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Multipath diffusion in geochronology

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Abstract

Recent developments in microanalytical tools such as the ion and laser microprobe have revealed spatial distributions of radiogenic isotopes in minerals which cannot be explained by a simple volume diffusion mechanism. Although it is known that diffusion of a substance along extended defects (such as dislocations, exsolution lamellae, micropores, microfractures, fission tracks, etc.), which may serve as high-diffusivity pathways in a crystal, can significantly influence the bulk diffusivity of a mineral, this has largely been ignored in the field of geochronology. A general numerical model has been developed, which solves coupled multipath diffusion equations that describe the simultaneous diffusion of a solute species through both the crystal lattice (via volume diffusion) and high-diffusivity pathways (via short-circuit diffusion) under non-steady state conditions. Addition of a radioactive source term to the appropriate equations further allows for the modelling of integrated cooling ages and closure temperatures, and has direct pertinence to geochronological and thermochronologial studies. Three key criteria can be used to distinguish multipath diffusion mechanisms from volume diffusion mechanisms: (a) non-Fickian concentration profiles, (b) enhanced solute diffusivity with increasing mineral grain size, and (c) a lack of any correlation between closure temperatures (and cooling ages) and larger grain sizes. With multipath diffusion, the effective diffusion dimension a for certain minerals appears to remain on the order of the grain size, and the model can adequately explain observed increases in the bulk diffusion coefficient D b with a in the hydrothermal bomb data of previous Ar diffusion studies. Arrhenius diagrams of a multipath diffusion D b vs 1/T will consist of curves that have a kink in them, reflecting a continuous change in the relative importance of the different diffusion mechanisms with temperature. The most important consequence of multipath diffusion is that the overall bulk diffusion coefficient D b of a diffusing species can be enhanced significantly above its volume diffusion coefficient D v . As a result, integrated ages and effective closure temperatures (T c ) can be much lower than those predicted assuming only a volume diffusion mechanism, to the extent that minerals normally characterized by low volume-diffusion T c may potentially have older integrated ages that minerals normally associated with higher volume-diffusion T c .

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References

  • Aifantis EC (1979) A new interpretation of diffusion in high-diffusivity paths — a continuum approach. Acta Metall 27:683–691

    Google Scholar 

  • Atkinson A, Taylor RI (1986) Impurity diffusion in NiO grain boundaries. J Phys Chem Solids 47:315–323

    Google Scholar 

  • Balluffi RW (1970) On measurements of self-diffusion rates along dislocations in FCC metals. Phys Status Solidi 42:11–34

    Google Scholar 

  • Burgess R, Kelley SP, Parsons I, Walker FDL, Worden RH (1992) 40Ar-39Ar analysis of perthite microtextures and fluid inclusions in alkali feldspars from the Klokken syenite, south Greenland. Earth Planet Sci Lett 109:147–167

    Google Scholar 

  • Compston W, Williams IS, Meyer C (1984) U-Pb geochronology of zircons from lunar brecia 73217 using a sensitive high mass-resolution ion microprobe. Proc 14th Lunar Planet Sci Conf, J Geophys Res Suppl 89:B525-B534

    Google Scholar 

  • Crank J (1975) The mathematics of diffusion. Oxford University Press, Oxford

    Google Scholar 

  • Darlymple GB, Lanphere MA (1969) Potassium-argon dating: principles, techniques and applications to geochronology. Freeman, San Francisco

    Google Scholar 

  • Davidson CM (1991) Tectonometamorphic evolution of the Maclaren Glacier metamorphic belt, south-central Alaska. PhD dissertation, Princeton Univ, Princeton, New Jersey

  • de Jong K, Wijbrans JR, Féraud G (1992) Repeated thermal resetting of phengites in the Mulhacen Complex (Betic Zone, southeastern Spain) shown by 40Ar/39Ar step heating and single grain laser probe dating. Earth Planet Sci Lett 110:173–191

