The Hadean era 44 to 38 Gyr ago

To reconstruct the rate of mantle fractionation in the Hadean era, we have assumed that this rate (equal to the rate of MORB + OIB production) and the corresponding "degassing" flux of liquid silicates was intense in early Earth history and then decreased gradually through time down to the present-day value. Taking into account (1) that no significant energy input from external sources (impacts) into the Earth is expected (at least after the late bombardment event at ~ 3.9 Gyr ago), (2) that radioactive heat-producing isotopes are decaying and (3) that the Earth is gradually releasing energy acquired during accretion and core segregation, this assumption appears to be reasonable. We varied the rate of mantle-melt production (and adequate degassing) through time until the calculated present-day mantle ratio for 136Xe(Pu)/136Xe(U) approached the observed value (Table 28.3). In the reference solution thus obtained, the time-averaged rate of mantle fractionation and the attendant flux of silicate melt are ~ two orders of magnitude greater during the Hadean era than they are at present.

Extremely efficient mantle degassing is a very robust result, constrained by the low 136Xe(Pu)/136Xe(U) ratio in mantle xenon. The effective mantle 130Xe-depletion factor is of the order of 10-6, and a similar value was derived by Tolstikhin and Marty (1998).

Because mantle convection governs post-accretion melt generation and degassing, the high rate of degassing during the first 1 Gyr or so of Earth history indicates vigorous convection within this reservoir. Energy released in the course of accretion and core formation and still available in the Earth was probably the major moving force of this early intense convection and degassing. However, the degassing rate could also have been enhanced by late impacts (between 4.5 and 3.9 Gyr ago) that disrupted the crust, leading to the uplift of hot mantle material, melting and degassing. Such effects could have been considerable even if the total flux of impactors was small (Pritchard and Stevenson, 2000). Correspondingly, in this model we assume that the late bombardment caused intense melt production and degassing.

Geological evolution (from 4.0 Gyr ago to the present): Sm-Nd, Lu-Hf and

Rb-Sr isotope systematics

The rate of crustal growth and mass fluxes into and from the crust are very similar to those constrained by the Th-U-Pb systematics (Kramers and Tolstikhin, 1997). A similar crustal-growth curve was derived by Jacobsen (1988) and Azbel and Tolstikhin (1988). Other parameters that govern the distribution of the elements of interest among the three reservoirs are the melt fractions in the mantle and subduction fractionation zones and the respective partition coefficients.

The mean fraction of liquid silicates in the mantle fractionation zone (MFZ) during accretion, 0.3, is constrained by the modelling of siderophile-element partitioning into the metal phase (Kramers, 1998). Afterwards this fraction smoothly decreases to the present-day value, ~ 0.1, derived from models of mantle melt generation at ridges (e.g. McKenzie and O'Nions, 1991).

The melt fraction in the subduction fractionation zone (SFZ) appears to be a more complicated parameter. Enhanced values, ~ 0.1, were derived for the major-element compositions of arc volcanics (Chapter 25). These values do not allow sufficient fractionation of the melts produced and their enrichment in highly incompatible elements. This is illustrated by the Rb/Sr ratio of modern arc basalts, ~ 0.04 (well below the mean crustal value, 0.15; see Tables 24.1 and 26.3). To reconcile the crustal budget of highly incompatible elements, small melt fractions in the subduction fractionation zone have been invoked: 0.005 (Jacobsen and Wasserburg, 1979), 0.01 (Albarede, 1998a), 0.015 (Azbel and Tolstikhin, 1988; Kramers and Tolstikhin, 1997; Nagler and Kramers, 1998). An estimate inferred from our model, 0.01, is similar to those above.

