Gubbins D., Herrero-Bervera E. Encyclopedia of Geomagnetism and Paleomagnetism

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and O

are much less mobile than is Mg

and the migrations

of these two ions do not work as effective conduction mechanisms.

Ionic conduction is also a thermally activated process, and can be

written as:

s ¼ s

expðDE

=kTÞ (Eq. 3)

where DE

is the activation energy for ionic conduction. The bodily

motion of ions causes a very strong distortion of the lattice and so

the activation energy for ionic conduction would be much larger than

that of a small polaron (DE

 DE

). This indicates that the tempera-

ture dependence of ionic conduction is much larger than that of small

polaron conduction. Ionic conduction can dominate small polaron con-

duction at higher temperatures.

The population of V

increases with that of Fe

so that the

charge balance is maintained. The increase in oxygen partial pressure

increases Fe

and, therefore increases V

. Hence, the ionic con-

ductivity of V

increases with increasing oxygen partial pressure.

Ionic conductivity is linked with the diffusion coefficient by the

Nernst-Einstein relation:

s ¼ q

nD=kT (Eq. 4)

where q is the charge of the carrier, n is the concentration of the car-

rier, and D is the diffusion coefficient. The diffusion is a thermally

activated process:

D ¼ D

expðDH

=kTÞ (Eq. 5)

From Eqs. (4) and (5), we have

s ¼ðq

=kTÞexpðDH

=kTÞ (Eq. 6)

Therefore, the preexponential term for ionic conduction is inversely

proportional to the absolute temperature. The migration of a small

polaron is also a diffusion process and its preexponential term should

also be inversely proportional to the absolute temperature.

A certain amount of water could be transported into the deep mantle

by the subduction process. Although water should form hydrous

minerals, olivine and its high-pressure polymorphs can contain a cer-

tain amount of water. The rate of diffusion of a proton is very high

and so transportation of an electric carrier by H

(proton conduction)

could have an important role in electrical conduction in the deep

mantle. Proton conduction is a form of ionic conduction and so its

temperature dependence should be also expressed by Eq. (3).

Though it is usually difficult to specify the electrical conduction

mechanism, an indication may come from the sign of the dominant

charge carrier that can be inferred from the thermopower. The thermo-

power, Q, is the ratio of the voltage, DV, generated across a sample

with a temperature difference, DT,toDT:

Q ¼DV

=DT: (Eq. 7)

The voltage, DV

, is generated because the charge carrier has a larger

energy at a higher temperature. Hence, the sign of the charge carrier is

the same as that of the thermopower, Q.

At high pressures, compression can change the energy barrier. We

introduce the activation enthalpy, DH, as follows:

DH ¼ DE þ PDV (Eq. 8)

where P is pressure and DV is the activation volume.

In small polaron conduction, the energy barrier for migration of a

hole decreases with increasing pressure because the distance between

ions shortens. Hence, it is expected that small polaron conductivity

should increase with an increasing pressure (DV

< 0). In ionic

conduction, the corridor for the bodil y migration of ions narrows with

increasing pressure, resulting in an increase in the energy barrier.

Hence ionic conduction is expected to have negative pressure depen-

dence (DV

> 0).

Electrical conductivity of mantle minerals

In this section, the electrical conductivities of the major mantle miner-

als are explained, which are summarized in Figure M185.

Olivine

The electrical conductivity of olivine has been extensively studied.

The measurement of thermoelectric effects has shown that the charge

of the dominant carrier of olivine is positive at temperatures below

1600 K, whereas it becomes negative above 1700 K. This suggests that

there should be two electrical conduction mechanisms. The mechanism

dominant at lower temperatures is considered to be the small polaron

conduction by Fe

. The mechanism dominant at higher temperatures

is considered to be the migration of V

(ionic conduction).

Figure M184 Ionic conduction. Mg

diffuses through V

which causes the migration of V

Figure M185 Electrical conductivity of olivine, wadsleyite,

ringwoodite, Al-free perovskite, and Al-bearing perovskite against

reciprocal temperature. The shaded area denotes the conductivity

of various kinds of silicate magmas.

686 MANTLE, ELECTRICAL CONDUCTIVITY, MINERALOGY

It is reported that the electrical conductivity of natural olivine with

Mg/(Mg þ Fe) ¼ 0.91 at temperatures of 1000–1770 K under an oxy-

gen partial pressure of 10

4

Pa can be expressed as the sum of two

exponential functions:

s ¼ 10

2:4

ðSm

1

Þexp½1:6ðeVÞ=kT þ10

9:2

ðSm

1

exp½4:2ðeVÞ=kT: (Eq: 9Þ

The activation energy of ionic conduction (4.2 eV) is much larger than

that of small polaron conductivity (1.6 eV). The conductivity increases

by a power of 1.8 of the Fe/(Mg þ Fe) ratio. Conductivity also

increases by one-seventh power of the oxygen partial pressure. The

pressure dependence is small. It is reported that the activation volume

is þ0.6 cm

mol

1

. The plus sign of the activation volume is not

consistent with the small polaron model.

Olivine has an orthorhombic crystal structure, resulting in aniso-

tropy of the electrical conductivity. Conductivity in the [001] crystallo-

graphic direction is about twice those in the [100] and [010] directions.

Anisotropy of electrical conductivity in the upper mantle could be

observed in the future.

Olivine has an M

SiO

stoichiometry, where M ¼ Mg, Fe, Ni,

Ca..., and does not contain H

as a first approximation. However, a

small amount of H

up to the order 1000 ppm can be contained in oli-

vine at high pressures. Diffusion of H

in olivine is very fast so that

even a small amount of H

cause high-electrical conductivity.

Wadsleyite and Ringwoodite

Ringwoodite has a spinel structure, in which structural units A and B are

arranged alternatively. Unit A consists of a SiO

tetrahedron, and unit B

consists of MgO

octahedra. Wadsleyite has a modified spinel structure.

The structural units of wadsleyite are the doubles of those of ring-

woodite. Unit AA is a Si

unit, and unit BB consists of MgO

octa-

hedra. Thus, although wadsleyite has a more complex structure than

ringwoodite, the structures of these two minerals are fairly similar.

The electrical conductivities of these two minerals also have similar

values, which may reflect their structural similarity. The conductivities

of these minerals are about two orders of magnitude higher than oli-

vine. The conduction mechanisms of these minerals have not been

clarified. They could be a small polaron of Fe

, because the carrier

charge is plus. Their activation enthalpies are about 1 eV, which are

considerably smaller than that of olivine (1.7 eV). That is, the tempera-

ture dependences of the electrical conductivities of these two minerals

are much smaller than that of olivine. The conductivities of these two

minerals were measured over only a reasonably small temperature

range, that is, 1173–1473 K. The preexponential terms are 100–1000

1

, which are indistinguishable from that of olivine.

The electrical conductivity of wadsleyite is about two orders of

magnitude higher than that of olivine. Hence the olivine-wadsleyite

transition causes a significant conductivity jump. In contrast, because

conductivities of wadsleyite and ringwoodite are quite similar, the

wadsleyite-ringwoodite transition does not cause a conductivity jump.