    Google Scholar 

  • Dodson MH (1973) Closure temperature in cooling geochronological and petrological systems. Contrib Mineral Petrol 40:259–274

    Google Scholar 

  • Faure G (1986) Principles of isotope geology (2nd ed). Wiley, New York

    Google Scholar 

  • Fechtig H, Kalbitzer S (1966) The diffusion of argon in potassium-bearing solids. In: Schaeffer OA, Zähringer J (eds), Potassium argon dating. Springer, New York, pp 68–107

    Google Scholar 

  • Felix FW (1966) Rare-gas diffusion in neutron-irradiated potassium halides. Proc Brit Ceram Soc 9:273–277

    Google Scholar 

  • Fick A (1855) Ueber diffusion (in German). Annal Phys Chem 94:59–86

    Google Scholar 

  • Fisher JC (1951) Calculation of diffusion penetration curves for surface and grain boundary diffusion. J Appl Phys 22:74–77

    Google Scholar 

  • Fryer BJ, Jackson SE, Longerich HP (1993) The application of laser ablation microprobe-inductively coupled plasma-mass spectrometry (LAM-ICP-MS) to in situ (U)-Pb geochronology. Chem Geol 109:1–8

    Google Scholar 

  • Giletti BJ (1974) Studies in diffusion I: argon in phlogopite mica. Carnegie Inst Washington Publ 634:107–115

    Google Scholar 

  • Hacker BR, Christie JM (1991) Observational evidence for a possible new diffusion path. Science 251:67–70

    Google Scholar 

  • Hames WE, Hodges KV (1993) Laser 40Ar/39Ar evaluation of slow cooling and episodic loss of 40Ar from a sample of polymetamorphic muscovite. Science 261:1721–1723

    Google Scholar 

  • Harrison LG (1961) Influence of dislocations on diffusion kinetics in solids with particular reference to the alkali halides. Trans Faraday Soc 57:1191–1199

    Google Scholar 

  • Harrison TM (9181) Diffusion of 40Ar in hornblende. Contrib Mineral Petrol 78:324–331

    Google Scholar 

  • Harrison TM, Fitz Gerald JD (1986) Exsolution in hornblende and its consequences for 40Ar/39Ar age spectra and closure temperature Geochim Cosmochim Acta 50:247–253

    Google Scholar 

  • Harrison TM, Duncan I, McDougall I (1985) Diffusion of 40Ar in biotite: temperature, pressure and compositional effects. Geochim Cosmochim Acta 49:2461–2468

    Google Scholar 

  • Hart EW (1957) On the role of dislocations in bulk diffusion. Acta Metall 5:597

    Google Scholar 

  • Hess JC, Lippolt HJ, Gurbanov AG, Michalski I (1993) The cooling history of the late Pliocene Eldzhurtinskiy granite (Causasus, Russia) and the late thermochronological potential of grain-size/age relationships. Earth Planet Sci Lett 117:393–406

    Google Scholar 

  • Hodges KV, Hames WE, Bowring SA (1994) 40Ar/39Ar age gradients in micas from a high-temperature-low-pressure metamorphic terrain: evidence for very slow cooling and implications for the interpretation of age spectra. Geology 22:55–58

    Google Scholar 

  • Jam SC (1958) Simple solutions of the partial differential equation for diffusion (or heat conduction). Proc R Soc London Ser A 243:359–374

    Google Scholar 

  • Joesten R (1991) Grain-boundary diffusion kinetics in silicate and oxide minerals. In: Ganguly J (ed) Diffusion, atomic ordering and mass transport. Springer, Berlin Heidelberg New York, pp 345–395

    Google Scholar 

  • Jost W (1952) Diffusion in solids, liquids, gases. Academic Press, New York

    Google Scholar 

  • Kelley SP, Turner G (1991) Laser probe 40Ar/39Ar measurements of loss profiles within individual hornblende grains from the Giants Range Granite, northern Minnesota, U.S.A. Earth Planet Sci Lett 107:634–648

