The role of iron partitioning in mantle composition ...authors.library.caltech.edu/51198/1/jgrb4072.pdf · J/mol• deg from the recently determined phase ly depleted in iron. diagram

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 87, NO. B7, PAGES 5631-5644, JULY 10, 1982

THE ROLE OF IRON PARTITIONING IN MANTLE COMPOSITION, EVOLUTION, AND SCALE OF CONVECTION

1 J. Peter Watt and Thomas J. Ahrens

Seismological Laboratory, California Institute of Technology, Pasadena, California 91125

Abstract. The effect on composition and evo- convection with the entire mantle passing through lution of the mantle of the recently-observed the partial melt zone. Thus the lower mantle was strong concentration of iron in (Mg, Fe)O-magne- depleted of iron relative to both the upper siow•stite (row) at the expense of (Mg, Fe)SiO•- mantle and the mantles of the small terrestrial perovskite (pv) structure is studied by calcO- planets and satellites, which do not have mantle lating a temperature- and pressure-dependent iron pressures sufficient to form perovskite-structure partitioning coefficient for the lower mantle. silicates, or which had lower accretional temper- The value of the standard entropy for atures and less extensive melting. On this basis,

MgSiO•-perovskite is found to be 69.4 + 10.3 Venus would be expected to have a mantle similar- J/mol• deg from the recently determined phase ly depleted in iron. diagram of forsterite. Iron remains concentrated in (Mg, Fe)O throughout the entire lower mantle Introduction if account is taken of an FeO phase change .... with

pv pv mw mw the partitioning coefficient (x_ /x•. )/(x_ /•. ) One of the major issues in the study of the increasing from 0.04 to 0.8 be•wee• 670 •m a•d earth's interior is the question of the radial the core-mantle boundary. Partitioning has chemical homogeneity of the mantle, the solution negligible effect on gross density and elastic of which has important implications for the properties of the lower mantle. By using recent evolution of the earth and for the style of shock wave and static compression results for FeO mantle convection. A chemical boundary at 670 km,

and MgSiO3-perovskite, we find that the lower say, would either restrict convection to the mantle is more pyroxene-rich than the upper upper mantle or require two-layer circulation. mantle and as iron-rich, or somewhat less so, The present state of the convection problem has than the upper mantle. Mg/(Mg + Fe) = 0.93-0.95 recently been reviewed by Stevenson and Turner for the lower mantle compared with 0.85-0.90 for [1979]. Arguments in favor of whole-mantle con- the uppermost mantle. The lower mantle Mg/Si vection have been presented by Ringwood [1975], ratio is closer to chondritic values (0.99 Davies [1977], O'Connell [1977], Sammis et al. + 0.03) than is the upper mantle (•1.5 for a [1977], Hager and O'Connell [1978], Sharpe and peridotite with px/ol = 0.4(molar)), thus sup- Peltlet [1979], and Davies [1981], among others. porting the idea of a chemically layered mantle The idea of layered convection has been supported with implications for the style of mantle by studies such as those of Richter and Johnson convection. While partitioning of iron has no [1974], Anderson [1979], Wasserburg and DePaolo significant effect on gross lower mantle density, [1979], Jeanloz and Richter [1979 ], Christensen we find that the (Mg, Fe)O and perovskite [1981], and Richter and McKenzie [1981], for components of the lower mantle have essentially example. the same densities. Mantles with higher bulk iron In this paper, we investigate the effects of contents have (Mg, Fe)O denser than the the high-pressure behavior of olivines and perovskite component; for a bulk magnesium mole pyroxenes on mantle composition, evolution, and

fraction of 3 0.80, the density difference is scale of convection. 0.7-0.8 g/cm . We investigate the feasibility of Ringwood [1962] suggested that the 670 km the Mac, Bell, and Yagi gravitational separation seismic discontinuity is caused by a phase trans- hypothesis of mantle evolution in which a mantle formation to perovskite-structure silicates. In more iron-rich than present loses iron through recent years, both experimental evidence for gravitational sinking of the denser (Mg, Fe)O, mantle minerals-see, for example, Liu [1979] for and we conclude that the process cannot a review of high-pressure products of olivines, successfully compete with solid state convection pyroxenes, and garnets-and studies of analog unless iraplausibly large grain sizes or materials, summarized by Liebermann [ 1979], have unacceptably low viscosities are invoked. A given strong support to the perovskite (pv) likely explanation for removal of iron from an hypothesis. Although there is evidence for initially iron rich lower mantle is upward additional minor discontinuities below 670 km, extraction of FeO-enriched basalts or picrites the properties of the lower mantle from 670 km to and concentration of iron in upper mantle garnets the core-mantle boundary appear to be dominated during accretion of the earth or subsequent by the perovskite transformation. Anderson [1977]

has argued that a pyrolite mantle transforming to

1 perovskite-structure silicates and (Mg, Fe)O Now at Department of Geology, Rensselaer cannot explain the 670 km discontinuity. It has

Polytechnic Institute, Troy, New York 12181. been proposed that the lower mantle is mainly FeO-poor perovskites [Sawamoto, 1977; Butler and

Copyright 1982 by the American Geophysical Union. Anderson, 1978]. Seismic data for the lower mantle appear to be consistent with a mainly

Paper number 2B0088. pyroxene stoichiometry [Anderson, 1970; Anderson 0148-0227/82/002B-0088505.00 et al., 1971; Gaffhey and Anderson, 1973; Burdick

5631

5632 Watt and Ahrens.- Iron Partitioning and Mantle Composition

0:30 , , • (3.$83)

--- I MgS•03 (p

ß io 20 3o 40

Pressure (GPo)

b where x is the mole fraction of element a in

phase b a Bell et al report K = 0 08 for pressures between 25 and 45 GPa and temperatures around 1000øC, indicating strong depletion of iron in pv with respect to m•. This segregation of iron is much more dramatic than that which

occurs for upper mantle phases and pressure and temperature conditions; theoretical estimates appear in the work of Ahrens [1972, 1973], while experimental results are given by Akimoto et al. [1976] and Akaogi and Akimoto [1979].

Since the density difference between the mw

iron 3 and magnesium end mõmbers (p(FeO) =25.865 g/cm , p(MgO) = 3.583 g/cm , Z%p= 2.28 g/cm •) is double that of the pv end members (p(FeSiO_- pv) = 5.23 gm/cm 3 extrapolated from the l•ttice parameter da•a of Y iet al.•[1979a], p (MgSiOR) = 4.10 g/era •, Z%p =•.13 g/em •), one might expe•t that for a given initial unpartitioned composition, the concentration of iron in • upon partitioning would yield a higher • + pv density than for an unpartitioned • + pv assemblage. Figure 1 shows that the relative densities of

Fig 1. Reciprocal density for MgO, FeO, MgSiOR MgO, FeO, Mg-pv, and Fe-pv persist at depth. (pv), and FeSiO• (pv) vs. pressure calculated Conversely, to produce a given gross density in from third-order finite strain theory and the the lower mantle, one might expect the parti- equation of state parameters in Table 1. ticned • + pv assemblage to require a lower Zero-pressure density values are given in overall iron content than an unpartitioned mix- parentheses. Relative densities are unchanged ture. One of the aims of this paper is to inves- with increasing pressure. The hatched regions tigate this possibility. enter the partitioning coefficient via equation Mac et al. [1979] found that for olivine with (5), where Z%V is proportional to 1/p. a bulk iron mole fraction of 0.1, which satisfies

the density of the Parametric Earth Model (PEM) [Dziewonski et al., 1975], the densities of the

and Anderson, 1975]. Of these studies, only the mw and pv components in the lower mantle are work of Sawamoto [ 1977] included experimental essentially equal, assuming that the experimental data on perovskite-structure silicates; the value of K (= 0.08) holds throughout the lower density of MgSiO•-pv was 2.5% lower than the most mantle. For higher bulk iron contents, p > P v' . mw recent results •described below, which now make They speculated that xf the mantle were m•re possible a more detailed study of the relation of iron-rich in the past, gravitational sinking of seismic models of the lower mantle to specific the denser mw could occur. Near the core-mantle compositional models. boundary, the iron-rich mw could lose some iron

