Canadian Journal of Earth Sciences Published by THE NATIONAL RESEARCH COUNCIL OF CANADA VOLUME 9 DECEMBER, 1972 NUMBER 12 Developnlent of the Early Continental Crust. Part 1. Use of Trace Element Distribution Coefficient Models for the Protoarchean Crust DENIS M. SHAW Deyurtment of Geology, McMaster University, Hamilfon, Ontario, Cunuda Received May 29, 1972 Revision accepted for publication August 11, 1972 The original continental crust developed as the residue from fractional crystallization of the mantle-crust system. Using measured distribution coefficients for K, Rb, Ba, Sr, La, Ce, Eu, Yb, and Ni, several crystallization models are tested for conformity with regional geochemical estimates of continental crustal composition. In spite of the uncertainties and approximations the predicted concentrations agree reason- ably well with observation, except in the case of Yb. La crofite continentale originelle s'est d6veloppCe comme le rCsidue de la cristalisation fractionnde du systkme crocte-manteau. L'utilisation des coefficients de distribution mesurCs pour K, Rb, Ba, Sr, La, Ce, Eu, Yb, et Ni, a permis de vCrifier la conformit6 de plusieurs modkles de cristalisation avec les Cvaluations gCochimiques rdgionales de la composition de la crofite continentale. MalgrC les incertitudes et les approximations, les concentrations prCdites se conforment raisonnablement bien avec l'observation, sauf dans le cas du Yb. [Traduit par le journal] Introduction Theories of the evolution of the outer parts of the earth, published prior to 1966, require radical rcthinking in the light of recent develop- ments in plate tectonics and sea-floor spreading. Hart ( 1969), Ringwood ( 1969), Turekian ( 1963), and others have indicated some of the problems, and Armstrong (1968) has pro- posed a model for crustal recycling to accom- modate the isotopic evidence. Concurrently with the geophysical revolution of the last decade, a resurgence of interest in Prccarnbrian terranes has brought to light (An- haeusser 1970, Anhrieusser et al. 1969, Clifford 1969, Coodwin 1968) important differences betwcen thc continental crust of the present day and that of Archean times, while others (e.g. Lambcrt and Heier 1968, Spooner and Fair- bairn 1970) have invcstigated vertical compo- sition changes in the Precambrian crust. Measurements of distribution coefficients be- tween solid and liquid silicate phascs have also recently become possible (see later) and now permit some very rough quantitative tests of models proposed (e.g. Gast 1968) to account for the accumulation of granitophile elements such as K, Rb, U, etc. near the earth's surface. The present paper attempts to synthesize re- sults in these diverse fields into a model of evolution of the continental crust. Starting with the simplistic assumption that the compositions of the different zones of the earth are known, a hypothesis for the origin of the primordial crust will be developed. A second paper will deal with the evolution of the crust after its initial consolidation. Element Abundances in the Earth The abundances and abundance ratios of granitophile or pegmatitic elements such as K, Rb, U, and the rare earth elements (REE) help intcrpret the evolution of the earth (e.g. Cast 1960, Haskin et ul. 1966, Taylor 1964). So also do the isotopic abundances of Sr, Pb, Ar, Canadian Journal of Earth Sciences, 9, 1577 (1972) Can. J. Earth Sci. Downloaded from www.nrcresearchpress.com by Entomology on 09/18/12 For personal use only.
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Canadian Journal of Earth Sciences Published by THE NATIONAL RESEARCH COUNCIL OF CANADA
VOLUME 9 DECEMBER, 1972 NUMBER 12
Developnlent of the Early Continental Crust. Part 1. Use of Trace Element Distribution Coefficient Models for the Protoarchean Crust
DENIS M. SHAW Deyurtment of Geology, McMaster University, Hamilfon, Ontario, Cunuda
Received May 29, 1972 Revision accepted for publication August 11, 1972
The original continental crust developed as the residue from fractional crystallization of the mantle-crust system. Using measured distribution coefficients for K, Rb, Ba, Sr, La, Ce, Eu, Yb, and Ni, several crystallization models are tested for conformity with regional geochemical estimates of continental crustal composition.
In spite of the uncertainties and approximations the predicted concentrations agree reason- ably well with observation, except in the case of Yb.
La crofite continentale originelle s'est d6veloppCe comme le rCsidue de la cristalisation fractionnde du systkme crocte-manteau. L'utilisation des coefficients de distribution mesurCs pour K, Rb, Ba, Sr, La, Ce, Eu, Yb, et Ni, a permis de vCrifier la conformit6 de plusieurs modkles de cristalisation avec les Cvaluations gCochimiques rdgionales de la composition de la crofite continentale.
MalgrC les incertitudes et les approximations, les concentrations prCdites se conforment raisonnablement bien avec l'observation, sauf dans le cas du Yb. [Traduit par le journal]
Introduction Theories of the evolution of the outer parts
of the earth, published prior to 1966, require radical rcthinking in the light of recent develop- ments in plate tectonics and sea-floor spreading. Hart ( 1969), Ringwood ( 1969), Turekian ( 1963), and others have indicated some of the problems, and Armstrong (1968) has pro- posed a model for crustal recycling to accom- modate the isotopic evidence.
