti diffusion in quartz. Chemical Geology, 236, 65–74.10.1016/j.chemgeo.2006.09.001Search in Google Scholar
Corfu, F., and Andrews, A.J. (1986) A U-Pb age for mineralized Nipissing Diabase, Gowganda, Ontario. Canadian Journal of Earth Sciences, 23, 107–109.10.1139/e86-011Search in Google Scholar
Corfu, F., and Muir, T.L. (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. Chemical Geology—Isotope Geoscience, 79, 201–223.10.1016/0168-9622(89)90030-4Search in Google Scholar
Crank, J. (1975) The Mathematics of Diffusion, 2nd ed., 414 pp. Oxford.Search in Google Scholar
Cruz-Uribe, A.M., Feineman, M.D., Zack, T., and Jacob, D.E. (2018) Assessing trace element (dis)equilibrium and the application of single element thermometers in metamorphic rocks. Lithos, 314–315, 1–15.10.1130/abs/2016AM-287145Search in Google Scholar
Davis, W.J. (1997) U-Pb zircon and rutile ages from granulite xenoliths in the Slave Province; evidence for mafic magmatism in the lower crust coincident with Proterozoic dike swarms. Geology, 25, 343–346.10.1130/0091-7613(1997)025<0343:UPZARA>2.3.CO;2Search in Google Scholar
Deer, W.A., Howie, R.A., and Zussman, J. (1992) An Introduction to the Rock-forming Minerals. Longman Scientific Technical.Search in Google Scholar
Degeling, H.S. (2003) Zr equilibria in metamorphic rocks. Unpublished Ph.D. thesis, Australian National University, 231 pp.Search in Google Scholar
Demiryont, H. (1985) Optical properties of SiO2-TiO2 composite films. Applied Optics, 24, 2647–2650.10.1364/AO.24.002647Search in Google Scholar
Dieckmann, R., Mason, T.O., Hodge, J.D., and Schmalzried, H. (1978) Defects and cation diffusion in magnetite (III.) Tracer diffusion of foreign tracer cations as a function of temperature and oxygen potential. Berichte der Bunsengesellschaft für Physikalische Chemie, 82, 778–783.10.1002/bbpc.19780820803Search in Google Scholar
Dodson, M.H. (1973) Closure temperature in cooling geochronological and petrological systems. Contributions to Mineralogy and Petrology, 40, 259–274.10.1007/BF00373790Search in Google Scholar
Dohmen, R., Chakraborty, S., and Becker, H.-W. (2002) Si and O diffusion in olivine and implications for characterizing plastic flow in the mantle. Geophysical Research Letters, 29, 26-1–26-4.10.1029/2002GL015480Search in Google Scholar
Dohmen, R., Marschall, H.R., Ludwig, T., and Polednia, J. (2018) Diffusion of Zr, Hf, Nb and Ta in rutile: effects of temperature, oxygen fugacity, and doping level, and relation to rutile point defect chemistry. Physics and Chemistry of Minerals. https://doi.org/10.1007/s00269-018-1005-710.1007/s00269-018-1005-7Search in Google Scholar
Escudero, A., and Langenhorst, F. (2012) Incorporation of Si into TiO2 phases at high pressure. American Mineralogist, 97, 524–531.10.2138/am.2012.3941Search in Google Scholar
Escudero, A., Langenhorst, F., and Müller, W.F. (2012) Aluminum solubility in TiO2 rutile at high pressure and experimental evidence for a CaCl2-structured polymorph. American Mineralogist, 97, 1075–1082.10.2138/am.2012.4049Search in Google Scholar
Ewing, T.A., and Müntener, O. (2018) The mantle source of island arc magmatism during early subduction: Evidence from Hf isotopes in rutile from the Jijal Complex (Kohistan arc, Pakistan). Lithos, 308-309, 262–277.10.1016/j.lithos.2018.03.005Search in Google Scholar
Ewing, T.A., Hermann, J., and Rubatto, D. (2013) The robustness of the Zr-in-rutile and Ti-in-zircon thermometers during high-temperature metamorphism (Ivrea-Verbano Zone, northern Italy). Contributions to Mineralogy and Petrology, 165, 757–779.10.1007/s00410-012-0834-5Search in Google Scholar