Data reported by Yagi et al. [1979a] for the to the core by processes such as chemical lattice parameters of (Mg, Fe)SiO•(pv) indicated reduction, direct solution of FeO in the core, that the iron-magnesium solid •olution extends [Ringwood 1977a], or chemical disproportionation only from 0.0 to 0.2 mole fraction FeSiO , [Mac and Bell, 1977]. The remaining mw, somewhat confirming the results of Liu [1976] who found3a depleted in iron, could float or convect to be maximum Fe mole fraction of 0.3 in the percy- reequilibrated with the pv. Repeated operation of skite-structure phase. For more iron-rich ortho- this cycle could lead to the present situation pyroxenes, (Mg^ 8Fen 2)SiO•(pv) and a mixture of where p N p , an• the process would cease. A ß mw N v stishovite an• mag•&siow•gtite- (Mg, Fe)O - were similar suggestion of separation of FeO because formed. Itc and Yamada [1982] reported that of density differences in a fictive Fe-Si-O perovskites were stable over an even smiler mantle was made by Shimazu [1956]. range of 0.0-0.1 mole fraction FeSiO_. Thus for We find this hypothesis appealing. It could realistic Mg mole fractions in the mantle (x M > explain the fact that the earth, the largest 0.85), oxide mixtures may also occur, gas terrestrial planet, has its mantle depleted in well as perovskite-structure silicates. The bulk iron relative to the mantles of other bodies such modulus of MgSiO_ was determined to be 260 + 20 as the moon, Mars, and the eucrite parent body GPa [Yagi et al., 31979b], in accord with --the (EPB). An overview of planetary compositions has estimate of Liebermann et al. [1977] based on been given by Smith [1979]. Figure 2 shows elasticity systematic relationships. Mg/(Mg + Fe) estimates for these bodies versus

The most important result of these studies is pressures at the base of their mantles. If the the very strong segregation of iron into the earth's mantle had a similarly high iron content magnesiow•stite (row) phase [Bell et al., 1979]. at some earlier time, the gravitational settling For the exchange of iron between mw and pv, mechanism could explain an evolution to its

FeO + MgSiO 3 • MgO + FeSiO 3 the partition coefficient K is defined as

row. mw -1

K = (x•;/x•).(XFe/XMg)

present iron content. Such a process would not (1) occur on the moon, the EPB, or Mars (except

perhaps near the bottom of the Martian mantle) because pressures required for formation of mw + pv from olivines and pyroxenes (>20 GPa) are

(2) higher than those at the bases of the mantles of

Watt and Ahrens: Iron Partitioning and Mantle Composition 5633

these bodies. On the other hand, internal pressures and accretional heating in Venus are similar to the earthß Thus if gravitational separation of m• is feasible for the earth, then it should also occur on Venus, making the composition of the Venusian mantle more similar to that of the earth than has previously been supposed [Ringwood and Anderson, 1977], a conclu- sion reached by Anderson [1980] on petrologic and tectonic grounds and by Morgan and Anders [1980] from a study of fractionation processes in the solar nebula.

1.0 I I I---- pv forms I I

M g•Fe I•Moo I

ø'75r• •Mors

Earth 9•.p venus----_!•-

_

Pressure at Base of Mantle (GPa)

We estimate that gravitational sinking of mw Fig. 2. Mg/(Mg + Fe) for the earth, Mars, the in a terrestrial mantle with initial m. = 0ß75 moon, the eucrite parent body (EPB), and Venus would account for between 10 and 20% of•gthe mass vs. pressure at the base of the mantles of these of the present core, assuming maximum efficiency bodies. Composition estimates for the earth are for the processß Thus this mechanism, while not from Ringwood [1975] (upper mantle) and present the dominant means of core formation, could still work (lower mantle), for Mars from Arvidsen et produce an appreciable portion of the core. al. [1980] and Anderson and Baumgardner [1980], Accordingly, a second aim of this paper is to for the moon from Ringwood [1977b], Goins et al. investigate the feasibility of the gravitational [1978], Binder [1980], and Buck and Toks•z settling of mw hypothesis. [1980], for the eucrite parent body from Stolper

[1977], and for Venus from Ringwood and Anderson Calculated Lower Mantle [1977] Anderson [1980], and present work.

Partitioning of Iron

In order to explore the geophysical con- We ignore the (Z%C_) ø integrals in (4) thus sequences of iron partitioning between • and pv, assuming either thatPthe four phases in (1 • have we calculate the variation of K with pressure and the same temperature variation of specific heat, temperature, in a manner similar to the studies or that temperatures are close to, or higher of Ahrens [1972, 1973] for iron partitioning than, the Debye temperatures of the phases. among upper mantle olivines, pyroxenes, and Acoustic Debye temperatures are 665øC for MgO garnets [Anderson et al.,_ 1968], 217øC for FeO [Jackson ß O

For an ideal solution, equation (2) can be et al., 1978], 722 C for MgSiO•(pv) (Yagi et al. written as [Kern and Weisbrod 1967] [1979b]; elasticity s_ystematiSs of Liebermann et

al. [1977]), and 599 C (systematics estimates)

K = exp [-(AG)TP/RT] (3) for FeSiO•(pv). Thus for the temperatures of the partitioning experiments [Bell et al., 1979], or

where (AG) P is the net change (E products - for temperatures in the lower mantle, this is an E reactants)Tin Gibbs free energy for reaction excellent assumption and equation (4) becomes (1) at pressure P and temperature T, R is the gas

constant, and T is the absoluteptemperature (AG)• (AH) O o fl P ß = - )298 Simple thermodynamics allows (•%G) T to be ex- 298 T(•%S + (•V)TdP' (5) pressed as The (•IV) T term in (5) requires a knowledge of

the variation of molar volume (or density) with

•G)T = 298 + 298 )øtiT' pressure, We use a third-order Birch-Murnaghan equation of state with the zero-pressure density

- 298[(Z%Cp)ø/T']dT ' + (Z%V)TdP' (4) o , bulk modulus K , and first pressure deriva- r O

o o t•ve of the bulk modulus K•' specified for each where QIH)__, and (•%S)2_^ are the net changes in phase, adjusted for temperature effects by using standard •halpy and e•ropy, respectively, for the thermal expansion coefficient • and the first reaction (1) (•C_) ø is the net change in spe- temperature derivative of the bulk modulus •K/•T, oifie heat 'at P•= 1 atto, and (AV) T is the net as in the work of Watt and O'Connell [1978]. change in molar volume at temperature-T. Evidence Third-order finite strain is adequate for for ideality of magnesiow•stites comes from the calculation of densities, and hence molar vol- lattice parameter-composition studies of Hahn and umes, to pressures at the core-mantle boundary- Muan [1962], Hentschel [1970], Jackson et al. see, for example, Banerdt and Sammis [1980]; [1978], Rosenhauer et al. [1976], and Bonozar and however fourth-order terms must be included to Graham[1982]. The situation is complicated by adequately represent elastic properties. The departures from a linear lattice parameter- parameters used for the phases in (1) are col- composition relationship at the iron-rich ,end of lected in Table 1. The bulk modulus of FeSiO•(pv) the series, caused by the presence of Fe 5+ and is estimated from elasticity systematics [Limber- associated vacancy concentrations [Simons, 1980]. mann et al., 1977]. The MgSiO3(PV) value of •K/•T The careful sample characterization of Bonczar is estimated from data on other perovskite- and Graham [1981] reveals a nearly perfect structure compounds, while the value of •(pv) is correlation between deviation from linear behav- estimated from the proportionality of • to the ior and degree of nonstoichiometry, indicating product of the cation and anion charge valence that • 'nonidealty' is not caused by imperfect [Jones, 1976]. The estimates for a high-pressure mixing. The limited data on perovskite-structure phase of FeO are derived from shook wave silicates [Liu, 1976; Yagi et al., 1979a] show no experiments of Jeanloz and Ahrens [1980]. A phase significant departures from ideality. transformation in FeO has been confirmed by Zou

5634 Watt and Ahrens: Iron Partitioning and Mantle Composition

TABLE 1. Equation of State Parameters

MgO FeO MgSiO FeSiO (pv) 3 (pv) 3

Pc' g/em3 3.583 a 5.865? 4.10 i 5.23 k (6 g GPa 163 a 182 260 j 250 g O • ß . ß

•K_/•P, 3.9 a (195')e 3.2 f 4.0 j 4.0 g

o dimensionless 6b (•.4) e •,o 10-o/o C 31. 37 5 B 35 35

Spetzler [1970]. Anderson and Andreatch [1966]. White and Anderson [1966]. Jackson et al. [1978].

