Earth’s Core

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Encyclopedia of Physical Science and Technology En004H-192 June 8, 2001 19:27

Earth’s CoreDavid LoperFlorida State University

I. StructureII. Composition and PropertiesIII. Evolution of the CoreIV. Core–Mantle InteractionsV. Core Energetics

VI. Core DynamicsVII. The Geodynamo

GLOSSARY

Convection Motion driven within a fluid body due to den-sity differences. The density differences may be of ther-mal or compositional origin.

Core–mantle boundary The boundary between theouter core and the mantle: a nearly spherical surface3480 km in radius.

Inner core The central, solid spherical region of the corehaving a radius of 1200 km.

Inner-core boundary The boundary between the innercore and the outer core: a nearly spherical surface1200 km in radius.

Mush A mixed region of solid and liquid phases.Outer core The molten part of the core lying between

1200 and 3480 km from the center.

THE EARTH’S METALLIC CORE occupies the centralportion of the planet and is surrounded by the rocky man-tle. To a first approximation the core is a sphere having aradius of 3480 km and a mean density of 10,480 kg/m3. It

comprises 16% by volume of earth and 32% by mass. Thecore is composed principally of iron, but contains a smallpercentage of nickel and a small but significant amount(∼10%) of one or more nonmetallic elements. The centralportion of the core, called the inner core, is solid, while theremainder, called the outer core, is liquid. Earth has had acore since it formed some 4.5 billion years ago. It is likelythat the entire core was initially molten, that the solid innercore crystallized from the outer core as earth cooled overearth history and that this process is continuing. The outercore is very likely to be convecting vigorously, driven prin-cipally by the release of latent heat and compositionallybuoyant material at the inner-core boundary. These con-vective motions provide energy to the geomagnetic fieldby means of dynamo action, sustaining it against ohmicdecay. Direct evidence of core motions is found in thesecular variations of the geomagnetic field. It is a remark-able fact that these variations occur on times of humanscale (decades), whereas continental drift takes roughly amillion times longer. This suggests that the core is far dif-ferent, both dynamically and structurally, from the mantleand may be likened more to the atmosphere or oceans.

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776 Earth’s Core

FIGURE 1 Seismologically determined elastic-wave speed, den-sity and gravity as functions of depth in the core. Uncertainties ofwave speeds are indicated by the multiple lines. [From Jeanloz,J. A. (1990). Annu. Rev. Earth Planet. Sci. 18, 357–386. Copyright1990 by Annual Reviews Inc.]

I. STRUCTURE

The internal properties of earth must be determined bymeans of external observations, which is a difficult in-verse problem. Seismology is the principal source of in-formation about most of the earth’s interior, particularlythe mantle. However, seismology provides relatively lit-tle information about the liquid outer core, and the secu-lar variations of the geomagnetic field are used to probeits topmost layer. Additional evidence regarding the corecomes from measurements of the length of day, gravity,and moment of inertia and from high-pressure experimen-tation (see Fig. 1).

To a good approximation, the core is a spherically sym-metric, self-gravitating body in hydrostatic equilibrium.The pressure, p, density, ρ, and local acceleration of grav-ity, g, of any such body are related by

dp

dr= −ρg, g = G

m

r2,

dm

dr= 4πρr2 and ρ = ρ(p),

where G = 6.67 × 10−11 N m2/kg2 is the gravitationalconstant and m is the amount of mass within a sphereof radius r . The last of these equations is an equation ofstate for density; the functional form of this relation de-termines the internal structure of a given planetary body.A good approximation to the equation of state for earth’score is that the incompressibility is a linear function ofpressure:

ρdp

dρ= k1(p + p1),

with p1 = 68 GPa and k1 ≈ 3.23. [Remarkably, this equa-tion with the same constants fits the lower mantle as well.]

The pressure at the center of earth is about 364 GPa (i.e.,several million atmospheres) and 135 GPa at the top of thecore. Iron compressibility is important at these pressures;core material exceeds the density of iron at zero pressureby 25% at the top of the core and by 65% at earth’s center.However, these densities are smaller than those of pureiron, strongly suggesting alloying with lighter elements.