Ferry, J.M., and Watson, E.B. (2007) New thermodynamic models and revised calibrations for the Ti-in-zircon and Zr-in-rutile thermometers. Contributions to Mineralogy and Petrology, 154, 429–437.10.1007/s00410-007-0201-0Search in Google Scholar
Fielitz, P., Borchardt, G., Schmücker, M., and Schneider, H. (2006) Al-26 diffusion measurement in 2/1-mullite by means of Secondary Ion Mass Spectrometry. Solid State Ionics, 177, 493–496.10.1016/j.ssi.2005.11.012Search in Google Scholar
Foley, S.F., Barth, M.G., and Jenner, G.A. (2000) Rutile/melt partition coefficients for trace elements and an assessment of the influence of rutile on the trace element characteristics of subduction zone magmas. Geochimica et Cosmochimica Acta, 64, 933–938.10.1016/S0016-7037(99)00355-5Search in Google Scholar
Gaetani, G.A., Asimow, P.D., and Stolper, E.M. (2008) A model for rutile saturation in silicate melts with application to eclogite partial melting in subduction zones and mantle plumes. Earth and Planetary Science Letters, 272, 720–729.10.1016/j.epsl.2008.06.002Search in Google Scholar
Gesenhues, U. (1997) Doping of TiO2 pigments by Al3+ Solid State Ionics, Diffusion & Reactions, 101-103, 1171–1180.10.1016/S0167-2738(97)00443-8Search in Google Scholar
Gesenhues, U., and Rentschler, T. (1999) Crystal growth and defect structure of Al3+-doped rutile. Journal of Solid State Chemistry, 143, 210–218.10.1006/jssc.1998.8088Search in Google Scholar
Golden, E.M., Giles, N.C., Shan Yang, and Halliburton, L.E. (2015) Interstitial silicon ions in rutile TiO2 crystals. Physical Review B, 91, 134110.10.1103/PhysRevB.91.134110Search in Google Scholar
Gonzalez-Elipe, A.R., Gracia, F., Yubero, F., Holgado, J.P., Espinos, J.P., and Girardeau, T. (2006) SiO2/TiO2 thin films with variable refractive index prepared by ion beam induced and plasma enhanced chemical vapor deposition. Thin Solid Films, 500, 19–26.10.1016/j.tsf.2005.10.061Search in Google Scholar
Guo, S., Tang, P., Su, B., Chen, Y., Ye, K., Zhang, L., Gao, Y., Liu, J., and Yang, Y. (2017) Unusual replacement of Fe-Ti oxides by rutile during retrogression in amphibolite-hosted veins (Dabie UHP Terrane); a mineralogical record of fluid-induced oxidation processes in exhumed UHP slabs. American Mineralogist, 102, 2268–2283.10.2138/am-2017-6120Search in Google Scholar
Hatta, K., Higuchi, M., Takahashi, J., and Kodaira, K. (1996) Floating zone growth and characterization of aluminum-doped rutile single crystals. Journal of Crystal Growth, 163, 279–284.10.1016/0022-0248(95)00972-8Search in Google Scholar
Hayden, L.A., Watson, E.B., and Wark, D.A. (2008) A thermobarometer for sphene (titanite). Contributions to Mineralogy and Petrology, 155, 529–540.10.1007/s00410-007-0256-ySearch in Google Scholar
Hoff, C.M., and Watson, E.B. (2018) Aluminum in rutile as a recorder of temperature and pressure. V.M. Goldschmidt Conference.Search in Google Scholar
Hoshino, K., Peterson, N.L., and Wiley, C.L. (1985) Diffusion and point defects in TiO2–x Journal of Physics and Chemistry of Solids, 46, 1397–1411.10.1016/0022-3697(85)90079-4Search in Google Scholar
Islam, M.M., Bredow, T., and Gerson, A. (2007) Electronic properties of oxygen-deficient and aluminum-doped rutile TiO2 from first principles. Physical Review B, 76, 045217.10.1103/PhysRevB.76.045217Search in Google Scholar
Jaoul, O., Poumellec, M., Froidevaux, C., and Havette, A. (1981) Silicon diffusion in forsterite: A new constraint for understanding mantle deformation. In Stacey, F.D., Paterson, M.S., Nicholas, A., Eds., Anelasticity in the Earth, pp. 95–100. American Geophysical Union.10.1029/GD004p0095Search in Google Scholar