A certain amount of water (up to 3%) can be contained in wad-

sleyite and ringwoodite through substituting silicon. However, the con-

tribution of proton conduction to the electrical conductivity of

wadsleyite and ringwoodite has not yet been clarified.

Perovskite

The composition of mantle perovskite is primarily (Mg,Fe)SiO

.Inaddi-

tion to these components, perovskite can also contain up to 25% Al

.In

the lower mantle, perovskite would contain up to 6% Al

. The Mg site

is probably too large for Al. Hence, Al should predominantly substitute

the Si site (Al

`). To keep the charge valance, the Fe in the Mg site tends

to be trivalent (Fe

) if perovskite contains an Al

component.

The electrical conductivity of Al-free (Mg

0.9

0.1

)SiO

perovskite is

0.8

–10

0.5

1

at 1700–1900 K. The conductivity of (Mg

0.9

0.1

)

SiO

perovskite with 3% Al

is about half an order of magnitude

higher than that of Al-free perovskite; that is, 10

0.3

–10

1

the same temperature range. The higher electrical conductivity of

the Al-bearing perovskite implies that the dominant conduction

mechanism is the small polaron of Fe

. The activation enthalpies of

Al-free and Al-bearing perovskites have similar values, 0.6–1.0 eV,

even smaller than those of wadsleyite and ringwoodite.

The electrical conductivity of perovskite at the top of the lower

mantle is 10

1

, and is about half order of magnitude higher than

that of ringwoodite. Therefore, the postspinel transition should cause a

conductivity jump by half an order of magnitude.

The electrical conductivity of perovskite has very little pressure

dependence. Activation volume is about 0.1 cm

mole

1

. The nega-

tive sign of the activation volume (i.e., conductivity increases with

increasing pressure) is consistent with the small polaron model.

Activation energy is relatively small, and the temperature gradient in

the mantle is small (0.2–0.5 K km

1

). Therefore, the electrical con-

ductivity of perovskite should be nearly constant and of the order of

1

throughout the lower mantle.

Magma

Silicate melts (magma) generally have higher conductivity than solid

minerals. Their conductivity is 10

–10

1

at temperatures above

1500 K. The high conductivity of silicate melts is probably because

of the high mobility of atoms in silicate melts. Hence the dominant

conduction mechanism is considered to be ionic conduction.

Under the conditions found in the mantle, the wetting angle of sili-

cate melts is significantly small. Hence, silicate melts easily form a

network structure in mantle rocks even though their fraction is very

low. The network of the melts works as a conduction path and there-

fore the presence of a small amount of silicate melts should drastically

increase electrical conductivity. The conductivity anomalies observed

in the mantle could be attributable to a certain degree of melting of

mantle rocks.

Explanation of the elect rical conductivity

of the mantle

A laboratory electrical conductivity model is shown with observations

in Figure M181. Generally, mantle minerals with a higher-pressure sta-

bility field have higher electrical conductivity. This fact is primarily

responsible for the increase of the electrical conductivity in the upper

mantle. The activation enthalpy of mantle minerals with a higher-

pressure stability field is lower, which means they have smaller

temperature dependence. This is one of the reason why the uniform

electrical conductivity is more in the deeper mantle.

Conductivity increases by two orders of magnitude with the olivine-

wadsleyite transition, whereas it increases by half an order of magni-

tude with the postspinel transition. The seismic velocity jumps asso-

ciated with the 410- and 660-km zone are both significant. By

contrast, the conductivity jump associated with the olivine-wadsleyite

transition is four times larger than that of the postspinel transition.

Therefore, the conductivity jump associated with the 410-km disconti-

nuity should be much larger than that of the 660-km discontinuity, if

indeed the latter is observed at all.

The conductivity of the HCL at the top of the upper mantle is too

high to be explained by the conductivity of normal mantle olivine.

Some additional contribution is required. One possibility is that partial

melting occurs in the region and the melt forms an electrically conduc-

tive path in the mantle rock. Another possibility is that olivine in the

region contains considerable amounts of hydrogen and hence the elec-

trical conductivity is significantly raised by proton conduction. For

now, the lack of sufficient experimental evidence means we cannot

posit an explanation for this situation.

Tomoo Katsura

MANTLE, ELECTRICAL CONDUCTIVITY, MINERALOGY 687

Bibliography

Poirier, J.-P., 2000. Introduction to the physics of the Earth’s interior,

2nd edn. Cambridge: Cambridge University Press.

Utada, H., Koyama, T., Shimizu, H., and Chave, A.D., 2003. A semi-

global reference model for electrical conductivity in the mid-

mantle beneath the north Pacific region. Geophysical Research

Letters, 30: 1194, doi:10.1029/2002GL016092.

Xu, Y., Shankland, T.J., and Poe, B.T., 2000. Laboratory-based electri-

cal conductivity in the Earth’s mantle. Journal of Geophysical

Research, 105: 27865–27875.

Cross-references

Earth Structure, Major Divisions

Electrical Conductivity of the Core

Electromagnetic Induction

Geomagnetic Deep Soundings

Magnetotellurics

MANTLE, THERMAL CONDUCTIVITY

The thermal conductivities of familiar igneous rocks, such as basalt,

at laboratory pressure, are typically k  2:5Wm

1

. Taking

a high-temperature specific heat, C

¼ 1200 J K

1

and

r ¼ 2800 kg m

3

as the basalt density, the corresponding thermal

diffusivity is  ¼ k

 7:4  10

7

1

. For mantle minerals

we find k  4.0 W m

1

,   1.0  10

6

1

. Thermal con-

ductivity of the crust and uppermost mantle (the lithosphere) can differ

little from the conductivities of laboratory samples, but for the deep

mantle, the effects of high pressure as well as high temperature must

be considered. If we nevertheless assume that there is no dramatic

variation in diffusivity, then thermal diffusion is too slow to influence

the deep structure or thermal history. Heat transport in the mantle is

by convection and conduction is important only in boundary layers with

steep temperature gradients. In the context of geomagnetism this means

especially the D

layer at the bottom of the mantle, adjacent to the core.

Lattice conductivity and the effect of pressure

We have only a crude theory of thermal conductivity for complex

materials, such as rocks. While we know that lattice conductivity is

due to phonons, the quanta of thermal vibration, a calculation of con-

ductivity requires an estimate of the mean free path of phonons, the

average distance traveled between the scattering events that randomize

them, and there are several scattering mechanisms, some of which

are difficult to quantify. In a hypothetical, perfect single crystal, scat-

tering would arise only from interactions between phonons. This is

the best understood of the scattering processes and so has received

most attention in discussions of mantle conductivity. It is a conse-

quence of anharmonicity, or nonlinearity in atomic bond forces. If

these forces were perfectly linear, that is, if the forces on displaced

atoms were simply proportional to their displacements, then their

oscillations would be harmonic or sinusoidal, with no interaction

between superimposed oscillations (phonons would not scatter one

another). The anharmonicity of real materials is apparent as positive

thermal expansion coefficients and is described theoretically in terms

of the Grüneisen parameter, g (q,v.). The fundamental physics of the

process is discussed by Kittel (1971); Poirier (1991) summarized its

application to geophysics, emphasizing an expression, due originally

to A.W. Lawson, representing the variation of conductivity with

temperature and pressure.

