Does infiltration of core material into the lower mantle affect the observed geomagnetic field?

Physics of the Earth and Planetary Interiors, 73 (1992) 29—37 Elsevier Science Publishers B.V., Amsterdam

29

Does infiltration of core material into the lower mantle affect the observed geomagnetic field?

a

Jean-Paul Poirier a and Jean-Louis le Mouël b Département des Géomatériaux, b Département de Géomagnétisme et Paléomagnétisme, Inst itut de Physique du Globe de Paris, 4, Place Jussieu, 75252 Paris Cedex 05, France (Received 7 November 1991; revision accepted 2 March 1992)

ABSTRACT Poirier, J.P. and le Mouël, J.-L., 1992. Does infiltration of core material into the lower mantle affect the observed geomagnetic field? Phys. Earth Planet. Inter., 73: 29—37. A quantitative estimate of the depth of penetration of liquid iron from the core into the base of the lower mantle has been obtained, from laboratory data and theoretical models. The thickness of the infiltrated layer is found to be of the order of 1—100 m depending on the grain size of the mantle material. Even with the assumption that convection in the D” layer entrains the electrically conducting core fluid over 100 km, the effective conductivity of the layer is hardly modified and the perturbation caused to the secular variation field is negligible. The same conclusion obtains in the improbable limiting case where all the infiltrated core fluid is gathered in a single mass.

1. Introduction With a view to investigating the nature of the core—mantle boundary and the D” zone, Knittle and Jeanloz (1989, 1991) melted iron foils embedded in silicate perovskite, in a laser-heated diamond-anvil cell at pressures up to 80 GPa. Visual inspection of the quenched samples suggested that a chemical reaction had taken place, and this was confirmed by X-ray diffraction and electron microprobe traverses across the iron—silicate boundary: molten iron preferentially dissolved FeO and penetrated into the silicate, presumably by migration of the liquid metal along the silicate grain boundaries. Jeanloz (1990) and Knittle and Jeanloz (1991) concluded that “some Fe may be drawn from the core into the D” region by a surface-tension driven capillary process”. The reaction zone could then be swept upward into the

mantle by convection, and Knittle and Jeanloz (1991) inferred that the “heterogeneous accumulation of reaction products is what makes up the D” layer”. Jeanloz (1990) further speculated that, as a consequence, there would be, dispersed within D”, sizeable ‘metallic regions’ with a high electrical conductivity, which could pin magnetic field lines. This pinning could influence the Earth’s magnetic field observed at the surface and could also result in an electromagnetic coupling between the mantle and the core, affecting fluid flow in the core. Goarant (1991) and Goarant et al. (1992) melted iron powder mixed with olivine in a laserheated diamond-anvil cell up to about the pressure of the core—mantle boundary (130 GPa), and they examined the recovered quenched samples by analytical transmission electron microscopy, on a scale of 10—100 A. They also observed penetration of liquid iron into the solid per-

Correspondence to: J.-P. Poirier, Département des ~ matériaux, Institut de Physique du Globe de Paris, 4, Place Jussieu, 75252 Paris Cedex 05, France.

ovskite—magnesiowustite assemblage along grain boundaries, in agreement with Knittle and Jeanloz.

0031-9201/92/$05.00 © 1992

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Elsevier Science Publishers B.V. All rights reserved

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Thus, infiltration of the liquid core alloy into the lower mantle seems to be a distinct possibility. The purpose of the present paper is to investigate the mechanisms by which iron can infiltrate the lower mantle and to place quantitative bounds on the extent of penetration and the time it takes for the infiltrated zone to fill the D” layer. Quantitative assessment of the possible influence of iron infiltration on the geomagnetic field leads to the conclusion that the effect is negligible, as are its effects on the field observed at the surface and on core—mantle coupling,

2. Intergranular wetting

CORE MATERIAL INFILTRATION INTO LOWER MANTLE

the grain boundaries must therefore be considered. Such mechanisms exist: a process, known in metallurgy as ‘intergranular wetting’ causes liquid embrittlement of materials. Typical examples are liquid gallium, which penetrates the grain boundaries of aluminium (Elbaum, 1959), and liquid bismuth, which penetrates the grain boundaries of nickel (Cheney et al., 1961), by forming a eutectic. Grain boundaries, being crystal defects, have a specific energy (per unit area) YGB; penetration of the liquid along a grain boundary destroys it and replaces it by two solid—liquid interfaces, with specific energy 71’ If the difference in energy: 77GB

