etters xx (2006) xxx–xxx

+ MODEL

EPSL-08365; No of Pages 12

www.elsevier.com/locate/epsl

ARTICLE IN PRESS

Earth and Planetary Science L

Slab dehydration in the Earth's mantle transition zone

Guillaume Richard ⁎, David Bercovici, Shun-Ichiro Karato

Department of Geology and Geophysics, Yale University, United States

Received 17 March 2006; received in revised form 18 July 2006; accepted 5 September 2006

Editor: C.P. Jaupart

Abstract

Because of the high water solubility in wadsleyite and ringwoodite, the mantle transition zone is possibly a large waterreservoir. The potentially high water content of the Earth's mantle transition zone is a key element of several global mantledynamic models. Nevertheless, to keep the transition zone relatively wet, the tendency for convection to distribute water over theentire mantle has to be offset by other mechanisms. One such mechanism could be linked to the dehydration of the slab. Studies ofslab dehydration mainly focus on hydrous minerals phase diagrams that provide the depth of water exsolution. In this study, weinvestigate the water diffusion process that occurs prior to such exsolution. The diffusion process is controlled by both chemicalgradients and thermal gradients via the temperature dependence of water solubility. We have addressed how this diffusionphenomenon influences slab water transport into the transition zone by developing a theoretical model of coupled thermal andchemical diffusion in a flat lying slab stalled in the transition zone.

Model solutions demonstrate that even if intrinsic water solubility is decreasing with increasing temperature (which normallywould act to impede a chemical diffusion from the slab), the water concentration profile adjusts to reduce the adverse effects oftemperature-dependent solubility. The self-adjustment entails the concentration of water reaching a local maximum below the topedge of the stagnant slab; under specific conditions, this concentration maximum can reach the solubility limit and thus exsolvefluid (i.e. create of hydrous melt or aqueous silicate fluid). Consequently, model water flux computations are relatively independentof solubility variation and indicate that much of the water flux introduced by relatively well hydrated slabs is taken up into thetransition zone by diffusion.© 2006 Published by Elsevier B.V.

Keywords: Water; Double diffusion; Stagnant slab; Transition zone; Water solubility

1. Introduction

Water plays various important roles in controlling thedynamics and evolution of the Earth's interior. Two areasin the Earth's mantle are able to store large amounts ofwater, i.e., the oceanic crust and lithosphere and the

⁎ Corresponding author.E-mail address: guillaume.richard@yale.edu (G. Richard).

0012-821X/$ - see front matter © 2006 Published by Elsevier B.V.doi:10.1016/j.epsl.2006.09.006

Please cite this article as: Guillaume Richard et al., Slab dehydration in the(2006), doi:10.1016/j.epsl.2006.09.006

transition zone (between 410 km and 660 km depths).The oceanic crust and shallow lithosphere undergolengthy traverses along the bottom of the oceans and arethus well hydrated. Subduction transports some of thiswater into the mantle, although how much water istransported this way remains unclear [1–3]. However,even if a large part of the subducted water was releasedback to the hydrosphere through arc volcanism, in coldslabs a significant amount (∼40% of its initial water

Earth's mantle transition zone, Earth and Planetary Science Letters

Fig. 1. The dehydration of a stagnant slab in the mantle transition zoneThe essence of the model hypothesis: The diffusion of water out of theslab and the diffusion of heat into the slab occur simultaneously andare coupled by the temperature dependence of the water solubility.

2 G. Richard et al. / Earth and Planetary Science Letters xx (2006) xxx–xxx

ARTICLE IN PRESS

content) is released by the breakdown of sediments,crust, and serpentinized mantle at high pressure andtemperature [2] is likely stored in various dense hydrousmagnesium–silicate phases (DHMS) that can be carriedto depths of 450 km [3–5]. At depths between 410 and660 km, in the transition zone, the water solubility is veryhigh and the water can be stored in ringwoodite (up to2.4 wt.%) or in wadsleyite (up to 2.7 wt.%) [6]. Theamount of water that slabs can carry down to the transi-tion zone storage area depends on the transit time of slabsacross the transition zone. In particular, tomographicimaging depicts many slabs deflected horizontally andlingering in the transition zone [7]. One unresolvedquestion concerns the way water, carried by a subductingslab, behaves when it enters and dwells in this highsolubility area. Global models like the transition zonewater-filter model [8] and electrical conductivity data [9]suggest that the transition zone water reservoir is slightlyhydrated (of order of 0.1 wt.% or less than 10% of itscapacity). Convective mixing on the mantle tends toprevent the transition zone from soaking up water bysimple diffusion from the lower and upper mantles,where water solubility is lower [10]. Therefore, otherprocesses are required to bring water into this reservoir.Previous studies have described two processes providingwater: one “from the bottom” and one “from the top”.Upward percolation of water expelled from slabsentering the low-solubility lower mantle at 660 kmdepth is likely to be one way to hydrate the transitionzone [8,11]. At the transition zone upper boundary(410 km depth), the possible melt layer of the water-filtermodel [8] caused by dehydration of supersaturated up-wellingmantle provides a trap and source of water whichwould be entrained back into the transition zone by slabs[8,12].

Another way to hydrate the transition zone is fromdehydration of slabs stagnating in the transition zone.This dehydration is controlled by the stability of densehydrous magnesium silicates (DHMS) [13]. Given thephase diagrams of these DHMS under the pressures ofinterest, fluid exsolution can be located at certain depthsand temperature. However, water can also leave the slabwithout invoking exsolution of fluids. Because waterconcentration in the slab is higher than in the surr-ounding mantle, diffusion will take place. In this case,one important effect influencing water transport is thetemperature-dependence of water solubility in thesystem MgO–SiO2–H2O. Under high temperature(TN200 °C) and pressure (i.e. transition zone) condi-tions, experiments done under wet conditions indicatethat the transition minerals wadsleyite and ringwooditealways coexist with a fluid (certainly close to a hydrous

Please cite this article as: Guillaume Richard et al., Slab dehydration in the(2006), doi:10.1016/j.epsl.2006.09.006

melt) that contains abundant dissolved oxides, and thepresence of such fluids is likely to influence solubilitymeasurements [14]. Because of these fluids and of thetemperature dependence of water fugacity [15], themeasured water storage capacity decreases with increas-ing temperature in wadsleyite [14] and in ringwoodite[16]. However, as shown below (see Appendix B.2),water fugacity does not play any role in the diffusionprocess and thus the effect of fugacity on the tempe-rature dependence of solubility must be removed beforeevaluating the chemical potential of water in transitionzone minerals. As detailed below (cf. Section 2.1), theintrinsic chemical potential mainly controls the temper-ature dependence of water solubility and thus influencesthe water diffusion process, and affects both the waterconcentration profile in this region as well as the flux ofwater out of the slab. Our goal is to understand how thetemperature dependence of water solubility influencesslab water transport into the transition zone. To do so,we have developed and explored a theoretical model todescribe the basic physical process of coupled chemicaland heat transport at the slab-mantle interface.

