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Analysis of experimental data on divalent cation diffusion kinetics in aluminosilicate garnets with application to timescales of peak Barrovian metamorphism, Scotland

  • Xu ChuEmail author
  • Jay J. Ague
Original Paper

Abstract

We present a new statistical framework to analyze the diffusion data for divalent cations (Fe, Mg, Mn, and Ca) in aluminosilicate garnet using published experimental data and an Arrhenius relationship that accounts for dependence on temperature, pressure, garnet unit-cell dimension, and oxygen fugacity. The regression is based on Bayesian statistics and is implemented by the Markov chain Monte Carlo approach. All reported experimental uncertainties are incorporated, and the data are weighted by the precision of the experimental conditions. We also include a new term, the inter-experiment bias, to compensate for possible inconsistencies among experiments and to represent any experimental variability not explicitly presented in the Arrhenius relationship (e.g., water content, defect density). At high temperatures where most experiments were conducted, the diffusion coefficients calculated with the new parameters agree well with previous diffusion models (e.g., Chakraborty and Ganguly in Contrib Mineral Petrol, 111:74–86, 1992; Carlson in Am Mineral, 91:1–11, 2006). However, the down-temperature extrapolation leads to notable differences at lower temperatures for common petrological applications. For example, at 600 °C, the diffusion coefficients of Fe and Mn are one half-to-one order of magnitude faster and the diffusion coefficient of Ca is about one order of magnitude slower than calculated with parameters in Carlson (2006). Our statistical analysis also provides well-defined uncertainty bounds for timescale estimates based on garnet diffusion profiles. Application of the newly derived coefficients indicates that the timescale of the thermal peak of Barrovian metamorphism (Dalradian belt of Scotland) is about four to seven times longer than that estimated using previously published diffusion coefficients. The peak is still geologically brief, however—of the order of 106 years (0.75 Myr +0.70/−0.36 Myr; ±1σ). This brevity requires pulsed advective heat input, as provided by syn-orogenic mafic magmatism in these rocks.

Keywords

Garnet Diffusion coefficient Markov chain Monte Carlo Barrovian metamorphic belt 

Notes

Acknowledgments

We are grateful to J. Korenaga, S. Chakraborty, Y. Yu, and Y. Liang for helpful discussions and comments. The paper benefited from careful and constructive reviews by J. Ganguly and F.S. Spear. We thank T.L. Grove for editorial handling. Support from the National Science Foundation Directorate of Geosciences (NSF EAR-0948092 and EAR-1250269) and Yale University is gratefully acknowledged. This work was also supported in part by the facilities and staff of the Yale University Faculty of Arts and Sciences High Performance Computing Center and by the National Science Foundation under Grant #CNS 08-21132 that partially funded acquisition of the facilities. MATLAB scripts developed in this study are available upon request.

Compliance with ethical standards

Conflicts of interest

This study was funded by National Science Foundation Directorate of Geosciences (NSF EAR-0948092 and EAR-1250269). The authors declare that they have no conflict of interest.

Supplementary material

410_2015_1175_MOESM1_ESM.pdf (584 kb)
Supplementary material 1 (PDF 583 kb)