In rocks of the upper crust of the Earth, mineral grains are often separated by thin intergranular cracks, through which fluids can circulate, This may have given rise to the misconception, widespread in earth sciences, that grain boundaries are open discontinuities between grains and that fluids can easily penetrate them by capillary infiltration, much like water in a sandbag. In reality, grain boundaries in a compact polycrystalline solid are crystal defects between grains of different orientations (e.g. American Society for Metals, 1980) or interfaces grains as of different minerals, and cannotbetween be considered channels open to the circulation of fluids. Intergranular cracking, which is responsible for some of the permeability of surface rocks, is impossible at lower-mantle pressures. Studies of capillary melt redistribution in partially molten rocks (Stevenson, 1986, 1990) have been used as a justification for the assumption of capillary invasion of the lower mantle by the liquid core (Jeanloz, 1990; Knittle and Jeanloz, 1991). Partial melting does indeed preferentially occur at grain boundaries (thus destroying them) and creates channels through which melt can circulate and redistribute. It is therefore perfectly correct to consider partially molten rock as a permeable medium (Stevenson, 1986), but application of this model to infiltration of the core liquid into the lower mantle is inappropriate, Mechanisms whereby liquid iron can infiltrate the lower-mantle material by opening a path along

71

is positive, penetration of the liquid along the grain boundary is energetically favourable. This mechanism accounts for preferential dissolution (corrosion) of a solid at grain boundaries. The equilibrium concentration C~of the dissolved solid material in the liquid close to a grain boundary is larger than the concentration far from grain boundaries, C 0, by a factor embodying the effect of the decrease in the energy of solution at 2~y the grain boundary: a C~=C 0 exp— (2) kT where a is the width of the grain boundary, k is the Boltzmann constant, and T is the absolute temperature. Although there is local equilibrium everywhere, there is a concentration gradient of solute, which drives a diffusive flux away from the grain boundary. Progression of the attack along the grain boundary, creating a channel of width a, may be controlled by the evacuation of the solute by diffusion along the length of the channel already created. We can now estimate the time it must take for liquid iron to infiltrate the lower-mantle material over a distance h from the solid—liquid interface. Let us assume, as inferred from the diamond-anvil cell experiments, that liquid iron dissolves FeO from the perovskite—magnesiowüstite assemblage. Oxygen atoms, constituting the framework

31

J.P. POIRIER AND J.L. LE MOUEL _

where D05 is the diffusion coefficient of oxygen in liquid iron and VC2z~y is given by C0 exp—~——1 a VC~—-~-(5)

GB h

In first approximation, the equilibrium concentration of oxygen in the liquid C 0 can be taken as 3 equal to that in the solid Equations (4) C0 and 4/a(5) give dh D 2~y 0~ a (6) =

and, by integration, h2 _________________

a

t

=

~-~~-—

a2~y exp

—h—

-i

—

1

(7)

Co 2 1 Coefficient of diffusion of oxygen The coefficient of diffusion of oxygen in liquid iron at its melting point and at ambient pressure Fig. 1. Penetration of fluid (shaded) by preferential dissolution at a grain boundary (GB). The concentration of dissolved oxygen is C the grain boundary. 0 far fromA the fluxgrain of oxygen boundary, awayand from C÷close the grain to boundary is created.

has been measured by several researchers. The best values found in the literature are 9 2 —i D °‘~ ~2 3 + 10 3\1 x 1~— m s (McCarron and Belton, 1969)

of the crystal structure, dissolve in the liquid iron. Neglecting the tortuosity of the grain boundary structure and assuming that the grain boundaries are planar, we consider a steady-state situation in which the liquid has already penetrated over the distance h along a grain boundary and created a flat channel of width a, which it wets perfectly (Fig. 1). A thin slab of unit length, height dh, and width a (the unit cell parameter of the crystal), contains 4dh/a2 atoms of oxygen (there are four oxygen atoms in a face-centred cubic cell). The diffusive flux transported through the cross-sectional area of the slab during time dt is 4 dh (3\

D

a3 dt ‘ ‘ Using Fick’s equation of diffusion we can write J

=

4 dh a dt

=

—D~VC

(4)

