Slope Year for the U-Pb Dating Method and Its Applications

Jie Yuan

Key Laboratory of Earth and Planetary Physics, Institute of Geology and Geophysics, Chinese Academy of Science, Beijing, China.

DOI: 10.4236/ojg.2015.55032                

Abstract

The slope year t_slope for the U-Pb dating method is given as , where λ₂₃₈ and λ₂₃₅ are the decay constants for ²³⁸U and ²³⁵U, respectively, and k is the slope of the tangent line at a point on either the Concordia or Discordia line. These two lines are determined by the initial ²⁰⁶⁽⁷⁾Pb_i concentrations in minerals. If , the line is the Concordia. However, if (∧ is the logical operator “and”, also known as the logical conjunction), or , the line is Discordia. The Concordia line is of the form (where p stands for the present), while the Discordia line has the form (where k and b are the slope and intercept of the straight line, respectively).

Keywords

Slope Year, U-Pb Dating, Zircon, Mass Spectrum, Isotope, Initial Pb Isotope Concentration

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Rutherford, E. and Soddy, F. (1903) The Radioactivity of Uranium. Philosophical Magazine, 5, 25-30, 441-445.
[2]	Audi, G., Bersillon, O., Blachot, J. and Wapstra, A.H. (2003) The Nubase Evaluation of Nuclear and Decay Properties. Nuclear Physics A, 729, 3-128. http://dx.doi.org/10.1016/j.nuclphysa.2003.11.001
[3]	Jaffey, A.H., Flynn, K.F., Glendenin, L.E., Bentley, W.C. and Essling, A.M. (1971) Precision Measurement of Half-Lives and Specific Activities of 235U and 238U. Physical Review C, 4, 1889-1906. http://dx.doi.org/10.1103/PhysRevC.4.1889
[4]	Pomme, S., Garcia-Torano, E., Sibbens, G., Richter, S., Wellum, R., Stolarz, A., et al. (2008) U-234/U-235 Activity Ratios as a Probe for the U-238/U-235 Half-Life Ratio. Journal of Radioanalytical and Nuclear Chemistry, 277, 207-210. http://dx.doi.org/10.1007/s10967-008-0731-6
[5]	Baker, T., Perkins, C., Blake, K.L. and Williams, P.J. (2001) Radiogenic and Stable Isotope Constraints on the Genesis of the Eloise Cu-Au Deposits, Cloncurry District, Northwest Queensland. Economic Geology, 96, 723-742. http://dx.doi.org/10.2113/96.4.723
[6]	Muller, R. (1996) Radiogenic Isotope Geology. Physics Today, 49, 60. http://dx.doi.org/10.1063/1.2807660
[7]	Panneerselvam, K., Macfarlane, A.W. and Salters, V.J.M. (2012) Reconnaissance Lead Isotope Characteristics of the Blackbird Deposit: Implications for the Age and Origin of Cobalt-Copper Mineralization in the Idaho Cobalt Belt, United States. Economic Geology, 107, 1177-1188. http://dx.doi.org/10.2113/econgeo.107.6.1177
[8]	Solomon, M., Gemmell, J.B. and Zaw, K. (2004) Nature and Origin of the Fluids Responsible for Forming the Hellyer Zn-Pb-Cu, Volcanic-Hosted Massive Sulphide Deposit, Tasmania, Using Fluid Inclusions, and Stable and Radiogenic Isotopes. Ore Geology Reviews, 25, 89-124. http://dx.doi.org/10.1016/j.oregeorev.2003.11.001
[9]	Ahrens, L.H. (1955) Implications of the Rhodesia Age Pattern. Geochimica et Cosmochimica Acta, 8, 1-15. http://dx.doi.org/10.1016/0016-7037(55)90013-2
[10]	Mezger, K. and Krogstad, E.J. (1997) Interpretation of Discordant U-Pb Zircon Ages: An Evaluation. Journal of Metamorphic Geology, 15, 127-140. http://dx.doi.org/10.1111/j.1525-1314.1997.00008.x
[11]	Tilton, G.R. (1960) Volume Diffusion as a Mechanism for Discordant Lead Ages. Journal of Geophysical Research, 65, 2933-2945. http://dx.doi.org/10.1029/JZ065i009p02933