The slope of the equilibrium line in P-T space is given by the Clausius-Clapeyron equation:

P P

dP/dT (AS)298/(AV = )298 and S;98 can then be obtained from

P _ o

(8)

(9)

where • is Gr•neisen's constant and C is the v

specific heat at constant volume. We assume that

Y/v is constant. (AH); is then calculated from equation (7). 98 Figure 3 shows the P-T diagram for forsteritc

(Mg SiO) The •• and •T phase boundaries 2 4 '

are from Suito [1977]; the • MgO + MgSiO3(PV) boundary is the recent determination of Itc and o o

Yamada [ 1982 ]. S and 6•H) values are com- 28 28 puted from the phase boundarie• successively for fo(•)• fo(Y) • and MgSiO•(pv), The necessary equation of state data are •iven in Table 3,

High-pressure phase [Jeanloz and Ahrens, 1980] Table 4 shows results for the calculation of Jeanloz and Ahrens [1980]. o o S2A 8 and ZIH2^. for the • and • phases of fors- .gEstimated. te•lte and W•or MgSiOq(pv). Ahrens and Syono n. caleulated from data in Clark [1966]. [1967] estimated the thermochemical properties of

1Calculated from lattice parameters of Yagi et T-forsterite, assuming formation directly from o

ß al. [1979a]. the phase, and found S2-^ = 75.3 J/mole deg wOYagi et al. [1979b]. from density-entropy systematics for normal spi- -Extrapolated from lattice parameters of Yagi nels and AHø - - 2144 3 (+3.3) kJ/mole assuming 29U - ' et al. [1979a]. that 7-forsterite has th• same P-p behavior as

MgO. These estimates are in good agreement with

et al. [1980]; however, it is not clear what the our results based on more complete data for o

Y-Mg SiO. The value of S.•, for MgSiO•(pv) is structure of the high-pressure phase is [Jackson 4 ß somewhat higher than t• of MgSiO•(e•statite) and Ringwood, 1981; Navrotsky and Davies, 1981]. (67.8 J/mole deg [Helgeson, 1978]), Elthough the

The standard enthalpies and entropies of the uncertainty is large. Navrotsky [1980] predicted foursphases in (1) are needed for the (AH)ø•^o and a larger entropy for MgSiO• (pv) compared to the (AS)•. terms in (5). These are availabl• •ø for low-pressure phase based o• metal-oxygen distance MgO •d FeO [Robie et al., 1978] and are listed and coordination change arguments. Similar in Table 2; however, these data do not exist for behavior has been observed in the ilmenite- perovskite-structure silicates and must be perovskite transformation in CdTiO• [Nell et al., estimated. 1971]. Since the errors in ent6opies obtained

Various empirical methods exist for estimating o from P-T diagrams are fairly large, calorimetric

S.298 values for minerals, su•arized by Helgeson investigations of MgSiO3(PV) will be of great e% al. [1978], but while they can yield good interest. approximations for certain groups of minerals, Since FeSiO•(pv) is not thermodyamieally none of them are of universal applicability. stable with regpect to FeO and SiO o (stishovite) Additional complications, the effects of which on [Yagi et al., 19•9a; Itc an• Yamad•, 1982], we the empirical relations are unknown, arise be- must estimate S- - and AH- - in Table 2 The

2 U 2 ' cause of the change of phase to the perovskite first values hav• been dete2•ned assuming that structure with its attendant changcoin coordina- o o (FeO + FeSiO 3- tion. Accordingly, we estimate S)oR(MgSiO•-pv) AH1273 (FeO + FeSiO3-PV) = AG1273 from the P-T diagram of forsterile and • fix

(AH)•oR (MgSiO•-pv) from the experimental K value TABLE 2. S ø and ZIH ø (With Respect to Elements) deteh•Ined by Bell et al. [1979]. Similar approaches have been used by Ahrens and Syono [1967] for the reactions forsteritc • oxides and enstatite • oxides and Mac et al. [1969] for the reaction fayalite (•)• fayalite (spinel).

For a given phase_ transformation occurring at pressure P and 298 C, the net Gibb's free energy for the reaction vanishes:

P o 0 = (AG)298 = (AG)298 + (AV)298dP' (6)

o o K o S298 • J/mole kJ/mole AH298 •

MgO 26.94 -601.49

FeO 59.80 -272.04 a3 .4 a -1430.1 MgSiO ?-pv 69 0b FeSiO pv(estimated)61 -1118.•eb 96.7 c -1073.

The P-p curves for the four phases can be used to calculate the pressure integral in (6) and the

o

(ZIG)298 term is given by o

(AG) o = (AH) ;98 298 (AS) 298 ( 7 ) 298 -

acalculated from MgpSiO a P-T diagram and _experimental partitiohing coefficient. u - fixed by experimental partitioning 28 c•e ffi cient. o

S298 fixed by am logy with MgSiO 3- pv.


pv) = -/1P(•V)1273dP ' and taking P( Y•FeO + TABLE 3. Equation of State Data for Forsteritc

FeSiO3-PV) as 15.5 GPa (Yagi et al. [1979b] for • • FeO + stishovite) and then fixing S ø (FeSiO_-pv) from the experimental partition•Sg coefficient. The second set of values was estimated by taking Søoc• (FeSiO•-pv) as 2.4% higher

than FeSiO• (fe•sillite)$ the same amount that o • o S•A• (MgSiO_-pv) is larger than SAA. (MgSiO•- Pc' g/cm3

e•atite), • and calculating (AH)•aRZ•eSiO•-p•) from the partitioning coefficienti•We prefer the K GPa O' first approach as being less artificial. The second set of values leads to a more rapid •K /•P, increase of the computed partitioning coefficient d•mensionless with depth for mantle pressures and temperatures. 7,

Phases

Fo(•) Fo(•) Fo(•) MgO M•SiO (pv) 3

3.222 a 3.467 c 3.549 c 3.584 f 4.10 h

129 a 166 c 213 c 163 f 260 i . ß ß ß ß

5.2 a 4.5 d 4.5 d 3.9 f 4.0 i

1.13 a 1.13 d 1.27 e 1.54 g 1.5 d Figure 4 shows the caIculated lower mantle dimensionless

partitioning coefficient as a function of pres- Cv, J/moleøK 118 b 120 d 120 d 37 3 b 120 j . ß ß ß ß

sure to the core-mantle boundary. We assume an adiabatic temperature profile and plot results for adiabats initiated at surface temperatures of

o 1000 and 1400 C, cor_responding to temperatures of about 1550 and 2250øC respectively, at 120 GPa (•2600 km depth). The solid curves were calculated assuming no phase change in FeO and indicate that the segregation of iron in n•a decreases rapidly with depth until at about 80 GPa (• 1900 km), K • 1. At greater depths, iron is segregated into the perovskite phase. The segregation decreases with increasing adiabat

Mg;,SiO 4 35-

30

25

20

(GPa) 15

I0

_

o 6()o

MgO + MgSiO3(pv) --

.... P = 2.7.3 -O.002T

- y

p = \\.5 0.0055__.

I I I

I000

aGraham and Barsch [1969] and Kumazawa and Anderson [ 1969 ] ß

b Robie et al. [1978]. Mizukami et al. [1975]. Est imat ed. Suzuki et al. [1979]. Spetzler [1 970].

hgAnderson and Andreatch [ 1969] ß Calculated from lattice parameters of Yagi et

. al. [1979a]. •.Yagi et al. [1979b]. OHelgeson et al. [1978] value for enstatite.

initial temperature. If the phase change in FeO is included, the dashed curves result, with K < 1 throughout the entire lower mantle, indicating that iron remains concentrated in mw at all

depths, although less markedly so with increasing depth. The segregation decreases with increasing adiabat initial temperature.

Thus the concentration of iron in mw at the

expense of pv decreases with depth in the lower mantle, with the high-pressure phase of FeO having a major influence on whether or not iron becomes concentrated in the pv phase in the lowermost mantle.

Effect of Partitioning on Lower Mantle Composition

We investigate the effect of iron partitioning on composition of the lower mantle by considering three simple chemical models: olivine, pyroxene, and a model peridotite (2 o1:1 px) that approxi- mates the composition of the upper mantle [Nokolds, 1954; Graham and Dobrzykowski, 1976].

In Figure 5, we examine the effect of partitioning on the gross zero-pressure density of our model peridotite. We plot the magnesium mole fractions for coexisting partitioned mw and pv phases versus bulk unpartitioned magnesium mole fraction for two values of K (= 0.1 and 0.01). We also plot the density of the mixed- oxide (Mg., Fe• )0 + st ishovite assemblage. It

[400 is apparen• tha•-•artitioning has only a very small effect on gross density, and for plausible

T (øC) mantle bulk magnesium mole fractions, XMg > 0.80, Fig. 3. Pressure-temperature diagram for for- the effect is negligible. sterite. The • • • and • • 7 phase boundaries We follow the approach of Watt and O'Connell are from Suito [1977], while the 7 • MgO + [1978] for both mixed-oxide and mw + pv assem-

MgSiO3(pv) boundary is from Itc et al. [1982]. blages, varying XMg , the bulk magnesium mole


o •H•_- Values Calculated for TABLE 4. S - and

H•-Pressure9•hases of Mg2SiO 4

o o K o S298, J/mole •H298, kJ/mole a

Fo(a) 95.19 b -2170.37 b (+0.84) (+1.32)

Fo(•) 85.3 -2143.2 (+3.5) (+4.1)

Fo(•) •2.3 -21 3-5.9 (+5.7) (+5.4)

MgSiO 3 ( pv ) 69.4 - 1430.1 (+10.3) (+15.1)

•With respect to elements. Robie et al. [1978].

has essentialy no effect on T . Fourth-order finite strain st ill fails to fit Othe lowermost 200-300 km mantle (region D"), where strong velocity gradients or lateral variations in properties have been proposed by Lay and Helmberger [1981] from studies of SH waves.

Table 5 summarizes the •oMg and T values required in the three models fit PEMøand C2 p and K profiles. It can be seen that the •4 + pv models require less iron than the mixed oxides, and that there are not large differences between olivine and py roxene x.. values. Significant differences arise in theMgtemperatures at which mantle adiabats must be initiated, with pyroxene- rich lower mantles requiring hotter geotherms than olivine-rich lower mantles.