Concurrently with the geophysical revolution of the last decade, a resurgence of interest in Prccarnbrian terranes has brought to light (An- haeusser 1970, Anhrieusser et al. 1969, Clifford 1969, Coodwin 1968) important differences betwcen thc continental crust of the present day and that of Archean times, while others (e.g. Lambcrt and Heier 1968, Spooner and Fair- bairn 1970) have invcstigated vertical compo- sition changes in the Precambrian crust.
Measurements of distribution coefficients be- tween solid and liquid silicate phascs have also
recently become possible (see later) and now permit some very rough quantitative tests of models proposed (e.g. Gast 1968) to account for the accumulation of granitophile elements such as K, Rb, U, etc. near the earth's surface.
The present paper attempts to synthesize re- sults in these diverse fields into a model of evolution of the continental crust. Starting with the simplistic assumption that the compositions of the different zones of the earth are known, a hypothesis for the origin of the primordial crust will be developed. A second paper will deal with the evolution of the crust after its initial consolidation.
Element Abundances in the Earth The abundances and abundance ratios of
granitophile or pegmatitic elements such as K, Rb, U, and the rare earth elements (REE) help intcrpret the evolution of the earth (e.g. Cast 1960, Haskin et ul. 1966, Taylor 1964). So also do the isotopic abundances of Sr, Pb, Ar,
Canadian Journal of Earth Sciences, 9, 1577 (1972)
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1578 CANADIAN JOURNAL OF EARTH SCIENCES. VOL. 9, I972
and the abundances of atmosphere and hydro- sphere constituents, considered later.
It will be assumed initially that the abun- dances of metallic elements in certain rocks and in meteoritic metal phase may be taken as equal to their abundances in various parts of the earth. It will also be assumed that the earth and meteorites had an origin in primordial solar material with common values for the isotopic ratios X7Sr/x6Sr, 20Tb/20Tb, 207Pb/204Pb, and 20TPb/HPb, some 4.5i x 109 years ago.
The elements chosen are mostly granitophile, i.4. they may be expected to be enriched in crustal rocks with respcct to the mantle (ex- cept pcrhaps Sr, Yb, and Wi, q.v.). U, Th, Pb, K, Rb, and Sr were chosen because of their significance to isotope petrology and heat-flow studies. In addition La. Ce, Eu, and Yb were taken to represent the KEE. Ba and TI were added, in spitc of sparse data, because of their coherence with K and because earlier studies (Gast 1960, Taylor 1 964) suggested they de- serve fuller study. Other elements which may provide critical evidcnce, when better docu- mented, include Li, W, Nb, and Sn.
The elements chosen are also lithophile, with the notable exceptions of Ni, Pb, and T1, whose distributions may be markedly influeinced by sulfur abundance behavior.
Table 1 presents estimates of elemental abuindances in different parts of the earth, and in certain meteorites. The upper continental crust (UCC) is represented by measurements on Precambrian surface exposures or appro- priate intermediate-silicic igneous rocks. The lower continental crust (LCC) is assumed to be dioritic but not basaltic (Ringwood and Green 1964), with abundances similar to high- grade granulite facies terranes now exposed at the surface: data were not available for this zone for '33, and are not satisfactory for Pb. Following Grecn et a&. ( l972), the LCC abun-
E arc taken as the same as in the UCC. Whether the lower crust does in fact consist of granulite facies rocks is controversial. but heat-flow evidence supports the lower abundances of U, Th, and K. For example, Tilling and Gottfried (1969) show that 35 km of Boulder batholith surface rocks would pro- duce the observed heat-flow of 2.2 pcal/cm%, yet the crustal thickness is 45 km indicating that the U, Th, and K abundances must de-
crease with depth. Oceanic crust (OC) is taken as equivalent to abyssal tholeiitic basalt, and for the mantle (M) values appropriate to lherzolite and dunite have been chosen. The earth's core (C) is estimated by abundances in meteoritic metallic phase, but few data are available.
The theory has recently been raised that much of the earth's K, Rb, and Cs occur in the core, depending on their possible chalcophile behavior and the possible occurrence of sub- stantial amounts of S in the core (Murthy and Hall 1970, Hall and Murthy 1971, Lewis 1971). In the absence of strong supporting evidence this theory will not be further con- sidered here.
Many assumptions and simplifications are embodied in Table 1. The nature of the lower continental crust is controversial, but the abun- dances are probably of the right order of magnitude. The variations in clement abun- dances between dunite and peridotite are con- siderable, and the upper mantle may consist of either or both primary or residual (de- pleted) combinations. Extrapolation af such values to the whole mantle may appear unwise in the extreme, but this will be explored later. Similar criticisms apply to abundances in the core.
The last line of Table 1 gives overall mantle/ crust abundances calcuBated from the estimates for different earthshelts, and may be compared with models such as basaltic achondrites (ACH) and ordinary chondrites (CH) . The relative merits of these models has recently been assessed by Larimer ( 197 1 ) . The values chosen here under ACH accord with Larimer's eucrites for K, Rb, Ba, Sr, and La but are 2~ lowcr than his for U and Th: values given here under CH agrce with Larimer's chondrites in the case of K, Rb, Ba, Sr, La, U, and Th. The estimates. co, here of bulk earth composition agree with Larimer's (similar) estimate within a 2x factor for K, Rb, Ba, Sr, U, and Th, and within a 4x factor for La: other elements can- not be compared. This relatively good agree- ment is encouraging, but it is mitigated some- what by the fact that much the same data was used in Larimer's model as here.