2. Model description

Our theoretical model describes transport of waterout of and heat into a slab temporarily floating in thetransition zone (Fig. 1). The two transport processes arecoupled by the temperature dependence of water solu-bility in transition zone minerals.

2.1. Coupling of the heat and water fluxes

One can employ the formalism of linear nonequilib-rium thermodynamics (see [17]) to define the fluxes andconjugate or thermodynamics forces of our system (seeAppendix B.1 for details). According to the second lawof thermodynamics, the rate of entropy production is

Earth's mantle transition zone, Earth and Planetary Science Letters

3G. Richard et al. / Earth and Planetary Science Letters xx (2006) xxx–xxx

ARTICLE IN PRESS

positive–definite and in general the heat flux JT (J m−2

s−1) and the chemical (water) flux JW (mol m−2 s−1) arecoupled such that:

JT ¼ L11j1T−L12j

lT

JW ¼ L12j1T−L22j

lT

8><>: ð1Þ

where Lij (i, j=1, 2) are called phenomenologicalcoefficients (or elements in a positive–definite matrix),μ is the chemical potential of water and T is the temp-erature. The Onsager reciprocal theorem tells us thatL12=L21 [18]. In our system, the heat diffusivity is muchhigher than the water diffusivity and it can be shown(see Appendix B.1) that chemical heat transport L12j l

T

is negligible compared to L11j1

T. Assuming that L21

L22is a

constant, JW can also be recast to yield:

JT ¼ L11j1T¼ −kjT

JW ¼ −RL22jl− L21

L22

RT

8><>: ð2Þ

whereR is the gas constant and k the thermal conductivity.The chemical potential is given by μ=μ0+RT ln(a),where μ0 is the standard-state chemical potential of dis-solved water. Water concentration (–OH) is directlyproportional to the concentration ofmagnesium vacanciesVMg″ that we assume to be ideally mixed [19], thus the

Table D.1Used variables and parameters

Symbols Names

κ Thermal diffusivityk Thermal conductivityα Water diffusivityC⁎ Water solubilityμ0 Standard-state chemical potential of bonded watefH2OP0

Dimensionless water fugacityaMgO MgO chemical activityμi0 Standard-state chemicalppotential of element I

Δμ0 Standard-state chemical potential variation

C Water concentrationC̄ Average temperature on the studied profileδC ConcentrationT TemperatureT̄ Average temperature on the studied profileδT Temperature rangeρ Mantle densityCP Mantle thermal capacity at constant pressureη Similarity variableΦ(η) Normalized water concentrationθ(η) Normalized temperature

Please cite this article as: Guillaume Richard et al., Slab dehydration in the(2006), doi:10.1016/j.epsl.2006.09.006

activity a can be replaced by the water concentration C.Introducing the water solubility [6],

C⁎ ¼ fH2O

P0aMgOe−

l0−Dl0RT ð3Þ

the chemical potential reads (see Appendix A):

l ¼ l0 þ RT lnðCÞ ¼ Dl0 þ RT lnfH2O

P0aMgO

CC⁎

� �ð4Þ

wherefH2OP0

is the dimensionless water fugacity,Δμ0 is thestandard-state chemical potential variation (see Table D.1for definition) and aMgO is the magnesium oxide activity.

Introduction of Eq. (4) into the expression for the fluxJW in Eq. (2) (see Appendix B.2 for a detailed deri-vation) leads to:

JW ¼ −að−Cjln C̄⁎ þjCÞ ¼ J⁎W þ JCW ð5Þ

where a ¼ L22RC

is the water diffusivity which weassume is constant, and C̄* is the intrinsic (or effective)solubility defined as:

C̄⁎ ¼ P0aMgO

fH2Oe−

Dl0−L21L22

RT C⁎ ¼ e−l0−

L21L22

RT ¼ e−ERT ð6Þ

where we introduce E ¼ l0−L21L22

hereafter referred as the

‘intrinsic’ chemical potential. At high pressure, the water

Values Units

10−6 m2 s−1

3.3 Jm−1 s−1 K−110−8–10−10 m2 s−1fH2O

P0aMgOe−

l0−D0lRT mol−1

r −100–+100 kJ mol−1

109–1010 –0.5 –– kJ mol−1

μH2O0 +μMg

0 –μMgO0 kJ mol−1

C̄− dC2 UðgÞ wt.%

0.5–2 wt.%0.5–2 wt.%T̄− dT

2 h gð Þ °C1300–1400 °C300–400 °C3300 kg m3

103 J. kg−1

K− 1

z2ffiffiffijt

p –−1–+1 –−1–+1 –

Earth's mantle transition zone, Earth and Planetary Science Letters

4 G. Richard et al. / Earth and Planetary Science Letters xx (2006) xxx–xxx

ARTICLE IN PRESS

fugacity decreases strongly with increasing temperature[15] and thus the temperature dependence of C* and C̄*can have opposite trends (see Appendix D).

The water flux can be seen as the combination of twofluxes: JW

C =−α∇C, which depends on the concentrationgradient as expected; and JW⁎ =αC∇lnC̄*, which dependson the intrinsic solubility gradient. If the water solubilitywere the same between the slab and the surroundingmantle, then the flux would be JW=JW

C =−α∇C. Alter-natively, if the concentration were constant, the fluxwould be driven by the solubility gradient. The actualwater flux JW will be reduced or enhanced compared toJWC , depending on the sign of ∇lnC̄*. Because the

intrinsic solubility C̄* is temperature dependent theheat JT and chemical fluxes JW⁎ are coupled.