We test the plausibility of these T values. o

and hence of the chemical models, by computing adiabats for the lower mantle as in the work of

Watt and O'Connell [1978]. In Figure 8, we ecrupare the calculated profiles with two recent

fraction, and T ,the adiabat initial temperature, literature lower mantle geotherms which make no for the models ø until density and bulk modulus compositional assumptions-Stacey [1977a] and profiles for PEM and C2 [Anderson and Hart, 1976] Brown and Shankland [1981]; however, these geo- are matched below 670 kin. The differences between therms assume a homogeneous mantle with no ther- PEM and the most recent standard earth model- real boundary layers. We note that geotherms Preliminary Reference Earth Model (PREM) [Dzie- derived by Jeanloz and Richter [1979] and Ander- wonski and Anderson, 1981] are not significant son and Baumgardner [1980] using specific oompo- for our purposes. • Since we do not model the shear sitions lie between these two profiles. We esti- modulus, we cannot use the Hashin-Shtrikman mate uncertainties in the calculated model tern- bounds for the bulk modulus; instead, we use the perature profiles by considering the effect of Voigt-Reuss-Hill average. The resulting theoreti- errors in the equation of state parameters in cal uncertainty is at most +6 GPa. Although the Table 1. The chief uncertainties for • + pv finite-strain equations are c•upled in x• and occur in the •K/•P and •K/•T values for the •v TA, the coupling is very weak for the rh]•ge of

p•rameters used here: xN• basically controls the component and contribute an error of about +_800 C at the core-mantle boundary. Obviously, experi- density, while T controls the bulk modulus. We mental determination of these quantities is of use the data of ø Table 1 and assume linear great interest. The effect of a phase change in variation of density, bulk modulus, and •K/•P FeO or changes in the value of • forA the pv with XM_ , a good assumption for mw given the component have only a small effect (•50UC). Thus errors •nd scatter in the experimental data (see, it appears that an mw+ pv lower mantle more for example, Bonczar and Graham [1982]) and also pyroxene-rich than the upper mantle is needed to for pv where compositions are confined to the yield sufficiently high temperatures for eompati- Mg-rich end of the solid _solution. For stishovite, we take p• --4.29 g/cm 5, K• --280 GPa and 3K/3P.-- 5.0 [LieSermann et al., 1976], a -- 18. X 10-ø/•øC [Weaver et al., 1973], and 3K/3T -- -0.035 GPa/øC [Graham, 1973].

Figure 6 shows p versus P plots for the peridotire model with x.. : 0.94 to match the mw+ pv density to the PEMMgand C2 values. The solid line is the result for both partitioned and unpartitioned cases, so that the effect of partitioning is negligible• given the assumptions stated above.

Figure 7 shows the bulk modulus versus P results for the same model with T = 900øC to match PEM and C2. Again, the partitioning effect is negligible. Third-order finite strain is clearly inadequate to account for the seismic model bulk modulus throughout the entire lower mantle. In accord with the results of Banerdt and

Sammis [1980], significant deviations begin to occur when P • 0.15K and at lower pressures for more olivine-rich models. Fourth-order finite

bility with composition-independent geotherms. In order to produce the same temperatures in a

mixed-oxide lower mantle, we would require a higher stishovite •K/•P than used here; we estimate 7 or higher. The final Brillouin scattering

7

6-

5

4

// FeO phase // .... change

• - ••To= •00 •C ..... •-

ø • _x---_-œ__- 0 ..... ,----• ---•----r"---"• "---= •------T----•-- • 20 30 40 50 60 70 80 90 I00 I10 120 150

strain is needed to fit the _seismic models Pressure (GPa)

adequately, wit9 values of •2K/•PZ between -0.02 Fig. 4. Calculated iron partitioning coefficient and -0.05 GPa-, in agreement with the estimates for reaction (1) for adiabats initiated at the of Davies and Dziewonskil[1975] , but larger than surface at temperatures of 1000 ø and 1400øC. The the value of -0.10 GPa- suggested by Graham and dashed curves include the phase change in FeO Justice [1980]. Addition of fourth-order terms observed by Jeanloz and Ahrens [1980].


data of Weidner et al. [1980] on single-crystal stishovite, combined with existing static compression measurements, should provide the data necessary to resolve this question.

We estimate that uncertainties in the equation of state parameters could decrease the magnesium mole fractions in Table 5 by up to 0.08, so that the iron content of the lower mantle could be

similar to, or lower than, that of the upper

mantle; however, the preferred solutions have • values between 0.93 and 0.95 indicating that • lower mantle is more magnesium-rich than the upper mantle. The effect of an FeO phase change is very small (an increase of at most 0.01), as would be expected at the magnesium-rich end of

6.0

5.6

5.2-

4.8

4.4

i i i i

.... mixed oxides

_

_

$' o PEM • C2

I I I I 4.0• 40 80 120 160 200

the solid solution. Pressure (GPo)

Recent shock wave studies on (Mg 0 tF•a 0 )O by Vassiliou and Ahrens [1981] suggest6 •4 Fig. 6. Density versus pressure for mixed- inter- mediate composition mag•esiow•stites may be less oxide and mw+ pv lower mantles of peridotite (2 compressible at high temperatures than would be inferred from a linear interpolation between the end members. By using equation Of state parameters from the shook wave experiments, we find that the T values in Table 5 are increased by 500øC at mos• for mixed oxides and 300øC for mw+ pv, while the x•_ values are reduced by at most 0.02- a slightly•re iron-rich lower mantle results.

I.O

o 0.8

o

E 0.6

'o 0.4

o

.'•_

,.. 0.2-

•' ,5.0

4.8

Per,dotite

- k k - N _

K=O, 10

K=O.01

•,,,• 4.4 MO

_

ort•

4o0• - t i 1 3'81.0 0.9 0.8 0.7 0.6 (•.5

bulk Mg mole froction

o1:1 px) stoichiometry. A bulk magnesium mole fraction of 0.94 is used to match the mw+ pv curve to PEM and C2 profiles. The mw+ pv curve is for both partitioned and unpartitioned cases.

Pyroxene-rich lower mantles were excluded in the study of Watt and O'Connell [1978] because even iron-free MESiO• under lower mantle conditions was denser than • seismic mOdel values. The

estimate of •(pv) described above is the linear thermal expansion, and this value was incorrectly used by Watt and O'Connell rather than the volume thermal expansion given in Table 1. Additionally, the recent improved elasticity data of Jackson et a!. [1978], Jeanloz and Ahrens [1980], and Bon c- zar and Graham [1982] for FeO differ considerably from that of Mizutani et al. [1972] used by Watt and O' Cormell.

We can conclude that, within the uncertainties in our knowledge of mechanical and thermal properties, iron segregation in mw has no detectable effect on gross density and elastic properties of the lower mantle. A magnesiow•stite + perovskite lower mantle appears to be more pyroxene-rich (lower Mg/Si ratio) than the upper mantle and as iron-rich, or somewhat less so, than the upper mantle. A pyrOxene-rich lower mantle has been proposed earlier by Anderson [1970], Anderson et al. [1971], Gaffhey and Anderson [1973], Burdick and Anderson [ 1975], and Butler and Anderson [1978]. Thus the Mg/Si ratio in the lower mantle is closer to the chondritic

value of 0.99 + 0.03 [Ross and Aller, 1976], corresponding to pure pyroxene, than to the upper mantle, where Mg/Si•l.5 for a peridotite with px/oi = 0.4(molar) and x•, = 0.88, as suggested by Anderson [1977]. Thes•'•differences in Mg and Si contents would present a chemical barrier tO single-cell convection extending deep into the lower mantle, a barrier that does not necessarily appear if only Mg and Fe contents of the upper and lower mantles are considered [e.g., Mac, 1974; Watt et al., 1975].

The above arguments apply to a lower mantle Fig. 5. Magnesium mole fractions in coexisting mw and pv of peridotite stoichiometry (2 o1:1 px) modelled in terms of (Mg, Fe) silicates. Jackson as a function of bulk unpartitioned magnesium and Ahrens [1979] have considered the effect of mole fraction for values of 0.10 and 0.01 for the calcium and aluminum (11 weight % total) in a iron partition coefficient. Also plotted are the pyrolite mantle and used 120 GPa shock compres- gross densities of the mw+ pv assemblages sion data to estimate Hugoniot densities in the with and without partitioning, as well as the lowermost mantle. By using their analysis, we densities of simple mixed-oxide (MO) assemblages. calculate that including calcium and aluminum


8OO

720

...-.. 640

--= 560

o

-• 480

400

320

i i i i

mixed oxides

mw + pv /

o PEM

• C2

I

160 200

Pressure (GPe)

the lower mantle. For higher iron contents (

0.80), Prow > p from 6'70 to about 1800 km,XM•n; p > p to t• core-mantle boundary. Thus while t•e F• phase change plays only a small role in determining the lower mantle iron content, it has a major influence on the relative densities of lower mantle mw and pv.

