5.4       Model (galena) ages

 

As discussed above, different Pb isotope dating methods address the problem of uranium mobility in different ways. In the U)Pb zircon dating method, a mineral was chosen which held U well and in which Pb loss could be modelled and corrected. In common Pb)Pb dating the recent loss of U can be permitted, provided the system was closed for most of its life. In the galena method discussed here, a phase is analysed which contains no U, so there is no problem of U loss.

 

 

5.4.1    The Holmes)Houtermans model

 

Since there is no U decay in a galena, we are not measuring its age directly back from the present day, but are measuring the age of the galena source from the formation of the Earth until the isolation of the galena. This approach was conceived independently by Holmes (1946) and Houtermans (1946). They divided the isotopic evolution of galena Pb into two parts. The first was assumed to be a rock system, which must have remained closed to U and Pb from the formation of the Earth until galena separation. The second was in the galena itself, which must contain no significant amounts of uranium. This model for terrestrial Pb isotope evolution may be summarised as follows:

 

                            U decay                              no U decay

                            in rock                                 in galena

              T  )))))))))))))))>  t  )))))))))))))))>  P

 age of Earth                             age of galena                              present.

 

Given this model, the basic decay equation for 207Pb is:

 

            207Pbt  =  207PbT   +   235U  (e8235 T ! e8235 t)                  [5.12]

 

This decay equation is more complex than [5.2] because ‘t’ is not zero. Each term is next divided through by 204Pb and rearranged. The same procedure is applied to the corresponding equation for 206Pb to yield the following result:

 

(207Pb)              (207Pb)              235U

()))))  !       ()))))    =     ))))   (e8235 T ! e8235 t)                      [5.13]

(204Pb)t             (204Pb)T            204Pb

 

(206Pb)              (206Pb)              238U

()))))  !       ()))))    =     ))))   (e8238 T ! e8238 t)                      [5.14]

(204Pb)t             (204Pb)T            204Pb.

 

Equation [5.13] is now divided through by equation [5.14] and the result is simplified as follows:

 1)  204Pb terms are cancelled on the right-hand side of the equation. This leaves a factor for the U isotope ratio at the present day, which is a constant with the value 1/137.88.

 2)  (207Pb/204Pb)t and (206Pb/204Pb)t represent the present day compositions, since galena incorporates no U.

 3)  The Pb isotope compositions at time ‘T’ represent the composition of the solar nebula; which is the primordial composition of the Earth, now represented by Canyon Diablo troilite (C.D.).

 

The equation can then be written as:

 

(207Pb) 

()))))  !  C.D.

(204Pb)P                            1                  (e8235 T ! e8235 t)

))))))))))))   = ))))   @         ))))))))))                        [5.15]

(206Pb)                           137.88            (e8238 T ! e8238 t)

()))))  !  C.D.

(204Pb)P

 

If the isotope ratios on the left-hand side of the equation represent a sample extracted from the mantle at time t, then the term on the right-hand side corresponds to the slope of an ‘isochron’ line joining it to the solar nebula composition (Fig. 5.29).

Fig. 5.29. Pb)Pb isochron diagram showing present-day composition (P) of galena extracted from a Bulk Earth reservoir 3 Byr ago. After Russell and Farquhar (1960).

 

            To apply the Holmes)Houtermans model, the galena source rock is assumed to be a closed system with a ‘single stage’ Pb isotope history. A growth curve is then constructed for this galena source, which runs from the primordial Pb composition to that of the analysed galena, and is calibrated for various values of t. (Since this is a transcendental curve, t cannot be solved by direct algebra starting with a composition on the left hand side of equation [5.15]). The shape of the growth curve is determined by the two uranium decay constants, and its trajectory by the 238U/204Pb or ‘:’ value of the closed-system galena source. For the single stage model described, it is called the :1 value and would normally be between 7 and 9. According to the Holmes)Houtermans model, not every galena source rock need have the same growth curve defined by the same : value. Galena ore bodies were expected to have concentrated the metal from local continental basement in the vicinity. However, this presupposes that the basement in question has been in existence since near the time of formation of the Earth, which is now regarded as very unlikely (e.g. see section 4.4).