Phonon-phonon scattering, which leads to Lawson’s formula, is

observable only under highly idealized conditions. For common rocks

Lawson’s formula overestimates conductivity by a factor of order 10.

In these materials, phonon scattering is due to their interactions with

crystal imperfections and the random distribution of different ele-

ments, even including different isotopes of the same element. The tem-

perature and pressure dependences of “impurity scattering” are not

represented by the theory of phonon-phonon scattering. The extreme

case of an “imperfect crystal” is a glass, in which the atomic

arrangement resembles that of a liquid. Glasses have much lower ther-

mal conductivities than the corresponding crystalline solids and both

the temperature and pressure dependences are opposite to those of

pure, simple solids. The result is a very confused picture of phonon

scattering in chemically and crystallographically complicated materi-

als, such as rocks, making it impossible to extrapolate reliably to the

base of the mantle. It appears safest to assume that there is no dramatic

variation in conductivity with depth in the mantle and to verify that

this leads to no conflict with what we understand about the properties

of D

(see below).

Radiative heat transfer

Materials that are transparent at infrared wavelengths may transmit heat

radiatively, giving an additional component of thermal conductivity at

high temperature. This is an important heat transport mechanism in

the interiors of stars and was introduced to geophysics by S.P. Clark.

In the simple case of a “gray body,” a generalization of the ideal black

body of radiation laws, in which the absorption of radiation with

depth of penetration is the same for all wavelengths, the radiative

conductivity is

where n is refractive index, s ¼ 5:67  10

8

2

4

is the Stefan-

Boltzmann constant and 2 is the opacity, the reciprocal of the aver-

age distance traveled by a photon before absorption. For an idea of

how significant this may be we can calculate the value of 2 required

to give a radiative conductivity equal to a plausible lattice conductivity

at a temperature of 2500 K (near to the base of the mantle). We find

e  2500 m

1

, corresponding to a penetration depth of 0.4 mm. Thus,

a quite modest transparency would suffice to make this an important

consideration.

The opacities of mantle minerals are controlled primarily by their

iron contents, especially if the iron occurs as both Fe

2þ

and Fe

3þ

ions,

providing an absorption mechanism by charge transfer. Electron

energy bands are broadened by pressure, making this process easier

by spreading the wavelength range of absorption. Lower mantle miner-

als are believed to be primarily (Mg,Fe)SiO

perovskite and (Mg,Fe)O

magnesiowustite, both with substantial iron contents, so that, although

the question is not conclusively resolved, it appears unlikely that

radiative transfer is important in the lower mantle.

Conduction of core heat into the D

layer

The structure of D

is complicated by compositional heterogeneity, mak-

ing a direct interpretation of seismological observations in terms of tem-

perature difficult, at best. However, we have a reasonable idea of the

thickness of the D

zone and if this is accepted as representative of the

thickness of the thermal boundary layer (see D

as a boundary layer)

then we can use it to estimate the diffusivity and hence conductivity.

is modelled as a 150 km thick layer in PREM (Dziewonski and

Anderson, 1981) and this value is assumed here. An uncertainty of 50 km

or so is of no consequence as we can only make a rough calculation.

The temperature at the core-mantle boundary, estimated as 3740 K

from core properties (see Core, thermal conduction), is almost 1000

K higher than the lower mantle temperature estimated by extrapolating

adiabatically from the 670 km deep phase transition zone (2760 K).

We must, therefore, consider a 1000 K temperature increment across

the boundary layer. This means that the mantle material in contact with

688 MANTLE, THERMAL CONDUCTIVITY

the core has a viscosity that is lower by a factor of at least 10

than that

of the mantle a few hundred kilometers higher, concentrating convec-

tive flow in a very thin layer at the bottom. A theory of the mechanism

by which this flow feeds narrow hot plumes is given by Stacey and

Loper (1983), but a simple analog represents the essential features.

As the hot material is skimmed off into narrow buoyant plumes,

there is a general collapse of the mantle on to the core to replace it.

The analog is the ablation of materials from the surfaces of meteorites

and spacecraft entering the atmosphere. A steady, exponential profile

of temperature, T, is established, moving inward as surface material

is removed, so that

T  T

¼ðT

 T

Þexpðh=HÞ

where h is the distance from the heated surface, at temperature T

and T

is the temperature well removed from the ablating surface.

Our interest is in the scale height, H, which we identify with the

thickness of D

H ¼ 

 being thermal diffusivity and v is the speed of the collapse of the

mantle on to the core. If the core to mantle heat flux is



A (per

square meter) then



A ¼ vrC

 T

ðÞ

and if we estimate this as 0:033 W m

2

(5  10

W over the

surface of the core-mantle boundary) then these relationships give

 ¼ 7:6  10

7

1

, in fortuitously close coincidence with the

value for basalt at zero pressure.

Although this calculation is simplified and approximate, it

encourages the view that thermal diffusivity does not vary greatly

through the mantle. With the higher density at the core-mantle bound-

ary the corresponding conductivity is k  5W m

1

, higher than

for laboratory samples, but not dramatically so.

A general conclusion

Thermal conductivity of the deep mantle is poorly constrained by either

observation or theory, in spite of repeated efforts to understand it, but we

have no evidence that it differs greatly from the conductivity of the

uppermost mantle or laboratory samples of basic or ultrabasic rock. In

this circumstance core heat is conducted into a boundary layer at the base

of the mantle, 100 to 200 km thick, softening it and allowing for its

removal in buoyant plumes. Convection, not conduction, is responsible

for heat transport up the several thousand kilometer depth of the mantle.

Frank D. Stacey

Bibliography

Dziewonski, A.M., and Anderson, D.L., 1981. Preliminary reference

Earth model. Physics of the Earth and Planetary Interiors, 25:

297–356.

Kittel, C., 1971. Introduction to Solid State Physics, 4th edn. New

York: Wiley.

Poirier, J.-P., 1991. Introduction to the Physics of the Earth’s Interior.

Cambridge: Cambridge University Press.

Stacey, F.D., and Loper, D.E., 1983. The thermal boundary layer inter-

pretation of D

and its role as a plume source. Physics of the Earth

and Planetary Interiors, 33:45–55.

Cross-references

Core, Thermal Conduction

as a Boundary Layer

Grüneisen’s Parameter for Iron and Earth’s Core

MATUYAMA, MOTONORI (1884–1958)

Born in Oita Prefecture, Japan, as a son of a Buddhist priest, he

graduated from the physics department, Kyoto University, 1911. He

became lecturer in 1913, associate professor in 1916, and then profes-

sor in the Department of Geology, Kyoto University, from 1922 to

1946. He studied at the University of Chicago between 1933 and

1935. After retirement from Kyoto University, he served as president

of the Yamaguchi University, from 1949 to his death. For his contribu-

tion to paleomagnetism and gravity, Matuyama was elected to Member

of Japan Academy in 1950.