2.2. Diffusion equations and 1D similarity solution

In a Lagrangian coordinate system following thehorizontal motion of the slab, diffusion of a quantity X isgiven by dX

dt ¼ −jdJX . Thus, introducing the thermaldiffusivity j ¼ k

qCp¼ L11=T

2, which is assumed con-

stant, to recast Eq. (5), our system can be describedusing the following set of equations (see Appendix B.2):

dTdt

¼ jj2T

dCdt

¼ j aC̄⁎jC

C̄⁎

� �� �8>><>>: ð7Þ

In a one-dimensional system in which variation isonly along the z-axis (where z is the distance from theslab-mantle interface), the system (7) permits similaritysolutions for both the temperature and water concentra-tion profiles. We write T the temperature profile as

T ¼ T̄ þ dT2hðgÞ, where T̄ is the average temperature as

well as the temperature at the slab mantle interface, δTthe temperature step between slab and mantle and θ(η)is a function of the similarity variable g ¼ z

2ffiffiffiffiffijt

p . Thus,the heat diffusion equation becomes

−2gdhdg

¼ d2hdg2

ð8Þ

which yields the well-known error function solution;with boundary condition that T= T̄ at z=0, or θ=0 atη=0, the solution to Eq. (8) is

hðgÞ ¼ erf ðgÞ ð9Þ

Writing the water concentration C ¼ C̄ þ dC2 UðgÞ,

where C̄ is the average concentration as well as the

Please cite this article as: Guillaume Richard et al., Slab dehydration in the(2006), doi:10.1016/j.epsl.2006.09.006

concentration at the slab mantle interface and δC theconcentration step, we can recast the water diffusionequation as:

dC2

dUdt

¼ aA

AzdC2

AUAz

−C̄ þ dC

2 U

C̄⁎AC̄*Az

!ð10Þ

For the sake of simplicity, using a Taylor expansionaround T̄ we can rewrite the intrinsic solubility (6) as

C̄⁎ ¼ e−ERT ¼ BeAh ð11Þ

The parameters A ¼ E

RT̄

dT

2T̄and B ¼ e

− ER T̄ are not well

constrained for transition-zone minerals, mainly be-cause E, the intrinsic chemical potential of dissolvedwater, is unknown. The sign of E, controls the sense ofvariation of the intrinsic solubility with temperature: theintrinsic solubility increases with temperature when E ispositive and decreases when E is negative. Aftersubstitution of Eq. (11) and the similarity variable ηinto Eq. (10) we obtain the ordinary differential equationfor Φ:

d2Udg2

þ 2jga

−Adhdg

� �dUdg

−Ad2hdg2

U−2A C̄dC

d2hdg2

¼ 0

ð12Þ

The far-field boundary conditions are that Φ→∓1 asη→±∞. To solve (12), we employ a 1D second-orderfinite-differences implicit scheme. We use 10,000 gridpoints in the domain −10≤ η≤10 that is largecompared to the intrinsic diffusive length scales (i.e.η=10 is effectively equivalent to η → ∞) and preventsboundary effects.

3. Results

We seek to quantify the effects of the doublediffusion process on water transport from a slab intothe transition zone. Uncertainties in some of thecontrolling parameters, such as the intrinsic chemicalpotential E and water diffusivity α, are large. Unfortu-nately, high-pressure experiments [14,16] on transitionzone water solubility have included an aqueous phase ormelting of the transition zone mineral and are thus notrelevant to describe a solid state diffusion process.Consequently, we have explored a large range of valuesto investigate their influences, especially E ¼ l0− L21

L22, on

the water concentration profile and water flux awayfrom the slab.

Earth's mantle transition zone, Earth and Planetary Science Letters

Fig. 2. Temperature effect on water diffusion in the transition zone withμ0b0. Water concentration profile of a 1 wt.% hydrated slab diffusingin a dry surrounding mantle (0.01 wt.%). When Eb0 the intrinsicwater solubility decreases with increasing temperature and the doublediffusion effect induces the creation of local maximas within the waterconcentration. This feature also affects the water flux away from the

5G. Richard et al. / Earth and Planetary Science Letters xx (2006) xxx–xxx

ARTICLE IN PRESS

3.1. Water concentration profiles and diffusive coupling

Eq. (12) shows that the coupling effect is related tothe ratio between

ja

and A. Ifja

is relatively largeja≫A� �

,then the three temperature dependent terms(proportional to A) can be neglected leaving the waterconcentration largely independent of temperature.

For the case wherejafA, E becomes an important

parameter. Its sign controls the direction of the solubilitydriven water flux JW⁎ (see Eq. (5)) and its magnitudedictates the strength of this flux. In particular, if the signof E is negative, the water flux driven by chemical andsolubility gradients are opposite. The competition be-tween these two fluxes induces a local increase of thewater concentration at the edge of the slab. Underspecific initial conditions, this effect could yield waterconcentrations up to the solubility limit of the mantlemineral, which can then induce water exsolution and/ormelting.

slab (see Section 3.2). The three displayed profiles correspond to E=−1, −10, −100 kJ mol−1 to represent water solubilities that are isweakly to strongly temperature dependent. To emphasize the localmaxima, we have set a high water diffusivity (a ¼ 10−7m2s−1;ja¼ 10). The y-axis is the similarity variable g ¼ z

2ffiffiffiffiffijt

p , where κ the

thermal diffusivity is about 10−6 m2 .s−1.

3.1.1. Water accumulationUnder high pressure, in transition zoneminerals, water

fugacity decreases with increasing temperature [15].Experimental studies [14,16] suggest that water storagecapacity decreases with increasing temperature, butbecause of the presence of fluid (aqueous solution ormelt) in these experiments, obtaining the value of E is notstraight forward. Uncertainties on water fugacity, phe-nomenological coefficients, chemical potential and linkedto fluid presence have to be summed up and become large.Thus we make no assumptions on the trend of thistemperature dependence but instead explore the fullplausible range of E (E∈ [−100, +100]kJ mol−1).

We have run several simulations to understand how Einfluences the water concentration profile. If the intrinsicwater solubility increases with temperature (EN0), thetwo water fluxes (JW⁎, JW

C) are in the same direction. Thiseffect enhances the diffusion of water out of the coldregion to the warmer mantle and the shape of the con-centration profile is close to an error-function shape (seeFig. 4 and Section 3.2 below). In contrast, in negative Ecases (wherein intrinsic solubility decreases with increas-ing temperature), the resulting water concentrationprofiles (Fig. 2) depict a local maximum within the slabbelow the mantle-slab interface. On either side of thischemical flux convergence zone, the two forces that drivethe water flux are opposite. On the one hand, water tendsto diffuse, as usual, from a high concentration region (wetslab) to low concentration one (dry mantle), but on theother hand it tends to diffuse away from low solubilityarea (warm mantle) towards high solubility area (cold

Please cite this article as: Guillaume Richard et al., Slab dehydration in the(2006), doi:10.1016/j.epsl.2006.09.006

slab). It is evident in Fig. 2 that the ‘concentrationmaximum’ is more important when |E| is large.

3.1.2. Water supersaturationA consequence of the formation of a local maximum

of water concentration, if it is large enough, is thecrossing of the solubility limit and the formation of asuper-saturated region. To illustrate the effect of doublediffusion (coupling between thermal and water diffu-sion) on water supersaturation, we present a case wherethe true solubility C⁎ increases with increasing temp-erature. Here, supersaturation is more difficult to reachthan in a case where the true solubility decreases withincreasing temperature and can thus be considered alimiting case. Recall that the true C⁎ (Eq. (3)) andintrinsic solubility C⁎ (Eq. (6)) can have opposite temp-erature dependences (see Appendix D).