    Google Scholar 

  • Kelley SP, Parsons I, Worden RH, Walker FDL (1989) A laser 40Ar/39Ar study of preheated alkali feldspars. Terra Abstracts 1:353

    Google Scholar 

  • Kelley SP, Reddy SM, Maddock R (1994) Laser-probe 40Ar/39Ar investigation of a pseudotachylyte and its host rock from the Outer Isles thrust, Scotland. Geology 22:443–446

    Google Scholar 

  • Kober B (1986) Whole-grain evaporation for 207Pb/206Pb age investigations on single zircons using a double-filament thermal ion source. Contrib Mineral Petrol 93:482–490

    Google Scholar 

  • Krogh T (1982) Improved accuracy of U-Pb zircon ages by the creation of more concordant systems using an air abrasion technique. Geochim Cosmochim Acta 46:637–649

    Google Scholar 

  • Le Claire AD (1963) The analysis of grain boundary diffusion measurements. Br J Appl Phys 14:351–356

    Google Scholar 

  • Le Claire AD, Rabinovitch A (1984) The mathematical analysis of diffusion in dislocations. In: Murch GE, Nowick AS (eds) Diffusion in crystalline solids, Academic Press, Orlando, Florida, pp 257–318

    Google Scholar 

  • Lee JKW (1991) A quasi-random walk with argon diffusion in hornblende. PhD dissertation, Princeton Univ, Princeton, New Jersey

  • Lee JKW (1993) The argon relase mechanisms of hornblende in vacuo. Chem Geol (Isotope Geosci). 106:133–170

    Google Scholar 

  • Lee JKW, Aldama AA (1992) Multipath diffusion: a general numerical model. Computers and Geosciences 18:531–555

    Google Scholar 

  • Lee JKW, Williams IS (1993) Microstructural controls on U-Pb mobility in zircons. EOS Trans Am Geophys Union 74:650

    Google Scholar 

  • Lee JKW, Onstott TC, Hanes JA (1990) An 40Ar/39Ar investigation of the contact effects of a dyke intrusion, Kapuskasing Structural Zone, Ontario: a comparison of laser microprobe and furnace extraction techniques. Contrib Mineral Petrol 105:87–105

    Google Scholar 

  • Lee JKW, Onstott TC, Cashman KW, Cumbest RJ, Johnson D (1991) Incremental heating of hornblende in vacuo: implications for 40Ar/39Ar geochronology and the interpretation of thermal histories. Geology 19:872–876

    Google Scholar 

  • Love GR (1964) Dislocation pipe diffusion. Acta Metall 12:731–737

    Google Scholar 

  • Lovera OM, Richter FM, Harrison TM (1989) The 40Ar/39Ar thermochronometry for slowly cooled samples having a distribution of diffusion domain sizes. J Geophys Res 94:17917–17935

    Google Scholar 

  • Lux G (1987) The behavior of noble gases in silicate liquids: solution, diffusion, bubbles and surface effects, with applications to natural samples. Geochim Cosmochim Acta 51:1549–1560

    Google Scholar 

  • Maboko MAH, McDougall I, Zeitler PK, Fitz Gerald JD (1991) Discordant 40Ar−39Ar ages from the Musgrave Ranges, central Australia: implications for the significance of hornblende 40Ar−39Ar spectra. Chem Geol (Isotope Geosci) 86:139–160

    Google Scholar 

  • Megrue GH (1967) Isotopic analysis of rate gases with a laser microprobe. Science 157:1555–1556

    Google Scholar 

  • Miller WM, Fallick AE, Leake BE, Macintyre RM, Jenkin GRT (1991) Fluid disturbed hornblende K−Ar ages from the Dalradian rocks of Connemara, western Ireland. J Geol Soc London 148:985–992

