diffusion in earth’s deep interior: insights from high-pressure experiments

Diffusion in Earth’s Deep Interior: Insights from High-Pressure Experiments

Jim Van Orman

Department of Geological Sciences

Case Western Reserve University

COnsortium for Materials Properties Research in Earth Sciences

COMPRES is an NSF-supported consortium that supports study of Earth material properties, particularly at high pressures and temperatures (Earth interior conditions).

Interior of the Earth

In the deep mantle, these transform to denser high-pressure forms.

In the deep mantle, these transform to denser high-pressure forms.

The crust and upper mantle are composed of the familiar silicate minerals.

The crust and upper mantle are composed of the familiar silicate minerals.

Mantle Mineralogy

To study these and other materials, COMPRES supports user facilities, including several synchrotron X-ray facilities where high-pressure experiments are performed.

Advanced Photon Source

Synchrotron facilities also house very large presses that allow study of somewhat larger samples.

Mounted on a stage that can move the press with micron precision to put the sample at the focal point of the X-ray beam.

Mafic melt viscosity experiment by Lara Brown, Chip Lesher, et al., UC-Davis

http://www.johnkyrk.com/diffusion.html

What is Diffusion?What is Diffusion?

Diffusion in Earth’s Deep Interior: Insights from High-Pressure Experiments

Diffusion is the transport of matter by random hopping of atoms. It is a fundamental step in many important chemical and physical processes.

Atoms initially confined to a plane spread out with time according to a simple mathematical law, based on the theory of a random walk.

How rapidly they spread depends on the diffusion coefficient. Diffusion is *much* more rapid in gases and liquids than in minerals.

Gas

Crystal

How can diffusion happen in a crystal?

How can diffusion happen in a crystal?

In a perfect crystal, diffusion is extremely difficultIn a perfect crystal, diffusion is extremely difficult

dislocations

grain boundaries

But crystals are never perfect...But crystals are never perfect...

Diffusion by a vacancy mechanism

More vacancies = faster diffusion

Vacancies move much faster than the atoms themselves

Diffusion in the Deep Earth (1):Maintaining a Heterogeneous Mantle

Subduction makes the mantle chemically heterogeneous

On what length scales can the heterogeneity

be preserved?

Convective and diffusive mixingConvective and diffusive mixing

Diffusion in the Deep Earth (2):Chemical Transfer at the Core-Mantle Boundary

Diffusion in the Deep Earth (3):Diffusion and Viscosity

Stokes-Einstein Equation

diffusioncoefficient

viscosity

Diffusion in Deep Earth Materials at High Pressure

1. Solid Iron-Nickel Alloys (Inner Core)

2. MgO (Lower Mantle)

What are the fundamental controls on the diffusion rates?

High-Pressure Experiments

Pressure = Force/Area

Multi-AnvilPress

Sample size ~1 mm

Ni

Fe

1. Diffusion in Iron-Nickel Alloys at High Pressure

Homologous Temperature Scaling For Close-Packed Metals

Inner Core

Does it hold at high pressure?

Fe-Ni Diffusion Profiles12 GPa, 1600 oC

100

80

60

40

20

0

Fe concentration (atomic %)

6004002000-200

x-position (microns)

2 hours

10 hours

.5 hours

€

D ′ c ( ) =−12t

dxdc

⎛ ⎝ ⎜

⎞ ⎠ ⎟′ c

xdc0

′ c

∫

Boltzmann-Matano

Yunker and Van Orman, 2007

DFe-Ni vs Composition

-13.2

-13.0

-12.8

-12.6

-12.4

-12.2

-12.0

log Diffusion coefficient (m

2/s)

100806040200

Fe concentration (atomic %)

12 GPa1600 oC2 hr

Melting curve1 atmosphere

Yunker and Van Orman, 2007

DFe-Ni vs Pressure at Constant Homologous Temperature

-16

-15

-14

-13

-12

log Diffusion coefficient (m

2/s)

20151050

Pressure (GPa)

T/T m=.87490% Fe

Yunker and Van Orman, 2007

-16

-15

-14

-13

-12

log Diffusion Coefficient (m

2/s)

2520151050

Pressure (GPa)

Goldstein et al. (1965) Constant activation volume

1600°C90%Fe

logDFe-Ni vs PressureYunker and Van Orman, 2007

-16

-15

-14

-13

-12

log Diffusion Coefficient (m

2/s)

2520151050

Pressure (GPa)

Goldstein et al. (1965) Constant activation volume This experiment

1600°C90%Fe

logDFe-Ni vs PressureYunker and Van Orman, 2007

-16

-15

-14

-13

-12

log Diffusion Coefficient (m

2/s)

2520151050

Pressure (GPa)

Goldstein et al. (1965) Constant activation volume This experiment Homol. Temp scaling

1600°C90%Fe

€

D = D0 exp −gTm T( )

logDFe-Ni vs PressureYunker and Van Orman, 2007

Inner core viscosity (Harper-Dorn creep regime)

Suggests that inner core behaves like a fluid on the timescale of Earth rotation, and is free to super-rotate instead of being gravitationally locked to the mantle.