In the calculations displayed in Fig. 3, we haveconsidered a slightly under-saturated slab with an initialwater concentration Cslab

0 of 2.4 wt.% lingering in amantle containing 0.01 wt.% of water. The slab andmantle are composed of a 10 mineral whose watersolubility is 2.41 wt.% at 1100 °C and 3 wt.% at1500 °C. If E is strongly negative (Eb−200 kJ mol−1)then the local maximum in water concentration canreach the solubility limit and hence supersaturation.

Earth's mantle transition zone, Earth and Planetary Science Letters

Fig. 3. Double diffusion effect and liquid release Water concentrationprofile as a function of g ¼ z

2ffiffiffiffiffijt

p for a large negative chemical potential

E=−200 kJ mol−1, a high water diffusivity α=10−7 m2 s−1 and an initialwater concentration in the slab close to saturation (Cslab

0 =2.4 wt.%). Theconcentration profile (long dashed line) displays a local maxima belowthe edge of the slab that is larger than the solubility limit (solid line).κ=10−6 m2 s−1. See text for details.

Fig. 4. Water concentration profile for several values of E. Waterconcentration profile of a 1%-wet slab diffusing in a dry surroundingmantle (0.1 wt.%) for a range of intrinsic chemical potential E. Awaterdiffusivity α of 10−8 m2 s−1 is used (one order of magnitude smallerthan is Fig. 2). Axies are the same than in Fig. 2.

6 G. Richard et al. / Earth and Planetary Science Letters xx (2006) xxx–xxx

ARTICLE IN PRESS

Therefore if the slab entering the transition zone is closeto saturation, the water concentration (dashed line)intersects the true solubility limit (solid line). In thiscase, water is released from the minerals and producesaqueous fluid or hydrous melt. The likeliness of thisfluid release depends on the amount of water carried bythe slab down to the transition zone and by the waterconcentration of the surrounding mantle at this depth(410 km). If the initial slab water concentration is highenough, the peak water concentration can reach thesolubility limit and thus induce water exsolution ormelting at the edge of the slab even if the true solubilityof water is increasing with temperature. The flux ofwater from the slab would be strongly enhanced by sucha mechanism. It is worth noting that this mechanism ofwater exsolution is very similar to the exsolution ofwater from hydrous minerals that are unstable. In ourcase, exsolution occurs because the intrinsic watersolubility decreases while the slab temperature increaseswith time. In the case of unstable hydrous minerals,exsolution occurs because the mineral disappears whenthe temperature increases, thus expelling water.

3.2. Flux of water away from the slab

A subducted slab is likely to transport a relativelylarge amount of water into the transition zone. Labora-tory experiments [3,5] and numerical models [2] arguethat the top (5–10 km thick) of a cold subductingperidotitic lithosphere is able to carry a large part of the

Please cite this article as: Guillaume Richard et al., Slab dehydration in the(2006), doi:10.1016/j.epsl.2006.09.006

water released from sediments, crust, and serpentinizedmantle down to 410 km depth. Water concentration inthose dense hydrous magnesium silicates is generallyhigher than 5 wt.% (Phase A, C, D, E) [5]. Moreover,partial melting of upward mantle plastic flow at the topthe transition zone could induce a return flow of waterdown to the transition zone along subducted regions[8,12] and make portions of the slab well hydrated. Intotal, there is likely to be a significant slab flux of waterinto the top of the transition zone. The double diffusivemechanism described here can, in turn, extract this waterinto the transition zone.We therefore examine howmuchof the injected slab water flux is absorbed into thetransition zone by this double diffusion mechanism.

3.2.1. Effects of thermo-chemical coupling on waterflux

The flux of water away from the slab is given by Eq.(5) and can be inferred from Fig. 4 which displays thewater concentration profile as a function of η for Eranging from 100 to −100 kJ mol−1. At the interfacebetween the slab and the mantle the concentration isapproximately linear in η such that C ¼ b−gg ¼b−g z

2ffiffiffijt

p , where γ and β are two arbitrary constantsthat will be estimated from the fit of the concentrationprofile. In a constant solubility case, the water flux canthus be approximated as:

JCW jz¼0 ¼ −aACAz

¼ ag

2ffiffiffiffiffijt

p ð13Þ

If the solubility is temperature-dependent, using aTaylor expansion around zero of Eq. (6) and noting

Earth's mantle transition zone, Earth and Planetary Science Letters

Fig. 5. Effect of the initial concentration step δC on water flux awayfrom the slab Normalized water fluxes (total water flux over purechemical water flux ratio) as function of the initial water concentrationstep between slab and mantle(δC (wt.%)) for two water diffusivities(α=10−8, 10−7 m2 s−1) compared to the normalized flux if the heat andwater diffusion processes were uncoupled (dashed line, see AppendixB.3). The normalized water flux is almost constant and close to one forhigh slab concentration (δCN0.5 wt.%) and decreases rapidly forlower values. This plot demonstrates that the coupling stronglymitigates the decrease of water flux induced by the high solubility ofthe cold slab (see details in the text). The thermal diffusivity is set to be10−6 m2 s−1. The mantle water concentration is fixed to 0.1 wt.% andE=−100 kJ. mol−1.

7G. Richard et al. / Earth and Planetary Science Letters xx (2006) xxx–xxx

ARTICLE IN PRESS

that when η is small, θ=erf (η) =η, we see thatC

C̄⁎¼ bV−gVg

1þ Agis approximately (Taylor expansion around

zero)C

C̄⁎fbV− gVþ bVAð Þg ¼ bV− gVþ bVAð Þ z

2ffiffiffiffiffijt

p , where

γ′ and β′ are two arbitrary constants similar to γ, β.The total water flux is therefore given by:

JW jz¼0 ¼ −aC̄⁎A

AzC

C̄⁎¼ aC̄⁎

gVþ bVA2ffiffiffiffiffijt

p ¼ ag⁎

2ffiffiffiffiffijt

p ð14Þ

Because the intrinsic solubility C̄⁎=eAθ=eAerf (η) =1 atthe edge of the slab (η= z=0),γ*=γ′+β′ A.

A useful variable to look at is the normalized waterflux JW

JCW. Using Eq. (5) at the slab-mantle interface we

have:

JWJCWjz¼0

¼ 1þ J⁎WJCWjz¼0

¼ g⁎

gð15Þ

In the numerical experiment displayed in Fig. 4,A ¼ E

RT̄

dT

2 T̄is known and the parameters γ, γ* can be

evaluated. For this case the normalized water flux goesfrom 1.09 to 0.91 for E∈ [100, −100] (kJ mol−1). Asexpected, when the solubility increases with temperature(EN0) the flux of water away from the slab is higherthan in the constant temperature case and converselywhen the solubility decreases with temperature (Eb0).