A. Core–Mantle Boundary

The outer boundary of the core is often denoted by itsacronym: CMB (core–mantle boundary). Above the CMBis the low-density and electrically insulating elastic sili-cate mantle, while below is the high-density and electri-cally conducting fluid outer core. The CMB is identifiedby a strong and sharp change in seismic and electromag-netic properties. Primary or compressive (P) wave speedsdrop from 13.6 km/s in the lower mantle to 10.0 km/s atthe top of the core, while secondary or shear (S) wavespeeds drop from 7.3 km/s in the mantle to zero in thecore. (Fluids cannot sustain shear waves.) Reflections ofseismic phases such as PcP , ScS, and PnKP at the CMBindicate that the CMB is less than 2 km thick. The seis-mically determined mean CMB radius, as codified in thePreliminary Reference Earth Model, is 3480 km. This ra-dius may be estimated independently from geomagnetism,assuming that the mantle is an electrical insulator and thecore is perfectly conducting. The geomagnetic CMB isthe depth at which the unsigned magnetic flux does notvary with time. The radius of the CMB determined bythis method depends on the magnetic-field model used,but is in good agreement with the seismically determinedvalue.

The shape of the CMB deviates from spherical due tothe centrifugal force of rotation, making the polar radiusabout 9 km less than the equatorial. Smaller scale devia-tions of the CMB from its mean radius can be estimatedin principle by seismic tomography, but observations areconfused by strong heterogeneities in the lower mantleand there is no clear consensus on the shape or magnitudeof the deviations. Estimates of the root mean square (rms)deviations typically lie in the range from 0.5 to 5.0 km.

B. Inner-Core Boundary

The inner-core boundary (ICB) is believed to be a phase-change boundary between the metallic liquid outer coreabove and the metallic solid inner core below. Sincethe outer core is electromagnetically opaque, we mustrely on seismic studies for direct information aboutthis feature. The mean radius of the ICB is 1220 km.



Earth’s Core 777

Geographical deviations of the ICB from its mean ra-dius are difficult to quantify, due to the small numberand poor geographical distribution of relevant seismicmeasurements. Indirect information regarding the struc-ture of the ICB comes from metallurgy; see Section III.B.

C. Outer-Core Structure

The primary evidence for existence of the outer core comesfrom the shadow zone for direct P waves at angular dis-tances between 100 and 143 degrees from the seismicsource. There is no reliable evidence that the outer coreis other than a well-mixed homogeneous liquid. The rel-atively rapid secular variations of earth’s magnetic fieldobserved at the surface are strong, but indirect, evidenceof vigorous motions within the core which maintain thisstate. Furthermore, the dynamo process believed to be op-erating in the outer core (see Section V) provides fur-ther strong, but indirect, argument for vigorous motionsthroughout most of the outer core.

D. Inner-Core Structure

The first evidence of structure within the inner core camefrom studies of seismic attenuation, which found relativelyhigh levels of attenuation in the uppermost 200–300 kmof the inner core. More recently, it has been determinedthat the inner core is seismically anisotropic, with P-wavespeeds being larger in the direction parallel to earth’s rota-tion axis than in the perpendicular direction. There is alsoevidence of seismic anisotropy in the western hemisphereof the inner core. The most likely cause of these struc-tures is crystal alignment, induced by asymmetrical coregrowth and deformation by relaxation toward equilibriumellipticity.

II. COMPOSITION AND PROPERTIES

A. Overall Composition

Strong, but indirect, evidence that the core is composedprincipally of iron comes from cosmochemistry, from theexistence of iron meteorites, and from high-pressure ex-perimentation. There is also strong evidence from the lastof these that the core must contain a significant percentageof light, nonmetallic material. The nature of this material isuncertain, but the most likely elements are sulfur, silicon,and oxygen.

An important, but undetermined, issue is whether thecore contains significant amounts of heat-producing ra-dioactive elements. This has bearing on the energetics ofthe core, the age of the inner core, and the energy sourcefor the geodynamo.