In order to see whether the denser mw in a

mantle more iron rich than present can sink to the core-mantle boundary in sufficiently short times for the gravitational separation cycle to function over geologic time, we require an estimate of mw settling .velocity. We use the results of the modified Stokes problem of a spherical drop of fluid of radius r, density p', and viscosity •' moving under gravity in a fluid of density p and viscosity • [Landau and Lif- shitz, 1959]. The velocity of the particle is given by

v = 2r2g(p- p')(•+ •')/[3•(2• + 3•')] (10)

Fig. 7. Bulk modulus versus pressure for mixed- where g is the acceleration of gravity. We assume oxide and mw+ pv lower mantles of peridotite (2 that • = •' and ignore effects such as departures o1:1 px) stoichiometry. An adiabat initial from sphericity [McNown and Malaika, 1950] and temperature of 900øC is used to match the mw+ pv the influence of unequal particle sizes and curve to PEM and C2 below 700 kin. The mw+ pv suspensions of mineral grains on viscosity curve is for both partitioned and unpartitioned [Walker et al., 1976, 1978]. We estimate that cases. Note that third-order finite strain lacks these effects could alter the calculated sufficient curvature to match the bulk modulus in velocities by no more than a factor of 2. the lowermost mantle. For a peridotite. model with x•o =A 0.8,

p - p = 0.8 g/cm •, and g = 1000 c•sec z (700 k•Wvalu•, we find that •l•settling times would

should increase the density of an (Mg, Fe) be unacceptably long3>(•10 • Gy) for the present silicate lower mantle by at most 0.2%, so that mantle viscosity (10 •- poise) and for reasonable our results for x. in the lower mantle are grain sizes (1 ram). In order to compete slightly low, and a•gmore realistic chemical model successfully with convection, with net vertical would only reinforce our present conclusions. velocities of a few centimeters per year [Davies,

1977; Hager and O'Connell, 1979], mw grain sizes Feasibility of Gravitational Separation of about 12 km would be required, an unrealistic

of mw and pv value given the fact that • and pv form as an intimate mixture on the microscopic level. If we

Concentration of iron in mw at the expense of suppose • separation was completed early in man-

pv appears not to affect the overall density of tie evolution and use •hub•t et al.'s [1978] an mw+ pv assemblage under lower mantle condi- viscosity estimates of 10 -10 -v poise at the end ticns. In order to investigate the plausibility of Earth accretion and Stevenson's [1982] of the gravitational separation of mw hypothesis, estimate of net vertical convective velocity of we must consider the densities of mw and pv about 4.5 m/yr, we still require mw grain sizes individually. of at least 25-250 m. Thus it is unlikely that

In Figure 9, we plot the individual densities gravitational separation of mw could compete for mw and pv in a peridotite lower mantle with successfully with solid state convection. T = 900øC, the value needed to match PEM and C2 A more likely mechanism for removal of iron buølk modulus profiles, by using a calculated from an initially iron-rich lower mantle is partitioning coefficient including an FeO phase melting during accretion or subsequent convection change (Figure 2). The solid curves are for x. = with the entire mantle passing through the 0.95, the value matching PEM and C2 densities.gwe melting zone. FeO will become concentrated in the see that the two phases have essentially equal densities throughout the lower mantle. The fine-

dashed curves are for x M = 1.0, an iron-free lower mantle. AIn this case,gthe pv density is about 0.3 g/cm 5 higher than that of mw. For XM_ = 0.90, more iron rich than the present lo•er mantle, the long-dashed curves indicate that the mw density is about 0.2 g/cm • greater than that of pv. Thus the present lower mantle has an iron content such that p • p , in accord with the mw • v end point of the gravitational separation cycle. If an FeO phase change is not included in the partitioning calculation (Figure 2), for iron

contents satisfying PEM and C2, .Prow • P-, just below 670 km, then Ppv > Prow for th'• remaiSder of

TABLE 5. Magnesium Mole Fractions and Adiabat Initial Temperatures Inferred for Chemical Models of the Lower Mantle

Model

, , ,

mixed oxides mw+ pv

ø C ø C T o , XMg T , o XMg

olivine 100 0.93 700 0.93 peridotit e 600 0.91 900 0.94 pyroxene 1200 O. 92 1500 0.95


low density melt [Stolper and Walker, 1980], and also in upper mantle garnets [Akaogi and Akimoto, 1979]. Thus FeO will be preferentially removed upward in basaltic-picritic melts. Additionally, picritic melts are Si09-poor compared with the primitive mantle. Accordiffgly, the residual mantle would be Si02-rich and FeO-poor.

Another possibl• mechanism for gravitational separation is partial melting of iron-rich mw in the lower mantle. The partial melt could perco- late along pv grain boundaries to the core-mantle boundary. This process would require • to have a lower melting point than pv and would require the mw melt to be denser than the remaining solid. Jackson [1977a, b] reviewed various approaches to the variation of mineral melting points with pressure and concluded that an expansion of melting temperature (T_) •n a polynomial in pressure is probably best. TM Because of the lack of T -P data for the materials of interest here, we adorapt the Lindemann melting law, as advocated by Stacey [ 19 77b ]:

Bln T -- 2(7 - 1/3) (11) •1 n m

6.0 Peridotite

5.5

5.o

4.5 --

T O -- 900oc

4'00 20 40 60 80 Ioo Pressure (GPa)

We use a third-order finite strain equation of Fig. 9. Individual mw and pv densities versus state and assume that 7p-- constant (= .7oPo ). In pressure in a peridotite lower mantle for x M Figure 10, we plot our estimated melting cu•rves 0.95 (which satisfies PEM and C2 densities, •nd

for MgO, FeO, and MgSiO: (pv). We take T• for forlmore iron-rich (xM• --0.90) and iron-free (x.o MgO from Johnson and Mua• [1965] and for FeO from = .0) lower mantles: • These results include t•õ Lindsley [1965], and 7 for MgO from Anderson and FeO phase change of Jeanloz and Ahrens [1980]. Andreatch [1969] and f•r FeO from Jeanloz and Ahrens [1980]. The hatched region represents T -P behavior for magnesiow•stite compositions betwemen x = 0.80, assuming congruent melting. Also giv- (Mg 0 ?Fe O •)0 and (Mg n •5Feo 45)0, the values for en Mg is an MgSiO• (enstatite) T -P curve based on a pa•titi6•ed peridotf• lower mantle with bulk the 0-5.0 GPa m•lting data of Bomyd et al. [1964],

4000 , I ' I ß Stacey (1977)

ß Brown 8, Shankland (1981)

I ......... mixed oxides

3000 t '-- mw + pv 2OO0

I000

l

........... ; .......... 1 .......... l .......... i ......... ; .... o 50 I00 150

Pressure (GPa)

Fig. 8. Adiabatic temperature profiles calculated from the x. and T values of Table 5

o (which allow the •gchemical models to satisfy PEM

using a fit to Simon's law extrapolated to 670 km; below this depth, we use Lindemann's law for MgSiO• (pv). The error bars represent the uncertainty introduced by an error of +_0.5 in 7 o . The estimated melting behaviors of mw and pv are very similar, so that partial melting of mw is not iraplausible. Below 670 kin, mw and pv appear to melt at temperatures 500-1000øC above those of present lower mantle, so that partial melting and gravitational settling of mw and removal of iron at the core-mantle boundary would have to be completed considerably before the lower mantle had cooled to its present state. On the other hand, such elevated temperatures may be higher than one might expect for a mantle cooling by convection; see, for example, Sharpe and Peltier, [1979], Cook and Turcotte [1981], Arkani-Hamad et al. [1981]. Accordingly, the relative melting points of mw and pv and the density of molten mw .... • ...... pv are problems • •J•A •.•A•AA •.

investigation. Stolper eta!. •1981• considered the analogous problem of segregation of basaltic melts.

Conclusions

We have investigated the effect of the strong and C2 density and bulk modulus profiles) for segregation of iron into magnesiow•stite at the olivine (ol), pyroxene (px), and peridotitc (pd) expense of perovskite-structure silicates on the stoichiometries. Included for comparison are the composition and evolution of the lower mantle. In geotherms of Stacey [1977] and Brown and Shank- calculating the variation of the iron partition- land [198!] which were derived without assuming ing coefficient with mantle pressures and specific compositions. temperatures, we required the standard entropy of

5640 Watt and Ahrens.' Iron Partitioning and Mantle Composition

5OOO

4000

T m (oc)

3000

2000

iooo o 20 40 60 80

Pressure (GPc])

conclude that a pyroxene-rich lower mantle is about 1000øC hotter than an olivine-rich lower mantle. For compatibility with geotherms based on other independent approaches, the lower mantle appears to be more pyroxene-rich than the upper mantle and as iron rich, or somewhat less so, than the upper mantle, but not more iron rich. Our preferred values for the lower mantle magnesium mole fraction are 0.93-0.95, compared with 0.85-0.90 for the upper mantle. Thus the Mg/Si ratio in the lower mantle is closer to chondritic values (0.99 + 0.03) .than to the upper mantle-a peridotitc upper mantle with px/ol = 0.4(molar) and x. = 0.88 has Mg/Si • 1.5. This difference in Mgm•nd Si content between upper and lower mantles would pose a barrier to single-cell whole mantle circulation, as would a lower mantle somewhat depleted in Fe relative to the upper mantle. Some previous arguments for major element chemical homogeneity of the mantle, for example, those of Watt et al. [1975], were based on differences in Fe content and were not sensitive

to variations in Mg and Si content. The present study strengthens the arguments for a pyroxene-rich lower mantle and hence for layered mantle convection.