    Google Scholar 

  • Mortlock AJ (1960) The effect of segregation on the solute diffusion enhancement due to the presence of dislocations. Acta Metall 8:132–134

    Google Scholar 

  • Mussett AE (1969) Diffusion measurements and the potassiumargon method of dating. Geophys J R Astron Soc 18:257–303

    Google Scholar 

  • Nicolaysen LO (1957) Solid diffusion in radioactive minerals and the measurement of absolute age. Geochim Cosmochim Acta 11:41–59

    Google Scholar 

  • Norgett MJ, Lidiard AB (1968) The migration of inert gases in ionic crystals. Philos Mag (8th ser). 18:1193–1210

    Google Scholar 

  • Onstott TC, Peacock MW (1987) Argon retentivity of hornblendes: a field experiment in a slowly cooled metamorphic terrane. Geochim Cosmochim Acta 51:2891–2903

    Google Scholar 

  • Onstott TC, Hall CM, York D (1989) 40Ar/39Ar thermochronometry of the Imataca Complex, Venezuela. Precambrian Res 42:255–292

    Google Scholar 

  • Onstott TC, Phillips D, Pringle-Goodell L (1991) Laser microprobe measurement of chlorine and argon zonation in biotite. Chem Geol 90:145–168

    Google Scholar 

  • Parsons I, Rex DC, P Guise, Halliday AN (1988) Argon-loss by alkali feldspars. Geochim Cosmochim Acta 52:1097–1112

    Google Scholar 

  • Phillips D (1991) Argon isotope and halogen chemistry of phlogopite from South African kimberlites: a combined stepheating, laser probe, electron microprobe and TEM study. Chem Geol (Isotope Geosci) 87:71–98

    Google Scholar 

  • Phillips D, Onstott TC (1988) Argon isotopic zoning in mantle phlogopite. Geology 16:542–546

    Google Scholar 

  • Reichenberg D (1953) Properties of ion-exchange resins in relation to their structure. III. Kinetics of exchange. J Am Chem Soc 75:589–597

    Google Scholar 

  • Ruoff AL, Balluffi RW (1963) Strain-enhanced diffusion in metals II: dislocation and grain-boundary short-circuiting models. J Appl Phys 34:1848–1853

    Google Scholar 

  • Scaillet S, Féraud G, Lagabrielle Y, Ballèvre M, Ruffet G (1990) 40Ar/39Ar laser-probe dating by step heating and spot fusion of phengites from the Dora Maira nappe of the western Alps, Italy. Geology 18:741–744

    Google Scholar 

  • Scaillet S, Féraud G, Ballèvre M, Amouric M (1992) Mg/Fe and [(Mg,Fe)Si−Al2] compositional control on argon behaviour in high-pressure white micas: a 40Ar/39Ar continuous laser-probe study from the Dora-Maria nappe of the internal western Alps, Italy. Geochim Cosmochim Acta 56:2851–2872

    Google Scholar 

  • Schärer U, Allègre CJ (1982) Uranium-lead system in fragments of a single zircon grain. Nature 295:585–587

    Google Scholar 

  • Skrotzki W (1990) Microstructure in hornblende of a mylonitic amphibolite. In: Knipe RJ, Rutter EH (eds) Deformation mechanisms, rheology and tectonics, Geol Soc London Spec Pub 54:321–325

  • Smoluchowski R (1952) Movement and diffusion phenomena in grain boundaries. In: Shockley W, Hollomon JH, Maurer R, and Seitz F (eds) Imperfections in Nearly Perfect Crystals, John Wiley and Sons, New York, pp 451–475

    Google Scholar 

  • Steiger RH, Jäger E, (1977) Subcommission on geochronology: convention on the use of decay constants in geo- and cosmochronology. Earth Planet Sci Lett 36:359–362

    Google Scholar 

  • Tilton GR (1960) Volume diffusion as a mechanism for discordant lead ages. J Geophys Res 65:2933–2945