FIGURE 2 A typical phase diagram for a binary eutectic alloy. T istemperature and ξ is mass fraction of constituent B. Within the re-gion labeled mush, solid having the solidus composition and liquidhaving the liquidus composition coexist at a common temperature.

B. Radial Variations of Composition

It is very likely that the outer core is homogeneous to a highdegree of precision; the relative density differences associ-ated with convective motions are on the order of 10−9. Thelargest and most significant change of composition is thatwhich occurs across the ICB. In general, the solid whichforms by solidification of an alloy has a composition thatdiffers from the parent liquid (see Fig. 2). The outer coreis dominantly iron and the inner core is likely to be com-posed of iron crystals containing less of the nonmetallicelements. The density contrast attributed to the composi-tional difference is roughly 0.5 g/cc = 500 kg/m3.

C. Physical Properties and State

The physical properties and state of the core are summa-rized in Table I. The first entry in columns 2 and 3 is thatat the top and the second is that at the bottom. For moredetail, see Appendices F and G of Stacey (1992).

III. EVOLUTION OF THE CORE

A. Initial Formation

The existence of stony and iron meteorites provides strongevidence that planetary cores, in general, and earth’s core,in particular, formed by separation of less dense silicatephases and more dense metallic phases as they accreted



778 Earth’s Core

TABLE I Physical Properties and State of the Core

Outer core Inner coreProperty (top–bottom) (top–bottom) Units

P-wave speed 8,065–10,356 11,028–11,266 m/s

S-wave speed 0–0 3,504–3,668 m/s

Incompressibility 644–1,304 1,343–1,425 GPa

Poisson’s ratio 0.5–0.5 0.444–0.441 —

Specific heat 707–659 641–637 J/kg K

Thermal expansivity 15.6–7.8 6.7–6.4 10−6/K

Thermal conductivity 28–36.8 49.5–50.9 W/m K

Electrical conductivity 3 4 105 S/m

Pressure 136–329 329–364 GPa

Density 9,903–12,166 12,764–13,088 kg/m3

Gravity 10.7–4.4 4.4–0.0 m/s2

Temperature 3,750–4,960 4,960–5,100 K

during the formation of the solar system some 4.5 billionyears ago. This was a strongly exothermic process; thegravitational potential energy released by this process issufficient to heat earth by some 2000◦. It follows that earthlikely was very hot soon after its formation and has beencooling since then.

B. Formation and Growth of Inner Core

It is very likely that the inner core has grown by solidifi-cation from the outer core as earth has cooled during thepast 4.5 billion years and that solidification and growthis continuing. The inner core may well be a relatively re-cent feature; in some models of the evolution of the coreit begins to grow roughly 2 billion years ago.

The core is cooled by transfer of heat to the mantle,and the rate of cooling is largely controlled by the thermalstructure of the lowermost mantle (the D′′ layer). The outercore is coolest at the top, near the CMB, but freezingproceeds from the center outward because the increase ofthe freezing (liquidus) temperature with pressure is greaterthan the adiabatic gradient:

dTL

dp>

dTA

dp.

As the inner core grows, both latent heat and buoyantmaterial are released at the base of the outer core. Thesework in parallel to drive convective motions in the outercore.

Solidification of outer-core material at the ICB is sim-ilar to the metallurgical process of unidirectional solidifi-cation of molten metallic alloys; the mathematical modelis called a Stefan problem. The simplest solution to theStefan problem involves the steady advance of a planarsolidification front into a quiescent liquid. This simple so-lution has two known forms of instability. If the freezing

process involves a change of composition (see Fig. 2) andthe material rejected by the solid phase is buoyant com-pared with the parent liquid, the static state is prone to acompositional convective instability. It is very likely thatthis instability occurs in the outer core and that the result-ing convective motions participate in the dynamo processwhich sustains earth’s magnetic field.

Solidification of an alloy at a planar interface is prone toa second, morphological instability. The material rejectedby the solid phase accumulates on the liquid side of thefreezing interface, depressing the liquidus and making thatliquid compositionally (or constitutionally) supercooled.This causes the flat freezing interface to be unstable andbecome convoluted. These convolutions can become ex-treme, forming a so-called mushy zone. Again, it is verylikely that this instability occurs in the core and that the in-ner core is, in fact, an intimate mixture of solid and liquid.Dynamic processes cause the fraction of liquid phase tobe small, so that the inner core acts structurally as a solideven though, thermodynamically, it behaves as a solid-liquid mixture.