As with Larimer's conclusions, achondrites provide a bctter earth-model for K, Rb, and REE (except Yb): chondrites are better for
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TABLE 1. Concentration of some elements in various parts of the earth -- -- -- --
Mass Cr Th (lOz5g) (ppm) References (PPm) References
--
UCC 0.944 2.5 1, 2, 32, 34 10 1, 2, 32 LCC 0.944 0.4 19, 34 2 19, 34 OC 0.479 0.1 3 ,4 0.2 3 ,4 M 407.2 0.02 5, 6 0.0: 5, 6 C 187.6 3 x 10-z 6 10 - 6 ACH - 5.0 x 10- 1 ,22 0 .2 1, 23 CH -- 1.1 x I ,22,29
10. Hess 1964 1 I . Hamilton and Mountjoy 1965 12. Stueber and Murthy 1966
crust + mantle.
carbonaceous chondrites. 13. Morgan and Goode 1966 14. Pinson et al. 1958 15. Taylor 1964 16. Murthy 1964 17. H e m and Billings 1970a 18. Heier and B~llings 1970b 19. Lambert and Heier 1968 20. Herrman 1970 21. Haskin et al. 1966 22. Rogers and Adams 1969n 23. ~ o g e r s and Adams 3969b 24. Goles 1967 25. Greenland and Lovering 1965
26. Gast 1960 27. Hutchison and Dawson 1970 28. Spooner and Fairbairn 1970 29. Morgan and Lovering 1968 30. Albuquerque and Shaw (in press) 31. Albuquerque et al. (1972) 32. Eade and Fahrig 1971 33. Lanl et al. 1972 34. Heier and Thoresen 1971 35. Siehinolfi 1971 36. S&oner and +airbairn 1970 37. Green et al. 1972 38. Keil 1969
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CANADIAN JOURNAL OF EARTH SCIENCES. VOt. 9. 1972
FIG. 1. Sr isotope ratios (atomic) in rocks as a function of (Rb/Sr) ppm relative to the 4.55 X 10" year geochron. Data points are averages taken from Gast (1960), Hurley (1968a, h ) , Murthy and Compston (1965), Shaw et nl. (1967), Stueber and Murthy (l966), Tatsumoto et nl. (1965). ACH, achondrites; CHG, chondrite (Gast) ; CHM, chondrite (Murthy and Compston); PC, Precambrian Shield; S: stratiform peridotite; C, whole crust; P, peridotite inclusions in basalt; B, basalt etc.; A, alpine peridotite; T, oceanic tholeiite.
Ba, Sr. U, Th, Pb, TI, and Yb. Strontium iso- isotope abundances and element ratios for the tope ratios also favor an achondritic earth, as Rb-Sr and U-Th-Pb decay systems may be first pointed out by Gast (1960, see also Fig. 1). roughly estimated from Figs. 1 and 2. For if
Assuming the age of the earth ( t o ) to be the whole earth must lie on the geochrons about 4.55 x 1 0 9 r , the present-day daughter shown in these figures. then any part of the
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SHAW: DEVELOPMENT OF THE EARLY CONTINENTAL CRUST. PART 1
FIG. 2. Pb isotope ratios (atomic) in rocks as a function of U/Pb and Th/Pb (ppm), relative to the 4.55 X 10' year isochron. Data points taken from Chow and Patterson (1962), Doe ( 1967), Murthy and Patterson ( 1961 ), Tatsumoto ( 1966). T, oceanic tholeiitic basalt; A, oceanic alkalic basalt; B, continental basalt; C, continental crust; V, silicic volcanics; P, Precambrian sediments; S, Phanerozoic sediments.
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CANADIAN JOURNAL OF EARTH SCIENCES. VOL. 9, 1972
TABLE 2. Element ratios deduced from isotopic systems compared with assumed composition of earth zones
From Figs. 1, 2 0.01 - 0.07 0.15 0.5 -0.6 3 -4 From Table 1 0.017 0.21 0.6 3
earth now cnriched in Rb relative to Sr (or U and Th relative to Pb) will plot below the geochron, and must be balanced (by the lever rule) by other parts of the earth falling above the gcochron: initial ratios are accepted as identical with meteorites. Few points are avail- able to plot on diagrams of this sort but those used suggest the element ratios given in Table 2. These compare favorably with ratios ob- tained from co in Table 1, which gives mean abundances in the earth outside the core. The general agreement in orders of magnitude strengthens belief that the model is reasonable.
The U, Th, and K values for co are similar to Hanks and Anderson's (1969) Model III and may be used to calculate the present-day radio- active heat flux. Taking heat production figures for U, Th, and K to be 0.73, 0.20, and 2.5 X 10- %al/g yr respectively, the mass of mantle plus crust as 409.567 x 102Q and the earth's surface area as 5.10 1 x 1 018 cm" a heat flux of 1 .O1 NFU (the NFU is ,xal/s cm" is obtained. This is lower than the measured figure of 1.65 (Von Herzen and Lee l969) , but not exees- sively so.