References

  1. Ague JJ, Baxter EF (2007) Brief thermal pulses during mountain building recorded by Sr diffusion in apatite and multicomponent diffusion in garnet. Earth Planet Sci Lett 261:500–516CrossRefGoogle Scholar
  2. Ague JJ, Carlson WD (2013) Metamorphism as garnet sees it: the kinetics of nucleation and growth, equilibration, and diffusion relaxation. Elements 9:439–445CrossRefGoogle Scholar
  3. Ague JJ, Baxter EF, Eckert Jr. JO (2001) High \( f_{{{\text{O}}_{2} }} \) during sillimanite zone metamorphism of part of the Barrovian type locality, Scotland. J Petrol 42:1301–1320Google Scholar
  4. Andrae R, Schulze-Hartung T, Melchior P (2010) Dos and don’ts of reduced chi squared. arXiv:1012.3754
  5. Atherton MP (1977) The metamorphism of the Dalradian rocks of Scotland. Scott J Geol 13:331–370CrossRefGoogle Scholar
  6. Ayres M, Vance D (1997) A comparative study of diffusion profiles in Himalayan and Dalradian garnets: constraints on diffusion data and the relative duration of the metamorphic events. Contrib Mineral Petrol 128:66–80CrossRefGoogle Scholar
  7. Barrow G (1893) On an intrusion of muscovite-biotite gneiss in the south-eastern highlands of Scotland, and its accompanying metamorphism. Q J Geol Soc Lond 49:330–354CrossRefGoogle Scholar
  8. Baumgartner LP, Floess D, Podladtchikov Y, Foster CT (2010) Pressure gradients in garnet induced by diffusion relaxation of major element zoing. Geol Soc Am Abstr Prog 42:629Google Scholar
  9. Baxter EF, Scherer EE (2013) Garnet geochronology: timekeeper of tectonometamorphic processes. Elements 9:433–438CrossRefGoogle Scholar
  10. Baxter EF, Ague JJ, DePaolo DJ (2002) Prograde temperature-time evolution in the Barrovian type-locality constrained by Sm/Nd garnet ages from Glen Clova, Scotland. J Geol Soc 159:71–82CrossRefGoogle Scholar
  11. Baxter EF, Caddick MJ, Ague JJ (2013) Garnet: common mineral, uncommonly useful. Elements 9:415–419CrossRefGoogle Scholar
  12. Bertka CM, Holloway JR (1988) Martian mantle primary melts: An experimental study of iron-rich garnet lherzolite minimum melt composition. Proc Lunar Planet Sci 18:723–739Google Scholar
  13. Bertran-Alvarez Y, Jaoul O, Liebermann RC (1992) Fe-Mg interdiffusion in single crystal olivine at very high-pressure and controlled oxygen fugacity: technological advances and initial data at 7 GPa. Phys Earth Planet Inter 70:102–118CrossRefGoogle Scholar
  14. Borinski SA, Hoppe U, Chakraborty S, Ganguly J, Bhowmik SK (2012) Multicomponent diffusion in garnets I: general theoretical considerations and experimental data for Fe–Mg system. Contrib Mineral Petrol 164:571–586CrossRefGoogle Scholar
  15. Boyd FE, England JL (1960) Apparatus for phase equilibrium measurements at pressures up to 50 kilobars and temperatures up to 1750C. J Geophys Res 65:741–748CrossRefGoogle Scholar
  16. Brady JB (1995) Diffusion data for silicate minerals, glasses and liquids. AGU Ref Shelf 2:269–290CrossRefGoogle Scholar
  17. Buening DK, Buseck PR (1973) Fe–Mg lattice diffusion in olivine. J Geophys Res 78:6852–6862CrossRefGoogle Scholar
  18. Caddick MJ, Bickle MJ, Harris NBW, Holland TJB, Horstwood MSA, Parrish RR, Ahmad T (2007) Burial and exhumation history of a Lesser Himalayan schist: recording the formation of an inverted metamorphic sequence in NW India. Earth Planet Sci Lett 264:375–390CrossRefGoogle Scholar