A possible interpretation of this result is that these small melt fractions reflect a difference between the total amount of melt that was generated at subduction zones and underwent crystallization differentiation and a mafic cumulate that was delaminated and sank back into the mantle (Section 26.7). Although delamination was been included in the modelling, in a simple batch-melting model the enrichment of incompatible elements in a small primary melt fraction is similar to that for a large melt fraction when followed by crystal fractionation giving the same final fraction of melt. The result is the accepted crustal composition for the elements of interest. The discrepancy discussed above implies that delamination is substantial; the melt flux into the crust should be ~ 10 times that shown in Fig. 28.2, of which 90% would have been delaminated. Further, the model-derived value of the upper-crustal erosion flux, mainly constrained by Pb and U recycling to solve the second lead paradox, exceeds the value indicated by direct observations on sediment subduction by a factor ~ 2 (Section 25.1). Because the model does not include a delamination flux from the crust, the reference solution generates a more intense sedimentary

Age, Gyr

Age, Gyr

Fig. 28.2 Mass fluxes inferred from the reference model solution. The accretion mass flux is constrained by the Earth's mass and the Earth accretion time scale (obtained from the Hf-W systematics, e.g. Section 18.3), and by the mass of D" (which is similar to the present-day value, Table 28.3), its formation time scale (~ 70 Myr, from mantle xenology, e.g. Kunz et al., 1998) and the fraction of chondritic material in D" (0.2, see the footnotes to Table 28.3); correspondingly, the flux of proto-terrestrial material constitutes one-fifth of the total flux into D". The core-segregation mass flux is constrained by the core mass and the accretion time scale, with a tailing-off constrained by the noble-metal abundances in the mantle (Chapter 18). The melt production in the mantle is constrained by the core segregation rate for the first ~ 100 Myr and by mantle xenology thereafter (Section 27.5); this flux in turn constrains the mantle fractionation rate via the melt fraction coefficient (see footnote 11 to Table 28.2). The mass flux from D" is constrained by the mantle noble-gas systematics (Section 27.4). The crustal-growth flux (right-hand bottom corner of the figure) and the erosion flux (not shown) have been adopted from the Th-U-Pb model (Kramers and Tolstikhin, 1997). After Tolstikhin et al. (2006), © Elsevier Science 2006, reproduced by permission.

flux instead. Even though the delaminated material is predicted to be depleted, the delamination/sediment flux ratio, ~ 20, implies that a comparable rate of U removal could be associated with delamination.

The model-derived abundances of Lu, Hf, Sm and Nd, along with the isotopic compositions of the daughter elements in differentiated reservoirs rely on the melt-solid partition of these elements. The REE bulk partition coefficients are reasonably well constrained for mantle mineralogy (see Table 24.2 and its footnotes). For a mantle peridotite residue with 3% garnet, we used D(Sm) = 0.065 and D(Nd) = 0.03 (very similar to the values inferred by Jacobsen and Wasserburg (1979) for fractionation processes occurring in both MFZ and SFZ zones. This gives good agreement between the calculated and observed abundances of the species of interest in the accessible reservoirs, the mantle and the continental crust (Table 28.2 and Fig. 27.13). Because D" largely consists of fractionated material that was separated from the bulk silicate Earth very early, its time-integrated isotopic effect on the mantle is large, e143 ~ +5. continuous extraction of the continental crust over time leads to the value e 143 ~+4 for the mantle, ending up with a present-day total e 143 ~ +9 (Figs. 27.2(a), 27.18).

The bulk partition coefficient for Hf, like those for Sm and Nd, is considered in the model to be identical in both mantle fractionation processes occurring in MFZ and SFZ (Fig. 28.1). It is adjusted to produce a crustal Hf/Nd ratio of 0.18 (Table 26.3). The value derived from the model is D(Hf) = 0.0385. The partition coefficient for Lu in the mantle fractionation zone MFZ, D(Lu, MFZ) = 0.190, is adjusted to obtain a somewhat Lu-enriched mantle, so that the mixing line between the mantle and crustal end-members approaches the regression of the observed terrestrial Hf-Nd array in Fig. 27.13. This enhanced value leads to relatively low Lu/Hf ratios and ultimately low e176 values in D" (Table 28.2). This could reflect deep partial mantle melting (in the presence of garnet) in the early, hotter, mantle, when D" was formed. Such partitioning of Hf allows an explanation of the Hf-Nd isotope relationships (Fig. 27.13).