Jones, A.G. (2014) Compensation of the Meyer-Neldel Compensation Law for H diffusion in minerals. Geochemistry, Geophysics, Geosystems, 15, doi:10.1002/2014GC005261.10.1002/2014GC005261Search in Google Scholar
Karvinen, S. (2003) The effects of trace elements on the crystal properties of TiO2 Solid State Science, 5, 811–819.10.1016/S1293-2558(03)00082-7Search in Google Scholar
Kohn, M.J., Penniston-Dorland, S.C., and Ferreira, J.C.S. (2016) Implications of near-rim compositional zoning in rutile for geothermometry, geospeedometry, and trace element equilibration. Contributions to Mineralogy and Petrology, 171, 78.10.1007/s00410-016-1285-1Search in Google Scholar
Le Gall, M., Lesage, B., and Bernardini, J. (1994) Self-diffusion in Al2O3 I. Aluminum diffusion in single crystals. Philosophical Magazine, 70, 761–773.10.1080/01418619408242929Search in Google Scholar
Liu, L., Xiao, Y., Aulbach, S., Li, D., and Hou, Z. (2014) Vanadium and niobium behavior in rutile as a function of oxygen fugacity: evidence from natural samples. Contributions to Mineralogy and Petrology, 167, 1026.10.1007/s00410-014-1026-2Search in Google Scholar
Marschall, H.R., Dohmen, R., and Ludwig, T. (2013) Diffusion-induced fractionation of niobium and tantalum during continental crust formation. Earth and Planetary Science Letters, 375, 361–371.10.1016/j.epsl.2013.05.055Search in Google Scholar
Marucco, J.-F., Gautron, J., and Lemasson, P. (1981) Thermogravimetric and electrical study of nonstoichiometric titanium dioxide TiO2–x between 800 and 1100 °C. Journal of Physics and Chemistry of Solids, 42, 363–367.10.1016/0022-3697(81)90043-3Search in Google Scholar
Mezger, K., Rawnsley, C.M., Bohlen, S.R., and Hanson, G.N. (1991) U-Pb garnet, sphene, monazite, and rutile ages; implications for the duration of high-grade metamorphism and cooling histories, Adirondack Mts., New York. Journal of Geology, 99, 415–428.10.1086/629503Search in Google Scholar
Mezger, K., Hanson, G.N., and Bohlen, S.R. (1989) High-precision U-Pb ages of metamorphic rutile; application to the cooling history of high-grade terranes. Earth and Planetary Science Letters, 96, 106–118.10.1016/0012-821X(89)90126-XSearch in Google Scholar
Mitchell, R.J., and Harley, S.L. (2017) Zr-in-rutile resetting in aluminosilicate bearing ultra-high temperature granulites: Refining the record of cooling and hydration in the Napier Complex, Antarctica. Lithos, 272–273, 128–146.10.1016/j.lithos.2016.11.027Search in Google Scholar
Moore, D.K., Cherniak, D.J., and Watson, E.B. (1998) Oxygen diffusion in rutile from 750 to 1000 °C and 0.1 to 1000 MPa. American Mineralogist, 83, 700–711.10.2138/am-1998-7-803Search in Google Scholar
Morton, A.C., and Hallsworth, C.R. (1999) Processes controlling the composition of heavy mineral assemblages in sandstones. Sedimentary Geology, 124, 3–30.10.1016/S0037-0738(98)00118-3Search in Google Scholar
Mosenfelder, J.D., Kim, N., and Stebbins, J.F. (2010) Silicon coordination in rutile and TiO2-II at ambient and high pressures. American Mineralogist, 95, 968–973.10.2138/am.2010.3491Search in Google Scholar
Nakayama, T., and Sasaki, T. (1963) The diffusion of barium in a rutile single crystal. Bulletin of the Chemical Society of Japan, 36, 569–574.10.1246/bcsj.36.569Search in Google Scholar
Nowotny, M.K., Bak, T., and Nowotny, J. (2006a) Electrical properties and defect chemistry of TiO2 single crystal. III. Equilibrium kinetics and chemical diffusion. Journal of Physical Chemistry B, 110, 16292–16301.10.1021/jp060623kSearch in Google Scholar PubMed
Nowotny, M.K., Bak, T., and Nowotny, J. (2006b) Electrical properties and defect chemistry of TiO2 single crystal. IV. Prolonged oxidation kinetics and chemical diffusion. Journal of Physical Chemistry, B, 110, 16302–16308.10.1021/jp060624cSearch in Google Scholar PubMed