  19. Caddick MJ, Konopasek J, Thompson AB (2010) Preservation of garnet growth zoning and the duration of prograde metamorphism. J Petrol 51:2327–2347CrossRefGoogle Scholar
  20. Carlson WD (2002) Scales of disequilibrium and rates of equilibration during metamorphism. Am Mineral 87:185–204Google Scholar
  21. Carlson WD (2006) Rates of Fe, Mg, Mn, and Ca diffusion in garnet. Am Mineral 91:1–11CrossRefGoogle Scholar
  22. Chakraborty S, Ganguly J (1991) Compositional zoning and cation diffusion in aluminosilicate garnets. In: Ganguly J (ed) Diffusion atomic ordering and mass transfer, advances in physical geochemistry, vol 8. Springer, New York, pp 120–175CrossRefGoogle Scholar
  23. Chakraborty S, Ganguly J (1992) Cation diffusion in aluminosilicate garnets: experimental determination in spessartine-almandine diffusion couples, evaluation of effective binary diffusion coefficients, and applications. Contrib Mineral Petrol 111:74–86CrossRefGoogle Scholar
  24. Chakraborty S, Rubie DC (1996) Mg tracer diffusion in aluminosilicate garnets at 750–850 °C, 1 atm and 1300 °C, 8.5 GPa. Contrib Mineral Petrol 122:406–414CrossRefGoogle Scholar
  25. Cherniak DJ, Dimanov A (2010) Diffusion in pyroxene, mica and amphibole. Rev Mineral Geochem 72:641–690CrossRefGoogle Scholar
  26. Cherniak DJ, Ryerson FJ (1993) A study of strontium diffusion in apatite using Rutherford backscattering spectroscopy and ion implantation. Geochim Cosmochim Acta 57:4652–4662Google Scholar
  27. Christensen JN, Rosenfeld JL, DePaolo DJ (1989) Rates of tectonometamorphic processes from rubidium and strontium isotopes in garnet. Science 244:1465–1469CrossRefGoogle Scholar
  28. Cygan RT, Lasaga AC (1985) Self diffusion of magnesium in garnet at 750 °C to 900 °C. Am J Sci 109:57–77Google Scholar
  29. Dewey JF (2005) Orogeny can be very short. Proc Natl Acad Sci USA 102:15286–15293CrossRefGoogle Scholar
  30. Dewey JF, Mange MA (1999) Petrography of Ordovician and Silurian sediments in the western Irish Caledonides: traces of short-lived Ordovician continent-arc collision orogeny and the evolution of the Larentian Appalachian-Caledonian margin. In: MacNiocaill C, Ryan PD (eds) Continental tectonics, vol 164. Geol Soc Lond Spec Publ, London, pp 55–107Google Scholar
  31. Elphick SC, Ganguly J, Loomis TP (1985) Experimental determination of cation diffusivities in aluminosilicate garnets I. Experimental methods and interdiffusion data. Contrib Mineral Petrol 90:36–44CrossRefGoogle Scholar
  32. England PC, Thompson AB (1984) Pressure–temperature–time paths of regional metamorphism. I. Heat transfer during the evolution of regions of thickened continental crust. J Petrol 25:894–928CrossRefGoogle Scholar
  33. Erambert M, Austrheim H (1993) The effect of fluid and deformation on zoning and inclusion patters in poly-metamorphic garnets. Contrib Mineral Petrol 115:204–214CrossRefGoogle Scholar
  34. Farver JR, Yund RA (1990) The effect of hydrogen, oxygen and water fugacity on oxygen diffusion in alkali feldspar. Geochim Cosmochim Acta 54:2953–2964CrossRefGoogle Scholar
  35. Faryad SW, Chakraborty S (2005) Duration of Eo-Alpine metamorphic events obtained from multicomponent diffusion modeling of garnet: a case study from the Eastern Alps. Contrib Mineral Petrol 150:306–318CrossRefGoogle Scholar
  36. Florence FP, Spear FS (1991) Effects of diffusional modification of garnet growth zoning on PT path calculations. Contrib Mineral Petrol 107:487–500CrossRefGoogle Scholar