Also the mean concentrations of U, Th, and K in the continental crust obtained from Table 1 lead similarly to an estimate that the average continental heat-flow is 0.7% HFW (assuming continental surface area of 2.4 x 101* cm2). This value is similar to many shield areas (Lubimova and Polyak 1969) but is decidedly lower than the eastern North American average of 1.2 HFU (Simmons and Roy 1969): of course it omits any contribution from the sub- continental mantle. The oceanic average heat flow, obtained by assuming that all the U, Th, and K not in the continental crust is below the sea, is 1.27 HFU: this is less than the measured value of 1.65 (Von Herzen and Lee 1969).
The concentrations of U, Th, and K in Table 1 are thus of the right order of magnitude to produce the observed heat flow. They may however be somewhat low : alternatively the observed heat flow may still include an original
heat component. It is to be noted that only 33% of the heat-producing elements are in the crust.
The Proto-Earth It will be accepted that the earth formed by
accretion oi cold solid condensates from the solar nebula, these being the same materials which were elsewhere organized into asteroidal objects, now fragmented and seen as meteorites. Recent arguments that the sequence of accre- tion began with high temperature condensates and concluded with %ow temperature, volatile- element enriched surface materials ( e .g . Was- son 1971) are not yet well enough established to modify the following arguments.
Accretion led to gravitational collapse of a nebula vortex, to a sphere of radius r and mean density p, liberating heat energy E given by the following expression:
E = 16/15 6 ; ~ ~ ~ " ~
where G is the gravitational constant (Lubi- mova 1967, p. 244). Taking the heat capacity of most inorganic solids as 1.25 x IO7ergs/OK/g, the expected temperature rise is T, where
This gives, for the earth, T > 3 x lo4 OK. In fact, such high temperatures would not be reached because of heat losses by radiation and evaporation.
Lubimova ( 1967, Fig. 6 ) concluded that this accretional energy (25 x 10% ergs) was effec- tively dissipated by radiation into space during the period of accretion which lasted from 0.6-1.7 x 1 0"r, and can be ignored. Birch ( 1 965) reached a similar conclusion, such heat- ing nowhere exceeding temperatures of 1 000".
Lubimova also estimated the energy release from core separation (1.5 x ergs) was insufficient to melt the earth, which was initially cold (surface and center temperatures 400 and 1200 OK). Subsequent accumulation of radio- active heat and frictional tidal heat (totals over
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SHAW: DEVELOPMENT OF THE EARLY CONTINENTAL CRUST. PART 1 1583
4.5 x 1 0 9 1 - were 0.6-2 x 10% and 3.6 x ergs) led to core separation after 0.6 x 10"r, and melting in the outer parts of the earth, whereby the continental crust mostly separated by zone-melting over a period of 0.3-0.4 x lo9 yr, some 2.0-3.0 x 1 0 9 1 - ago (Lubimova 1967, pp. 3 1 3-3 1 7) and continued separating until the present.
Hanks and Anderson ( 1969) however, cal- culated the minimum heating effect of accre- tional energy, by assuming black-body radiative heat loss proportional to TVhroughout the accretion process. Constraints on the various models developed from this approach include (a) core formation must have antedated the oldest Precambrian rocks which exhibit paleo- magnetism, (b) heating by gravity and radio- activity was not so fast that a core separated during accretion, otherwise Mars would also have a corc. Their models led to the conclusions that the duration of accretion was < 5 x lo5 yr, and, if the core formed no later than 3.4 X lo9 yr ago, temperatures in the mantle must have exceeded 1700 "K after accretion and core separation. In other words, the mantle passed through an early liquid stage, and must since have crystallized to solid (except possibly for the low-velocity zone near the surface). Recent studies of lcad partition between metal and silicate (Oversby and Ringwood 197 1 ) , com- bined with primitive isotopic ratios, suggest that core formation required a period of the order of 107-108 years, similar to Birch's ( 1 965 estimate of about 5 x 1 OX years.
The mantle of the earth thus passed through a high temperature stage, during which it was largely or wholly molten, and subsequently crystallized. During this period, the earth de- gassed, losing most of its initial content of noble gases and other volatile constituents. Escape of such material would inhibit any extensive solid crust forming at the surface, although radiative cooling would establish a steep surface tem- perature gradient. Convective overturn would continually bring hot magma to the surface and atmospheric retention would be minimal.
The timc to of 'origin of the earth' in a geo- chemical scnse, may be equated to reaching the prcsent mass, the beginning of this stage. The surface temperature was about 1200 "C, the atmosphcrc did not yet exist, the metallic core had scparated. and the globe was a two-phase
liquid system. Evaporation losses of light metals such as K and Rb, had terminated and the isotopic clocks were set. The earth was hence- forth a closed isotopic system except for gaseous decay products such as *OAr. If the abundances in Table 1 may be accepted, the elements shown there were partitioned between the proto-mantle and the coie.
Cooling, proceeding by black-body radiation at the surface, was unimpeded by atmospheric insulation. Within the earth, heat transfer took place by conduction and radiation (Elsasser 1 966, Lubimova 1967). High temperatures, low viscosity, and the great thickness of the mantle layer gave a high Reynolds number, so that effective convection developed and aided heat transfer to the surface: the initial tem- perature gradient (neglecting radioactivity) was approximately adiabatic, of the order of 0.3 "K/km (Jacobs et al. 1959, p. 107). Near the surface a more efficient surface radiation steepened the thermal gradient as shown in Fig. 3. The intersection with the mantle solidus (slope about 1 "K/km) suggests that crystal- lization proceeded outwards from the interior (Adams 1924).