Paladino, A.E., and Kingery, W.D. (1962) Aluminum ion diffusion in aluminum oxide. Journal of Chemical Physics, 37, 957–962.10.1063/1.1733252Search in Google Scholar
Pape, J., Mezger, K., and Robyr, M. (2016) A systematic evaluation of the Zr-in-rutile thermometer in ultra-high temperature (UHT) rocks. Contributions to Mineralogy and Petrology, 171, 44.10.1007/s00410-016-1254-8Search in Google Scholar
Ren, Y., Fei, Y., Yang, J., and Bai, W. (2009) SiO2 solubility in rutile at high temperature and high pressure. Journal of Earth Sciences, 20, 274–283.10.1007/s12583-009-0025-0Search in Google Scholar
Ryerson, F.J., and Watson, E.B. (1987) Rutile saturation in magmas; implications for Ti-Nb-Ta depletion in island-arc basalts. Earth and Planetary Science Letters, 86, 225–239.10.1016/0012-821X(87)90223-8Search in Google Scholar
Sakaguchi, I., Yurimoto, H., and Sueno, S. (1992) Impurities dislocation diffusion in single crystal MgO. Materials Science and Engineering, B 13, LI–L4.10.1016/0921-5107(92)90175-9Search in Google Scholar
Sasaki, J., Peterson, N.L., and Hoshino, K. (1985) Tracer impurity diffusion in single-crystal rutile (TiO2–x Journal of Physics and Chemistry of Solids, 46, 1267–1283.10.1016/0022-3697(85)90129-5Search in Google Scholar
Schandl, E.S., Davis, D.W., and Krogh, T.E. (1990) Are the alteration halos of massive sulfide deposits syngenetic? Evidence from U-Pb dating of hydrothermal rutile at the Kidd volcanic center, Abitibi Subprovince, Canada. Geology, 18, 505–508.10.1130/0091-7613(1990)018<0505:ATAHOM>2.3.CO;2Search in Google Scholar
Slepetys, R.A., and Vaughan, P.A. (1969) Solid solution of aluminum oxide in rutile titanium oxide. Journal of Physical Chemistry, 73, 2157–2162.10.1021/j100727a010Search in Google Scholar
Smye, A.J., and Stockli, D.F. (2014) Rutile U–Pb age depth profiling: A continuous record of lithospheric thermal evolution. Earth and Planetary Science Letters, 408, 171–182.10.1016/j.epsl.2014.10.013Search in Google Scholar
Stalder, R., Foley, S.F., Brey, G.P., and Horn, I. (1998) Mineral-aqueous fluid partitioning of trace elements at 900–1200 °C and 3.0–5.7 GPa; new experimental data for garnet, clinopyroxene, and rutile, and implications for mantle metasomatism. Geochimica et Cosmochimica Acta, 62, 1781–1801.10.1016/S0016-7037(98)00101-XSearch in Google Scholar
Stebbins, J.F. (2007) Aluminum substitution in rutile titanium dioxide: New constraints from high-resolution 27Al NMR. Chemistry of Materials, 19, 1862–1869.10.1021/cm0629053Search in Google Scholar
Tailby, N.D., Cherniak, D.J., and Watson, E.B. (2018) Al diffusion in quartz. American Mineralogist, 103, 839–847.10.2138/am-2018-5613Search in Google Scholar
Taylor-Jones, K., and Powell, R. (2015) Interpreting zirconium-in-rutile thermometric results. Journal of Metamorphic Geology, 33, 115–122.10.1111/jmg.12109Search in Google Scholar
Thomas, J.B., Watson, E.B., Spear, F.S., Shemella, P.T., Nayak, S.K., and Lanzirotti, A. (2010) TitaniQ under pressure: the effect of pressure and temperature on the solubility of Ti in quartz. Contributions to Mineralogy and Petrology, 160, 743–759.10.1007/s00410-010-0505-3Search in Google Scholar
Tomkins, H.S., Powell, R., and Ellis, D.J. (2007) The pressure dependence of the zirconium-in-rutile thermometer. Journal of Metamorphic Geology, 25, 703–713.10.1111/j.1525-1314.2007.00724.xSearch in Google Scholar
Tual, L., Möller, C., and Whitehouse, M.J. (2018) Tracking the prograde P–T path of Precambrian eclogite using Ti-in quartz and Zr-in-rutile geothermobarometry. Contributions to Mineralogy and Petrology, 173, 56.10.1007/s00410-018-1482-1Search in Google Scholar