  37. Florence FP, Spear FS (1993) Influences of reaction history and chemical diffusion on PT calculations for staurolite schists from the Littleton Formation, northwestern New Hampshire. Am Mineral 78:345–359Google Scholar
  38. Florence FP, Spear FS (1995) Intergranular diffusion kinetics of Fe and Mg during retrograde metamorphism of a politic gneiss from the Adirondack Mountains. Earth Plant Sci Lett 134:329–340CrossRefGoogle Scholar
  39. Freer R, Edwards A (1999) An experimental study of Ca-(Mg, Fe) interdiffusion in silicate garnets. Contrib Mineral Petrol 134:370–379CrossRefGoogle Scholar
  40. French BM, Eugster HP (1965) Experimental control of oxygen fugacities by graphite-gas equilibriums. J Geophys Res 70:1529–1539CrossRefGoogle Scholar
  41. Friedrich AM, Hodges KV, Bowring SA, Martin MW (1999) Geochronological constraints on the magmatic, metamorphic and thermal evolution of the Connemara Caledonides, western Ireland. J Geol Soc Lond 156:1217–1230CrossRefGoogle Scholar
  42. Gaidies F, de Capitani C, Abart R, Schuster R (2008) Prograde garnet growth along complex PTt paths: results from numerical experiments on polyphase garnet from the Wolz Complex (Austroalpine basement). Contrib Mineral Petrol 155:673–688CrossRefGoogle Scholar
  43. Gaidies F, Pattison DRM, de Capitani C (2011) Toward a quantitative model of metamorphic nucleation and growth. Contrib Mineral Petrol 162:975–993CrossRefGoogle Scholar
  44. Ganguly J (2010) Cation diffusion kinetics in aluminosilicate garnets and geological applications. Rev Mineral Geochem 72:559–601CrossRefGoogle Scholar
  45. Ganguly J, Bhattacharya RN, Chakraborty S (1988) Convolution effect in the determination of compositional profiles and diffusion coefficients by microprobe step scans. Am Mineral 73:901–909Google Scholar
  46. Ganguly J, Cheng W, Chakraborty S (1998) Cation diffusion in aluminosilicate garnets: experimental determination in pyrope-almandine diffusion couples. Contrib Mineral Petrol 131:171–180CrossRefGoogle Scholar
  47. Geiger CA, Feenstra A (1997) Molar volumes of mixing of almandine-pyrope and almandine-spessartine garnets and the crystal chemistry and thermodynamic-mixing properties of the aluminosilicate garnets. Am Mineral 82:571–581Google Scholar
  48. Gerasimov VY (1987) An experimental study of interdiffusion of iron and magnesium in garnets. Dokl Acad Nauk SSSR 295:684–688Google Scholar
  49. Graham CM, Elphick SC (1991) Some experimental constraints on the role of hydrogen in oxygen and hydrogen diffusion and Al-Si interdiffusion in silicates. In: Ganguly J (ed) Diffusion atomic ordering and mass transfer, advances in physical geochemistry, vol 8. Springer, New York, pp 248–285CrossRefGoogle Scholar
  50. Hickmott DD, Shimizu N, Spear FS, Selverstone J (1987) Trace element zoning in a metamorphic garnet. Geology 15:573–576CrossRefGoogle Scholar
  51. Hier-Majumder S, Anderson IM, Kohlstedt DL (2005) Influence of protons on Fe-Mg interdiffusion in olivine. J Geophys Res 110:B02202Google Scholar
  52. Hollister LS (1966) Garnet zoning: an interpretation based on the Rayleigh fractionation model. Science 154:1647–1651CrossRefGoogle Scholar
  53. Jakobsson S, Oskarsson N (1994) The system C–O in equilibrium with graphite at high pressure and temperature: an experimental study. Geochim Cosmochim Acta 8:9–17CrossRefGoogle Scholar