We have studied the feasibility of the gravitational settling of mw mechanism for mantle

Fig. 10. Speculated melting curves for mw and evolution in which an iron rich lower mantle

magnesium-rich MgSiO• (perovskite) calculated by would lose iron at the core-mantle boundary using Lindemann's law. • The enstatite curve (above because of sinking of denser magnesiow•stite and 670 kin) is based on a Simon's law fit to the cycle to its present state where the densities of 0-5.0GPa melting data of Boyd et a1.[1964], shown the magnesiowastite and perovskite phases were as crosses. The hatched region is for • composi- hypothesized to be essentially equal. We find ticns in a partitioned peridotitc lower mantle. that the present lower mantle does have The error bars represent an uncertainty of +0.5 p_. • p_. and that for a more iron-rich mantle, in the zero-pressure Gr•neisen constant. -The o '"w > o •Vthroughout the entire lower mantle; Stacey [1977a] and Brown and Shankland [1981] '•oWr ex•le,• for a bulk •. of 0.80, • - p = temperature curves are included for comparison. 0.7-0.8 g/era J, but only ifm•n FeO phasem•hang•Vis

included.

Investigation of the sinking velocities of

MgSiO•(pv), which we have determined from the P-T denser magnesiow•stite through the lower mantle diagrEm of forsterite, including the recently indicates that iraplausibly large grain sizes and determined 7-MgASiO,. • (Mg, Fe)O + MgSiO• (pv) unacceptably low viscosities are necessary for E 4 o

phase boundary. The value of Sgo R of 69.4($10.3) the gravitational separation hypothesis to J/mole deg for MgSiO:(pv) is'•5out 2.5% •arger compete successfully with convection in the solid than that of MgSi0 3 (•nstatite), in agreement state over geologic time to a state of mw and pv with the prediction of Navrotsky. density equality. The likely mechanism for

The iron partitioning coefficient increases depletion of iron in an initially iron rich lower with depth in the lower mantle, from 0.06 at 670 mantle is upward extraction of FeO-rich melts km to about 6 at the core-mantle boundary, but if during accretion and subsequent convection. If mw the recently discovered FeO phase change is were to partially melt in the lower mantle, the included, the partitioning coefficient remains gravitational separation process could perhaps less than unity throughout the lower mantle operate, but we estimate only at temperatures at (• 0.8 at the base of the mantle), indicating least 500 to 1000øC higher than those in the that iron remains concentrated in magnesiow•stite present lower mantle. If partial melting occurred to the core-mantle boundary. Our calculations early in Earth history, the combination of a demonstrate that the partitioning is not suffici- lower melting point for (Mg, Fe)O enriched in ent to produce a lower mantle of essentially pure iron, and the higher density of this phase, which FeO in equilibrium with essentially pure results from equilibrium with perovskite-

MgSiO3(PV). structure silicates, could perhaps give rise to We find that partitioning of iron has no this lower mantle differentiation. Since the

detectable effect on lower mantle gross density elevated temperatures estimated for this process and elastic properties, so that its presence is to occur are higher than those calculated in most likely transparent to seismic studies. We parameterized convection studies, investigation assume simple chemical models, third-order Finite of the relative melting temperatures of mw and pv strain, an adiabatic lower mantle, a linear and of the effect of partial melting on relative variation of density and elastic properties densities and iron partitioning in • and pv is within mw and pv solid solutions, and by using needed to test the viability of the partial melt- recent ultrasonic, shook wave, and static corn- ing hypothesis. pression results for FeO and MgSiO3(PV) , we The concentration of iron in the • component


of the high-pressure products of mantle silicates Anderson, O. L., and P. Andrearch, Pressure deri- could explain the depletion of iron in the vatives of elastic constants of single-crystal earth's mantle with respect to the upper mantle MgO at 23 ø and-195.8øC, J. Am. Ceram. Soc., and the mantles of other planetary bodies for 4__9, 404-409, 1966ß which we have estimates of compositionß In the Anderson, O. L., and J. R. Baumgardner, Equations earth, mw and pv will form from silicates and of state in planet interiors, Proc. Lunar Plan-. removal of iron from the iron-enriched mw phase et. Sci. C0nfß , 11th, 1999-2014, 1980. could occur either in the upper mantle by upward Anderson, O. L., E. Schreiber, R. C. Liehermann, extraction of FeO-rich melts or at the base of and N. Soga, Some elastic constant data on the mantle after gravitational settling of mw as minerals relevant to geophysics, Rev. Geophys., a consequence of partial melting, leaving the 6, 491-524, 1968. mantle depleted in iron relative to the mantles Arkani-Hamed, J., M. N. Toksõz, and A. T. Hsui, of smaller bodies, which have internal pressures Thermal evolution of the Earth, Tectonophysics, too low for formation of perovskite-structure 7__5, 19-30, 1981. silicates or lower accretional temperatures and Arvidson, R. E., K. A. Goettel, and C. M. Holen- less extensive melting. Accordingly, we propose that the mantle of Venus has an iron content much

more similar to the earth's mantle than to that

of other terrestrial planets and satellites.

Acknowled•ents. We appreciate discussions with D. L. Anderson, A. Navrotsky, D. J. Steven-

berg, A post-Viking view of Martian geologic evolution, Rev. Geophys. Space Phys., 18, 565- 603, 1980.

Bartertit, W. B., and C. G. Samis, An evaluat'ion of finite strain equations of state using a lattice model, Phys. Earth Planet. Inter., 23, 31-38, 1980.

son, J.M. Vizgirda, and E. B. Watson. E. Itc Bell, P.M., T. Yagi, and H. K. Mac, Iron-magne- kindly made available a preprint. D. L. Anderson slum distribution coefficients between spinel

offered detailed comments on the manuscript; [(Mg, Fe)oSiO,], magnesiow•stite [•(Mg, Fe)O], B. H. Hager and an anonymous reviewer provided and perov•kit• [(Mg, Fe)SiO•], Year Book Carne- helpful suggestions. Supported by NSF grants EAR gie Inst. Washington, 1•78,•618•-• - 1979- 79-06766 and EAR 79-26384. Contribution 3647, Binder, A. B., On the internal structure of a Division of Geological and Planetary Sciences, moon of fission origin, J. Geophys. Res., 85, California Institute of Technology, Pasadena, 4872-4880, 1980ß California 91125ß Bonczar, L. J., and E. K. Graham, The pressure

and temperature dependence of the elastic prop- References erties of polycrystal magnesiow•stite, J. Geo-

phys. Res., 87, 1061-1078, 1982. Ahrens, T.J., The state of mantle minerals, Boyd, F. R., J. L. England, and B. T. C. Davis,

Tectonophysics, 13, 189-219, 1972. Effects of pressure on the melting and polymor- Ahrens, T. J., Petrologic properties of the upper phisin of enstatite, MgSi03, J. Geophys. Res.,

670 km of the Earth's mantle: Geophysical ira- 69, 2101-2109, 1964. plications, Phys. Earth Planet. Inter., 7_, 167- Brown, J. M., and T. J. Shankland, Thermodynamic 186, 1973. parameters in the earth from seismic profiles,

Ahrens, T. J., and Y. Syono, Calculated mineral Geophys. J. R. Astron. Soo., 66, 579-596, 1981. reactions in the Earth's mantle, J. Geophys. Buck, W. R., and M. N. Toksõz, The bulk composi- Res,, 72, 4181-4188, 1967. tion of the moon based on geophysical con-

Akaogi, M., and S. Akimoto, High-pressure phase straints, Proc. Lunar Planet. Sci. Conf., 11.th, equilibria in a•arn•t lherzolite, with special 2043-2058, 1980. reference to Mg•-Fe •+ partitioning among con- Burdick, L., and D. L. Anderson, Interpretation stituent minerals, Phys Earth Planet Inter., of velocity profiles of the mantle, J. Geophys e, ß ß

19, 31-51, 1979. Res., 80, 1070-1074, 1975. Akimoto, S.-I., M. Akaogi, K. Kawada, and O. Butler, R., and D. L. Anderson, Equation of state

Nishizawa, Mineralogic distribution of iron in fits to the lower mantle and outer core, Phys. the upper half of the transition zone in the Earth Planet. Inter., 17, 147-162, 1978. earth's mantle, in The Geophysics of the Pacif- Christensen, U., Numerical experiments on convec- ic Ocean Basin and its Margins, Geophys. Mono- tion in a chemically layered mantle, J. Geo- gr. Ser., vol. 19, edited by G. H. Sutton, M. phys., 4__•9, 82-84, 1981ß H. Manghnani, and R. Moberly, pp. 399-405, AGU, Clark, S.P., Handbook of Physical Constants, Washington, DC, 1976.