    Google Scholar 

  • Tucker R, Laskar A, Thomson R (1963) Pipe diffusion in LiF. J Appl Phys 34:445–452

    Google Scholar 

  • Turner G (1968) The distribution of potassium and argon in chondrites. In: Ahrens LH (ed) Origin and distribution of elements. Pergamon, New York, pp 387–398

    Google Scholar 

  • Veblen DR, Buseck PR (1980) Microstructures and reaction mechanisms in biopyriboles. Am Mineral 65:599–623

    Google Scholar 

  • Walker FDL (1990) Ion microprobe study of intragrain micropermeability in alkali feldspars. Contrib Mineral Petrol 106:124–128

    Google Scholar 

  • Wartho J, Dodson MH, Rex DC, Guise PG, Knipe RJ (1991) Mechanisms of Ar release from Himalayan metamorphic hornblende. Am Mineral 76:1446–1448

    Google Scholar 

  • Wasserburg GJ (1954) Argon-40: potassium-40 dating. In: Faul H (ed) Nuclear geology. Wiley, New York, pp 341–349

    Google Scholar 

  • Wetherill GW (1966) K−Ar dating of Precambrian rocks. In: Schaeffer OA, Zähringer J (eds) Potassium argon dating. Springer, New York, pp 107–117

    Google Scholar 

  • Whipple RTP (1954) Concentration contours in grain boundary diffusion. Philos Mag (7th Ser) 45:1225–1236

    Google Scholar 

  • Williams IS, Claesson S (1987) Isotopic evidence for the Precambrian provenance and Caledonian metamorphism of high grade paragneisses from the Serve Nappes, Scandinavian Caledonides II. Ion microprobe zircon U-Th-Pb. Contrib Mineral Petrol 97:205–217

    Google Scholar 

  • Worden RH, Walker FDL, Parsons I, Brown WL (1990) Development of microporosity, diffusion channels and deuteric coarsening in perthitic alkali feldspars. Contrib Mineral Petrol 104:507–515

    Google Scholar 

  • Wright N, Layer PW, York D (1991) New insights into thermal history from single grain 40Ar/39Ar analysis of biotite. Earth Planet Sci Lett 104:70–79

    Google Scholar 

  • Yang, J, Lewis RS, Anders E (1982) Sorption of noble gases by solids, with reference to meteorites. I. Magnetite and carbon. Geochim Cosmochim Acta 46:841–860

    Google Scholar 

  • York D, Hall CM, Yanase Y, Hanes JA, Kenyon WJ (1981) 40Ar/39Ar dating of terrestrial minerals with a continuous laser. Geophys Res Lett 8:1136–1138

    Google Scholar 

  • Yund RA, Smith BM, Tullis J (1981) Dislocation-assisted diffusion of oxygen in albite. Phys. Chem Mineral 7:185–189

    Google Scholar 

  • Yund RA, Quigley J, Tullis J (1989) The effect of dislocations on bulk diffusion in feldspars during metamorphism. J Metamorphic Geol 7:337–341

    Google Scholar 

  • Yurimoto H, Nagasawa H (1989) The analysis of dislocation pipe radius for diffusion. Mineral J 14:171–178

    Google Scholar 

  • Yurimoto H, Morioka M, Nagasawa H (1989) Diffusion in single crystals of melilite: I. Oxygen. Geochim Cosmochim Acta 53:2387–2394

    Google Scholar 

  • Yurimoto H, Morioka M, Nagasawa H (1992) Oxygen self-diffusion along high-diffusivity paths in forsterite. Geochem J 26:181–188

    Google Scholar 

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  1. Research School of Earth Sciences, The Institute of Advanced Studies, The Australian National University, 0200, Canberra, A.C.T., Australia

    James K. W. Lee

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Lee, J.K.W. Multipath diffusion in geochronology. Contr. Mineral. and Petrol. 120, 60–82 (1995). https://doi.org/10.1007/BF00311008

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