  54. Kelly ED, Carlson WD, Ketcham RA (2013a) Crystallization kinetics during regional metamorphism of porphyroblastic rocks. J Metamorph Geol 31:963–979CrossRefGoogle Scholar
  55. Kelly ED, Carlson WD, Ketcham RA (2013b) Magnitudes of departures from equilibrium during regional metamorphism of porphyroblastic rocks. J Metamorph Geol 31:981–1002CrossRefGoogle Scholar
  56. Kohn MJ (2004) Oscillatory- and sector-zoned garnets record cyclic (?) rapid thrusting in central Nepal. Geochem Geophys Geosyst 5:Q12014. doi: 10.1029/2004GC000737 CrossRefGoogle Scholar
  57. Kohn MJ (2014) Geochemical zoning in metamorphic minerals. In: Holland HD, Turekian KK (eds) The crust. Treatise on Geochemistry, vol 4, 2nd edn. Elsevier, Oxford, pp 249–280CrossRefGoogle Scholar
  58. Korenaga J, Karato S-I (2008) A new analysis of experimental data on olivine rheology. J Geophys Res 133:B02403Google Scholar
  59. Krawczynski MJ, Grove TL (2012) Experimental investigation of the influence of oxygen fugacity on the source depths for high titanium lunar ultramafic magmas. Geochim Cosmochim Acta 79:1–19CrossRefGoogle Scholar
  60. Kretz R (1983) Symbols for rock-forming minerals. Am Mineral 68:277–279Google Scholar
  61. Lasaga AC (1979) Multicomponent exchange and diffusion in silicate. Geochim Comochim Acta 43:455–469CrossRefGoogle Scholar
  62. Liu JS (2001) Monte Carlo strategies in scientific computing. Springer, New YorkGoogle Scholar
  63. Loomis TP, Ganguly J, Elphick SC (1985) Experimental determination of cation diffusivities in aluminosilicate garnets. II. Multicomponent simulation and tracer diffusion coefficients. Contrib Mineral Petrol 90:45–51CrossRefGoogle Scholar
  64. Lyubetskaya T, Ague JJ (2010a) Modeling metamorphism in collisional orogens intruded by magmas: I. Thermal evolution. Am J Sci 310:427–458CrossRefGoogle Scholar
  65. Lyubetskaya T, Ague JJ (2010b) Modeling metamorphism in collisional orogens intruded by magmas: II. Fluid flow and implications for Barrovian and Buchan metamorphism, Scotland. Am J Sci 310:427–458CrossRefGoogle Scholar
  66. Médard E, McCammon CA, Barr JA, Grove TL (2008) Oxygen fugacity, temperature reproducibility, and H2O contents of nominally anhydrous piston-cylinder experiments using graphite capsules. Am Mineral 93:1838–1844CrossRefGoogle Scholar
  67. Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E (1953) Equations of state calculations by fast computing machines. J Chem Phys 21:1087–1091CrossRefGoogle Scholar
  68. Morioka M, Nagasawa H (1990) Ionic diffusion in olivine. In: Ganguly J (ed) Diffusion atomic ordering and mass transfer, advances in physical geochemistry, vol 8. Springer, New York, pp 176–197CrossRefGoogle Scholar
  69. Novak GA, Gibbs GV (1971) The crystal chemistry of silicate garnet. Am Mineral 83:546–552Google Scholar
  70. Oliver GJH, Ghen F, Buchwaldt R, Hegner E (2000) Fast tectonometamorphism and exhumation in the type area of the Barrovian and Buchan zones. Geology 28:459–462CrossRefGoogle Scholar
  71. Perchuk AL, Burchard M, Schertl H-P, Maresch WV, Gerya TV, Bernhardt H-J, Vidal O (2009) Diffusion of divalent cations in garnet: multi-couple experiments. Contrib Mineral Petrol 158:573–592CrossRefGoogle Scholar
  72. Press WH, Teukolsky SA, Vetterling WT, Flannery BP (2007) Numerical recipes, 3rd edn. Cambridge University Press, New YorkGoogle Scholar