To estimate the effect of the coupling between heatand chemical diffusion on the flux, let us define anarbitrary reference by estimating the normalized fluxassuming that the two diffusive processes are indepen-dent and uncoupled (uc). In this case (see Appendix B.3for details), the two water fluxes at z=η=0 are:

JCW jucz¼0 ¼ −adC

2ffiffiffip

p ffiffiffiffiffijt

p ð16Þ

and

J⁎W jucz¼0 ¼ −aC̄

2ffiffiffip

p ffiffiffiffiffijt

p EdT

RT̄2ð17Þ

Thus the ‘uncoupled’ normalized flux is:

JWJCWjucz¼0

¼ 1þ EdT

RT̄ 2

C̄dC

ð18Þ

Now we can compare this ‘uncoupled’ normalizedflux with the ‘actual’ normalized flux given by ourmodel. The study of the two normalized water fluxes forE=−100 kJ mol−1 displayed for a range of δC in Fig. 5yields two conclusions.

Please cite this article as: Guillaume Richard et al., Slab dehydration in the(2006), doi:10.1016/j.epsl.2006.09.006

First, ‘actual’ normalized flux follows a relation such asJWJCW

jz¼0 ¼ 1−f 1dC where f is a constant. This 1

dC-depend-ence is similar to the ‘uncoupled’ flux dependence (cf.Eq. (18)). Nevertheless, in this case, f is a function of j

ain addition to the other variables (E, C̄, δT, T̄ ). In bothcases, for a well hydrated slab (large initial concentra-tion step between the slab and the mantle, i.e.δCN0.5 wt.%), the water flux is weakly δC-dependent.When δC is smaller, the temperature driven flux is moreimportant and its effects on the water flux becomesstronger. The total water flux away from the slab islower and eventually, when δC is small enough, thetemperature driven flux prevails, the total flux becomesnegative and the water diffuses towards the slab.

Secondly, the coupled normalized flux is clearlyhigher than the ‘uncoupled’ normalized flux, by a factorof four for large δC and by more than a factor of ten forsmall δC (as said above the coupling can even changethe sign of the flux for very small δC). The coupling ofchemical and heat transport diminishes the influence ofvariable intrinsic solubility on the flux of water from theslab. By forming local maxima in concentration whichincrease the concentration gradients, the couplingmitigates the reduction in water flux (see Section3.1.1). This self-regulation effect controls the strengthof the chemically driven flux; it is constant for highinitial water concentration δC and becomes stronger forlow δC. As an example, for E=100 kJ mol−1 withmantle-like parameters (Cmantle

0 =0.1 wt.%, T̄ =1300 °C,

Earth's mantle transition zone, Earth and Planetary Science Letters

Fig. 6. Effect of the initial slab water concentrationCslab0 on the mass of

water removed from the slab. R— the ratio between the incoming andthe removed mass after 50 My for E ¼ l0− L21

L22¼ −100kJmol−1, as

function of the initial slab water concentration Cslab0 (wt.%) for two

water diffusivities (α=10−8, 10−7 m2 .s−1). Higher water diffusivityleads to larger amounts of water removed to the transition zone. R—decreases significantly as the initial concentration Cslab

0 falls below0.5 wt.%. The thermal diffusivity is set to be 10−6 m2 .s−1 and themantle water concentration is fixed to 0.1 wt.%.

8 G. Richard et al. / Earth and Planetary Science Letters xx (2006) xxx–xxx

ARTICLE IN PRESS

δT=300 °C), the threshold at which self-regulationbecomes significant takes place around δC=0.5 wt.%and seems independent of j

a.

3.2.2. Net water extractionLet us consider a slab entering the transition zone,

which initially (at t=0) holds C slab0 in wt.% of water in a

d-thick layer. The amount of water extracted from thisslab lingering in the transition zone can be calculatedusing our model formulation. The amount of water in avertical slice of this slab is C slab

0 d.We integrate JW intime over the area of the slab in the transition zone, toobtain the mass of water removed from this slice of slabduring its transit across the transition zone. The mass ofwater removed is thus:

M remH2O ¼ q

ZS

Z ttrans

0JW jz¼0dtdS

¼ ag⁎ffiffiffij

p ffiffit

p� �ttranso

Sq ð19Þ

where S is the top surface area of the slab slice lyinghorizontally in the transition zone, ttrans the transit time andρ is bulk mantle density. We can look at the ratio betweenthe incoming and the removed mass of water in the slabfor the two extreme cases when E=−100 kJ mol−1

and +100 kJ mol−1.

RF ¼ M remH2O

M incomingH2O

¼g⁎Faffiffij

p ffiffiffiffiffiffiffiffittrans

p

C0slabd

ð20Þ

where γ±⁎ corresponds to E=±100 kJ mol−1.Consider the first case displayed in Fig. 4 as an exam-

ple where the initial concentrations are C slab0 =1 wt.% and

Cmantle0 =0.01 wt.%. Measuring the slope of the curves

at the slab-mantle interface, we obtain values for γ±⁎.For E=100 (kJ mol−1), γ+*= 6.08 and for E=−100(kJ mol−1), γ-⁎=5.10. According to tomographic im-aging [7], we can assume a typical transit time ofttrans=50 My. Considering that the hydrated region of theslab is about d=5 km thick and the water diffusivityα=10−8 m2 s−1, the percentages of initial water removedfrom the slab are R+ ∼48% and R− ∼40.5% (or, re-spectively 68% and 57% for 100 My transit time).

The water flux is obviously diffusivity dependent(see Fig. 5). However, the water diffusivity of transitionzone minerals is still not well constrained, firstly due toits temperature and pressure dependence, and secondlybecause grain boundary diffusion is likely to be ordersof magnitude more effective than volumetric diffusion.The possible range for volumetric diffusivity α is from10−10 m2 s−1 [20] to 10−7 m2 s−1 [21] which yields

Please cite this article as: Guillaume Richard et al., Slab dehydration in the(2006), doi:10.1016/j.epsl.2006.09.006

another degree of freedom to the system in that ja varies

from 100 to 10,000. Considering a higher water diffu-sivity, α=10−7 m2 s−1, that could be relevant if grainboundary diffusion is efficient at this depth, leads tohigh R values: R+ ∼174% and R− ∼107%. In this case,the slab is totally dry after 50 My, regardless of the valueor sign of E (see Fig. 6). For α=10−9 m2 s−1, R decreasesto around 15%.

For higher Cmantle0 , the values of R± are lower. For

example (see Fig. 6), with Cmantle0 =0.1 wt.% and Cslab

0 =1 wt.%, we obtain R− ∼36%. For less hydrated slabs (i.e.with smallerCslab

0 and δC), the flux andR± start to decreasefor slabs with concentration Cslab

0 b0.5 wt.%.