In the 1920s, Matuyama conducted a systematic survey of the nat-

ural remanent magnetization (NRM) of Quaternary and late Tertiary

volcanic rocks in Japan, Korea, and Northeast China (Manchuria at

that time). The determination of the dipole moment was done by the

method of Gauss (spherical harmonic analysis). In the results, he noted

that the youngest rocks are always magnetized to directions similar to

the present day field, while many of the early Quaternary and Tertiary

rocks had NRMs almost oppositely directed. In all cases, there were

not many rocks with the NRMs in the intermediate directions. On

the basis of these observations, Matuyama concluded that the Earth’s

magnetic field was in the reversed state in the late Tertiary (Miocene)

and again in the early Quaternary (Matuyama, 1929). This early report

was later picked up by Allan Cox and Richard Doell, who named the

reversed interval just before the current normal period (Brunhes epoch)

after him (Matuyama epoch). “Matuyama” thus became one of the most

often referred personal names of Japanese origin. “Matuyama chron” is

often quoted in the studies such as magnetostratigraphy, seafloor

spreading, sedimentology, geomagnetic reversal timescale, and so on.

Earlier in his career, Matuyama performed gravity survey of a coral

reef in the Marshall Islands using an Eötvös deviatoric gravimeter.

This was one of the earliest application of gravity methods to the study

of the crustal structure, especially in the coral islands. Gravity contin-

ued to be one of his main research subjects and, inspired by the work

of Vening Meinesz in the Indonesian Archipelago, he also measured

the gravity near the Japan Trench in a submarine of the Japanese Navy

(Matuyama, 1934). This led to the discovery of the westward offset of

the center of the negative gravity belt from the trench axis, which later

became an important factor for considering the origin of the great

earthquakes in the Sanriku region. Other subjects he studied include

the rheological properties of the ice, which was undertaken in colla-

boration with T.C. Chamberlin of the University of Chicago when he

stayed in the United States

Masaru Kono

Bibliography

Matuyama, M., 1929. On the direction of magnetization of basalt in

Japan, Tyosen, and Manchuria. Proceedings of the Imperial Acad-

emy (Tokyo), 5: 203–205.

Matuyama, M., 1934. Measurement of gravity over the Nippon Trench

on board the I.J. submarine Ro–57, Preliminary report. Proceed-

ings of the Imperial Academy (Tokyo), 10: 626–628.

MELTING TEMPERATURE OF IRON IN THE

CORE, EXPERIMENTAL

Introduction

There are two major techniques commonly used for ultrahigh pressure

melting studies: shock wave experiments and the internally heated dia-

mond anvil cell (DAC). In shock compression experiments, the sample

is subjected to high pressures and high temperatures by dynamic pro-

cesses (see Shock wave experiments). In DAC experiments, pressure is

MATUYAMA, MOTONORI (1884–1958) 689

generated by pressing two opposing diamond anvils, while heating is

applied resistively and/or using laser heating. Both techniques have

been extensively applied to study high pressure melting of iron. How-

ever, accurate determination of melting is exceedingly difficult at

extremely high pressure and temperature conditions. The associated

weaknesses—the short timescale in shock compression and the small

sample size in DAC—are reflected by the large uncertainties and the

discrepancy among literature values on melting temperature of iron

in the core.

In this section, we begin with a brief description of the generation of

simultaneous high pressures and temperatures in the DAC, followed

by a discussion on the observation of the onset of the melting transi-

tion and the determination of pressure-temperature conditions asso-

ciated with the observation. A brief review is given on DAC

experiments in studying the melting temperature of iron at high

pressures. The effect of light elements on the melting temperature is

discussed in the end.

For more details on this topic, the following review articles are sug-

gested. See Melting temperature of iron in the core, theory for theore-

tical approaches in this area.

1. Jephcoat, A.P., and Besedin, S.P., 1996. Temperature measurement

and melting determination in the laser-heated diamond-anvil cell.

Philosophical Transactions of the Royal Society of London, Series

A, 354(1711): 1333–1360.

2. Shen, G., and Heinz, D.L., 1998. High pressure melting of deep

mantle and core materials. In Hemley, R.J. (ed.), Ultrahigh Pressure

Mineralogy: Physics and Chemistry of the Earth’s Deep Interior.

Washington, DC: Mineralogical Society of America, pp. 369–396

3. Boehler, R., 2000. High pressure experiments and the phase dia-

gram of lower mantle and core materials. Reviews of Geophysics,

38: 221–245.

Diamond cell technique

Diamond as anvil and window

Diamond is a premier anvil material because it is the hardest material

known, and it is transparent from infrared to hard X-rays, thus provid-

ing a window for probing samples by various methods and for heating

samples by lasers. With the DAC technique, pressures beyond that at

the center of the Earth have been reported (Xu et al., 1986). The prin-

cipal components of a DAC are two opposing diamond anvils with a

gasket in between. A drilled hole in the center of the gasket serves

as sample chamber. For melting experiments at very high pressures,

typical dimensions of a sample chamber are 10–20 mm thick and

50 mm in diameter.

Heating diamond anvil cells

An easy way to provide heating is to heat the entire DAC externally.

However, there is a temperature limit of 1500 K with this method.

To generate extreme high temperatures to melt iron at high pressures,

internal heating methods are generally employed. One is the resistive

wire heating, in which iron is used as a conductor wire and heating

is applied electrically (Boehler, 1986; Mao et al., 1987). With this

method, temperatures can go as high as its melting point, but pressures

are limited because of deformation of the electrical leads as pressure

increases. The other is the laser-heating technique, in which near- or

mid-infrared lasers (Nd:YAG, Nd:YLF, CO

) are used for heating sam-

ples in DAC. There are, in principle, no pressure and temperature lim-

itations associated with this technique. The challenge is to control

pressure and temperature conditions, to measure them accurately, and

to characterize the sample at defined conditions. A typical sample con-

figuration is shown in Figure M186.

Pressure measurement

Pressures in the laser-heated DAC are often measured by the ruby fluor-

escence method (Mao et al., 1986) before and after laser heating or

during heating from unheated ruby chips away from the heating

area. When the laser-heating experiment is coupled with synchro-

tron radiation, pressures are estimated by measuring unit cell

volumes of samples whose pressure-temperature-volume equations

of state are known. For pressures measured before and after laser

heating, thermal pressure (caused by the material’s thermal expan-

sion) has to be considered in estimating pressures at high tempera-

ture. Thermal pressure may be minimized by choosing a hydrostatic

pressure medium and a small sample-to-medium ratio, and/or char-

acterized with the use of highly collimated synchrotron radiation.

Temperature measurement

Temperature measurement is based on the collected radiation from

thermal emission through the Planck radiation law: I

¼ c

e(l)l

–5

[exp(c

/lT)1], where I

is spectral intensity, l is wavelength, T

is temperature, c

¼ 2 phc

¼ 3.7418  10

–16

, c

¼ hc/k ¼

0.014388 mK, and e(l) is emissivity with e(l) ¼ 1 for a black body.