  73. Reed BC (1989) Linear least-squares fits with errors in both coordinates. Am J Phys 57:642–646CrossRefGoogle Scholar
  74. Reverdatto VV, Polyansky QP (2004) Modelling of the thermal history of metamorphic zoning in the Connemara region (western Ireland). Tectonophysics 379:77–91CrossRefGoogle Scholar
  75. Righter K, Hauri EH (1998) Compatibility of rhenium in garnet during mantle melting and magma genesis. Science 280:1737–1741CrossRefGoogle Scholar
  76. Rubie DC, Karato S, Yan H, O’Neil HStC (1993a) Low differential stress and controlled chemical environment in multianvil high-pressure experiments. Phys Chem Mineral 20:315–322CrossRefGoogle Scholar
  77. Rubie DC, Ross CRII, Carroll MR, Elphick SC (1993b) Oxygen self-diffusion in Na2Si4O9 liquid up to 10 GPa and estimation of high-pressure melt viscosities. Am Mineral 78:574–582Google Scholar
  78. Schwandt CS, Cygan RT, Westrich HR (1995) Mg self-diffusion in pyrope garnet. Am Mineral 80:483–490Google Scholar
  79. Schwandt CS, Cygan RT, Westrich HR (1996) Ca self-diffusion in grossular garnet. Am Mineral 81:448–451Google Scholar
  80. Smit MA, Scherer EE, Mezger K (2013) Peak metamorphic temperatures from cation diffusion zoning in garnet. J Metamorph Geol 31:339–358CrossRefGoogle Scholar
  81. Smye AJ, Bickle MJ, Holland TJB, Parrish RR, Condon DJ (2011) Rapid formation and exhumation of the youngest Alpine eclogite: a thermal conundrum to Barrovian metamorphism. Earth Planet Sci Lett 306:193–204CrossRefGoogle Scholar
  82. Sorcar N, Hoppe U, Dasgupa S, Chakraborty S (2014) High-temperature cooling histories of migmatites from the High Himalayan Crystallines in Sikkim, India: Rapid cooling unrelated to exhumation? Contrib Mineral Petrol 167:1–34Google Scholar
  83. Spear FS (1991) On the interpretation of peak metamorphic temperatures in light of garnet diffusion during cooling. J Metamorph Geol 9:379–388CrossRefGoogle Scholar
  84. Spear FS (1993) Metamorphic phase equilibria and pressure–temperature–time paths. Mineralogical Society of America, Washington DCGoogle Scholar
  85. Spear FS (2004) Fast cooling and exhumation of the Valhalla metamorphic core complex, southeastern British Columbia. Int Geol Rev 46:193–209CrossRefGoogle Scholar
  86. Spear FS (2011) Prograde P–T paths: How steep, how fast, and what they mean. AGU Fall Meeting 2011, abstract #V13G-01Google Scholar
  87. Spear FS (2014) The duration of near-peak metamorphism from diffusion modelling of garnet zoning. J Metamorph Geol 32:903–914CrossRefGoogle Scholar
  88. Spear FS, Florence FP (1992) Thermobarometry in granulites: pitfalls and new approaches. Precambrian Res 55:209–241CrossRefGoogle Scholar
  89. Spear FS, Parrish RR (1996) Petrology and cooling rates of the Valhalla complex, British Columbia, Canada. J Petrol 37:733–765CrossRefGoogle Scholar
  90. Spear FS, Selverstone J (1983) Quantitative PT paths from zoned minerals: theory and tectonic applications. Contrib Mineral Petrol 83:348–357CrossRefGoogle Scholar
  91. Spear FS, Ashley KT, Webb LE, Thomas JB (2012) Ti diffusion in quartz inclusions: implications for metamorphic time scales. Contrib Mineral Petrol 164:977–986Google Scholar
  92. Storm LC, Spear FS (2005) Pressure, temperature and cooling rates of granulite facies migmatitic pelites from the southern Adirondack Highlands, New York. J Metamorph Geol 23:107–130CrossRefGoogle Scholar