 

            A major problem encountered using the Holmes)Houtermans model was that as more galenas were analysed they were found to scatter more and more widely on the Pb)Pb isochron diagram (Fig. 5.30). Some of the ages determined were clearly erroneous, since they were in the future. Others, which were outliers to the main trend, often gave ages which could be shown to be geologically impossible. Since galenas of these two types contradicted the Holmes) Houtermans model, they were called ‘anomalous leads’. However, the crucial problem with this situation was the lack of an a priori test which could be performed to predict whether a galena would be anomalous, in the absence of other evidence of its age.

Fig. 5.30. Pb)Pb isochron diagram showing a compilation of many analysed galenas from different environments. After Stanton and Russell (1959).

 

 

5.4.2    Conformable leads

 

Given the complexity of Earth evolution, it was realised even in the 1950s that the country-rock source of a given galena ore was unlikely to have been a closed system since the formation of the Earth. Alpher and Herman (1951) attempted to overcome this problem by attributing Pb isotope evolution in the galena source rock to a single world-wide homogeneous reservoir, regarded by Russell (1956) as the Earth’s mantle. As an explanation of the observed galena Pb isotope variation this model is quite obviously inadequate, but it was the basis of a more geologically realistic model proposed by Stanton and Russell (1959).

 

            A certain class of Pb ores was found by Stanton and Russell which did lie on a single closed-system growth curve. These were sulphides associated with sediments and volcanics in greenstone belts and island arcs, which were structurally conformable with the host rocks (in contrast to cross-cutting veins). Stanton and Russell regarded these ores as being formed by syngenetic deposition in sedimentary basins associated with volcanic centres, and therefore as representing galena derived directly from the upper mantle without crustal contamination.

 

            Stanton and Russell selected nine deposits of various ages that satisfied these criteria, and fitted a single stage (upper mantle) growth curve with a :1 value of 9.0 (Fig. 5.31). These ores were termed ‘conformable’ leads because of their structural occurrence, and all galenas that didn’t fit this curve were by inference ‘anomalous’. Anomalous leads were divided into groups such as ‘J-type leads’ after a deposit at Joplin, Missouri which gave ages in the future, and some other types such as the ‘B’ type which gave ages in the past.

Fig. 5.31. Pb)Pb isochron diagram showing galena ores that form the basis of the ‘conformable’ Pb model. After Stanton and Russell (1959).

 

            Unfortunately, due to the mobility of Pb during crustal processes, it is difficult to develop a priori criteria to recognise galenas which will fit the conformable Pb evolution model. Therefore, the galena method is largely discredited as a dating tool. Nevertheless, it may provide powerful constraints on the Earth’s evolution, which will be examined below.

 

 

5.4.3    Open-system Pb evolution

 

As early as 1956, Russell considered the possibility that the mantle might not have been a closed system to U and Pb, but might have had a variable : value over time, due to some kind of differentiation mechanism. However, the success of the conformable lead model to explain uncontaminated galena compositions with a closed-system mantle militated against such complications.

 

            In the early 1970s, new measurements of the uranium decay constants (Jaffey et al., 1971) and a better estimate of primordial Pb from Canyon Diablo necessitated a re-examination of the conformable Pb model. For example, using the new values, a curve calculated to yield a reasonable fit to conformable galenas gave a low apparent age for the Earth of 4.43 Byr (Doe and Stacey, 1974). Alternatively, a terrestrial age of 4.57 Byr based on Pb)Pb dating of meteorites (Tatsumoto et al., 1973), caused the Geochron to lie to the left of most Phanerozoic galenas and young oceanic volcanics. This problem became known as the ‘Pb paradox’ and meant that single stage Pb models gave ‘future ages’ up to 1 Byr in error for Phanerozoic rocks.

 

            To rectify these problems, Oversby (1974) proposed a model for an evolving (mantle) source of galena Pb with a progressive increase in : value over time (approximated by a series of small increments in :). This model was elaborated upon by Cumming and Richards (1975), who modelled a galena source with a linear increase in : value. Surprisingly perhaps, Cumming and Richards regarded the galena source as a regional average of the crust. However, this may not be as strange as it sounds, since later work would show that mantle and crustal Pb evolution are in fact coupled together, and that upper mantle Pb is largely buffered by the crust (section 6.3.3). The model of Cumming and Richards yields a good fit to the ages of selected galena data, but still implies a young apparent age for the Earth of 4.50 Byr.