[12]	Wetherill, G.W. (1956) An Interpretation of the Rhodesia and Witwatersrand Age Patterns. Geochimica et Cosmochimica Acta, 9, 290-292. http://dx.doi.org/10.1016/0016-7037(56)90029-1
[13]	Goldich, S.S. and Fischer, L.B. (1986) Air-Abrasion Experiments in U-Pb Dating of Zircon. Chemical Geology, 58, 195-215. http://dx.doi.org/10.1016/0168-9622(86)90010-2
[14]	Goldrich, S.S. and Mudrey, M.G. (1972) Dilatancy Model for Discordant U-Pb Zircon Ages. In: Tugarinov, A.I., Ed., Contributions to Recent Geochemistry and Analytical Chemistry, Nauka Publishing Office, Moscow, 415-418.
[15]	Holmes, A. (1954) The Oldest Dated Minerals of the Rhodesian Shield. Nature, 173, 612-614. http://dx.doi.org/10.1038/173612a0
[16]	Silver, L.T. and Deutsch, S. (1961) Uranium-Lead Method on Zircons. Annals of the New York Academy of Sciences, 91, 279-283.
[17]	Wasserburg, G.J. (1963) Diffusion Processes in Lead-Uranium Systems. Journal of Geophysical Research, 68, 4823-4846.
[18]	Chew, D.M., Sylvester, P.J. and Tubrett, M.N. (2011) U-Pb and Th-Pb Dating of Apatite by LA-ICPMS. Chemical Geology, 280, 200-216. http://dx.doi.org/10.1016/j.chemgeo.2010.11.010
[19]	Thomson, S.N., Gehrels, G.E., Ruiz, J. and Buchwaldt, R. (2012) Routine Low-Damage Apatite U-Pb Dating Using Laser Ablation-Multicollector-ICPMS. Geochemistry, Geophysics, Geosystems, 13, 1. http://dx.doi.org/10.1029/2011GC003928
[20]	Allibon, J., Ovtcharova, M., Bussy, F., Cosca, M., Schaltegger, U., Bussien, D., et al. (2011) Lifetime of an Ocean Island Volcano Feeder Zone: Constraints from U-Pb Dating on Coexisting Zircon and Baddeleyite, and 40AR/39AR Age Determinations, Fuerteventura, Canary Islandssp. Canadian Journal of Earth Sciences, 48, 567-592. http://dx.doi.org/10.1139/E10-032
[21]	Bayanova, T.B. and Yakovenchuk, V.N. (1994) U-Pb Dating of Baddeleyite and Zircon from Imandrites on the Kola Peninsula. Doklady Earth science sections, 323, 147-150.
[22]	de Assis Janasi, V., de Freitas, V.A. and Heaman, L.H. (2011) The Onset of Flood Basalt Volcanism, Northern Parana Basin, Brazil: A Precise U-Pb Baddeleyite/Zircon Age for a Chapeco-Type Dacite. Earth and Planetary Science Letters, 302, 147-153. http://dx.doi.org/10.1016/j.epsl.2010.12.005
[23]	Li, Q.-L., Li, X.-H., Liu, Y., Tang, G.-Q., Yang, J.-H. and Zhu, W.-G. (2010) Precise U-Pb and Pb-Pb Dating of Phanerozoic Baddeleyite by SIMS with Oxygen Flooding Technique. Journal of Analytical Atomic Spectrometry, 25, 1107-1113. http://dx.doi.org/10.1039/b923444f
[24]	Soderlund, U. (2006) U-Pb Baddeleyite Ages of Meso- and Neoproterozoic Dykes and Sills in Central Fennoscandia: A Review. 5th International Dyke Conference: Dyke Swarms—Time Markers of Crustal Evolution, IDC-5. Rovaniemi, 31 July 2005-3 August 2005, 75-84.
[25]	Wahlgren, C.H., Heaman, L.M., Kamo, S. and Ingvald, E. (1996) U-Pb Baddeleyite Dating of Dolerite Dykes in the Eastern Part of the Sveconorwegian Orogen, South-Central Sweden. Precambrian Research, 79, 227-237. http://dx.doi.org/10.1016/0301-9268(95)00094-1
[26]	Aleinikoff, J.N., Lack, J.F.S., Lund, K., Evans, K.V., Fanning, C.M., Mazdab, F.K., et al. (2012) Constraints on the Timing of Co-Cu Au Mineralization in the Blackbird District, Idaho, Using SHRIMP U-Pb Ages of Monazite and Xenotime Plus Zircon Ages of Related Mesoproterozoic Orthogneisses and Metasedimentary Rocks. Economic Geology, 107, 1143-1175. http://dx.doi.org/10.2113/econgeo.107.6.1143