=

—

2 s~ 0~ (3—4)and x i0~ (Suzuki Mori,m1971) D 2 s~ 0~ (2.5—5.5) x iO~ m1977) (Otsuka and Kozuka, =

=

The self-diffusion coefficient of liquid metals scales with the melting temperature; thus the self-diffusion coefficient of iron at its melting point at the pressure of the inner core boundary is the same as at its melting point at ambient pressure (Poirier, 1988). If we assume that the coefficient of diffusion of oxygen behaves in the same way, its value at the melting point of iron, at the pressure be taken as of the core—mantle boundary, may

D ~3x109m2

—i

°~

With an apparent activation energy ~H 3Tm (Poirier, 1988) and taking the temperature of the core at the depth of the core—mantle boundary

32

CORE MATERIAL INFILTRATION INTO LOWER MANTLE

equal to 3800 K (Brown and McQueen, 1980; Spiliopoulos and Stacey, 1984; Poirier, 1986), the value of the diffusion coefficient in these conditions is not significantly different from the above value. 2.2. Grain boundary and interfactal energies

There are very few absolute measurements of large-angle grain boundary energy in solids. Friedel (1964) quoted ~ 0.85 J m2 for yiron, and Cooper and Kohlstedt (1982) gave YGB 0.9 J m2 for olivine. The grain boundary energy should be only slightly sensitive to pressure. In the absence of more relevant data, we will assume that for perovskite and magnesiowüstite YGB 0.9 J m2. The interfacial energy between solid oxides and liquid iron is even less well known than grain boundary energies. The interfacial energy between solid A1 andand liquid 2 (Nicholas, 203 1988) the Fe is equal energy to 2.4 Jbetween m interfacial solid MgO and liquid Fe can be estimated to be about 2.3 J m2, from =

=

3. Capillary rise Liquid iron can corrode grain boundaries and rise in the lower mantle at a rate dh/dt given by eqn. (6). However, it cannot rise higher than the height of the capillary rise hcap, for which the weight of the liquid column equilibrates the capillary forces. The height of capillary rise between two flat plates separated by a distance 6 is given by 2y cos 6 hcap L (9) =

where YL is the surface tension of the liquid (interfacial specific energy between the liquid and its vapour), 6 is the angle of wetting, p is the density of the liquid and g is the value of gravity. The surface tension of pure iron at its melting temperature, at ambient pressure, is YL 1.8 J m2 (lida and Guthrie, 1988); it also approximately scales with melting temperature decreases with increasing activity of oxygen and in solution (lida and Guthrie, 1988): =

values of the surface tension of liquid Fe, solid MgO and the wetting angle (130°). Clearly, at atmospheric pressure, liquid iron does not wet oxides and eqn. (1) is not satisfied, making preferential attack along the grain boundary impossible. However, there seems to be good evidence of wetting higheffect pressure, which is probably caused more byatthe of dissolved oxygen than by the effect of pressure itself. Indeed, the interfacial energy between liquid metals and oxides usually decreases as the oxygen content of the liquid metal increases: for 1 at.% 0 in liquid Fe, the interfacial energy with A1 203 has already 2 (Chakiader et deal., creased from 2.4 to 0.6 J m 1981). We will therefore assume perfect wetting, and take the interfacial energy y~ 0, which will give us an upper bound for L~yfrom eqn. (1) and a lower bound for the time t necessary to create a channel of height h and width a (eqn. (7)). With D 2 s—i, a 5 X 10— ~° m, 3 xkiO~ m x 1023 J K~,we obT 3800 K0~and 1.38 tam, with h in metres and t in seconds, =

=

=

t

=

2.3 X 106 h2

=

(8)

1.8—240 ln(1

+

)

220a

(10)

°x

Making the (incorrect, but unavoidable) assumption that the solution is ideal, the activity of oxygen in the solution a 05 is equal to the atomic fraction of oxygen. For about 10 wt.% oxygen in the core, we have a0~ 0.23 and the surface 2. Assumtension is then equal to YL 0.8 J m ing, as we have done all along, that wetting is perfect (6 0) and taking p iO~ kg m3 and g 10 m s2, we obtain 1 6>< io—~ heap (11) =

=

=

=

=

While the6 liquid corrodes the grain boundary at the tip of the channel and rises higher, the thin intergranular channel (originally of width a) widens by dissolution of the walls. To obtain a width 6 over a distance heap in time t, the quantity of solid dissolved per unit area of wall is 6/2. We will verify later that the rate of dissolution of the walls is fast enough to be compatible with the assumption that the channels are of constant width over their height. The height of capillary rise obviously decreases as the channels widen.