The residual mantle liquid was enriched in the radioactive elements U, Th, and K (see later), whose disintegration heat would tend to prolong the molten stage. Figure 4 demonstrates this effect, using a model (Jacobs et al. 1959) in which these elements are concentrated in a 60 km layer overlying dunite (and pallasitic material below 1600 km). If this interpretation
FIG. 3. Thermal gradients in the early earth, with successive adiabatic curves (1 and 2) and the approxi- mate solidus from Clark (1963). The adiabatic curves steepen near the surface by radiative cooling (Elsasser 1966).
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1584 CANADIAN JOURNAL OF EARTH SCIENCES. VOL. 9, 1972
is correct, the final consolidation of the crust took place 4.0 to 3.5 x 10"r ago, i.e. in early Archean times. The more thoroughgoing analy- sis by Hanks and Anderson (1969, Fig. 7 ) suggests a similar conclusion, although recent discovery of 3.9 x lo9 yr rock ages in S.W. Greenland (Black et al. 1971) indicates faster cooling than envisaged here.
The viscosity of molten mafic rock under zero pressure near the melting point is of the order of 104 poises, decreasing by an order of magnitude for approximately every 100 OC temperature elevation. By contrast the viscosity of solid deep-mantle material is of thc order of 102"oises. During the period of rapid, radia- tive cooling, the evolution of the mantle may be treated as a convecting residual magma overlying a solid stationary crystal accumulate, the whole resembling a cooling magma cham- ber (Fig. 5 ) . The essential features of this process werc worked out fifty years ago by Adams (1924) and need little modification except for the age of the earth, which he took as 1.6 x 10"r. In this situation at least two mechanisms will lead to an enrichment of granitophile elements towards the surface : frac- tional crystallization and gravitational potential. The effects of these processes-and also zone melting, which becomes important at a later stage-will bc investigated shortly.
As the volume of residual liquid decreased, the initial peridotite composition evolved to- wards a basaltic composition. As the abundance of escaping volatiles and the surface tempera- ture decreased, floating rafts of solid phases began to coalesce into more rigid crust. This would be further aided when lower temperature and prcssure permitted plagioclase to crystal- lize, with greater tendency to float. This had two important consequences; firstly, to decrease the surface radiative cooling rate, by restricting heat flow from the interior; secondly, to act as a lid on a saucepan, further restricting evapora- tion of gases and compounds. Concentration of all the basalt (about 1 5 9% of the overall perido- tite composition), from the residual melt would yield a surface layer about 280 km thick, at the beginning of this phase. Actually the thick- ness must have been less, because inantle xeno- liths in reccnt basalts include peridotite and dunite as well as eclogite. As the volume of the residual magma decreased, fast convection be-
Time, lo9 yeors
FIG. 4. Mantle temperatures at various depths as a function of time, assuming all thle earth's radio- activity to be concentrated (early) in a 60 km surface layer (after Jacobs et 01. 1959, Figs. 5, 7) .
G A S LOSS , -.
FIG. 5. Convective fractional crystallization of the cooling mantle.
came less important. Slow convection in the solid mantle must presumably have started by about this time.
The conclusion of this stage (Fig. 6 ) may be identified as time tl, marking the near-com- pletion of inantle solidification and the rapid coolinrr of the earth's surface. The thin molten
U
layer beneath must have been highly charged with volatiles. As these escaped (intermittently) the cooler surface conditions (<I000 " C ) led to a reduction in molecular velocities, increasing the residence time before escape and a slow growth of the protoatmosphere.
The hypothesis is proposed that the con- clusion of this stage yielded all the materials of the present continental crust, as a thin ( 14 km j layer extending over the whole sur- face of the earth, with the overall composition
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SHAW: DEVELOPMENT OF THE EARLY CONTINENTAL CRUST. PART 1 1585
FIG. 6. Outer parts of the earth at time t l . Fast convection continues in the residual liquid below a thin crust. Slow (solid) convection is under way in the mantle beneath.
of quartz-diorite and the mass given in Table 1 (0.46 x times the mass of the mantle). This primitive crust was underlain by basalt. The crustal mass did not increase substantially in subsequent times.
This model will be examined after discussing the fractionation mechanisms.
Fradianation Mechanisms The prediction of concentration trends re-
sulting from heterogeneous phase equilibria re- quires knowledge of partition coefficients DlcY-8 for component i between phases and p.
Aspects of the theory, developed initially by Lord Rayleigh, are discussed in many articles. Assuming a closed system containing a unit mass of a polycomponent solution, crystallization of phases a, p, etc. in constant proportions P,, Pa, etc. leaves a residual fraction F of liquid at a given time. For a given trace element the relative concentration in the liquid phase is x, and two limiting cases may be recognized; xL will be the concentration if the liquid con- tinuously equilibrates with the solids already separated; x' will correspond to continuous fractionation, whereby crystals are in effect isolated from the residual liquid (Shaw 1970)
Granitophile elements will have values of the bulk partition coefficient in the range 0 <: D < 1. For a given value of F the maxi- mum possible fractionation is given by
e41 xL = x1 = 1 / F
The relationships arc seen in Fig. 7 which
gives x as a function of D for values of F equal to 0.15 and 0.0046, i.e. residual basaltic liquid (maximum) and residual continental Gust liquid respectively.