Van Orman, J.A., Li, C., and Crispin, K.L. (2009) Aluminum diffusion and Al-vacancy association in periclase. Physics of Earth and Planetary Interiors, 172, 34–42.10.1016/j.pepi.2008.03.008Search in Google Scholar
Vlassopoulos, D., Rossman, G.R., and Haggerty, S.E. (1993) Coupled substitution of H and minor elements in rutile and the implications of high OH contents in Nb- and Cr-rich rutile from the upper mantle. American Mineralogist, 78, 1181–1191.Search in Google Scholar
Wark, D.A., and Watson, E.B. (2006) TitaniQ: A titanium-in-quartz geothermometer. Contributions to Mineralogy and Petrology, 152, 743–754.10.1007/s00410-006-0132-1Search in Google Scholar
Watson, E.B., and Cherniak, D.J. (2013) Simple equations for diffusion in response to heating. Chemical Geology, 335, 93–104.10.1016/j.chemgeo.2012.10.054Search in Google Scholar
Watson, E.B., and Harrison, T.M. (2005) Zircon thermometer reveals minimum melting conditions on earliest Earth. Science, 308, 841–844.10.1126/science.1110873Search in Google Scholar PubMed
Watson, E.B., Wark, D.A., and Thomas, J.B. (2006) Crystallization thermometers for zircon and rutile. Contributions to Mineralogy and Petrology, 151, 413–433.10.1007/s00410-006-0068-5Search in Google Scholar
Watson, E.B., Wanser, K.H., and Farley, K.A. (2010) Anisotropic diffusion in a finite cylinder, with geochemical applications. Geochimica et Cosmochimica Acta, 74, 614–633.10.1016/j.gca.2009.10.013Search in Google Scholar
Wong, L., Davis, D.W., Krogh, T.E., and Robert, F. (1991) U-Pb zircon and rutile chronology of Archean greenstone formation and gold mineralisation in the Val d’Or region, Quebec. Earth and Planetary Science Letters, 104, 325–336.10.1016/0012-821X(91)90213-2Search in Google Scholar
Yamazaki, D., Kato, T., Yurimoto, H., Ohtani, E., and Toriumi, M. (2000) Silicon self-diffusion in MgSiO3 perovskite at 25 GPa. Physics of Earth and Planetary Interiors, 119, 299–309.10.1016/S0031-9201(00)00135-7Search in Google Scholar
Zack, T., Kronz, A., Foley, S.F., and Rivers, T. (2002) Trace element abundances in rutiles from eclogites and associated garnet mica schists. Chemical Geology, 184, 97–122.10.1016/S0009-2541(01)00357-6Search in Google Scholar
Zack, T., von Eynatten, H., and Kronz, A. (2004a) Rutile geochemistry and its potential use in quantitative provenance studies. Sedimentary Geology, 171, 37–58.10.1016/j.sedgeo.2004.05.009Search in Google Scholar
Zack, T., Moraes, R., and Kronz, A. (2004b) Temperature dependence of Zr in rutile: empirical calibration of a rutile thermometer. Contributions to Mineralogy and Petrology, 148, 471–488.10.1007/s00410-004-0617-8Search in Google Scholar
Zener, C. (1952) Theory of diffusion. In W. Shockley, J.H. Hollomon, R. Maurer, and F. Seitz, Eds., Imperfections in Nearly Perfect Crystals, pp. 289–314. Wiley.Search in Google Scholar
Zhu, L., Ackland, G., Hu, Q.-M., Zhou, J., and Sun, Z. (2017) Origin of the abnormal diffusion of transition metal atoms in rutile. Physical Review B, 95, 245201.10.1103/PhysRevB.95.245201Search in Google Scholar
Zhukova, I., O’Neill, H., and Campbell, I.H. (2017) A subsidiary fast-diffusing substitution mechanism of Al in forsterite investigated using diffusion experiments under controlled thermodynamic conditions. Contributions to Mineralogy and Petrology, 172, 53.10.1007/s00410-017-1365-xSearch in Google Scholar
Ziegler, J.F., and Biersack, J.P. (2006) The stopping and range of ions in matter. Computer code SRIM 2006, http://www.srim.orgSearch in Google Scholar
© 2019 Walter de Gruyter GmbH, Berlin/Boston
