Concordia Discordia 206 Pb204 Pbm 206 Pb204 Pbi
Concordia- Discordia (206 Pb/204 Pb)m = (206 Pb/204 Pb)i + (238 U/204 Pb) (e λt -1 ) (206 Pb)m = (206 Pb)i + (238 U) (e λt -1 ) (206 Pb)m - (206 Pb)i = 238 U (e λt -1 ) 206 Pb*/ 238 U = (e λ 1 t -1 ) 207 Pb*/ 235 U = (e λ 2 t -1 ) Instead of finding the age (t), we can reverse the procedure and use the two eq to calculate compatible sets of (206 Pb*/ 238 U) and (207 Pb*/ 235 U) for specified values of t
The U-Pb-Th System Concordia = Simultaneous co- evolution of 206 Pb and 207 Pb via: 238 U 234 U 206 Pb 235 U 207 Pb
U-Pb discordia - open system behavior Indeed, Pb loss does not often occur in a single metamorphic event - it can be quite complicated (i. e. multiple events or even continous Pb loss) Age Upper intercept = age Lower intercept = any Pb-loss event
Concordia/Discordia Plot 207 Pb*/238 U vs. 206 Pb*/235 U All points with the same age form a curve = Concordia; If the data fall along a line instead = Discordia Use zircons; exclude Pb, all Pb is radiogenic Discordia beneath Concordia = Pb loss (usually) or U gain Discordia above Concordia = U loss Most rocks are discordant and can be explained by Pb loss Intersection of Discordia line with Concordia curve gives age of formation and age of Pb loss
Concordia discordia • The concordia curve is the locus of points for which the 206 Pb/238 U age equals the 207 Pb/235 U. • It is curved due to different half-lives of 238 U and 235 U.
Evolution of Pb isotopes with time • Growth of daughter isotopes • Because there are so many variables in Pb isotopic system (three diff decay const), it is convenient to display the data as concordia diagram. • On this diagram, families of concordia (growth) curves can be calibrated for different 238 U/204 Pb ratios (called µ). Each curve can be calibrated for time and equal time points can be joined to give isochrons.
The Geochron is the Pb-Pb isochron with a slope corresponding to T=4. 56 Ga that passes through the composition of primordial Pb - reflects closed system evolution of lead in solar system • Plot data from several meteorites, which define a line • Initial ratio determined by the Canyon Diablo troilite (Fe. S, incorporates Pb, but not U; initial Pb isotope ratios are preserved) which plots along the geochron If U/Pb, sample is right of geochron If U/Pb, sample is left of geochron
Uranium-Thorium-Lead 238 U/235 U = 137. 88 206 Pb, t½ = 4. 47 Gyr 235 U 207 Pb, t = 0. 70 Gyr everywhere (today) ½ 232 Th 208 Pb, t = 14. 0 Gyr m = 238 U/204 Pb ½ No longer in pseudolinear decay regime k = 232 Th/235 U ~ 4. 0 (chondrites) 238 U Can derive equations relating the Pb isotopes – useful because don’t need to measure parents Plot 207 Pb/204 Pb vs. 206 Pb/204 Pb Line = isochron if it passes through initial ratios Steeper slope = older age Evolution lines depend on m
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