 

            An alternative solution to this problem proposed by Stacey and Kramers (1975), was to break terrestrial Pb isotope evolution into two parts. Stacey and Kramers used Canyon Diablo Pb and average modern Pb (from a mixture of manganese nodules, ocean sediments and island arc rocks) to anchor the ends of a composite growth curve. This curve was produced by two closed systems (1 and 2) with different : values (:1 and :2), separated in time by a world-wide differentiation event. The closed systems consisted of a combination of the upper mantle and upper crust (lower crust, lower mantle and core being isolated). The model gave the best fit to a selection of conformable galenas (dated by the enclosing sediments) when :1 = 7.2, :2 = 9.7, and the event was at 3.7 Byr (Fig. 5.32). This time was regarded as a peak of crust forming events, an interpretation made particularly attractive by the 3.7 Byr age determined for the Amitsoq gneisses of western Greenland (section 5.5.1). However Stacey and Kramers noted that their model was only an approximation of Pb isotope evolution in the real Earth. For example, the discrete 3.7 Byr event in the model might actually represent a slow change in the Earth’s evolution during the Early Archean.

Fig. 5.32. Pb isotope diagram showing a two-stage lead isotope evolution model proposed for the source of galenas ( ! ). After Stacey and Kramers (1975).

 

            The above observations suggested that the galena source evolved for the last 3.8 Byr along a higher-: growth curve than the geochron, but the reason for this behaviour was not clear. Armstrong (1968) and Russell (1972) argued that these observations could be explained by recycling (bi-directional transport) of Pb between the crust and mantle. This concept was developed further by Doe and Zartman (1979) and presented as a computer program which modelled the Pb isotope evolution of the Earth, termed ‘Plumbotectonics’.

 

            Doe and Zartman defined three reservoirs: upper crust, lower crust and upper mantle (< 500 km depth). Based on evidence that continental accretion began ca. 4 Byr ago, and that frequent orogenies mixed mantle and crustal sources to yield differentiated crustal blocks, they modelled orogenies at 400 Myr intervals, with a decreasing mantle contribution through time. Crustal contributions represented erosion and continental foundering. Orogenies instantaneously extracted U, Th and Pb from the three sources, mixed them, and redistributed them back to the sources (Fig. 5.33). U fractionation into the upper crust represented granulite-facies metamorphism.

Fig. 5.33. Schematic illustration of the operation of the ‘plumbotectonics’ model, showing mixing of crustal and mantle reservoirs into the orogene (galena source) reservoir. After Doe and Zartman (1979).

 

            The orogene composition generated by the plumbotectonics model was constrained empirically to fit galena ores, and consequent growth curves generated for the other reservoirs are shown in Fig. 5.34. The upper crust develops radiogenic Pb, which is balanced by the development of an unradiogenic lower crustal reservoir, due to preferential retention of Pb relative to U during granulite-facies metamorphism of the lower crust. The calculated upper mantle : value is similar to that for the total crust, but recycling of radiogenic upper crustal Pb into the mantle yields an apparent increase in mantle : value with time. Despite this effect, it is important to note that the plumbotectonics model was not designed to solve the Pb paradox. Thus, in the first and second models (Zartman and Doe, 1981) Pb evolution started with an arbitrary isotope composition 4 Byr ago, whereas in the fourth model (Zartman and Haines, 1988) Pb evolution began 4.45 Byr ago from the Canyon Diablo composition (100 Myr after terrestrial accretion).

Fig. 5.34. Pb)Pb isochron diagram showing isotopic evolution of the four reservoirs computed by the plumbotectonics model. After Doe and Zartman (1979).

 

            The curved arrays inherent in the two-isotope system make it hard to evaluate the goodness of fit of conformable Pb data to terrestrial Pb isotope evolution models, as well as making conceptual understanding of the system difficult. Therefore, Manhes et al. (1979) developed an alternative presentation which overcame the problem of non-linearity. However, their formulation was rather complex, which detracted from its usefulness. To simplify the data presentation, Albarede and Juteau (1984) analysed each of the U)Pb systems (and Th)Pb) on a separate diagram of Pb isotope ratio against time, as is done for Nd (section 4.2). However, because of the effectively finite half-lives of U and Th relative to the age of the Earth (unlike Nd), the time dimension must be presented as the exponent (Fig. 5.35) in order to achieve linear evolution lines.