33

J.P. POIRIER AND J.L. LE MOUEL

4. Geophysical constraints on the quantity of infiltrated liquid Fe in D” layer 4.1. Seismic velocity decrease in D” layer and fluid fraction In some velocity profiles, it is found that the seismic velocities V~and V~,decrease by about 3% over 100 km at the base of the mantle (Young and Lay, 1987). We will assume that the thickness of the D” layer is 100 km (Doornbos, 1983) and that the observed 3% decrease in velocities is entirely the result of the presence of liquid core alloy between the grains of the lower-mantle material. This, of course, implies that the temperature 100 km above the core—mantle boundary is still higher than the melting point of the iron— oxygen alloy at the corresponding pressure (about 130 GPa). Interpolation of experimental data of Boehler (1986) and Brown and McQueen (1980, 1986) by Ross et al. (1990) gave a melting temperature for pure iron of about 3600 K, 100 km above the core—mantle boundary. Considering that the core alloy has a lower melting temperature than pure iron and that the thermal boundary layer may have a thickness of more than 100 km, the assumption of liquid iron 100 km above the core—mantle boundary may be marginally tenable. Williams et al. (1987) derived a melting temperature of 3800 K for the core alloy at the core—mantle boundary, which leads to the same tentative conclusion, We then need a relationship between the yelocity decrease and the fluid fraction in the mantie. With a view to constraining the amount of partial melt in the upper mantle, Stocker and Gordon (1975) measured the extensional velocity decrease in metallic alloys exhibiting a eutectic point. For a Cu—Pb alloy they found a relative velocity decrease of 1.75% per percent of fluid, and for Cu—Ag they found a velocity decrease of 14% per percent of fluid. In the absence of more and better data, we will derive an order of magnitude of the fluid fraction in the D” layer by assuming an average value for LW/V of 8% per percent of fluid. Thus, if all the decrease in velocity of 3% is due to core fluid in connected pores, the porosity CF equal to the fluid fraction may be roughly 0.4%.

If we imagine the infiltrated mantle material as formed of spherical or cubic grains, of characteristic dimension d, coated by a layer of fluid of thickness 6, we have F 66/d. The grain size in the lower mantle is, of course, unknown, but it is currently accepted that it probably does not differ much from that of the upper mantle, as inferred from the grain size of xenoliths, i.e. of the order of 1 mm or 1 cm. We can therefore calculate an order of magnitude of the width of the channels 6, the corresponding height of capillary rise heap (eqn. (11)), and the time taken to reach this height by grain boundary wetting (eqn. (8), for a width of channel equal to the cell parameter a), for T 0.4% and for the two grain sizes: for d 1 mm 8 0.7 ~am heap 20 m = =

30 years 1 cm 6 7 jsm heap 2 m t 3.5 months The widening of the channel from the cell parameter a to the width 6 corresponds to dissolution rates of about 120 A year’ and 120 ~m year~ for grain sizes of 1 mm and 1 cm respectively. Both figures are compatible with the assumption that widening of the channels keeps pace with their opening. If convection sweeps the infiltrated layer upward, as suggested by Jeanloz (1990) and Knittle and Jeanloz (1991), the time taken to fill a D” layer of 100 km thickness, assuming an average velocity of the convection flow of 10 cm year is about 1 million years. The average residence time of the infiltrated layer at the contact with the core is about 200 years and 20 years for a layer thickness of 20 m and 2 m, respectively. These times are much longer than the infiltration times of 30 years and 3.5 months respectively. It is therefore possible to imagine that the D” layer is filled with fluid iron—oxygen alloy in connected channels, corresponding to a porosity of 0.4%. t

for d

=

~,

5. Electrical conductivity of the infiltrated D” layer This semi-quantitative physical assessment of the infiltration process is compatible with the

34

CORE MATERIAL INFILTRATION INTO LOWER MANTLE

qualitative suggestion of Jeanloz (1990) and Knittie and Jeanloz (1991) that the D” layer may be infiltrated with liquid iron alloy from the core. We will now investigate the effect of the quantity of conducting fluid on the electrical conductivity of the D” layer, and the possible perturbations of the geomagnetic field that might result. Assuming that the conducting fluid is distributed in the connected porosity CF of the lower-mantle rock and that the conductivity of the fluid is much smaller than that of the rock, the ratio of the effective electrical conductivity of the rock u (on a scale much larger than that of the cracks) to the conductivity of the fluid o’~is given by Archie’s law: CF”~