IV. CORE–MANTLE INTERACTIONS

The core and the mantle may exchange heat, material,and angular momentum. The geodynamo operating in theouter core requires transfer of heat from core to the mantle.In addition, the heat conducted down the adiabatic gradi-ent must be transferred to the mantle. It is an open questionwhether the rate of heat conduction down the adiabat isgreater or less than the rate of transfer from core to mantle.If greater, then the top of the outer core may be thermallystratified. In this case, compositional buoyancy has thecapacity to maintain the adiabat all the way to the top.

Four types of material exchanges across the CMB arepossible: silicate from core to mantle, silicate from mantleto core, metal from core to mantle, and metal from mantleto core; but which occurs, if any at all, remains uncertain.During the accretion of earth, silicates and metals werechemically equilibrated at low pressure. It is an open ques-tion whether silicates and metals are equilibrated acrossthe CMB. If metals are leaching into the mantle and/orsilicates into the core, the top of the core may be compo-sitionally stratified.

Angular momentum transfers between the core andthe mantle are responsible for the long-term (decade andlonger) changes in the length of day. The principal mech-anism of transfer is unclear; possible coupling mecha-nisms include electromagnetic, topographic, and gravita-tional torques. Electromagnetic torques require significantelectrical conductivity in the lowermost mantle, topo-graphic torques require variations in the shape of the CMB,and gravitational torques require density anomalies in the



Earth’s Core 779

mantle plus a nonspherical ICB. The existence of the req-uisite electrical conductivity within the lower mantle isuncertain, but it appears that irregularities of the shape ofthe CMB and of the density of the lower mantle are suffi-cient to produce topographic and gravitational torques ofthe required magnitude.

V. CORE ENERGETICS

The core is cooling by transfer of heat to the mantle. Therate of transfer is controlled by the thermal structure of thelowermost mantle (i.e., the D′′ layer). The possible sourcesof energy within the core include sensible heat (i.e., theheat capacity of the core plus gravitational energy releasedby thermal contraction) released by the slow cooling ofthe core, latent heat of fusion released by the progressivesolidification of the inner core (plus gravitational energyreleased by the volume change), gravitational potential en-ergy released by the selective solidification of the densermetallic constituents in the core, and radioactive heating.The first three of these are linked to the cooling of thecore and have released approximately 3.0 × 1029 J of en-ergy since the inner core formed. Gravitational energy hassupplied about 13% of this total.

The magnitude of radioactive heating is difficult to esti-mate, as the partition coefficients of the relevant elements(U, Th, K) between the core and the mantle are very poorlyknown. Due to the finite half-lives of the isotopes 238U,235U, 232Th, and 40K, radioactive heating was more signif-icant early in earth history than it is now. If these elementscontribute significantly to the present heat budget, then thecore would have been heating for much of its history, andit would not have been possible to form a solid inner coreby cooling. It is quite likely that the present amount ofradioactive heating in the core is relatively insignificant.

If the outer core is well mixed by convective motions,as appears very likely, the temperature decreases signifi-cantly with increasing radius due to adiabatic decompres-sion. The adiabatic gradient is given by

dT

dr= αTg

Cp,

where α is the coefficient of thermal expansion and C p isthe specific heat; see Table I. The rate, Q̇, that heat is con-ducted radially outward along this adiabat is quantified by

Q̇ = 4πr2kdT

dr= 4πr2k

αTg

Cp,

where k is the thermal conductivity. If Q̇ is less than therate of transfer of heat to the mantle across the CMB, thenthermal buoyancy contributes to convective motions at thatlevel. Conversely, if Q̇ exceeds the rate of transfer, then the

top of the outer core is thermally stably stratified. Currentestimates of the properties of the outer core, particularlythe thermal conductivity, are not known with sufficient ac-curacy to determine which possibility in fact occurs. Usingvalues from Table I, Q̇ ≈ 3.5 × 1012 W. [If thermal con-ductivity is as high as 47 W/m K, then Q̇ ≈ 6 × 1012 W.]