[27]	Baltybaev, S.K., Levchenkov, O.A., Glebovitskii, V.A., Rizvanova, N.G., Yakubovich, O.V. and Fedoseenko, A.M. (2010) Timing of the Regional Postmigmatitic K-Feldspar Mineralization on the Base of U-Pb Dating of Monazite (Metamorphic Complex of the Northern Ladoga Region). Doklady Earth Sciences, 430, 186-189. http://dx.doi.org/10.1134/S1028334X1002008X
[28]	Bose, S., Dunkley, D.J., Dasgupta, S., Das, K. and Arima, M. (2011) India-Antarctica-Australia-Laurentia Connection in the Paleoproterozoic-Mesoproterozoic Revisited: Evidence from New Zircon U-Pb and Monazite Chemical Age Data from the Eastern Ghats Belt, India. Bulletin of the Geological Society of America, 123, 2031-2049. http://dx.doi.org/10.1130/B30336.1
[29]	Dunning, G.R., Macdonald, A.S. and Barr, S.M. (1995) Zircon and Monazite U-Pb Dating of the Doi Inthanon Core Complex, Northern Thailand: Implications for Extension within the Indosinian Orogen. Tectonophysics, 251, 197. http://dx.doi.org/10.1016/0040-1951(95)00037-2
[30]	Evans, J. and Zalasiewicz, J. (1996) U-Pb, Pb-Pb and Sm-Nd Dating of Authigenic Monazite: Implications for the Diagenetic Evolution of the Welsh Basin. Earth and Planetary Science Letters, 144, 421. http://dx.doi.org/10.1016/S0012-821X(96)00177-X
[31]	Peterman, E.M., Mattinson, J.M. and Hacker, B.R. (2012) Multi-Step TIMS and CA-TIMS Monazite U-Pb Geochronoogy. Chemical Geology, 312-313, 58-73. http://dx.doi.org/10.1016/j.chemgeo.2012.04.006
[32]	Rasmussen, B., Fletcher, I.R. and McNaughton, N.J. (2001) Dating Low-Grade Metamorphic Events by SHRIMP U-Pb Analysis of Monazite in Shales. Geology, 29, 963-966. http://dx.doi.org/10.1130/0091-7613(2001)029<0963:DLGMEB>2.0.CO;2
[33]	Rasmussen, B., Fletcher, I.R., Muhling, J.R., Mueller, A.G. and Hall, G.C. (2007) Bushveld-Aged Fluid Flow, Peak Metamorphism, and Gold Mobilization in the Witwatersrand Basin, South Africa: Constraints from in Situ SHRIMP U-Pb Dating of Monazite and Xenotime. Geology, 35, 931-934. http://dx.doi.org/10.1130/G23588A.1
[34]	Baumgartner, R., Romer, R.L., Moritz, R., Sallet, R. and Chiaradia, M. (2006) Columbite-Tantalite-Bearing Granitic Pegmatites from the Serido Belt, Northeastern Brazil: Genetic Constraints from U-Pb Dating and Pb Isotopes. Canadian Mineralogist, 44, 69-86. http://dx.doi.org/10.2113/gscanmin.44.1.69
[35]	Camacho, A., Baadsgaard, H., Davis, D.W. and Cerny, P. (2012) Radiogenic Isotope Systematics of the Tanco and Silverleaf Granitic Pegmatites, Winnipeg River Pegmatite District, Manitoba. Canadian Mineralogist, 50, 1775-1792. http://dx.doi.org/10.3749/canmin.50.6.1775
[36]	Melcher, F., Graupner, T., Henjes-Kunst, F., Oberthur, T., Sitnikova, M., Gabler, E., et al. (2008) Analytical Fingerprint of Columbite-Tantalite (Coltan) Mineralisation in Pegmatites—Focus on Africa. 9th International Congress for Applied Mineralogy, ICAM 2008, 8-10 September 2008, Brisbane, 615-624.
[37]	Melleton, J., Gloaguen, E., Frei, D., Novak, M. and Breiter, K. (2012) How Are the Emplacement of Rare-Element Pegmatites, Regional Metamorphism and Magmatism Interrelated in the Moldanubian Domain of the Variscan Bohemian Massif, Czech Republic? Canadian Mineralogist, 50, 1751-1773. http://dx.doi.org/10.3749/canmin.50.6.1751
[38]	Schmitt, A.K. and Zack, T. (2012) High-Sensitivity U-Pb Rutile Dating by Secondary Ion Mass Spectrometry (SIMS) with an O2+ Primary Beam. Chemical Geology, 332-333, 65-73. http://dx.doi.org/10.1016/j.chemgeo.2012.09.023
