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. 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

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?

In a perfect crystal, diffusion is extremely difficult dislocations grain boundaries 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 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 diffusion coefficient 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-Anvil Press 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 Profiles 12 GPa, 1600 o C Boltzmann-Matano Yunker and Van Orman, 2007

D Fe-Ni vs Composition 12 GPa 1600 o C 2 hr Melting curve 1 atmosphere Yunker and Van Orman, 2007

D Fe-Ni vs Pressure at Constant Homologous Temperature Yunker and Van Orman, 2007

logD Fe-Ni vs Pressure Yunker and Van Orman, 2007

logD Fe-Ni vs Pressure Yunker and Van Orman, 2007

logD Fe-Ni vs Pressure Yunker 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? ~ 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) MgO Van Orman and Crispin, in press, Reviews in Mineralogy & Geochemistry

Diffusion in MgO at High Pressure 25 Mg, 18 O enriched Experiments were designed to measure lattice and grain boundary diffusion of both Mg and O Sample retrieved from experiment at 2000 o C and 25 GPa 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 polyxtlMgO xtl Al 2 O 3 A surprise: Al 3+ diffuses rapidly in MgO Van Orman et al., 2003

Al 3+ impurities in MgO: Cation vacancies are created to maintain electrical neutrality. These are attracted to Al 3+ 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).

MgO Spinel MgAl 2 O 4 Diffusion experiments to determine Al- vacancy binding energy and pair diffusivity 1 atm to 25 GPa 1577 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 cm 3 /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 cm 3 /mol) Van Orman et al., 2009 However…

Al (0.535 Å) What about other trivalent cations? Crispin and Van Orman, 2010

Diffusivity and Ionic Radius Sc Crispin and Van Orman, 2010

Why is chromium so slow? Cr 3+ 1s 2 2s 2 2p 6 3s 2 3p 6 3d 3 Crystal field effect

Wuensch and Vasilos, 1962 Fe 2+ 6 d electrons –3 t 2g, 2 e g, 1 t 2g Co 2+ 7 d electrons –3 t 2g, 2 e g, 2 t 2g Ni 2+ 8 d electrons –3 t 2g, 2 e g, 3 t 2g (Similar to Cr 3+ ) The crystal field effect seems to explain differences in the diffusivity of other transition metals.

Crispin and Van Orman, 2010

A transition in the electronic structure of Fe 2+ 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 e g orbitals in Fe 2+ move to t 2g 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

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.