This method covering a range of wavelengths is often called spectral

radiometry, as compared to the general pyrometry in which thermal

radiation at only one wavelength is measured. One major advantage

of spectral radiometry is that, assuming wavelength-independent emis-

sivity, temperatures can be measured independently from the absolute

emissivity. However, emissivity is often found to be wavelength

dependent. Use of the available data on the wavelength-dependent

emissivity at ambient pressure (de Vos, 1954) gives about a 5% tem-

perature correction downward at 3000 K and about 12% downward

at 5000 K when compared with the results from the assumption of

wavelength-independent emissivity. Unfortunately, such a correction

cannot be accurately made because the wavelength dependence of

emissivity is not currently known at high pressures and high tempera-

tures, and it can be strongly dependent on the surface finish of a DAC

sample. This is the main limitation in the absolute accuracy of tem-

perature measurement by the spectral radiometry method.

Melting criteria

Melting is thermodynamically defined as equilibrium between a solid

and a liquid. When materials melt, their physical properties, such as

density, viscosity, absorption properties, and electrical resistance,

undergo a sudden change. Such property changes are characteristic

for a first-order phase transition and are often used for recognition of

Figure M186 A typical sample configuration in laser-heated

diamond anvil cell experiment.

690 MELTING TEMPERATURE OF IRON IN THE CORE, EXPERIMENTAL

melting. Unlike other first-order phase transitions, melting is character-

ized by the loss of long-range order and resistance to shear. To defini-

tively identify melting, both of these two characteristics should be

documented. Visual optical observation is a common way to determine

whether melting has taken place. It is obvious that fluid flow observa-

tion is a good measure of the loss of resistance to shear. Therefore it

has been widely used by almost all groups in the world (Saxena

et al., 1994; Jeanloz and Kavner, 1996; Jephcoat and Besedin, 1996;

Boehler, 2000). However, visual observation (fluid flow) is less obvious

as pressure increases, making it difficult to unambiguously define the

onset of melting. Synchrotron X-ray diffraction has been combined with

laser-heated DAC and used for melting studies to document the loss

of long-range order upon melting. Melting at high pressure was iden-

tified by the appearance of diffuse scattering from the melt with the

simultaneous loss of crystalline diffraction signals (Shen et al., 2004).

Synchrotron Mössbauer spectroscopy (SMS) provides another pro-

mising method to identify melting. SMS measures the atomic thermal

displacement that can be used for documenting rigidity of a material.

Upon melting the strong elastic resonance signal diminishes in SMS.

The mean-square thermal displacement of atoms (Lamb-Mössbauer

factor) can be measured as a function of temperature, providing a plot

for determining the onset of melting. Since measurement of SMS takes

only a few seconds to minutes, it holds a great potential for high

pressure melting studies.

Melting of core material at high pressures

Iron

Iron is the major component of the core. Knowledge of the melting

curve of iron can constrain the temperature of the inner core boundary

and anchor the Earth’s temperature profiles (see Core temperature). At

pressures below 50 GPa, the phase diagram of iron is reasonably well

known (Figure M187). At ambient pressure, the stable phase is a-Fe

with a body-centered-cubic (bcc) structure. At high pressure it trans-

forms to e-Fe with hexagonal-close-packed (hcp) structure. At high

temperature there is a large stability field for g-Fe with face-cen-

tered-cubic (fcc) structure. Although a controversial new solid phase

(called b-Fe) was reported (Saxena et al., 1995; Andrault et al.,

1997; Dubrovinsky et al., 1998), the existence of this phase was not

confirmed in later experiments (Shen et al., 1998; Kubo et al., 2003;

Ma et al., 2004). For the melting curve, there is a converging consen-

sus at pressures below 60 GPa, reflected by a narrow uncertainty range

in Figure M187. As pressure increases, uncertainties in phase bound-

aries, including the melting curve, become large as shown by wide

bands in Figure M187. The width of the bands represents the scatter

in literature data from recent years. Factors causing these uncertainties

include those in pressure determinations (neglecting thermal pressure,

different equations of state, and/or different standard materials), in

temperature determinations (large temperature gradient and temporal

variation, chromatic aberration in optics), and in sample characteriza-

tions (different melting criteria, transition kinetics).

Uncertainties in the melting curve and the g-e transition lead to sig-

nificant variations in the location of g-e-liquid triple point. Knowledge

of its location is important because it is the starting point used for

extrapolating the melting curve of e-Fe to core pressures. As shown

in Figure M187, the slope of g-e transition ranges from 25 to 40 K

GPa

1

, placing the triple point between 60 and 100 GPa. Such large

uncertainties in the slope of the g-e transition mainly arise from the

coexisting nature of these two phases in the pressure-temperature

range, causing difficulties in identifying the boundary. The uncertain-

ties are also contributed by the pressure-temperature determination

associated with the use of different standard materials and/or different

equations of state.

The melting data for iron above the triple point are scarce and scat-

tered, reflecting the difficulty level of such experiment. It appears that

the early DAC data (Boehler, 1993; Saxena et al., 1994) represent a

lower bound of the melting curve in this region. The later experimental

data falls at higher melting temperatures (Shen et al., 1998; Ma et al.,

2004). The shock wave data (Brown and McQueen, 1986; Nguyen and

Holmes, 2004) lie close to the upper bound. Extrapolating the data to

the inner core boundary, the melting temperature of iron is between

4800 and 6000 K at 330 GPa (see e.g., Grüneisen’s parameter for iron

and Earth’s core).

Effects of light elements

As shown by Birch (1952), the density of the Earth’s outer core is about

10% too low to be pure iron, so the core must also contain some light

elements. At present, there is no consensus on the dominant light ele-

ment in the core (see Core composition and Inner core composition).

At ambient pressure, the addition of a small amount of light elements

decreases the melting temperature of iron by up to a few hundred

degrees. Data at high pressure are scarce and limited in the Fe-

FeO-FeS system (Usselmann, 1975; Urakawa et al., 1987; Ringwood

and Hibberson, 1990; Knittle and Jeanloz, 1991; Williams et al.,

1991; Boehler, 1992; Fei et al., 1997). Eutectic melting was found in

the Fe-FeS system, while a solid solution mechanism was suggested

for Fe-FeO system (Knittle and Jeanloz, 1991; Boehler, 1992). Boehler

(1996) pointed out that the melting curves in the Fe-FeS-FeO system

converge instead of diverge with increasing pressure to that of pure iron.

However, several difficulties need to be addressed and overcome in

melting experiments of multicomponent systems using DAC. The

laser-heating spot could be on a scale similar to nonuniform samples,

which could cause large experimental errors. Large temperature gradi-

ents in radial and axial directions could lead to compositional gradients

(e.g., Soret diffusion), causing incomplete mixing during heating and

melting. Significant developments are thus needed for constraints of

light element effects on the melting temperature of iron.

Guoyin Shen

Figure M187 Iron phase diagram. Shaded areas represent the

range of literature values in recent years with static diamond anvil

cell experiments. Symbols are shock-wave data: square, Ahrens

et al. (2002); diamonds, Brown and McQueen (1986); circle,

Nyuyen and Holmes (2004). Brown and McQueen’s point at

200 GPa was interpreted as a solid-solid transition. All other

points are referred as melting.

MELTING TEMPERATURE OF IRON IN THE CORE, EXPERIMENTAL 691

Bibliography

Ahrens, T.J., Holland, K.G., and Chen, G.Q., 2002. Phase diagram of

iron, revised-core temperatures. Geophysical Research Letters, 29:

doi:10.1029/2001GL014350.