(12)

with in 1—2 4~e.g.Brace ct al., 1965). The infiltrating core fluid is a solution of oxygen (and probably sulphur) in iron and can be assimilated to liquid iron oxides FeO and Fe203. At the pressure of the core—mantle boundary the iron oxides are metallic, and hence are good conductors of electricity. Knittle et al. (1986) found that the conductivity of FeO between 72 and 155 GPa is approximately 106 5 m and Knittle and Jeanloz (1986) found that the conductivity of Fe203 is about 3 x i0~S m’ at 61 GPa. The conductivity of pure liquid iron at pressures and temperatures expected in the Earth’s core is estimated to be between 6.7 x iO~and 8.3 X i0~ S m~(Secco and Schloessin, 1989). Altogether it is reasonable to assume an electrical conductivity of the liquid alloy equal to that of the core, about 106 5 m~. With CF 0.004, Archie’s law (12), for 1 a~m ~ 2, gives a2 X iO~ ~ 4 X iO~ (13) ~,

~

—

magnitude smaller than that of the fluid. Without attempting a more quantitative treatment, we can conclude that the effective conductivity of the infiltrated D” layer is not significantly different from that of the lower-mantle material. We thus find that infiltration of conducting core fluid is possible in the D” layer, but despite the high conductivity of the fluid, the effective conductivity of the layer is practically unchanged. Even if the infiltration is heterogeneous, as suggested by Knittle and Jeanloz (1991) on the basis of the observation of lateral variations in the decrease of seismic velocities, the lateral variations in conductivity will be totally negligible, unless the iron segregates in large masses by some mysterious process. 6. Consequences for the geomagnetic field In the case where the infiltrated fluid is uniformly distributed, as there is no need to call for any particularly significant increase of the electrical conductivity o- of the D” layer, it is sufficient to consider models for which a- increases regularly, albeit possibly rapidly, in the lower mantle down to the core—mantle boundary. In this case, of course, the D” layer, in itself, has no influence at all on the electromagnetic coupling between the core and the mantle (e.g. Jault and le Mouël, 1991), or on the secular variation. Let us now consider the case where the iron could segregate in masses whose conductivity could be as great as that of the core itself. Could those metallic regions pin the magnetic field lines as proposed by Jeanloz (1990)? To obtain an upper limit for the possible effect, let us consider the case where the totality of the iron that has infiltrated into the D” layer, according to the former estimates (CF 0.4%, thickness 100 km), is segregated in a single mass S (boundary ~S). The radius of this inclusion (assumed to be spherical for the sake of simplicity) would be about 250 km (Fig. 2). Let B(r,t) be the main field and B(r,t) aB/~it be its temporal change, i.e. the secular variation field, which can be assumed to have time constants of the order of a few tens of years. =

For a value of fluid conductivity of 106 S rn_i and m 1, the effective conductivity a~is found to be 20 S m However, the effective conductivity given by Archie’s law is that of a perfectly insulating medium imbued with a conducting fluid; the conductivity of the lower-mantle assemblage is about 100 s m~ (Achache et al., 1981; Peyronneau and Poirier, 1989), four orders of =

-

35

J.P. POIRIER AND J.L. LE MOUEL

Let us consider the limiting (worst) case, where the conductivity of the core, as well as that of the inclusion, is infinite, whereas the mantle is insulating. Let u be the velocity field in the core. In the body of the core

the horizontal field fit the potential field (16); the presence of the inclusion does affect the surface layer of currents. We consider the simplest case where hr is approximately uniform over horizontal distances

B

greater than 250 kin, and we write

aB/at

=

V x (u X B)

(14)

and, at the core—mantle boundary,

E ‘P

[V x (u XB)]

=

=

B

b

(15)

where P is the unit radial vector. As the radial component of B is continuous through the core—mantle boundary, the secular variation B in r ~ a is a solution of the potential problem -

E= —VV E ‘P hr

for r>a(r

B

on ~j5

=

=

0

for r

=

not inside S)