Anderson, D. L., Petrology of the mantle, Miner- ß ß ß ai. Soc Am Spec Pap., 3__, u•-•3, ß

Anderson, D.L., Composition of the mantle and core, Ann. Rev. Earth Planet. Sci., 5_, 179-202, 1977.

Anderson, D. L., Chemical stratification of the mantle, J. Geophys. Res., 84, 6297-6298, 1979.

Mem., vol. 97, Geological Society of America, Boulder, Colo., 1966.

convection and the thermal evolution of the

earth, Tectonophys. ics, 7_•5, 1-17, 1981. Davies, G. F., Whole-mantle convection and plate

tectonics, Geophys. J. R. Astron. Soc., 4_•9, 459-486, 1977ß

Anderson, D.L., Tectonics and composition of Davies, G.F., Earth's neodymium budget and Venus, Geophys. Res. Lett.., 7_, 101-102, 1980. structure and evolution of the mantle• Nature,

Anderson, D. L., and R. S. Hart, An earth model 290, 208-213, 1981. based on free oscillations, J. Geophys. Res., Davies, G. F., and A.M. Dziewonski, Homogeneity 81, 1461-1475, 1976. and constitution of the earth's lower mantle

Anderson, D. L., C. Sammis, and T. Jordan, Corn- and outer core, Phys. Earth Planet. Inter., 10, position and evolution of the mantle and core, 336-343, 1975. Science., 171, 1103-1112, 1971. Dziewonski, A.M., and D. L. Anderson, Prelimi-


nary reference earth model, Phys. Earth Planet. Jeanloz, R., and T. J. Ahrens, Equations of state Inter., 25, 297-356, 1981. of FeO and CaO, Geophys. J. R. Astron. Soc.,

Dziewonski, A.M., A. L. Hales, and E. R. Lap- 62, 505-528, 1980. wood, Parametrically simple earth models con- Jeanloz, R., and F. M. Richter, Convection, com- sistent with geophysical data, Phys.. Earth position, and the thermal state of the lower Planet. Inter., 10, 12-48, 1975. mantle, J. Geophys. Res., 84, 5497-5504, 1979.

Gaffney, E. S.,2+and D. L. Anderson, Effect of Johnson, R. E., and A. Muan, Phase equilibria in low-spin Fe on the composition of the lower the system CaO-MgO-iron at 1500øC, J. Am. Ce- mantle, J. Geoph¾s. Res., 78, 7005-7014, 1973. ram. Soc., 48, 359-364, 1965.

Goins, N.R., M. N. Toksõz, and A.M. Dainty, Jones, L. E. A., High temperature elasticity of Seismic structure of the lunar mantle: An fluoride and oxide analogues, Ph.D. thesis, overview, Proc. Lunar Planet. Sci. Conf., 9th, Australian National University, Canberra, 1976. 3575-3588, 1978. Kern, R., and A. Weisbrod, Thermodynamics for

Graham, E. K., On the compression of stishovite, Geologists, translated from French by D. McKie, Geophys. J.•R. Astron. Soc•, 3•2, 15-34, 1973. 304 pp., Freeman, Cooper, San Francisco, 1967.

Graham, E. K., and G. R. Barsch, Elastic con- Kumazawa, M., and O. L. Anderson, Elastic moduli, stants of single-crystal forsteritc as a func- pressure derivatives, and temperature deriva- tion of temperature and pressure, J. Geophys. tives of single-crystal olivine and single- Res., 74, 5949-5960, 1969. crystal forsteritc, J. Geophys. Res., 74, 5961-

Graham, E. K., and D. Dobrzykowski, Temperatures 5972, 1969. in the mantle as inferred from simple composi- Landau, L. D., and E. M. Lifshitz, Fluid Mecha- tional models, Am. Mineral., 61, 549-559, 1976. nics, p. 69, Addison-Wesley, Reading, Mass.,

Graham, E. K., and P. R. Justice, Temperature in 1959. the lower mantle using compositional con- Lay, T., and D. V. Helmberger, A lower mantle SH straints, paper presented at International wave triplication and lateral varations in D" Conference on Mathematical Problems of the (abstract), Eos Trans. AGU, 62, 333, 1981. Thermal and Dynamic State of the Earth, IUGG Liebermann, R. C., Elasticity of the mantle, in Inter-Association Committee on Mathematical

Geophysics, U.S. Geodynamics Committee, and European Geophysical Society, sponsors, Lake Arrowhead, Calif., 1980.

Hager, B.H., and R. J. O'Connell, Subduction zone dip angles and flow driven by plate motion, Tectonophysics, 50, 111-133, 1978.

Hager, B.H., and R. J. O'Connell, Kinematic models of large-scale flow in the earth's mantle, J..Geophys. Res., 84, 1031-1048, 1979.

Hahn, W.C., and A. Muan, Activity measurements

The Earth-Its Origin• Structure• and Evolution, edited by M. W. McElhinny, pp. 203-226, Acade- mic, New York, 1979.

Liebermann, R. C., A. E. Ringwood, and A. Major, Elasticity of polycrystalline stishovite, Earth Planet. Sci. Lett., 32, 127-140, 1976.

Liebermann, R.C., L. E. A. Jones, and A.E. Ringwood, Elasticity of aluminate, titanate, stannate, and germanate compounds with the perovskite structure, Phys. Earth Planet. In-

ter., 14, 165-178, 1977. in oxide solid solutions: The system_ "FeO"-M_gO Lindsley, D.H., Pressure-temperature relations in the temperature interval 1100 ø to 1300øC, in the system FeO-SiO Year Book Carnegie Trans Metall Soc AIME, 224, 416-420, 1962 Inst. Washington, 1965, 2' .... . __ 226-230, 1965.

Helgeson, H.C., J.M. Delaney, H.W. Nesbitt, Liu, L.-G., Orthorhombic perovskite phases ob- and D. K. Bird, Summary and critique of the served in olivine, pyroxene, and garnet at high thermodynamic properties of rock-forming miner- pressures and temperatures, Phys. Earth Plan- als, Am. J. Sci.., 278A, 1-229, 1978. et. Inter., 11, 289-298, 1976.

Hentschel, B., Stoichiometric FeO as metastable Liu, L.-G., Phase transformations and the consti- intermediate of the decomposition of w•stite at tution of the deep mantle, in The Earth-It_•s 225-C, Z. Naturforsch., 25a, 1996-1997, 1970. Origin• Structure• and Evolution, edited by M.

Ito, E., and H. Yamada, Stability relations of W. McElhinny, pp. 177-202, Academic, New York, silicate spinels, ilmenites, and perovskites, 1979. Proc. U.S.-Jpn. Seminar Hi•h-Pressure Res.: Mao, H. K., and P.M. Bell, Disproportionation Appl. Geop•hys., in press, 1982. equilibrium in iron-bearing systems at pres-

Jackson, I., Melting of some alkaline-earth and sures above 100 kbar with applications to chem- transition-metal fluorides and alkali fluoro- istry of the earth's mantle, in Energetics of beryllates at elevated pressures: A search for Geological Processes, edited by S. K. Saxena melting systematics, Phys. Earth Planet. In- and S. BhattacharJi, pp. 236-249, Springer- ter., 14, 143-164, 1977a. Verlag, New York, 1977.

Jackson, I., Phase relations in the system LiF- Mao, H.K., T. Takahashi, W. A. Bassett, and J. MgF 2 at elevated pressures: Implications for S. Weaver, Effect of pressure and temperature the proposed mixed-oxide zone of the earth's on the molar volumes of w•stite and of three mantle, Phys. Earth Planet. Inter., 14, 86-94, (Fe, Mg) SiOn, spinel solid solutions, J. Geo- 1977b. -- phys. Res2., 774, 1061-1069, 1969.

Jackson, I., and T. J. Ahrens, Shock wave corn- Mao, H. K., P.M. Bell, and T. Yagi, Iron-magne- pression of single-crystal forsterite, J. Geo- sium fractionation model of the earth, Year phys. Res., 84, 3039-3048, 1979. Book Carnegie Inst. Washinston, 1978, 621-625,

Jackson, I., and A. E. Ringwood, High-pressure 1979. polymorphism of the iron oxides, Geophys. J.R. Mao, N.-H., Velocity-density systematics and its Astron. Soc., 64, 767-783, 1981. implications for the iron content of the man-

Jackson, I., R. C. Liebermann, and A. E. Ring- tle, J. Geophys. Res., 7•9, 5447-5452, 1974. wood, The elastic properties of (Mg., Fe )0 McNown, J. S., and J. Malaika, Effects of parti- x 1-x solid solutions, Phys. Chem. Minerals, 3, cle shape on settling velocity at low Reynolds 11-31, 1978. numbers, Eos Trans. AGU, 31, 74-82, 1950.