  93. Tirone M, Ganguly J, Dohmen R, Langenhorst F, Herwig R, Becker H-W (2005) Rare earth diffusion kinetics in garnet: experimental studies and applications. Geochim Cosmochim Acta 69:2385–2398CrossRefGoogle Scholar
  94. Tracy RJ, Robinson P, Thompson AB (1976) Garnet composition and zoning in the determination of temperature and pressure of metamorphism, central Massachusetts. Am Mineral 61:762–775Google Scholar
  95. Vielzeuf D, Clemens JD (1992) The fluid-absent melting of phlogopite + quartz: experiments and models. Am Mineral 77:1206–1222Google Scholar
  96. Vielzeuf D, Saul A (2011) Uphill diffusion, zero-flux planes and transient chemical solitary waves in garnet. Contrib Mineral Petrol 161:683–702CrossRefGoogle Scholar
  97. Vielzeuf D, Baronnet A, Perchuk AL, Laporte D, Baker MB (2007) Calcium diffusivity in alumino-silicate garnets: an experimental and ATEM study. Contrib Mineral Petrol 154:153–170CrossRefGoogle Scholar
  98. Viete DR, Richards SW, Lister GS, Oliver GJH, Banks GJ (2010) Lithospheric-scale extension during Grampian orogenesis in Scotland. Geol Soc Lond Spec Publ 335:121–160CrossRefGoogle Scholar
  99. Viete DR, Hermann J, Lister GS, Stenhouse IR (2011a) The nature and origin of the Barrovian metamorphism, Scotland: diffusion length scales in garnet and inferred thermal time scales. J Geol Soc Lond 168:115–132CrossRefGoogle Scholar
  100. Viete DR, Forster MA, Lister GS (2011b) The nature and origin of the Barrovian metamorphism, Scotland: 40Ar/39Ar age patterns and the duration of metamorphism in the biotite zone. J Geol Soc Lond 168:133–146CrossRefGoogle Scholar
  101. Viete DR, Oliver GJH, Fraser GL, Forster MA, Lister GS (2013) Timing and heat sources for the Barrovian metamorphism, Scotland. Lithos 177:148–163CrossRefGoogle Scholar
  102. Vorhies SH, Ague JJ (2011) Pressure–temperature evolution and thermal regimes in the Barrovian zones, Scotland. J Geol Soc 168:1147–1166CrossRefGoogle Scholar
  103. Vorhies SH, Ague JJ, Schmitt AK (2013) Zircon growth and recrystallization during progressive metamorphism, Barrovian zones, Scotland. Am Mineral 98:219–230CrossRefGoogle Scholar
  104. Wang Z, Hiraga T, Kohlstedt DL (2004) Effect of H + on Fe-Mg interdiffusion in olivine, (Fe, Mg)2SiO4. Appl Phys Lett 85:201–211Google Scholar
  105. Wasylenki LE, Baker MB, Kent AJR, Stolper EM (2003) Near-solidus melting of the shallow upper mantle: partial melting experiments on depleted peridotite. J Petrol 44:1163–1191CrossRefGoogle Scholar
  106. Watson EB, Baxter EF (2007) Diffusion in solid-earth systems. Earth Planet Sci Lett 253:307–327CrossRefGoogle Scholar
  107. Watson EB, Harrison TM, Ryerson FJ (1985) Diffusion of Sm, Sr, and Pd in fluorapatite. Geochim Cosmochim Acta 49:1813–1823CrossRefGoogle Scholar
  108. Wilbur DE, Ague JJ (2005) Chemical disequilibrium during garnet growth: Monte Carlo simulations of natural crystal morphologies. Geology 34:689–692CrossRefGoogle Scholar
  109. Zhang Y, Stolper EM, Wasserburg GJ (1991) Diffusion of a multi-species component and its role in oxygen and water transport in silicate. Earth Planet Sci Lett 103:228–240CrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Department of Geology and GeophysicsYale UniversityNew HavenUSA
  2. 2.Peabody Museum of Natural HistoryYale UniversityNew HavenUSA

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