4. Conclusion and discussion

We have analyzed the hydration of the Earth's mantletransition zone by diffusion of water out of slabs coolingwithin the transition zone. During this process, thecoupling of water transport to thermal diffusion throughtemperature-dependent water solubility has two mainconsequences. First, if the intrinsic solubility of water isdecreasing with increasing temperature (Eb0), thecoupling mitigates the effect of solubility variabilityon diffusive flux, thus the water flux estimation throughsimple (genuinely chemically driven) diffusion law canbe seen as relatively robust. Indeed, when the water fluxdiminishes because of the low solubility in the warm

Earth's mantle transition zone, Earth and Planetary Science Letters

9G. Richard et al. / Earth and Planetary Science Letters xx (2006) xxx–xxx

ARTICLE IN PRESS

mantle, the system self-adjusts through the formation ofa local concentration maxima below the edge of the slab,which in return increases the flux of water out of theslab. High water diffusivity and a low initial hydrationof the slab both allow the thermal diffusion effect to bemore efficient to keep water within the slab. If thestandard-state chemical potential E of water in themineral is strongly negative and the slab is close tosaturation, the coupling mechanism can allow the waterconcentration to reach the saturation limit and thusinduce fluid exsolution or melting. In particular, theformation of a peak water concentration at the edge ofthe slab can result in a super saturated area, whereminerals will have to dehydrate and thus the formationof a fluid is likely. The partitioning of incompatibleelements into this fluid implies that part of the slab couldbe depleted as it enters the lower mantle. Additionally,in case the solubility limit is reached, the presence offluid (or melt) could enhance the water flux away fromthe slab because water preferentially partitions intoaqueous solution or melt.

The main limitation of our model concerns the slabside boundary condition, since we assume that the con-centration in the slab is fixed at infinity to allow simi-larity solution; thus we don't take into account waterdiffusion from the edge of the slab to its center. Thisassumption is correct for the early stage of the slab'straverse across the transition zone, when the thermal andchemical boundary layer are thin, but its validity dimi-nishes with time. This potentially reduces the flux ofwater away from the slab. However, when the slab entersthe transition zone, it has already undergone somechemical equilibration which would broaden the thick-ness of the slab's hydrated layer, which is consistent withour assumption of a uniform water concentration deep inthe slab.

To infer quantitative predictions from our model,several parameters need to be constrained. The first is thetemperature dependence of the solubility. At lowtemperature b1200 °C, only pure water is present inthe reaction and its fugacity is known. Assuming that theSoret effect is weak, E can be evaluated. In wadlseyite,known solubility is increasing with increasing tempera-ture and E≈20 kJ mol−1 (cf. Appendix C). On thecontrary at higher temperature Demouchy et al. [14]noted the presence of the fluid phase in measurements ofwadsleyite water storage capacity at high P–T condi-tions, which influences interpretation of water solubility(mainly because the fugacity of the liquid phase isunknown. The thermal state of the slab also needs to beconstrained. In addition to affecting the solubilitytemperature-dependence, the slab temperature field

Please cite this article as: Guillaume Richard et al., Slab dehydration in the(2006), doi:10.1016/j.epsl.2006.09.006

(like the pressure field) controls the initial waterconcentration of the slab (when it enters into thetransition zone). However, the geotherm of a slab attransition-zone depths is still under discussion. A coldslab [22] is likely to carry a lot of water down to thetransition zone and the temperature difference with thesurrounding mantle is high (∼1000 °C) thus thesolubility difference would be large and the effect ofpeak concentration could be considerable. In a warmerslab [23], these effects would be less efficient but in themeantime a younger, warmer, slab is likely to float muchlonger in the transition zone than will an old slab [24] andthis will increase the time-integrated slab dehydration.Our model points out the importance of consideringsolubility variation with temperature in the study ofwater circulation in the mantle and should provide im-petus for laboratory experiments to explore watersolubility and transport properties in the deeper mantle.

Acknowledgements

We are grateful to Professor M. Bickle and ananonymous reviewer for their thoughtful comments. Wealso thank S. Hier-Majumder for encouragements andhelpful comments. This work was supported by theNational Science Foundation grant EAR0330745.

Appendix A. Basic thermodynamics of watersolubility

Chemical potential is the main controlling parameterof the diffusion process [17]. For water dissolved insolid, the general chemical potential is given by:

l ¼ l0 þ RT lnðaÞ ¼ l0 þ RT lnðCÞ ðA:1Þwhere, the activity a equals the concentration C and μ0

is the standard-state chemical potential of the substancein the state it assumes when dissolved (namely H+).

The chemical reaction between water and the mantletransition-zone phases is commonly described, in Krö-ger–Vink notation [25] (where in superscripts indicate thecharge with respect to an ideal crystal such that X isneutral, • is positive and ′ is negative; alphabetic sub-scripts represent the crystallographic site), as :

H2OþMgXMg⇄ð2HÞxMg þMgOsrg ðA:2Þ

where the hydroxyl incorporation is charge-balanced byMg vacancies (VMg), a Mg atom being replaced by two H(or more rigorously by [2OHo

U−VMgʺ ]X), the magnesiumatom (Mg) will form oxide and go to sites of repeatablegrowth (srg) such as grain boundaries [6].

Earth's mantle transition zone, Earth and Planetary Science Letters

10 G. Richard et al. / Earth and Planetary Science Letters xx (2006) xxx–xxx

ARTICLE IN PRESS

When the minerals are in equilibrium with free fluid,the water concentration is the solubility C* and we canwrite the equality of chemical potentials for the hy-dration reaction:

lH2O þ lMg ¼ lþ lMgO ðA:3Þ

Or using μX=μX0 +RT lnaX,

l0H2O þ RT ln

fH2O

P0

� �þ l0

Mg

¼ l0 þ RT lnðC⁎Þ þ l0MgO þ RT lnðaMgOÞ

ðA:4ÞWe can eliminate μ0 between Eqs. (A.4) and (A.1),

to obtain the final expression for chemical potential ofdissolved water in terms of solubility limit C⁎ (4) usedin the Section 2.1.

Appendix B. Fluxes and water diffusion

B.1. Phenomenological coefficients estimate

Following De Groot and Mazur [17], we can write anexplicit form of the entropy balance equation, which inour case only includes thermal and chemical fluxes:

qdsdt

¼ −jdJT−lJW

T

� �−JTT2

djT−JW djlT

ðB:1Þ

where ρ is the total density, s is total specific entropy, Tis the temperature, μ the chemical potential of water andJT and JW are respectively the heat and chemical (water)flux. It follows that the expressions for the entropy fluxand the entropy production rate are given by:

Js ¼ 1TðJT−lJW Þ ðB:2Þ

r ¼ −1T2

JT djT−JW djlT

ðB:3Þ

By inspecting the local entropy production rate σ, onecan define the fluxes and conjugate forces describing oursystem. According to the second law of thermodynamics,the rate of entropy production is positive definite, thus theheat flux JT and the chemical (water) flux JW are coupledby the positive definite matrix presented in Eq. (1).