[39]	Essex, R.M. and Gromet, L.P. (2000) U-Pb Dating of Prograde and Retrograde Titanite Growth during the Scandian Orogeny. Geology, 28, 419-422. http://dx.doi.org/10.1130/0091-7613(2000)28<419:UDOPAR>2.0.CO;2
[40]	Nesterova, N.S., Kirnozova, T.I. and Fugzan, M.M. (2011) New U-Pb Titanite Age Data on the Rocks from the Karelian Craton and the Belomorian Mobile Belt, Fennoscandian Shield. Geochemistry International, 49, 1161-1167. http://dx.doi.org/10.1134/S0016702911120081
[41]	Spencer, K.J., Hacker, B.R., Kylander-Clark, A.R.C., Andersen, T.B., Cottle, J.M., Stearns, M.A., et al. (2013) Campaign-Style Titanite U-Pb Dating by Laser-Ablation ICP: Implications for Crustal Flow, Phase Transformations and Titanite Closure. Chemical Geology, 341, 84-101. http://dx.doi.org/10.1016/j.chemgeo.2012.11.012
[42]	Richards, J.P., Cumming, G.L., Krstic, D., Wagner, P.A. and Spooner, E.T.C. (1988) Pb Isotope Constraints on the Age of Sulfide Ore Deposition and U-Pb Age of Late Uraninite Veining at the Musoshi Stratiform Copper Deposit, Central African Copper Belt, Zaire. Economic Geology, 83, 724-741. http://dx.doi.org/10.2113/gsecongeo.83.4.724
[43]	Votyakov, S.L., Ivanov, K.S., Khiller, V.V., Bochkarev, V.S. and Erokhin, Y.V. (2011) Chemical Microprobe Th-U-Pb Age Dating of Monazite and Uraninite Grains from Granites of the Yamal Crystalline Basement. Doklady Earth Sciences, 439, 994-997. http://dx.doi.org/10.1134/S1028334X1107018X
[44]	Li, X.-H., Li, W.-X., Wang, S.-C., Li, Q.-L., Liu, Y. and Tang, G.-J. (2009) Role of Mantle-Derived Magma in Genesis of Early Yanshanian Granites in the Nanling Range, South China: In Situ Zircon Hf-O Isotopic Constraints. Scientia Sinica Terrae, 39, 872-887. http://dx.doi.org/10.1007/s11430-009-0117-9
[45]	Zheng, J.P., Griffin, W.L., Ma, Q., O’Reilly, S.Y., Xiong, Q., Tang, H.Y., et al. (2012) Accretion and Reworking beneath the North China Craton. Lithos, 149, 61-78. http://dx.doi.org/10.1016/j.lithos.2012.04.025
[46]	Compston, W., Williams, I.S. and Clement, S.W. (1982) U-Pb Ages within Single Zircons Using a Sensitive High Mass-Resolution Ion Microprobe. The 30th Annual Conference on Mass Spectrometry and Allied Topics, Abstracts, Honolulu, 15 February 1984, B525-B534.
[47]	Compston, W., Williams, I.S. and Meyer, C. (1984) U-Pb Geochronology of Zircons from Lunar Breccia 73217 Using a Sensitive High Mass-Resolution Ion Microprobe. Journal of Geophysical Research, 89, 525-534. http://dx.doi.org/10.1029/JB089iS02p0B525
[48]	Feng, R., Machado, N. and Ludden, J. (1993) Lead Geochronology of Zircon by Laser Probe-Inductively Coupled Plasma Mass Spectrometry (LP-ICPMS). Geochimica et Cosmochimica Acta, 57, 3479-3486. http://dx.doi.org/10.1016/0016-7037(93)90553-9
[49]	Srinivasan, G., Whitehouse, M.J., Weber, I. and Yamaguchi, A. (2004) U-Pb and Hf-W Chronometry of Zircons from Eucrite A881467. The 35th Lunar and Planetary Science Conference, League City, TX, 19 March 2004, 1709.
[50]	Fong, C.F.C.M., Kee, D.D. and Kaloni, P.N. (2002) Advanced Mathematics for Engineering and Science. World Scientific Publishing Co. Pte. Ltd, Singapore.
[51]	Wang, J., Qian, Z., Qian, W., Zhuang, Y., He, Y. and Pan, C. (1999) Analysis of Regression and Variance, in Probability Statistics (Engineering Mathematics). Tongji University, Shanghai, 240-247. (In Chinese)
[52]	Bühlmann, P. and M?chler, M. (2008) Computational Statistics, 4-10. https://stat.ethz.ch/education/semesters/ss2012/CompStat/sk.pdf