The bulk partition coefficients for Sm, Nd, Lu and Hf listed above can be independently derived for a melt equilibrated with mantle peridotite consisting of Ol = 67%, Opx = 20%, cpx = 10% and Garnet = 3%, applying the mineral partition coefficients from McKenzie and O'Nions (1991). A similar abundance of garnet in a mantle mineral assemblage (a few per cent) was derived by Blichert-Toft and Arndt (1999) from their study of how mantle fractionation causes enhanced initial 176Hf/177Hf ratios in ancient komatiites.

The subduction-fractionation bulk partition coefficient for Lu, 0.145, fits the mantle and crustal end-members, so that the mean e176 values approach the regression line of the terrestrial Hf-Nd array (Fig. 27.13).

The Rb and Sr isotope abundances in the two accessible reservoirs, the mantle and crust (Table 28.2), are in overall agreement with observation (chapter 27). Thus, Jacobsen (1988) inferred from a layered mantle model that Sr = 15 ppm and Rb/Sr = 0.022 for the MORB-source mantle. Recently Workman and Hart (2005) suggested a much lower Rb/Sr ratio, 0.0065. The reason for the difference is that in the latter model a late start for mantle depletion is assumed (3 Gyr), based on the concept of gradual crustal growth. Further, Workman and Hart (2005) assumed the

Table 28.2 Calculated abundances ofSm, Nd, Lu, Hf, Rb and Sr isotopes in the principal terrestrial reservoirs: D" (DDP), the mantle (DMM) and the continental crust (CCR) together with the solid-melt bulk partition coefficients11

Table 28.2 Calculated abundances ofSm, Nd, Lu, Hf, Rb and Sr isotopes in the principal terrestrial reservoirs: D" (DDP), the mantle (DMM) and the continental crust (CCR) together with the solid-melt bulk partition coefficients11

DDP

DMM

CCR

Parameter

Dimension

a

b

c

1

mass

1025 g

24.5

372

2.26

2

Nd

PPm

5.4

0.86

22.6

3

147Sm/144Nd (Sm/Nd)

ratio

0.17

0.22

0.115

(0.28)

(0.37)

(0.19)

4

e143

ratio

-15

9

-17

5

Hf

PPm

1.150

0.203

4.370

6

176Lu/177Hf (Lu/Hf)

ratio

0.021

0.040

0.012

(0.15)

(0.29)

(0.087)

7

e176

ratio

-35

16.4

-20

8

Sr

PPm

83

14

360

9

87Rb/86Sr

ratio

0.092

0.045

0.28

(Rb/Sr)

(0.03)

(0.015)

(0.1)

10

87Sr/86Sr

ratio

0.7048

0.7029

0.7102

I Mass ratios are shown within parentheses.

2b Comparable with 0.8 ppm from McKenzie and O'Nions (1991), 0.77 ppm from Nagler and Kramers (1998), 0.7 ppm from Salters and Stracke (2004, Table 24.1) and somewhat above 0.58 ppm from Workman and Hart (2005).

2c 3c Calculated crustal Nd concentrations and Sm/Nd, Hf/Nd ratios are within the range of estimates suggested by different authors (see Table 11 in Rudnick and Fountain, 1995). 3b Indistinguishable from the ratio derived by Chauvel and Blichert-Toft (2001) from MORB-source mantle-melting models.

4,7 Present-day SOS ratios (to calculate e values): 143Nd/144Nd = 0.512 638 and 176Hf/177Hf = 0.282772.

4b,c'lb,c The e -coordinates of mantle and crustal end-members lie on the Hf-Nd isotope terrestrial array regression line (Fig. 27.13). 143Nd/144NdDMM = 0.513 13 (e143 = +9) as in Workman and Hart (2005); 176Hf/177HfDMM is in between estimates presented by these authors, e176 = +17.6, and by Salters and Stracke (2004), e176 = +15.5.

