2Common Lead vs Radiogenic Lead Pb derived from decay of U and Th is described as radiogenic lead.In a system containing U and Th, the isotopic composition of Pb is controlled by the decay of the U and Th parent isotopesHowever, in many systems, Pb is hosted in rock and minerals that contain no U and Pb and hence its evolution is independent of radioactive decay of U and ThHence, the isotopic composition of Pb varies between highly radiogenic Pb in very old U- and Th-bearing minerals to the comon Pb in Galena and other minerals that have low U/Pb and Th/Pb ratios
3Common PbCommon Pb dating is focussed on minerals whose U/Pb and Th/Pb ratios are so low that the isotope composition of Pb does not change with time.The principle common Pb mineral is Galena but sulphides of other base metals and K-feldspar, in which Pb2+ replaces K+1 also contain common PbThe isotope composition of common Pb was first determined by Aston (1927)It was known that the atomic weight of Pb associated with uranium was significantly less than that of common Pb, the differences being the presence of varying amounts radiogenic 206Pb.In contrast common Pb had a vary constant atomic weight, suggesting a constant isotopic composition
4Common PbIn 1938 A.O. Nier published a series of papers in which he reported systematic variations in the isotopic composition of Pb from different Galena ores.He found that these Pb’s had nearly constant atomic weights in spite of significant variations in isotopic compositions because of complimentary variations in the different isotopes.He subsequently showed that Pb ores have very variable isotope compositions likely to be related to mixing of radiogenic Pb with primeval Pb.This work led many scientists to hypothesize that the age of the Earth and the age of common Pb minerals could be determined using quantitative models based on the isotopic evolution of Pb in the Earth.
5The Holmes – Houterman Model The first general model for determining the age of the Earth from the evolution of Pb was determined independently by Holmes and by Houterman both in 1946This model makes the following assumptionsOriginally the earth was fluid and homogeneousAt that time U, Th and Pb were uniformly distributedThe isotopic composition of the primeval Pb was everywhere the sameSubsequently the Earth became rigid and small regional differences arose in the U/Pb ratioIn any given region the U/Pb ratio changed only as a result of radioactive decay of U to PbAt the time of formation of a common Pb mineral, such as galena, the Pb was separated from U and Th and its isotopic composition has remained constant since that time
6The Holmes-Houterman Model The 206Pb/204Pb ratio of a uranium-bearing system of age T that has remained closed to U and all of its daughters is given by:You can see that this equation has the form of the standard decay equationIf Pb was withdrawn from such a system without isotope fractionation t years ago, then the 206Pb/204Pb of that Pb is given by a modified form of this equationEqn 1
7The Holmes–Houterman Model Which is this one….Eqn 2Eqn 3Where ….
9The Holmes-Houterman Model Equations can also be written for the 207Pb and 208Pb systems. In order to make the equations less cumbersome, simplifying nomenclature was introduced.
10The Holmes-Houterman Model Introducing this simplifying nomenclature gives the following three equationsEqn 4Eqn 5Eqn 6
11The Holmes-Houterman Model We can combine equations 4 and 5 to eliminate m which gives usThis is the Holmes-Houterman Equation for Single-Stage Dating of PbEqn 7
12The Holmes-Houterman Model This equation can be simplified by introducing the simplifying nomenclatureEqn 8
13So where do the Meteorites come in…? Meteorites are fragments of larger parent bodies that formed early in the history of the solar systemDuring partial melting and chemical differentiation, an iron sulphide phase formed, known as troilite (FeS)Troilite contains appeciable concentrations of common Pb but is virtually free of U and ThTherefore the isotopic composition of Pb in troilite has remained very nearly constant since crystallisationIt is the least radiogenic Pb known and considered representative of the primeval Pb in the Earth because Earth and meteorites are believed to have formed at the same time from an isotopically heterogeneous solar nebula
14Single-Stage Pb Dating In order to use the Holmes-Houterman Equations for determining the age of the Earth the primeval Pb isotope ratios of the Earth had to be known.These were determined from iron-meteorites and in particular the Canyon Diablo troilite meteoriteIsotope ratios of Pb in troilite of the iron meteorite Canyon Diablo, ie equivalent to initial values206Pb/204Pb = a0 207Pb/204Pb = b0 208Pb/204Pb = c0 ReferenceTatsumoto et al., 1973Chen and Wasserburg (1983)
15Single-Stage Dating of Common Pb Using equations 4, 5, 6 and 8 it is possible to date common Pb’s that have had a single stage history.However, equation 8 is called transcendental which means that it cannot be solved algebraically and must be solved graphically or by using a set of table such as was calculated in practical 04.To interpolate between two points on a table use the following equationt = (age (t) that has the slope (m) or (207Pb/206Pb)* value that is the closest below your value of m) + (0.2 x your value of m - the slope (m) or (207Pb/206Pb)* value that is the closest below your value of m)/(the difference between the slope (m) or (207Pb/206Pb)* value that is the closest below your value of m and the next highest value)
16Problems with Single-Stage Pb Dating When more single-stage Pb dates were obtained it was found that often the dates where far away from the date given by the rocks that the Pb minerals and ores were hosted in.In the ore deposits where the Pb could be shown to have followed a single-stage model evolution, the ore deposits were stratigraphic sequences of volcanic and sedimentary rocks of marine origin in volcanic island arcs and the Pb, although derived from the lower crust and mantle was emplaced without contamination from crustal radiogenic PbMost ore deposits around the world though give anomalous Pb ages, that is they don’t agree with the ages of the rocks in which they are hosted.Thus the two-stage model was developed
17The Two-Stage ModelThe basic premise of the two-stage model is that there is an initial period of time when the evolution of Pb started with primordial values at the beginning of Earth’s history, time =TAfter a period of time, the U/Pb ratio of the reservoir was changed by geochemical differentiation and then remained constant to the presentThis two-stage evolution model was named after Stacey and Kramers (1975) in which they proposed that Pb evolved between 4.57 Ga and 3.70 Ga in a reservoir having uniform 238U/204Pb(m) and 232Th/204Pb(w) ratios of and respectivelyAt time 3.70Ga the values of m and w were changed by geochemical differentiation to and respectively.Subsequently the reservoir remained undisturbed until the present.
18The Stacey and Kramers Model The time of separation from the reservoir can be calculated from the equation of the isochron. For the Stacey and Kramers model this equation has the formWhere T’ = 3.70 x 109 years