It is useful to note that by introducing a new flux JT′=JT−hW JW (where hW is the specific partial enthalpy of thewater) (B.3) can be also written as:

r ¼ −1T2

JTVdjT−1TJW d ½jl�T ðB:4Þ

Please cite this article as: Guillaume Richard et al., Slab dehydration in the(2006), doi:10.1016/j.epsl.2006.09.006

where the [∇μ]T is taken at constant temperature. Thus,the fluxes and forces can be related by another, physicallyequivalent, positive definite matrix:

JTV¼ L11VjT−L12V ½jl�TJW ¼ L21VjT−L22V ½jl�T

(ðB:5Þ

where the off-diagonal coefficients L12′ , L21′ are respec-tively referred to as the Dufour and Soret coefficients.

To estimate the value of the diagonal coefficients L11and L22 in Eq. (1), let us look at the heat flux at a fixedchemical potential JT |μ and the chemical flux at aconstant temperature JW |T. The two fluxes become :

JT jl ¼ þL11j1T¼ −kjT ¼ −jqCqjT ðB:6Þ

JW jT ¼ −L22T

jl ¼ −L22T

jðl0 þ RT lnCÞ¼ −

RL22C

jC ¼ −ajC ðB:7Þ

where we see that L11=κρCPT2 and that L22 ¼ aC

R . In oursystem, the heat diffusivity is κ=10−6 m2.s−1, the waterdiffusivity α=10−8 m2 .s−1, the temperature T ∼1300,the water concentration C=0.1–1 wt.%=1.9/, 102−19/,102 mol . m− 3 and the chemical potential μ=±100 kJ mol−1. So, we have L11 ∼5.106 (J. K. m−1 .s−1)and L22 ∼1.9 10−6 (mol2. K. J−1. m−1 .s−1).

If we consider that the two parts of the chemical fluxJW defined in (1) are of the same order of magnitude, wesee that L21 ∼ μL22 ∼19 10−2 (mol. K. m−1 .s−1). TheOnsager theorem tells us that L12=L21 [18]. Thus, wecan compare the two terms of the total heat flux JT (cf.Eq. (1)), and see that L11 ∼5.106 ≫ μL12 ∼1.9 104

(J. K. m−1 .s−1). Consequently, we have neglected theoff diagonal part of the heat flux.

B.2. Water solubility and diffusion

The water diffusive flux JW can be recast in term ofwater solubilityC⁎. Using Eq. (4), JW in Eq. (2) becomes:

JW ¼ −L22T

j Dl0 þ RT lnfH2O

P0aMgO

CC⁎

� �� �ðB:8Þ

or after some algebra:

JW ¼ −RL22jlnfH2O

P0aMgO

C

C⁎e−Dl0

RT

!ðB:9Þ

Earth's mantle transition zone, Earth and Planetary Science Letters

11G. Richard et al. / Earth and Planetary Science Letters xx (2006) xxx–xxx

ARTICLE IN PRESS

From Eq. (A.4), we can obtain an expression for thesolubility C⁎ given in Eq. (3) and we define the intrinsicsolubility C̄⁎ given in Eq. (6); introducing these into Eq.(B.9), the water diffusion equation dC

dt ¼ −jðzdJW Þ canbe written as (see Eq. (7)):

dCdt

¼ aj C̄⁎jC

C̄⁎

� �ðB:10Þ

where a ¼ RL22C

is the water diffusivity, which is assumedto be constant.

B.3. Uncoupled fluxes

To evaluate the effect of the coupling between heatdiffusion and water diffusion through water solubility,we compare it to a reference flux. This reference fluxcorresponds to the sum of the two water sub-fluxes (JW⁎ ,JWC ) described in (5) in an uncoupled case. Using the

definition of the concentration C ¼C̄ þ dC2

UðgÞ:

JCW ¼ −ajC ¼ −adC2

jUuc ðB:11Þ

where Φuc is the solution of the uncoupled water diffu-

sion equation

dCdt

¼ aj2C ðB:12Þ

that is a simple error function Uuc ¼ erf z2ffiffiffiat

p

¼erf g

ffiffiffija

p . Thus, we read:

JCW ¼ −adC

2ffiffiffiffiffijt

p ffiffiffip

p e−jag

2d z ðB:13Þ

Similarly, with T ¼ T̄ þ dT2hðgÞ and using the solu-

bility approximation, the flux due to solubility gradientsis C̄⁎=BeAθ (see Eq. (11))

J⁎W ¼ aCjln C̄ ⁎ ¼ a C̄ þ dC2

Uuc

� �jAh ðB:14Þ

where θ is the solution of the heat diffusion Eq. (8),a simple error function h ¼ erf z

2ffiffiffijt

p

¼ erf ðgÞ Eq. (9).Eq. (B.14) becomes:

J⁎W ¼ aEdT

RT̄2

e−g2

2ffiffiffiffiffijt

p ffiffiffip

p C̄ þ dC2

erf g

ffiffiffija

r� �� �d z

ðB:15Þ

At the interface z=η=0 and the fluxes are given byEqs. (16) and (17) and the uncoupled normalized fluxpresented in Fig. 5 is given by Eq. (18).

Please cite this article as: Guillaume Richard et al., Slab dehydration in the(2006), doi:10.1016/j.epsl.2006.09.006

Appendix C. Considerations on the term E ¼ l0−L21L22

One of the main parameters of the diffusion processis E the sum of μ0 the standard-state chemical potentialand L21

L22which, in a sense, describes the importance of

the thermal diffusion (Soret effect) compared to thechemical diffusion. Both of these terms are poorlyconstrained in transition zone minerals. A first orderapproximation of the standard-state chemical potentialof water in wadsleyite could be drawn using recentexperimental data and the solubility expression (3).Using only low temperature (Tb1200 °C) solubilitydata from Fig. 3(a) in Demouchy et al. 2005 [14] toavoid the solid–liquid partitioning effect, a linear fitgives an approximate value of μ0 ≈20 kJ mol−1.

The Soret effect is non-negligible in silicate liquidswhere it has beenmeasured to be equal to a few dozens ofkJ mol−1 [26], nevertheless to our knowledge, it has notbeen evaluated in solid-state diffusion at high pressureand temperature. Thus we have taken into account all theuncertainties considering a large range of possible valuesfor these parameters E∈ [−100, +100] (kJ mol−1).