6b Same as inferred by Blichert-Toft and Arndt (1999) for the source of ancient komatiites. Chauvel and Blichert-Toft (2001) derived Lu/Hf = 0.28 from MORB-source mantle-melting models. 6c The model-derived 176Lu/177Hf ratio is indistinguishable from the average ratio in sedimentary rocks, 0.0117, which could be a proxy for the continental crust (see Table 2 in Vervoort et al., 1999). 8c Slightly above the value in Table 26.3. 9b Slightly above that proposed by Salters and Stracke (2004).

9c Between those suggested by Jacobsen and Wasserburg (1979) and Taylor and McLennan (1985). 10b Corresponds to the MOR-segment-arranged data base (307 MOR segments, totally 1300 ratios) of Su (2002), 87Sr/86Sr = 0.702 85 ± 0.000 39 (±1a). Salters and Stracke (2004) and Workman and Hart (2005) suggested somewhat lower ratios, 0.7027 and 0.70263, respectively. 10c Within the limits suggested for the total continental crust by Jacobsen and Wasserburg (1979).

II Solid-melt bulk partition coefficients are as follows. In the mantle fractionation zone (MFZ, Fig. 28.1): Nd, 0.025; Sm, 0.065; Hf, 0.0385; Lu, 0.19; Sr, 0.033; Rb, 0.001. In subduction-related fractionation (SFZ, Fig. 28.1): Nd, 0.03; Sm, 0.065; Hf, 0.0385; Lu, 0.145; Sr, 0.033; Rb, 0.0002. The model melt fraction in the mantle fractionation zone is a linear function of time decreasing from 0.3 at t = 0 (the start of accretion) to 0.1 (at the present time); it is a constant equal to 0.01 in the subduction fractionation zone (see the main text for a discussion).

From Tolstikhin et al. (2006), © Elsevier Science 2006, reproduced by permission.

depletion of a relatively small portion of the mantle only. Our reference-solution ratio, 0.015, is intermediate between the two models. A low Sr for the mantle was obtained from the Sr-Ce correlation in MORB samples and a Ce concentration derived from mantle-melting models (Workman and Hart, 2005). However, in other investigations of mantle melting (e.g. McKenzie and O'Nions, 1991) Ce (and Sr) concentrations for the depleted mantle ~ 1.5 higher have been adopted, closer to our estimate.

The model Sr concentration and the Rb/Sr ratio in the bulk continental crust shown in Table 28.2 are close to the value [Sr] = 325 ppm of Rudnick and Fountain (1995) and the value Rb/Sr = 0.12 of Taylor and McLennan (1985) respectively.

Geological evolution from 4.0 Gyr until the present: the noble gases

According to the reference solution of our model, the D" layer is an important reservoir of the radioactive heat-generating elements, U, Th and K: the model-derived abundances of these elements in D" are ~ 20% of the BSE amounts (Table 28.3). The high abundance of K means that the amount of 40Ar* hidden in D" allows a terrestrial inventory of the 40K-40Ar* systematics having K/UBSE = 12 000. The abundances of light solar noble gases are constrained by a low (U and Th)/3He ratio, indicating an almost-solar isotope composition of He. The 3He concentration in the model terrestrial regolith is about 0.01 times that observed in lunar ilmenites (Benkert et al., 1993). From the concentrations of other solar nuclides implanted in the terrestrial regolith can be derived (see the entries for 4He/3HeSiN, 36Ar/3HeSiN and 130Xe/3HeSiN in Table 28.1). The contribution of solar-particle-implanted material in the flux from D" into the mantle is less than 0.05% of the Earth's mass over geological time. A prediction (which also follows from the model of Tolstikhin and Marty, 1998) is that very primitive He and Ne may be found in plume-derived samples, in which a D"-derived solar-like component prevails over mantle radiogenic and recycled atmospheric noble gases.