Andrault, D., Fiquet, G., Kunz, M., Visocekas, F., and Hausermann,

D., 1997. The orthorhombic structure of iron: an in situ study at

high-temperature and high-pressure. Science , 278: 831–834.

Birch, F., 1952. Elasticity and composition of Earth’s interior. Journal

of Geophysical Research, 57: 227–286.

Boehler, R., 1986. The phase diagram of iron to 430 kbar. Geophysical

Research Letters, 13: 1153–1156.

Boehler, R., 1992. Melting of Fe-FeO and Fe-FeS systems at high

pressures: constraints on core temperatures. Earth and Planetaty

Science Letters, 111: 217–227.

Boehler, R., 1993. Temperatures in the Earth’s core from melting-point

measurements of iron at high static pressures. Nature, 363:

534–536.

Boehler, R., 1996. Melting of mantle and core materials at very high

pressures. Philosophical Transactions of the Royal Society of

London, Series A, 354: 1265–1278.

Boehler, R., 2000. High pressure experiments and the phase diagram

of lower mantle and core materials. Reviews of Geophysics, 38:

221–245.

Brown, J.M., and McQueen, R.G., 1986. Phase transitions, Grüneisen

parameter, and elasticity for shocked iron between 77 GPa and 400

GPa. Journal of Geophysical Research, 91: 7485–7494.

de Vos, J.C., 1954. A new determination of the emissivity of tungsten

ribbon. Physica, 20: 690–714.

Dubrovinsky, L.S., Saxena, S.K., and Lazor, P., 1998. Stability of

b-phase: a new synchrotron x-ray study of heated iron at high

pressure. European Journal of Mineralogy, 10:43–47.

Fei, Y., Bertka, C.M., and Finger, L.W., 1997. High pressure iron sul-

fur compound, Fe

, and melting relations in the Fe-FeS system.

Science, 275: 1621–1623.

Jeanloz, R., and Kavner, A., 1996. Melting criteria and imaging

spectroradiometry in laser-heated diamond-cell experiments.

Philosophical Transactions of the Royal Society of London, Series

A, 354: 1279–1305.

Jephcoat, A.P., and Besedin, S.P., 1996. Temperature measurement and

melting determination in the laser-heated diamond-anvil cell. Phi-

losophical Transactions of the Royal Society of London, Series A,

354: 1333–1360.

Knittle, E., and Jeanloz, R., 1991. The high pressure phase diagram

of Fe

0.94

O: a possible constituent of the Earth’s core. Journal of

Geophysical Research, 96: 16169–16180.

Kubo, A., Ito, E., Katsura, T., Shinmei, T., Yamada, H., Nishikawa, O.,

Song, M., and Funakoshi, K., 2003. Phase equilibrium study of

iron using sintered diamond (SD) anvils: absence of beta phase.

PEPI, 30: 1126.

Ma, Y.Z., Somayazulu, M., Mao, H.K., Shu, J.F., Hemley, R.J., and

Shen, G., 2004. In situ x-ray diffraction studies of iron to the Earth

core conditions. Physics of the Earth and Planetary Interiors, 144:

455–467.

Mao, H.K., Xu, J., and Bell, P.M., 1986. Calibration of the ruby pres-

sure gauge to 800 kbar under quasi-hydrostatic conditions. Journal

of Geophysical Research, 91: 4673–4676.

Mao, H.K., Bell, P.M., and Hadidiacos, C., 1987. Experimental phase

relations of iron to 360 kbar and 1400 C, determined in an intern-

ally heated diamond anvil apparatus. In Manghnani, M.H., and

Syono, Y. (eds.), High Pressure Research in Mineral Physics.

Tokyo: Terra Scientific Publishing Company/American Geophysi-

cal Union, pp. 135–138.

Nguyen, J.H., and Holmes, N.C., 2004. Melting of iron at the physical

conditions of the Earth’s core. Nature, 427: 339–342.

Ringwood, A.E., and Hibberson, W., 1990. The system Fe-FeO revis-

ited. Physics and Chemistry of Minerals, 17: 313–319.

Saxena, S.K., Shen, G., and Lazor, P., 1994. Temperatures in Earth ’s

core based on melting and phase transformation experiments on

iron. Science, 264: 405–407.

Saxena, S.K., Dubrovinsky, L.S., and Haggkvist, P., 1995. X-ray

evidence for the new phase b-iron at high pressure and high tem-

perature. Geophysical Research Letters, 23: 2441–2444.

Shen, G., Mao, H.K., Hemley, R.J., Duffy, T.S., and Rivers, M.L.,

1998. Melting and crystal structure of iron at high pressures. Geo-

physical Research Letters, 25: 373–376.

Shen, G., Prakapenka, V.B., Rivers, M.L., and Sutton, S.R., 2004.

Structure of liquid iron at pressures up to 58 GPa. Physical Review

Letters, 92: 185701.

Urakawa, S., Kato, M., and Kumazawa, M., 1987. Experimental study

of the phase relation in the system Fe-Ni-O-S up to 15 GPa. In

Manghnani, M.H., and Syono, Y. (eds.), High Pressure Research

in Mineral Physics. Tokyo: Terra Scientific Publish ing Company,

pp. 95–111.

Usselmann, T.M., 1975. Experimental approach to the state of

the core. I. The liquidus relations of the Fe-rich portion of the

Fe-Ni-S system from 30 to 100 kb. American Journal of Science,

275: 278–290.

Williams, Q., Knittle, E., and Jeanloz, R., 1991. The high pressure

melting curve of iron: a technical discussion. Journal of Geophysi-

cal Research, 96: 2171–2184.

Xu, J., Mao, H.K., and Bell, P.M., 1986. High pressure ruby and dia-

mond fluorescence: observations at 0.21 to 0.55 TPa. Science, 232:

1404–1406.

Cross-references

Core Composition

Core Temperature

Grüneisen’s Parameter for Iron and Earth’s Core

Inner Core Composition

Melting Temperature of Iron in The Core, Theory

Shock Wave Experiments

MELTING TEMPERATURE OF IRON IN THE

CORE, THEORY

An accurate knowledge of the melting properties of Fe is particularly

important, as the temperature distribution in the core is relatively

uncertain and a reliable estimate of the melting temperature of Fe at

the pressure of the inner-core boundary (ICB) puts a constraint on core

temperatures. However, there is much controversy over its high pressure

melting behavior (e.g., see Shen and Heinz, 1998). Static compression

measurements of the melting temperature (T

) with the diamond anvil

cell (DAC) have been made up to 200 GPa, but even at lower pressures

results for T

disagree by several hundred kelvins. Shock experiments

are at present the only available method to determine melting at higher

pressures, but their interpretation is not simple, and there is a scatter of

at least 2000 K in the reported T

of Fe at ICB pressures.

Since both quantum mechanics and experiments suggest that Fe

melts from the hexagonal close-packed (hcp) structured phase in the

pressure range immediately above 60 GPa, this entry will focus on

the equilibrium between hcp Fe and liquid phases. Several approaches

for determining T

from theory have been adopted, including quantum

mechanically based methods (e.g., Alfè et al., 2002a,b), and more

empirical methods such as dislocation melting models (Poirier and

Shankland, 1993), or those based on thermal physics (Stacey and Irvine,

1977).