It is important to distinguish between thermal and com-positional (i.e., gravitational) energy sources, because, asnoted above, thermal energy is “short circuited” by con-duction down the adiabat. On the other hand, moleculardiffusion is ineffective in redistributing matter, and com-positional convection is much more likely than thermalconvection in the outer core.

VI. CORE DYNAMICS

A. Oscillations

The outer core may sustain oscillations involving inertial(Coriolis), magnetic (Lorentz), and/or buoyancy forces.Oscilations involving all three are referred to as MACwaves (M = magnetic, A = Archimedian, C = Coriolis).The role of buoyancy forces in sustaining oscillations may,in fact, be negligible, in which case MC waves result. IdealMC waves, involving the fluid velocity, u, pressure, p,and perturbation magnetic field, b, are governed by themomentum, mass, and magnetic-diffusion equations:

∂u∂t

+ 2 × u = −∇p + 1

ρµ(B · ∇)b,

∇ · u = 0 and∂b∂t

= (B · ∇)u,

where is the rotation rate of earth, ρ is the density of corefluid, µ is the magnetic permeability, and B is the magneticfield (assume locally constant). Plane-wave solutions obeythe dispersion relation[

ω2 − (B · k)2

ρµ

]2

= 4( · k)2

k2ω2.

The solutions are of two distinct types; one is the same asclassic, nonmagnetic rotational oscillations to dominantorder, and the second is a strongly modified Alfven wavewhich has a slow phase and group speeds. The phase speedof this latter type of wave is consistent with the speed ofmotions at the top of the outer core inferred from secularvariations of the magnetic field.

B. Convection

Convective motions in the outer core are driven by sourcesof buoyancy at the ICB or sinks at the CMB; in the absence



780 Earth’s Core

of forcing, thermal conduction drives the outer core towardan isothermal state, which is strongly stable. The sourcesand sinks may be compositional or thermal.

A compositional sink of buoyancy at the CMB resultsfrom the transfer of silicate to the mantle or metal to thecore. A thermal sink of buoyancy at the CMB results fromthe transfer of heat from core to mantle at a rate greaterthan the rate heat is conducted radially outward withinthe outer core to the CMB. It is uncertain whether anysignificant transfer of material occurs at the CMB andwhether the rate of transfer of heat from core to mantleexceeds that conducted down the adiabat.

Compositional and thermal sources of buoyancy at theICB result from the growth of the inner core; latent heat isreleased at too great a rate to be conducted down the adi-abat, and molecular diffusion is quite ineffective in redis-tributing the buoyant material released by solidification. Itis very likely that both thermal and compositionally buoy-ant material is released at the ICB and that this materialdrives the convective motions in the bulk of the outer core.

C. Outer-Core Stratification

Given that the only plausible explanation for the existenceof the geomagnetic field is a convective dynamo in theouter core, the bulk of the outer core must be convectingand hence unstratified. However, the outer core might bestratified at the top. If the rate of heat conduction down theadiabat were greater than the rate of transfer from core tomantle, then thermal buoyancy forces would tend to strat-ify the top of the outer core. Similarly, if silicate materialwere leaking into the core and/or metallic material wereleaking into the mantle, then the top of the outer core wouldbe compositionally stratified. The rates of transfer of heatand material at the CMB are not known with sufficientaccuracy to determine whether the top of the outer coreis stratified. Any possible stratification is too weak to bedetected seismically. The best observational evidence ofthe dynamic state of the top of the outer core comes fromgeomagnetic secular variation, which can be inverted togive velocity fields. Current models of core motion do notshow any tendency for stratification. If the top layer of theouter core were stably stratified and if the rate of transferof heat from core to mantle were geographically variable(as seems likely), then strong thermal winds would be gen-erated at the top of the outer core. Such winds are not seenin the models of core surface motion.