The D" layer is the source of early produced 129Xe(I) and 131-136Xe(Pu) in the solid Earth. A high 129Xe(I)/136Xe(Pu) ratio, inferred for mantle xenon, constrains the early formation of the layer (Fig. 28.2). The contribution of a heavy-noble-gas-enriched unfractionated Q component (Table 28.3) is derived using the ratio of 129Xe(I) and unfractionated 130Xe, ~ 12, as observed in CO2-gas Xe (Phinney et al., 1978; Tolstikhin and O'Nions, 1996; Caffee et al., 1999); our reference solution gives a slightly higher ratio. The concentrations of Q gases in D" predicted by the reference solution (Table 28.3) appear to be quite reasonable: they are a factor ~ 103 lower than those observed in C1 chondrites (Fig. 11.5). The mixing proportion is XeQ/XeSIN = 340, and Q noble gases contribute ~ 0.4 of the 36ArQ in D". The occurrence of Q noble gases in D" allows a more general

Table 28.3 Calculated abundances of noble-gas species13'14 and parent elements in the principal terrestrial reservoirs

D" Mantle Cont. crust

D" Mantle Cont. crust

Table 28.3 Calculated abundances of noble-gas species13'14 and parent elements in the principal terrestrial reservoirs

Parameter

Dimensions

a

b

c

1

Mass

1025 g

24.5

372

2.26

2

U

ppb

71.5

7.7

1300

3

3 He

cm3 STP g-1

2.5 x

10-

■7

6.7 x

10-

11

5 x 10-12

4

4 He/3 He

ratio

2.8 x

103

8.5 x

104

1 x 108

5

40 Ar

cm3 STP g-1

6.7 x

10-

5

2.3 x

10-

6

1.7 x 10-4

6

40Ar/36Ar

ratio

2.9 x

103

4.8 x

104

7

130Xe

cm3 STP g-1

1.4 x

10-

11

3.5 x

10-

14

0

8

129Xe/130Xe

ratio

17.5

7.6

9

136Xe/130Xe

ratio

2.47

2.54

10

136Xe(U)

cm3 STP g-1

2.3 x

10-

13

1.2 x

10-

14

1.1 x 10-12

11

129Xe(I)/136Xe(U)

ratio

664

4.5

0

12

136Xe(Pu)/{136Xe(U) +136Xe(Pu)}

ratio

0.97

0.28

0.02

1a The initial model D" mass is 2.46 x 1026 g, so only 6% of the D" mass (< 0.05% Me) was entrained by mantle convective flow and maintained the D"-sourced noble gas flux through the mantle in the course of Earth history.

2a,b,c The crustal concentration of U is equal to that suggested by Weaver and Tarney

(1984) and is ~ 10% below the estimate of Rudnick and Fountain (1995). The mantle U concentration is the same as that derived from U-Th-Pb modelling by Kramers and Tolstikhin (1997) for the depleted upper mantle.

3a This concentration of 3HeDDP corresponds to 3HesiN = 1.25 x 10-6 cm3 STP g-1 implanted in the "terrestrial regolith", e.g. slightly below the concentrations actually observed in solar-noble-gas-rich meteorites (e.g. Acfer, Table 11.3). 3b The model-derived [4He]DMM and [3He]DMM are somewhat higher than those derived for layered mantle models (Marty and Tolstikhin, 1998), because of the higher U and Th concentrations and their mantle residence time.