=

B~1+ B,

(17)

where theand subscripts wi inclusion’, and i mean ‘without inclusion’ ‘due to the respectively. Let R be the distance from the centre of the inclusion and c the radius of the inclusion. On ~S (R c), B111 —B~,and as the typical magnitude of Bwjn is br, we have =

=

E1~b~(~)

a

(16)

B 0 for r a is the core radius and B,, is the component of E along the normal n to ~3S.It should be noted that li ‘P (on r a) is not affected by the presence of the inclusion, as it is entirely determined by processes inside the core. A layer of electric currents at the surface of the core (r a) makes —~

=

=

(18)

Equation (18) results from the well-known fact that the field due to electric currents induced in a uniform sphere by a uniform external field is dipolar. The assumption that br is almost uniform is the most efficient: more complicated geometries of hr give higher-degree multipoles instead of the simple dipole. With c 250 km, B~is reduced by a factor 7 x iO~at the surface of the Earth, compared with its value on which is of the same order of magnitude as the unperturbed =

as,

/ /

/

/

/ / / / / MANTLE

/

/

/ /

‘•‘

~

Fig. 2. Sketch of the lines of force of the field B~1,without conducting inclusion (dashed line) and B~1+ B1, with a conducting inclusion (continuous line). The lines of force are locally deflected by the inclusion, but are not perturbed at the surface of the Earth.

36

secular variation hr. The field B,,1 is itself reduced by geometrical attenuation from the core— mantle boundary to the Earth’s surface. However, all the energy of the secular variation field is carried by terms with degree five or less in its harmonic expansion, for which the attenuation is smaller than 1/30 (e.g. le Mouël et al., 1985). One can conclude that such an inclusion has no effect on the secular variation field observed at the surface. When continuing the observed secular variation field from the surface to the core—mantle boundary, one will obtain—with the well-known difficulties—the field B~1one cannot invent a field at the core—mantle boundary which one is not able to detect at the surface. In other words, qualitatively, the field lines of B~1 are not pinned by the inclusion, they are only locally deflected by it (Fig. 2). One could, of course, instead of one large inclusion, consider a number of smaller ones, the total amount of iron being constant. The perturbation3,Bk, the inclusion k, always varies as anddue thetosmaller c is, the smaller is the (c/R) perturbation at the Earth’s surface (Rk 3000 km). Alternatively, we could consider a number of less conducting inclusions with the same radius; however, the smaller the conductivity, the smaller is the perturbation. Up to now, we have neglected the conductivity a-rn of the mantle surrounding the inclusion. In fact, a-rn 0 and a toroidal field leaks into the mantle. The time-varying part of the toroidal field is distorted by the inclusion in the same way as is the poloidal secular variation field B; however, the perturbation at the Earth’s surface is even smaller (the toroidal field in the lower mantle is less than a tenth of the poloidal field if a-rn is of the order of a few hundreds of f1~ m~) (e.g. Jault, 1990).

7. Conclusions Using semi-quantitative materials science data on intergranular wetting and interfacial energies between liquid iron and ceramics, we found that infiltration of core material into the base of the lower mantle is indeed possible over distances of

CORE MATERIAL INFILTRATION INTO LOWER MANTLE

the order of 1—100 m, as was intuitively proposed by Jeanloz (1990). We then examined the effect that the infiltration might have on the secular variation of the geomagnetic field as observed at the surface of the Earth, using assumptions most favourable to the existence of such an effect. In particular, we assumed that mantle convection might somehow fill the D” layer over a thickness of 100 km, that the decrease in seismic velocities observed in some profiles is entirely the result of the presence of intergranular fluid, and that the electrical conductivity of this fluid is equal to that of the core. However, the effective conductivity of the infiltrated layer is found to be practically unchanged, and thus unable to affect the secular variation field observed at the surface. In the improbable case where all of the infiltrated conducting material is gathered in a single mass, it is found that the magnetic field lines are not pinned by the inclusion, but are locally deflected by it, without significant perturbation of the field lines at the surface. Acknowledgements We thank Francoise Goarant, François Guyot and Dominique Jault for fruitful discussions, and Alex Revcolevschi for providing much information on liquid metal—ceramic interfaces. Tom Shankland kindly read the manuscript and provided welcome criticism. This work was partly supported by CNRS (URA 734 and 729). This is IPGP contribution no. 1207.

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J.P. POIRIER AND J.L. LE MOUEL

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a

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