Inner core anisotropy an active deformation feature, rather than growth texture?

€

η =σ2 ˙ ε

≈1

2AHD

kTDb

~1011 - 1012 Pa s

2. Diffusion in MgO

(Mg,Fe)O is thought to represent ~15-20% of the lower mantle.

Prior Studies of Self-Diffusion in MgO (Atmospheric Pressure)

Mg O

Van Orman and Crispin, in press, Reviews in Mineralogy & Geochemistry

Diffusion in MgO at High Pressure

25Mg, 18O enriched

Experiments were designed to measure lattice and grain boundary diffusion of both Mg and O

Sample retrieved from experiment at 2000 oC and 25 GPa

Van Orman et al., 2003

Van Orman et al., 2003

Ab Initio Calculation

Cation diffusion in MgO is predicted to become slower with increasing depth in the lower mantle (except just above the core-mantle boundary).

MgO polyxtl MgO xtlAl2O3

A surprise: Al3+ diffuses rapidly in MgO

Van Orman et al., 2003

Al3+ impurities in MgO:

Cation vacancies are created to maintain electrical neutrality.

These are attracted to Al3+ and tend to form pairs (and higher order clusters at low temperature). These defect associates have been known about for decades, but their influence on diffusion has been largely neglected.

Al-vacancy pairs enhance the

mobility of Al, but diminish the mobility of the vacancy (and thus the mobility of other cations that diffuse using vacancies).

MgOSpinelMgAl2O4

Diffusion experiments to determine Al-

vacancy binding energy and pair

diffusivity

1 atm to 25 GPa1577 to 2273 K

E-probe scan

Van Orman et al., 2009

Diffusion profiles were fit to a theoretical model to determine binding energy and diffusivity of the Al-vacancy pairs. Binding energies for all experiments at atmospheric pressure are -50 ± 10 kJ/mol (2 ), consistent with theoretical values of -48 to -53 kJ/mol (Carroll et al., 1988) and have no clear pressure dependence.

Van Orman et al., 2009

V = 3.22 cm3/mol(+/- 0.25)

The diffusion coefficient of the Al-vacancy pair does depend on pressure.

Similar to pressure dependence for Mg self-diffusion (3.0 cm3/mol)

Van Orman et al., 2009

However…

Al (0.535 Å)

What about other trivalent cations?

Crispin and Van Orman, 2010

Diffusivity and Ionic RadiusDiffusivity and Ionic Radius

Sc

Crispin and Van Orman, 2010

Why is chromium so slow?Why is chromium so slow?

• Cr3+ 1s2 2s2 2p6 3s2 3p6 3d3 Crystal field effect

Wuensch and Vasilos, 1962

• Fe2+ 6 d electrons– 3 t2g, 2 eg, 1 t2g

• Co2+ 7 d electrons– 3 t2g, 2 eg, 2 t2g

• Ni2+ 8 d electrons– 3 t2g, 2 eg, 3 t2g

(Similar to Cr3+)

The crystal field effect seems to explain differences in the diffusivity of other transition metals.

0 -50 -100 -150 -200 -250160

180

200

220

240

260

Ga3+

Cr3+

Ni2+Co2+

Act

ivat

ion

Ene

rgy

(kJ/

mol

)

Crystal Field Stabilization Energy (kJ/mol)

Fe2+

Crispin and Van Orman, 2010

A transition in the electronic structure of Fe2+ in MgO is one of the exciting discoveries in mineral physics in the last decade (Badro et al., 2003).

• At high pressure, the two electrons in eg

orbitals in Fe2+ move to t2g orbitals.

• This so-called “spin” transition affects a wide range of properties (density, seismic wave speeds).

• It may also have a strong influence on diffusion.

Marquardt et al. (2009) Science

-350 -300 -250 -200 -150 -100 -50 0

-19

-18

-17

-16

-15

-14

-13

-12

Fe(ls)

Co(ls)

log

D (

m2 /s

)

Crystal Field Stabilization Energy (kJ/mol)

Fe

CoNi

Crispin and Van Orman, 2010

High Spin

Conclusion:How might electronic spin transitions affect diffusion

length scales in the mantle?

Low Spin?

Spin transitions may slow the diffusion of transition metals significantly. This would:1)Make chemical exchange across the core-mantle boundary more difficult.2)Make chemical heterogeneity in the deepest mantle more difficult to erase.