D. Inner-Core Rotation

There are strong dynamical reasons to believe that to a firstapproximation the inner core is corotating with the mantleand with the bulk of the outer core. If the inner core were

rotating about a different axis or at a different rate, enor-mous electromagnetic torques would be generated whichwould restore the state of corotation. In the late 1990s,several seismic studies produced evidence that the innercore is rotating slightly (from 0.2 to 3%) faster than themantle. This conclusion is controversial, as other studiesfind no significant difference in rotation rates of the innercore and the mantle.

VII. THE GEODYNAMO

Given the rapid secular variation of earth’s magnetic fieldand its episodic reversals of polarity, the only plausible ex-planation of its origin is the dynamo action of convectivemotions in the outer core. The so-called geodynamo prob-lem has proved to be one of the most difficult of mathemat-ical geophysics. Early results in the 1930s were negative,in the form of anti-dynamo theorems. Further progress onthis problem was slow until the 1970s when it was shownthat certain velocity fields were capable of sustaining amagnetic field. This kinematic dynamo problem requiredsolution of the magnetic diffusion equation

η∇2B + ∇ × (u × B) = ∂B∂t

in some spatial domain (e.g., a sphere) with suitableboundary conditions (e.g., insulating surroundings havinga potential field). Here, η is the magnetic diffusivity and uis a specified velocity. This is in effect a vector eigenvalueproblem.

Generalization of this kinematic problem to the dy-namic case has proved to be difficult. In the full problemthe velocity and pressure are determined by the momen-tum and continuity equations, e.g.,

∂u∂t

+ 2 × u = −∇p + Cg + 1

ρµ(B · ∇)B + ν∇2u

and

∇ · ρu = 0,

while the fractional density perturbation, C , which isthe driving force for the convective motions, obeys anadvective-diffusion equation

∂C

∂t+ u · ∇C = D∇2C.

This problem is too complex for analytic solution, and suc-cessful numerical simulation of dynamo action in a spher-ical body was first achieved by Glatzmaier and Robertsin 1995. As seen in Fig. 3, the output of this and similarmodels can appear quite realistic. The limitations in sizeand speed of current computers require the diffusivities ofmagnetic field (η), momentum (ν), and buoyancy (D) to



Earth’s Core 781

FIGURE 3 A representation of the magnetic field produced bythe Glatzmaier-Roberts dynamo model. The structure of thefield changes abruptly at the CMB. (Figure courtesy of GaryGlatzmaier.)

be parameterizations of small-scale turbulence rather thanassuming their molecular values.

The full dynamo problem is driven through the bound-ary conditions on the density perturbation, C , which pro-

vide gravitational potential energy to the system. Thisgravitational energy is converted to kinetic energy bymeans of convective instabilities and then to magnetic en-ergy through magnetic induction. Next, ohmic dissipationconverts the magnetic energy to heat, principally withinthe core. This heat is conducted and convected to the CMBand transferred to the mantle.

SEE ALSO THE FOLLOWING ARTICLES

CONTINENTAL CRUST • GEOMAGNETISM • HEAT FLOW

• HIGH-PRESSURE SYNTHESIS (CHEMISTRY) • MANTLE

CONVECTION AND PLUMES • OCEANIC CRUST • SEISMOL-OGY, THEORETICAL

BIBLIOGRAPHY

Jacobs, J. A. (1975). “The Earth’s Core,” Academic Press, San Diego.Jacobs, J. A. (1992). “Deep Interior of the Earth,” Chapman & Hall,

London.Jeanloz, J. A. (1990). “The nature of the Earth’s core,” Annu. Rev. Earth

Planet. Sci. 18, 357–386.Merrill, R. T., McElhinny, M. W., and McFadden, P. L. (1996). “The

Magnetic Field of the Earth: Paleomagnetism, the Core, and the DeepMantle,” Academic Press, San Diego.

Poirier, J. P. (1994). “Light elements in the Earth’s outer core: a criticalreview,” Phys. Earth Planet. Inter. 85, 319–337.

Stacey, F. D. (1992). “Physics of the Earth,” 3rd ed., Brookfield Press,Kenmore, Brisbane.

Stixrude, L., and Brown, J. M. (1998). “The Earth’s core,” Rev. Mineral.37, 261–282.

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