The condition for two phases to be in thermal equilibrium at a given

temperature, T, and pressure, P, is that their Gibbs free energies, G(P, T ),

are equal. To determine T

at any pressure from theory, it desirable to

692 MELTING TEMPERATURE OF IRON IN THE CORE, THEORY

calculate G for the solid and liquid phases as a function of T and deter-

mine where they are equal. In fact, it is usual to calculate the Helm-

holtz free energy, F(V, T ), as a function of volume, V, and hence

obtain the pressure through the relation P ¼ –(@F/@V )

and G through

its definition G ¼ F þ PV.

To obtain melting properties with useful accuracy, free energies

must be calculated with high precision, because the free energy curves

for liquid and solid cross at a shallow angle. It can readily be shown

that to obtain T

with a technical precision of 100 K, noncanceling

errors in G must be reduced below 10 meV. It has been shown that

ab initio molecular dynamics can be used to determine the free ener-

gies of liquid and solid of Al and Cu with sufficient accuracy as

to reproduce the known melting temperature to within 100 K. Alfè

et al. (1999, 2002a) used this method to calculate the melting curve

of Fe up to core pressures, and their results, shown in Figure M188,

give the melting temperature of Fe at ICB pressures to be 6200 K,

with an error of 300 K. For pressures P < 200 GPa (the range cov-

ered by DAC experiments) their curve lies 900 K above the values

of Boehler (1993) and 200 K above the more recent values of Shen

et al. (1998). Their curve falls significantly below the shock-based

estimates for the T

of Yoo et al. (1993), in whose experiments tem-

perature was deduced by measuring optical emission (however, the

difficulties of obtaining temperature by this method in shock experi-

ments are well known), but accords almost exactly with the shock data

value of Brown and McQueen (1986) and the new data of Nguyen and

Holmes (1999). For melting at ICB pressure, Alfè et al. (1999, 2002a)

calculate DV

/V ¼ 1.8%, DS

¼ 1.05R JK

1

mol

1

, and so obtain a

latent heat of fusion of 55 kJmol

1

There are other ways of determining the melting temperature of a

system by ab initio methods, including performing simulations that

model coexisting liquid and crystal phases. The melting temperature

of such a system can then be inferred by seeing which of the two

phases grows during the course of a series of simulations at different

temperatures. This approach has been used by Laio et al. (2000) and

by Belonosko et al. (2000) to study the melting of Fe. In their studies

they modeled Fe melting using interatomic potentials fitted to ab initio

surfaces. Alfè et al. (2002b) discovered, however, that these fitted

potentials did not simultaneously describe the energy of the liquid

and crystalline phases with the same precision, and so these simula-

tions do not represent the true melting behavior of Fe, but rather that

of the fitted potential. Alfè et al. (2002b) found a way to correct for

these shortcomings, by calculating the free energy differences between

the model and the ab initio system for both the liquid and solid phases.

This difference in free energy between liquid and solid can then be trans-

formed into an effective temperature correction. When this was done to

Belonosko’s data, there was excellent agreement (see Figure M188)with

previously determined melting curve for Fe determined by Alfè et al.

(2002a) using the technique based on direct determination of free energies.

Other more approximate theoretical approaches are also in accord

with the inferences from more accur ate quantum mechanical studies.

Poirier and Shankland (1993) obtained a value of T

for Fe at 330

GPa of 6100  100 K by using a dislocation melting model, Stacey

and Irvine (1977) estimated T

¼ 6 050 K from a Lindemann’s law-

based analysis, Stixrude et al. (1997) estimated T

to be 6150 K,

and Anderson (2003) found a T

of 5900  300 K on the basis of

thermodynamic analysis. Thus with ab initio calculations having been

shown to be robust, there now seems to be an emerging consensus on

the melting temperature Fe at ICB pressure to be between 6 000 and

6400 K. There is still scope for further work on the difficult problem

of the modeling of melting, but for the high pressure melting of Fe

at least, it now appears that there may be as many problems with

reconciling divergent experimental data than there are in obtaining

accurate predictions of T

from ab initio studies.

David Price

Bibliography

Alfè, D., Gillan, M.J., and Price, G.D., 1999. The melting curve of

iron at the pressures of the Earth’s core from ab initio calculations.

Nature, 401: 462–464.

Alfè, D., Price, G.D., and Gillan, M.J., 2002a. Iron under Earth’s

core conditions: liquid-state thermodynamics and high-pressure

melting curve from ab initio calculations. Physics Review, B65:

165118, 1–11.

Alfè, D., Gillan, M.J., and Price, G.D., 2002b. Complementary

approaches to the ab initio calculation of melting properties. Jour-

nal of Chemical Physics, 116: 6170–6177.

Anderson, O.L., 2003. The three-dimensional phase diagram of iron.

In Dehant, V., Creager, K.C., Karato, S-I., and Zatman, S. (eds.),

Earth’s Core. AGU, Geodynamics Series, 31:83–104.

Belonosko, A.B., Ahuja, R., and Johansson, B., 2000. Quasi-ab initio

molecular dynamic study of Fe melting. Physics Review Letters,

84: 3638–3641.

Boehler, R., 1993. Temperature in the Earth’s core from the melting point

measurements of iron at high static pressures. Nature, 363:534–536.

Brown, J.M., and McQueen, R.G., 1986. Phase transitions, Grüneisen

parameter and elasticity for shocked iron between 77 GPa and

400 GPa. Journal of Geophysical Research, 91: 7485–7494.

Laio, A., Bernard, S., Chiarotti, G.L., Scandolo, S., and Tosatti, E., 2000.

Physics of iron at Earth’s core conditions. Science, 287: 1027–1030.

Nguyen, J.H., and Holmes, N.C., 1999. Iron sound velocities in shock

wave experiments. In Furnish, M.D., Chhabildas, L.C., and

Hixson, R.S. (eds.) Shock Compression of Condensed Matter—

1999. Melville, NY: American Institute of Physics, pp. 81–84.

Poirier, J.P., and Shankland, T.J., 1993. Dislocation melting of iron and

the temperature of the inner-core boundary, revisited. Geophysical

Journal International, 115: 147–151.

Shen, G.Y., and Heinze, D.L., 1998. High pressure melting of deep

mantle and core materials. In Hemley, R.J. (ed.), Ultrahigh-pressure

Mineralogy. Reviews in Mineralogy, 37

:369–398.

Stacey, F.D., and Irvine, R.D., 1977. Theory of melting: the thermo-

dynamic basis of Lindemann’s Law. Australian Journals of

Physics, 30: 631–640.

Figure M188 The calculated high pressure melting curve of

Fe of Alfe

et al. (line 2) passes through the shock wave datum

(open circle) of Brown and McQueen. Other data shown includes:

The melting curve of Alfe

et al., corrected for the GGA pressure

error (line 3), Belonoshko’s melting curve (line 6), Belonoshko’s

melting data corrected for errors in potential fitting (black dots),

Laio et al.’s melting curve (line 4), Boehler’s DAC curve (line 5),

Shen’s data (diamonds), Yoo’s shock data (open squares),

William’s melting curve (line 1).