Fig. 5.35. Exponential plot of 206Pb/204Pb evolution against time, to test the fit of galena sources to a linear isotope evolution trend. After Albarede and Juteau (1984).

 

            Albarede and Juteau utilised a combined galena data set from Stacey and Kramers (1975) and Cumming and Richards (1975), with the addition of the galena data from Isua (Appel et al., 1978). This considerably strengthens the data-base, since it improves the constraints on early terrestrial Pb evolution. Fitting a linear growth line to the data (equivalent to a constant source : value) causes this line to intersect the Canyon Diablo Pb composition at an apparent age of 4.4 Byr, in close agreement to Doe and Stacey (1974) and Manhes et al. (1979). This is seen most clearly for 206Pb (Fig. 5.35) but also, albeit less strongly, for 207Pb. However, terrestrial accretion at a date as late as 4.4 Byr is inconsistent with the 4.55 Byr age of differentiated meteorites (section 3.2.4). Therefore, as an alternative, an Early Archean reservoir with lower : value was postulated. Hence the model of Stacey and Kramers is supported, but due to noise in the data set, continuous Pb isotope evolution models could not be ruled out.

 

            This situation remained essentially unchanged until some other research groups started to re-examine the behaviour of the U–Pb system during terrestrial accretion. For example, Allegre et al. (1995b) pointed out that the Bulk Silicate Earth (BSE) has a much higher : value (ca. 9) than bulk chondrites (ca. 0.7), which are regarded as equivalent to the Bulk Earth composition. This difference could be due to Pb volatilisation during terrestrial accretion, or to Pb partition into the Earth’s core. However, comparison of the partition coefficients of Pb and other siderophile–chalcophile elements suggested that core formation was the main cause of the high : value in the BSE (e.g. Galer and Goldstein, 1996).

 

            If this model is correct, terrestrial Pb isotope evolution can be constrained by the Hf–W extinct nuclide system (section 15.5.4). The Hf–W couple has similar chemical affinities to the U–Pb couple, in that both parents are lithophile (rock loving) and both daughters are siderophile (Fe core loving). The difference is that the parent isotope of Hf had a short half-life, which caused it to become extinct over approximately the same time period as that over which the Earth’s core developed. Therefore, W isotope analysis can be used to estimate the time of terrestrial core formation.

 

            Most Hf–W evidence appeared to favour late core formation, about 100 Myr after the main stage of terrestrial accretion (section 15.5.4). This model would then be consistent with the simplest interpretation of the Archean galena compositions (Fig. 5.35), involving a period of low : values in very early Earth history. Therefore, it was argued that a period of core formation lasting for ca. 100 Myr could largely explain the Pb paradox, since it would cause the BSE, and hence average MORB, to lie to the right of the geochron (section 6.3.1).

 

            Kramers and Tolstikhin (1997) challenged this explanation, arguing that delayed core formation could only explain one third of the Pb paradox. Instead, they further developed the Plumbotectonics model by allowing enhanced uranium recycling to the upper mantle over the last 1.5 Byr. This was caused by mobilisation of uranium in the sedimentary environment as a result of the gradual development of an oxygenated atmosphere. This modification of the Plumbotectonics model also improves the solution to a ‘second’ Pb paradox, also called the ‘kappa conundrum’ (section 6.3.3).

 

            Kramers and Tolstikhin’s rejection of the late-core model as an explanation of the Pb paradox turned out to be somewhat inspired, because subsequent W isotope work (section 15.5.4) implies significantly earlier core formation than the previous studies. Core formation can still have some effect on Pb if it is combined with a late giant impact, but the Plumbotectonics (crustal recycling) model must again be called upon to ‘solve’ at least part of the ‘Pb paradox’.

 

            It is concluded that the Kramers and Tolstikhin version of Plumbotectonics is probably the most realistic terrestrial Pb isotope evolution model yet developed, but it still has significant limitations. Like all of the earlier models, it assumes direct recycling of crustal material into the MORB source, and also assumes no exchange of material with the lower mantle. The combination of these features causes the MORB reservoir in the model to have a somewhat unusual trajectory (e.g. Kamber and Collerson, 1999). A fully realistic model would need to direct a fraction of recycled crust into the lower mantle. After 1)2 Byr of isolation in the deep mantle, such reservoirs generate mantle plumes that mix with and fertilise the upper mantle reservoir.

 

 

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