3c [3He]CCR in this cell is computed as a product of U and Th decay in the crust; this concentration and the 4He/3He ratio below (cell 4c) give the mean (U and Th)-He age of the continental crust as 1.7 Gyr, similar to the mean K-Ar age: for simplicity the crustal degassing coefficients for radiogenic Ar and He were assumed to be equal. 4a All 4He/3He and 21Ne/22Ne ratios, observed in plume-derived rocks, minerals and fluids, can be obtained by mixing of noble gases from D", plume-source and DMM. 5a The portion of terrestrial 40Ar* generated and preserved in D" amounts to 24% of the terrestrial inventory. Along with the atmospheric 40Ar* = 3.69 x 1022 cm3 STP, the values in cells (5a, b, c) add up to 6.55 x 1022 cm3 STP, which is 88% of the total40Ar* generated by terrestrial potassium; 12% of terrestrial40 Ar* was lost along with 129Xe(I) and 136Xe(Pu). 6b The 40Ar/36ArDMM ratio results mainly from 36ArATM recycling into the mantle. 7a [130Xe]Q,DDP is determined from the model-derived [129Xe(I)]DDP and Xe isotope sys-tematics in CO2-gas xenon (cell 8a). In turn, [130Xe]Q,DDP and [3He]SIN determine the mixing proportion of Q and solar initial noble gas components. The model-derived ratio of 130XeQ/130XeSiN = 340, and the ratio of 36ArQ/36ArSiN = 0.39. [130Xe]Q,DDP is a factor ~ 50 below those observed in bulk carbonaceous chondrites (Fig. 11.5).

solution of the model, which now does not require the degassing of Q noble gases from a chondrite matter at a late stage of accretion.

The values of the flux from D" into the mantle, the mantle degassing flux and the recycling rate of atmospheric Xe and Ar were adjusted to obtain model He, Ar and Xe isotope compositions and a 3He-concentration (Table 28.3) similar to the values accepted for the MORB-source mantle (Section 27.4). Atmosphere recycling into the mantle is essential: without it, the 40Ar/36Ar ratio derived for the mantle Ar could be as high as ~ 300 000.

As mentioned above the crust is not an important reservoir for the terrestrial inventory of radiogenic noble gases. Setting the value of the degassing coefficient £ccR,ATM to 0.5 Gyr-1 yields a mean 40Ar-40K age for the continental crust that is ~ 30% younger than the Sm-Nd age, 2.2 Gyr. Then the total present-day amount of radiogenic 40Ar* in the partially degassed crust is ~ 6% of the total terrestrial inventory of this nuclide. The model-derived crustal and mantle concentrations of U and other radioactive elements (Table 28.3) are in reasonable agreement with the available estimates (Table 17.1).

Summarizing, the reference solution shows that a D" layer of the type assumed in this model enables one to resolve terrestrial paradoxes of both solar and radiogenic noble gases and also of the inventory of incompatible elements (chapter 19). As D" was formed from slightly fractionated (enriched) matter and was isolated very early, it acts as a second enriched reservoir (in addition to the continental crust). The two reservoirs balance, within the framework of the chondritic Earth model, a wholly depleted mantle in terms of incompatible-element concentrations and the

Sm-Nd, Lu-Hf and Rb-Sr isotopic systematics. <-

ib 130xe in the present-day mantle is mainly air-derived recycled Xe (Tolstikhin and O'Nions, 1996; Tolstikhin and Marty, 1998).

8a Similar to the ratio of 129Xe over the light-isotope-enriched fraction of 130Xe observed in CO2-gas xenon (Tolstikhin and O'Nions, 1996).

8b'9b These ratios fit the observed 129Xe/130Xe versus 136Xe/130Xe mantle correlation (Fig. 27.8).

12a Xe(Pu) is by far the most important fission Xe component in D". 12b Contribution of Xe(Pu) as proposed by Kunz et al. (1998).

13 Noble gases are treated as incompatible elements with a solid-melt bulk partition coefficient = 0.001 for all noble gas species. In the course of mantle magmatism (for which the rate is shown in Fig. 28.2) all noble gases are transferred from the respective melt flux into the atmosphere and only this degassing flux is envisaged in the model.

14 Noble-gas recycling from the atmosphere into the mantle is treated as a flux proportional to the atmospheric abundances, with constant coefficients, 0.001 Gyr-1 for Ar and 0.004 Gyr-1 for Xe (see Tolstikhin and Marty, 1998, and Ballentine and Barfod, 2000, for a detailed discussion of the noble-gas-recycling contamination problem).

From Tolstikhin et al. (2006), © Elsevier Science 2006, reproduced by permission.

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