Appendix D. Solubility and intrinsic solubility

The intrinsic solubility C̄⁎ is essentially controlledby the standard-state chemical potential μ0, whereas thetrue solubility C⁎ includes the water fugacity. Conse-quently, even if these two variables are closely related,their temperature dependence can be opposite, depend-ing on the water fugacity's temperature dependence. Afirst order fit of the water fugacity [15] by an expo-nential law fH2O ¼ Xe−

YRT gives Y ≃ −140 kJ mol−1.

Using it and Δμ0 ≃ −351 kJ mol−1 [27] in Eq. (6)shows that μ0 could be as law as −211 kJ mol−1, whichstill allows the true solubility to increase with increasingtemperature as seen in the low temperature experiments[14] (i.e. E+Y−Δμ0N0). This demonstrates that thebehavior of the solubility C⁎ and the intrinsic solubilityC̄⁎ do not have to be the same.

References

[1] J. Dixon, L. Leist, C. Langmuir, J. Schilling, Recycled dehydratedlithosphere observed in plume-influencedmid-ocean-ridge basalt,Nature 420 (6914) (2002) 385–389.

[2] L. Ruepke, J. Phipps-Morgan, M. Hort, J. Connolly, Serpentineand the subduction zone water cycle, Earth Planet. Sci. Lett. 223(2004) 17–34.

[3] T. Komabayashi, K. Hirose, K.-i. Funakoshi, N. Takafuji,Stability of phase A in antigorite (serpentine) composition deter-mined by in situ X-ray pressure observations, Phys. Earth Planet.Inter. 151 (3–4) (2005) 276–289.

Earth's mantle transition zone, Earth and Planetary Science Letters

12 G. Richard et al. / Earth and Planetary Science Letters xx (2006) xxx–xxx

ARTICLE IN PRESS

[4] M. Schmidt, S. Poli, Experimentally based water budgets fordehydrating slab and consequences for arc magma generation,Earth Planet. Sci. Lett. 163 (1998) 361–379.

[5] E. Ohtani, K. Litasov, T. Hosoya, T. Kubo, T. Kondo, Watertransport into the deepmantle and formation of a hydrous transitionzone, Phys. Earth Planet. Inter. 143–144 (2004) 255–269.

[6] D. Kohlstedt, H. Keppler, D. Rubie, Solubility of water in thealpha, beta and gamma phases of (Mg, Fe)(2)SiO4, Contrib.Mineral. Petrol. 123 (4) (1996) 345–357.

[7] D. Zhao, Global tomographic images of mantle plumes andsubducting slabs: insight into deep Earth dynamics, Phys. EarthPlanet. Inter. 146 (1–2) (2004) 3–34.

[8] D. Bercovici, S. Karato, Whole-mantle convection and thetransition-zone water filter, Nature 425 (2002) 39–43.

[9] X. Huang, Y. Xu, S.-I. Karato, Water content in the transitionzone from electrical conductivity of wadsleyite and ringwoodite,Nature 434 (7034) (2005) 746–749.

[10] G. Richard, M. Monnereau, J. Ingrin, Is the transition zone anempty water reservoir? Inferences from numerical model ofmantle dynamics, Earth Planet. Sci. Lett. 205 (2002) 37–51.

[11] G. Richard, M. Monnereau, M. Rabinowicz, Slab dehydrationand fluid migration at the base of the upper mantle: implicationfor deep earthquake mechanisms, J. Geophys. Intl. (in press).

[12] G. Leahy, D. Bercovici, The dynamics of a heavy melt layer andwater entrainment in the transition-zone water filter model, EarthPlanet. Sci. Lett. (submitted for publication).

[13] T. Komabayashi, S. Omori, S. Maruyama, Petrogenetic grid inthe system MgO–SiO2–H2O up to 30 GPa, 1600 C: Applica-tions to hydrous peridotite subducting into the Earth's deepinterior, J. Geophys. Res. 109 (B03206) (2004), doi:10.1029/2003JB002651.

[14] S. Demouchy, E. Deloule, D. Frost, H. Keppler, Pressure andtemperature-dependence of water solubility in Fe-free wad-sleyite, Am. Mineral. 90 (7) (2005) 1084–1091.

[15] K. Pitzer, S. Sterner, Equations of state valid continuously fromzero to extreme pressures for H2O and CO2, J. Chem. Phys. 101(1994) 3111–3116.

Please cite this article as: Guillaume Richard et al., Slab dehydration in the(2006), doi:10.1016/j.epsl.2006.09.006

[16] E. Ohtani, H. Mizobata, H. Yurimoto, Stability of dense hydrousmagnesium silicate phases in the systems Mg2SiO4–H2O andMgSiO3–H2O at pressures up to 27 Gpa, Phys. Chem. Miner. 27(2000) 533–544.

[17] S.R. De Groot, P. Mazur, Non-Equilibrium thermodynamics,Dover Publication, 1984, pp. 48–53.

[18] L. Onsager, Reciprocal relations in irreversible processes, Phys.Rev. 37 (1931) 405–426.

[19] B.J. Wood, A. Pawley, D. Frost, Water and carbon in the Earth'smantle, Philos. Trans. R. Soc. Lond., A 354 (1771) (1996)1495–1511.

[20] R. Hae, E. Ohtani, T. Kubo, T. Koyama, H. Utada, Hydrogendiffusivity in wadsleyite and water distribution in the mantletransition zone, Earth Planet. Sci. Lett. 243 (2006) 141–148.

[21] J. Ingrin, H. Skogby, Hydrogen in nominally anhydrous upper-mantle minerals: concentration levels and implications, Eur. J.Mineral. 12 (2000) 543–570.

[22] T. Irifune, N. Kubo, M. Isshiki, Y. Yamasaki, Phase transforma-tion in serpentine and transportation of water into lower mantle,Geophys. Res. Lett. 25 (2) (1998) 203–206.

[23] P. Van Keken, B. Kiefer, S. Peacock, High resolution models ofsubduction zones: implications for mineral dehydration reactionsand the transport of water into the deep mantle, Geochem.Geophys. Geosyst. 3 (10) (2002), doi:10.1029/2001GC000256.

[24] U. Christensen, Influence of chemical buoyancy on the dynamicsof slabs in transition zone, Geophys. J. Res. 102 (B10) (1997)22,435–22,443.

[25] F. Kröger, H. Vink, Solid state physics 3, Academic Press, 1956.[26] C. Lesher, D. Walker, Solution properties of silicate liquids from

thermal diffusion experiments, Geochim. Cosmochim. Acta 50(1986) 1397–1411.

[27] J. Brodholt, K. Refson, An ab initio study of hydrogen in forsteriteand a possible mechanism for hydrolytic weakening, J. Geophys.Res. 105 (B8) (2000) 18,977–18,982.

Earth's mantle transition zone, Earth and Planetary Science Letters