MELTING TEMPERATURE OF IRON IN THE CORE, THEORY 693

Stixrude, L., Wasserman, E., and Cohen, R.E., 1997. Composition and

temperature of the Earth’s inner core. Journal of Geophysical

Research, 102: 24729–24739.

Williams, Q., Jeanloz, R., Bass, J., Svendsen, B., and Ahrens, T.J.,

1987. The melting curve of iron to 250 GPa—a constraint on the

temperature at Earth’s center. Science, 236: 181–182.

Yoo, C.S., Holmes, N.C., Ross, M., Webb, D.J., and Pike, C., 1993.

Shock temperatures and melting of iron at Earth core conditions.

Physics Review Letters, 70: 3931–3934.

Cross-references

Core Properties, Physical

Core Properties, Theoretical Determination

Core Temperature

Core, Adiabatic Gradient

Inner Core

Melting Temperature of Iron in the Core, Experimental

Shock Wave Experiments

MICROWAVE PALEOMAGNETIC TECHNIQUE

The microwave technique is used to determine the strength of the

Earth’s magnetic field in the past. It is usually applied to igneous rock

such as lava and dike or the surrounding material that has been heated

by them (baked contact), as well as heated archaeological material

(ceramics, fireplaces, etc.). Samples are placed inside a resonant cavity

and exposed to microwaves for a few seconds (typically 10 s). The

microwave exposure is directly analogous to raising the temperature

of the sample in the conventional Thellier technique, the main differ-

ence being that when the sample is exposed to microwaves most of

the energy is absorbed by the magnetic system whereas in direct heat-

ing the entire sample absorbs energy.

By concentrating the energy in the magnetic system the bulk sample

is not heated significantly. This reduces the probability of laboratory

thermal alteration and provides a more accurate determination of the

ancient magnetic field strength.

Microwaves magnons and temperature

A simple model for ferromagnetic minerals is a large number of spin-

ning electrons, one for each ion. Each spin has a magnetic moment

M ¼ gm

S, where g is the spectroscopic splitting factor, m

is the

Bohr magnetron, and S is the spin (Kittel, 1966).

In a ferromagnetic mineral there is a very strong force between

neighboring spinning electrons that tries to align all of the spins

(exchange coupling). At very low temperatures when the thermal energy

is near to zero the spins align and the total magnetization of the mineral

is greatest. This total magnetization is expressed as a strong internal field

in the mineral. As the temperature increases the energy increases and

the individual spin magnetic moments move away from perfect align-

ment. As the spin magnetic moments move away from perfect alignment

they precess around the internal field of the mineral so that only a com-

ponent (M

) remains aligned and the total magnetization of the mineral

reduces (Figure M189).

All of the spins precess at the same frequency (H where is the gyro-

magnetic ratio and H is the magnetic field) but each is slightly out of

phase with its neighbor. Looking along the field direction (M

direc-

tion) the M

components form a “spin wave” that passes through the

mineral (Figure M189). The amplitude of the spin wave increases in

quantized jumps equivalent to the complete reversal of one spin mag-

netic moment and so the total magnetization of the mineral changes by

2M. A spin wave that is quantized in this way is called a magnon. For

each magnon that is excited the magnetic moment reduces by 2M.

This is a simplified picture of spin wave generation in ferromagnetic

minerals but it helps us to understand how the magnetic moment of

a sample is reduced by the generation of magnons.

In the case of conventional thermal demagnetization, ferromagnetic

magnetization decreases with increasing temperature until it is comple-

tely removed at the Curie temperature. Looking at this process in more

detail, the external thermal energy (the high temperature in an oven,

say) generates phonons (lattice vibrations) in order to equilibrate the

external energy with the internal energy. The phonons in turn generate

magnons in the magnetic system in order to equilibrate the energy in

the magnetic system. When sufficient magnons are generated the sam-

ple is demagnetized and the equivalent external temperature that

caused this is called the Curie temperature.

Using microwaves it is possible to excite the magnons directly by

ferromagnetic resonance without applying heat to the sample (Walton

et al., 1992, 1993). If this can be done quickly the high-energy mag-

netic system will not have time to pass energy into the sample, gener-

ate phonons and raise its temperature. In theory microwaves can

demagnetize a sample in the same way as heating a sample but without

raising its temperature. In practice it takes a few seconds of microwave

exposure to generate sufficient magnons to completely demagnetize a

sample, the normal exposure time is 10 s and this means that some

phonons are generated. Also, since most samples are good insulators,

there is some dielectric heating of the sample in the microwave field.

The combination of these two effects is to raise the temperature of

the sample slightly, usually less than 150



C (Hill et al., 2000).

Dielectric heating is frequency-dependent, the higher the frequency

the more heat is generated. Magnon generation is also frequency-

dependent, higher frequency generates more magnons. The sample

size is also frequency-dependent, higher frequency means a smaller

resonant cavity and therefore smaller samples. Experiments at 8

and 14 GHz show clearly that at 14 GHz samples are more easily

demagnetized and are heated less than at 8 GHz. Much above

14 GHz dielectric heating becomes dominant and the samples are

heated more. For microwave demagnetization without heating the

14–16 GHz range seems optimal (Figure M190).

Recent experiments demonstrate that high (low) microwave power

is equivalent to high (low) temperature (Hill et al., 2002) and

so microwave demagnetization may be used instead of thermal

Figure M189 Magnons.

694 MICROWAVE PALEOMAGNETIC TECHNIQUE

demagnetization to determine paleomagnetic directions. Microwave

demagnetization has the added advantage that it can be used on sam-

ples that undergo severe alteration on heating and are unsuitable for

thermal analysis (i.e., sulfide-bearing rocks).

John Shaw

Bibliography

Hill, M.J., and Shaw, J., 2000. Magnetic field intensity study of the

1960 Kilauea lava flow, Hawaii, using the microwave palaeointen-

sity technique. Geophysical Journal International, 142: 487–504.

Hill, M.J., Gratton, M.N., and Shaw, J., 2002. A comparison of thermal

and microwave palaeomagnetic techniques using lava containing

laboratory induced remanence. Geophysical Journal International,

151: 157–163.

Walton, D., Shaw, J., Share, J.A., and Hakes, J., 1992. Microwave

demagnetisation. Journal of Applied Physics, 71: 1549–1551.

Walton, D., Share, J.A., Rolph, T.C., and Shaw, J., 1993. Microwave

magnetisation. Geophysical Research Letters, 20: 109–111.

Cross-references

Demagnetization

Depth to Curie temperature

Magnetization, Thermoremanent (TRM)

Paleointensity

Figure M190 Orthogonal 18 GHz microwave demagnetization plot (left) and 18 GHz microwave Thellier paleointensity plot with

PTRM checks and multidomain tail checks (right). The maximum microwave power used was 40 W for 10 s. H

pal

¼ 51.9  0.4 mT,

q ¼ 140.4.

MICROWAVE PALEOMAGNETIC TECHNIQUE 695