Mizukami, S., A. Ohtani, and N. Kawai, High-pres- solidus convective cooling of terrestrial plan- sure x-ray diffraction on •-and 7-Mg•SiOa, ets, Icarus, 38, 192-211, 1979. Phys. Earth Planet. Int. 10, 177-182, 1975. - Sharpe, H. N. an• W. R. Peltier, A thermal his-

Mizutani, H., Y. Hamano, and S.I. Akimoto, Elastic-wave velocities of polycrystalline sttshovtte, J. Geophys.. Res., 77, 3744-3749, 1972.

Morgan, J.W., and E. Anders, Chemical composition of Earth, Venus, and Mercury, Proc. Natl. Acad. Sct. U..S.., 77, 69 73-69 77, 1980.

Navrotsy, A., Lower mantle phase transitions may generally have negative pressure-temperature slopes, Geophys. Res. Lett., 7, 709-711, 1980.

tory model for the earth with parameterized convection, Geoph¾s. J. R. Astron. Soc., 59, 171-203, 1979.

Shimazu, Y., Chemical equilibrium within self- gravitating planets and internal constitution of the earth, J. phy. s.. Earth, 4, 43-47, 1956.

Simons, B., Composition-lattice parameter relationship of the magnesiow•stite solid solution series, Year Book Carnegie Inst. Washinstdn, 1979, 376-380, 1980. •

Navrotsky, A., and P. K. Davies, Cesium chloride Smith, J. V., Mineralogy of the planets: A voyage versus nickel arsenide as possible structures in space and time, Mineral. Ma•., 4_•3, 1-89, for (Mg, Fe)O in the lower mantle, J. Geophys. 1979. Res., 86, 3689-3694, 1981. Spetzler, H., Equation of state of polycrystal-

Netl, J. M., A. Navrotsky, and O. J. Kleppa, The line and single-crystal MgO to 800 kilobars and enthlapy of ilmenite-perovsktte transformation 800øK, J. Geophys...Res., 75, 2073-2087, 1970. in cadmium titanate, Inor•. Chem., 10, 2076- Stacey, F. D., A thermal model of the earth, 2077, 1971. Phys. Earth Planet. Inter., 15, 341-348, 1977a.

Noekolds, S. R., Average chemical composition of Stacey, F. D., Applications of thermodynamics to some igneous rocks, Bull. Geol. Soc. Am.., 65, fundamental earth physics, Geophys. Surv., 3, 1007-1032, 1954. 175-204, 1977b.

O'Connell, R. J., On the scale of mantle convet- Stevenson, D.J., The nature of the earth prior rich, Tectonophysics, 38, 119-136, 1977. to the oldest known rocks (the Hadean Earth),

Richter, F. M., and C. E. Johnson, Stability of a in Origin and Evolution of the Earth's Earliest chemically layered mantle, J. Geophys. Res., Biosphere: An InterdisciPlinary Study, edited 79, 1635-1639, 1974. by J. W. Schopf, Princeton University Press,

Richter, F. M., and D. P. McKenzie, On some con- Princeton, N.J., in press, 1982. sequences and possible causes of layered mantle Stevenson, D. J. and J. S. Turner, Fluid models convection, J. Geophys. Res., 86, 6133-6142, of mantle convection, in The Earth-Its Origin, 1981. Structure• and Evolution, edtbed by M. W. McE1-

Ringwood, A.E., Mineralogical constitution of birmy, pp. 227-263, Academic, New York, 1979. the deep mantle, J. Geophys. Res..., 67, 4005- Stolper, E.M., Experimental petrology of 4010, 1962. • eucritic meteorites, Geochtm. Cosmochtm. Acta,

Ringwood, A. E., Composition and Petrolo•y of the 41, 587-611, 1977. Earth's Int. er. i0r , 618 pp., McGraw-Hill, New Stolper, E., and D. Walker, Melt density and the York, 1975. average composition of basalt, Conbrtb. Miner-

Ringwood, A.E., Composition of the core and al. Petrol., 74, 7-12, 1980. implications for the origin of the earth, Geo- Stolper, E. M., D. Walker, B. H. Hager, and J. F. chem. J., 11, 111-135, 1977a. Hays, Melt segregation from partially molten

Ringwood, A. E., Basaltic magmatism and the bulk source regions: The importance of melt density composition of the moon, The Moon, 1_•6, 389-423, and source region size, J. Ge0phys. Res., 86, 1977b. 6261-6271, 1981.

Ringwood, A.E., and D. L. Anderson, Earth and Suito, K., Phase relations of pure Mg•SiOa up to Venus: A comparative study, Icarus, 30, 243- 200 kilobars, in High-Pressure Research:' Appl !- 253, 1977. cations in Geophysi.cs , edited by M. H. Manghna-

Robie, R. A., B. S. Hemingway, and J. R. Fisher, nt and S. I. Akimoto, pp. 255-266, Academic, Thermodynamic properties of minerals and re- New York, 1977. lated substances at 298.15K and 1 bar (105 Suzuki, I., E. Ohtant, and M. Kumazawa, Thermal Pascals) pressure and at higher temperatures, expansion of 7-Mg2Si04, J. Phys. Earth, 27, 53- U.S. Geol.. Surv. Bull..145.2 , 456 pp., 1978. 61, 1979. --

Rosenhauer, M., H. K. Mac, and E. Woermann, Corn- Vasstltou, M. S., and T. J. Ahrens, The equation pressibtltty of magnesiow•stite (Fe 0 aMgn 6 )0 of state of (Mgn•6Fe )0 to 200 GPa, Geophys. to 264 kbar, Year Book Carnesic Inst.'•as•n•.-. Res. Lett., 9_, 1•7-138;41982. ton, 1975, 513-515, 1976. Walker, D., J. Longhi, R. J. Kirkpatrick, and

Ross, -•. • , o-• L H "•er The chemical ecru- Differentiation of an Apollo 12 ......... a-- , J. F. Hays, position of the sun, Science , 19.1, 1223-1229, plcrite magma, Proc. Lunar Sct. Conf., 7th , 1976. 1365-1389, 1976.

sammis, c.G. , J. C. Smith, G. Schubert, and D. Walker, D., E. M. Stolper, and J. F. Hays, A A. Yuen, Viscosity-depth profile for the numerical treatment of melt/solid segregation: earth's mantle: Effect of polymorphic phase Size of the eucrtte parent body and stability transitions, J. Geop. hys. Res., 8_•2, 3747-3761, of the terrestrial low-velocity zone, J. Geo- 1977. phys. Res., 83, 6005-6013, 1978.

Sawamoto, H., Orthorhombic perovskite (Mg,Fe)SiO• Wasserburg, G.J., and D. J. DePaolo, Models of and the constitution of the lower mantle, i• earth structure inferred from neodymium and High-Pressure Research: Applications in Geo- strontium abundances, Proc. Natl. Acad. Sci. physics, edited by M. H. Manghnani and S.I. U.S., 76, 3594-3598, 1979. Akimoto, pp.219-244, Academic, New York, 1977. Watt, J.P., and R. J. O'Connell, Mixed-oxide and

Schubert, G., P. Cassen, and R. E. Young, Sub- perovskite-structure model mantles from 700-


1200 kin, Geophys. J. R. Astron.. Soc., 54, 601- perovskite phase of orthopyroxene composition 630, 1978. (Mg, Fe)SiO , in Year Book Carnegie Inst.

Watt, J.P., T. J. Shankland, and N.-H.Mao, Uni- Washington,31978, 612-613, 1979a formity of mantle composition, Geolo•.y, 3_, 91- Yagi, T., H. K. Mac, and P.M. Bell, Hydrostatic 94, 1975.

Weaver, J. S., T. Takahashi, and W. S. Bassett, Thermal expansion of stishovite (abstract), Eos Trans. AGU, 54, 475, 1973.

Weidner, D.J., J. D. Bass, A. E. Ringwood, and W. Sinclair, Elasticity of stishovite (abstract), Eos Trans. AGU, 61, 379, 1980.

White, G. K., and O. L. Anderson, Gr•neisen parameter of magnesium oxide, J. Appl. Phys., 37, 430-432, 1966.

Yagi, T., H. K. Mac, and P.M. Bell, Lattice parameters and specific volume for the

compression of MgSiO q of perovskite structure, Year Book Carnegie In•t. Washington, 1978, 613- 614, 1979b.

Zou, G. T., H. K. Mac, P.M. Bell, and D. Virgo, High-pressure experiments on the iron oxide wRstite (Fe )0, Year Book Carnegie Inst. Washington, 1•7_•9, 374-376, 1980.

(Received June 10, 1981; revised January 11, 1982;

accepted January 15, 1982. )

Documents

The role of iron partitioning in mantle composition ...authors.library.caltech.edu/51198/1/jgrb4072.pdf · J/mol• deg from the recently determined phase ly depleted in iron. diagram