The second fractionation mechanism is the e f ect of gravitational potential. In a multicom- ponent single-phase system the effect of gravity is to promote an equilibrium distribution of elements. For a simple binary system containing N molecules of a compcnent of molecular weight W and molar volume V, the following distribu- tion is stable:
h is height, p the phase density, T the tempera- ture, g and R the gravitational and gas con- stants.
If w/V < p, dN/dh is positive and the ele- ment coilcentrates upwards. In a more complex solution the effects of other components must be evaluated. Brewer ( 195 1 ) considered U in a solution containing Si, Mg, Fe, and 0 at 2000 "K and = 4g/cmY An order-of-magnitude solution suggested that X,T will double every 2 km upwards towards the surface of the earth (opposite of that expected in a simple binary solution of U ) . This result is an over-simplifica- tion, however, since it disregards the gravita- tional fractionation of the major elements Si, Mg, Fe, and 0 .themselves, and their effect on U. Nevertheless the conclusion is clear that, if gravitational equilibrium were attained. the surface concentration of uranium might be lower by a factor of up to 1000 at a depth of about 20 km. Equilibrium is clearly not to be expected, since by the same token Fe should not occur at the surface, but the tendency for U (and elements which behave in a similar fashion) to be less abundant in deep-crustal rocks has been claimed by several authors in recent years (e .g . Lambert and Heier 1968) and has been accepted in constructing Table 1. Moreover the tendency towards gravitational equilibrium should have been reached more readily within the mantle, because of (a) mechanical assistance of convection, and (b ) absence of complicating interactions of surface tectonic and atmospheric-oceanic factors. Brewer concluded that the earth as a whole has reached approximate gravitational equilibrium. Elements which behave similarly to U may
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FIG. 7. Relative concentrations of a trace element from fractional crystallization as a function sf D, for two values of F ; (a) x" and (b) xl.
therefore be expected to have been largely expelled from the mantle towards the crust.
A third mechanism to be considered is zone- refining. In the industrial process a narrow molten zone passes along a solid rod, scavenging impurities for which D < 1. Within the earth, the upper part of a convection cell within the solid mantle may reach a zone of low pressure, permitting partial melting. As the current ro- tates the molten zone will extract granitophile elements according to the relation
In this equation (Harris 1957) the ratio zone- thickness/rod length has been replaced by F, the mass fraction of liquid associated with the array of convection cells. With a given value of F, the maximum value of x, is (1 /F + 1 ), as shown in Fig. 8 (this limit applied to a rod of infinite length: for convection the limit is l /F as before).
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a oa I I I I 10 100 so00 10000
x z
FIG. 8. Relative concentration x, of a trace element as a function of D, for constant F, in a zone-refining process.
Equation 5 applies to a single zone-refining cycle. For two cycles of the convection cells the resulting concentration will be xS2, and so on.
Fractionation in the Protocrust The hypothesis proposed earlier may be
tested using distribution coefficients recently measured (Table 3) . These data suffer from the disadvantage of having been measured on phenocryst/lava systems, under low pressures. Knowledge of pressure and temperature varia- tions of D is not yet available. It is moreover uncertain how welf the phenocryst/lava systems represcnt equilibrium. It can be shown that the apparent partition coefficient d, measured erro- neously on an aggregate of fractionated (e.g. zoned) crystals which separated from a melt up to the stage of residual melt-fraction F is given by
D and d can therefore differ markedly. Assuming such problems were not in fact
present for the measurements assembled in Table 3, representative values may be chosen. These are not securely based, drawn as they are from individual values commonly ranging over an order of magnitude or more, but they may nevertheless be profitably used. Assuming
also that the bulk major element composition of the mantle-crust system may be approxi- mated by a peridotite-basalt mix of pyrolite composition (Ringwood 1969, l97O), such a magma could crystallize to various mineral assemblages (Green and Ringwood 1963, 1970) depending on p , T, fH&, etc. Phlogopite has been included since recent research has shown (Kushiro et al. 1967) that it may be stable to depths of 100 km. The modes most useful in the present context are given in Table 4 and, using representative D-values from Table 3, bulk partition coefficients are given in Table 5, except for U and Th, for which no coefficients are available for olivine.
Equations 1, 2, and 5, corresponding to mechanisms of continuous equilibration (XI.), continuous fractionation (xl), and zone refining (x,) were then evaluated for values of F equal to 0.15 (280 km depth residual liquid) and 0.0046 (continental crustal volume). In these calculations, the effect of ultra-high pressure assemblages deep within the mantle could not be assessed, but gravitational segregation would be expected to increase the tendency of any lithophile element to migrate upwards.
For the first 85% crystallization (Table 6) the three kinds of fractionation give similar concentrations, except where La > 1, as for Ni, in which case continuous fractionation ( 9 ) leads to very low final concentrations. Compar-
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TABLE 3. Distribution coefficients for several phases in equilibrium with basalt or peridotite magma -- - - -- -- - -- -- - - - -- -- - - -
DATA FROM: Gast 1968 Onuma et al. 1968 Higuchi and Nagasawa I969 Philpotts and Schnetzler 1990 Philpotts and Schnetzler 1970
Frey 1969 Griffin and Murthy 1969 Hakli and Wright 1969 Turekian 1963 Mercy and O'Hara 1967
ing the different mantle assemblages shown in Table 6, most elements have similar D-values for each assemblage, and consequently show similar concentration changes. Increases of 4 to 7 times the initial concentration are produced for K through Eu: Ni concentrations decrease to similar levels in each case. Contrasting trends are seen only for Yb whose large D-value in garnet lherzolite (4.2) leads to lower final con- centrations than in the other two assemblages.
The lower part of Table 6 presents the abso- lute concentrations in thc residual liquid, ob- tained by multiplying the mantle-crust bulk concentrations (co in Table 1 ) by the average of xL and x, for garnet lherzolite. Comparison with the adjacent columns shows this residue to resemble oceanic tholciite basalt for K, Rb, and Sr. The concentrations of Ba, La, Ce, Eu, and Ni are somewhat higher, more like continental basalt, and Yb is lower. Crystallization to spinel lherzolite would give a morc acceptable Yb coraceratration, but garnet is much more likely
to occur in the deep mantle than spinel. It is possible therefore that the estimate of co for Yb in Table 1 is somehow too low by an order of magnitude: of course the modal percentages chosen influence greatly the outcome of calcula- tions such as these. Minor differences are there- fore insignificant, but the fact that the use of distribution coefficients leads to residual trace element abundances consonant with basalt is encouraging. It is unnecessary to review the major element trends here, since they have been discussed exhaustively in many places (e.g. Green 1968).
The final aspect of Table 6 concerns the mass-fractions of trace elements in the residual basaltic liquid relative to the peridotitic mantle below. If the relative concentration in the re- sidual liquid is x, and the liquid mass-fraction is F, then the mass-fraction of the element in the liquid (relative to the whole system) is simply xF. Such values are given as per cent in Table 6 and show that fractional crystallization would
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NOTE: Values calculated from data in Tables 3 and 4.
expel virtually all the K, Rb, Ba, La, and Ce from the deep mantle. The same coilclusion would likely hold for U and Th (D-values in Table 3 for K, U, and Th are similar) and thus the heat-producing radioactive elements may be expected to have had negligible concentrations and negligible nlasses below 280 km depth, at the time of this separation and presumably subsequently also.
The major element composition of the re- sidual liquid will resemble column R in Table 7 : extraction of 15 5% of this composition from the assumed parent (column 4 ) cannot but be consonant with a peridotite assemblage. Con- tinued crystallization up to 99.46% solidifica- tion will leave the continental crustal residue, whose composition has been estimated as that given in column C (Taylor 1964) : solidification during this stage will give a bas.] ,z tic ' assem- blage, whose bulk composition is shown in coluinn D.
The subsequent crystallization of the residual 15% basaltic liquid may now be followed. In considering the options, the rough equality of oceanic and continental heat flow must be borne in mind. The present marked difference
in K, U, and Th abundances in continental and oceanic crust suggests compensating differences in the underlying uppcr mantle, extending no dceper than 280 km according to the analysis here: this hypothesis of lateral independence has been discussed by many authors (Taylor 1964, Birch 1965, Shaw 1968, and Ringwood 1969). Plate tectonics theory suggested to Ring- wood ( 1969, p. 1 19) that "there is no longer any justification for assuming that the mean chemical compositions beneath continents and oceans . . . are identical" but this conclusion is difficult to accept if radioactive heat drives convection.
The results expected from crystallization to a residual volume equal to the continental crust ( F = 0.0046) are in Table 8, where garnet lherzolite and phlogopite lherzol ite values closely similar to hose given for spinel lherzo- lite are omitted. The very small volume of residual liquid now leads to marked differences with continuous fractionation, as compared with continuous equilibration and zone refining, which produce similar results: only for D-values very close to unity would the results be similar. Table 9 shows the absolute concentrations ex-
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1590 CANADIAN JOURNAL O F EARTH SCIENCES. VOL. 9, 1972
TABLE 6. Concentrations remaining after 85% crystallization of the mantlexrust system, for three different phase assemblages and three fractionation mechanisms*
Spinel lherzolite Garnet lherzolite Phlogopite lherzolite Mean Mass in
F=0.15 x1 xL XZ x1 xL x, x1 xL XZ x liquid
Average tholeiitic basaltd
Absolute concentrations Oceanic thokiite in residual liquidc (Table 1)
NBTF.: Values omitted are the same as those given for spinel lherzolite crystallization. *Modal composition as in Table 4. aConcentration from spinel lherzolite crystallization. bConcentration from continuous fractionation (XI). =xL or x, from garnet lherzolite crystallization. dTurekian and Wedepohl 1961, except REE selected from Herrman's 1970 compilation.
TABLE 7. Major elements in the mantleuust system -- - - . .- . -- -
A B C D
Si02 Ti02 A1203 Fe203 FeO MnO
c F ~ o ~ NiO c o o Sum
NOTES: A. Parent material (3 alpine peridotite plus I Hawaiian basalt; Ringwood 1969, Table 1).
B. Residue after 85% crystallization (average of 1996 basalts; Manson 1968, Table VI).
C. Residue after 99.54:; crystallization (continental crust; Taylor 1964). D. Solids crystallized in going from B to C.
*Total Fe.
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TABLE 8. Relative concentrations remaining after 99.54% crystallization of mantle-crust system, for three different phase assemblages and three fractionation mechanisms - - -- - - - -- -- -- - -
NOTES: Values omitted are similar to those given for spinel lherzolite crystallization. e, is the mean concentration in the whole continental crust. S = spinel lherzolite assemblage. G = garnet lherzolite assemblage. P = phlogopite lherzolite assemblage.
pected in the continental crustal mass (values for xL and x, have been averaged). These are to be compared with the mean continental crust concentrations (c,) in the last column (mean concentrations in the continental crust plus oceanic crust are very similar). A graphical display is given in Fig. 9, in which the line with unit slope would be thc locus for an exact match.
Table 9 and Fig. 9 show that no single mineral assemblage or fractionation mechanism produces element concentrations in accord with the crustal composition from Table 1. Con- tinuous fractionation to garnet lherzolite gives concordant results for K, Rb, and Ba, excessive conccntrations for Sr, REE, and La/Yb, and negligiblc Ni : continuous equilibration or zone refining gives low values for K, Rb, and Ba.
Neverthcless the range in calculated values in- cludes the crustal valuc for all elements except La, Ce, and Eu, so a combination of mixed fractionation mcchanisrns with a less simplified phase assemblage sequence would give a better agrcernen t.
In the light of the many uncertainties in pro- ccss, asscmblagc, and B-values it is dubious whether the construction of a more detailed model is worthwhile. Nevertheless a factor which has not yet been accommodated is the possibility that upward migration of water might stabjljzc an amphibolc-bcaring assem- blage near the surface (now occurring in the suboceanic mantle) : it is now known that amphibole and phlogopite may be stable to pressures of 20 and 3 3 kb respectively (Kushiro et al. 1967, Kushiro 1970n, b ) . A model was
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CANADIAN JOURNAL OF EARTH SCIENCES. VOL. 9, 1972
1 I I I
1 0 lo2 lo3 I 04
c, PPm
FIG. 9. Predicted continental crust concentrations for garnet lherzolite crystallization ( C , ) by continuous fractionation (0) and continuous equilibration ( x ) , plotted against estimated continental crust composition ( c , ) . Exact agreement would place elements on the diagonal line.
therefore computed, in which the residual 15% basaltic composition would crystallize to spinel lherzolite between the depths of 279-100 km, phlogopite lherzolite from 100-60 km, am- pholite abovc 60 km, lcaving the same residue of 0.46% as the continental crust. These layers correspond to crystallizations successively of about 63, 78, and 97% of the initial 15% magma. The concentrations (C4) expected in the end-product of this 4-stagc process arc shown in Table 9. Thcse are about 10 timcs too large for Sr and the REE. low for Ba, Ni, and K/Rb, and high for Yb.
Summary The best conformity between calculated and
observed concentrations would be given by a fractionation mechanism intermediate between continuous fractionation and continuous equili- bration, during crystallization to garnet lhcrzo- litc followed, at higher levels, by spinel lherzo- lite. This is a completely plausibk proccss,
from present knowledge of phase petrology, and can hardly be refined until partition coeffi- cients (and their pressure and temperature dc- pendencc) are better known. As discussed previously, solidification of the residual magma into continental crust would still leave 67% of the U, Th, and K (and also Rb, La, etc.) retained in the subcontincntal mantle.
If, however, the effects of gravitational poten- tial be considered it is likcly that the model enrichment x would bc increased except for Yb and Ni.
Continued solid slow coiwection throughout geological time would undoubtedly assist (by zone refining) in the lifting of residual granito- phile elements towards thc surface. Present abundanccs in ultramafic rocks may thcrcfore somewhat overestimate the amounts left in the mantle, which will modify the preceding dis- cussion in a qualitative fashion.
It may i~everthelcss be coracluded that the hypothesis is not seriously at variance with
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SHAW: DEVELOPMENT OF THE EARLY CONTINENTAL CRUST. PART 1 1593
obscrvation, i.e. the concentrations of granito- phile elements in the continental crust are in general accord with what may be predicted. The theory does not jndicate when the con- centrations of granitophilc elements reached their present values, but the most rcasonable interpretation is that this situation was reached at the close of the primary differentiation: the tcndency of fast liquid convective overturn to establish thermal and chemical cquilibrium makes it. inevitable that crustal material was swept to the surface.
This crystallization requircd a period of 0.5-1.0 x 1 0 9 1 - aftcr core separation, as dis- cussed earlier. If time to is identified with the 4.55 x 10" yr event, then tl is in thc range 4.0-3.5 x 10" yr ago.
The protoarchean crust must have crystal- lized as a thin, widespread surface scum across the whole surface of the earth. The present disposition of continental land-masses with in- tervening ocean basins dcvcloped later, and a model will be prescnted in the second part of this article: isotopic evidence from Sr and Pb will be considered in that connection.
Acknowledgments Helpful suggestions have been contributed by
numerous friends and colleagues, in particular P. M. Clifford, S. R. Hart, R. L. Armstrong, and H. P. Schwarcz.
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