Some remarks on micro-physics of LPO (plastic anisotropy)��some tutorials

Shun-ichiro Karato

Yale University

Department of Geology & Geophysics

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transition zone

Visser et al. (2008) Trampert and van Heijst (2002) Panning and Romanowicz (2006)

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upper mantle

D” layer

Why LPO?

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• Seismic anisotropy is controlled mostly by LPO.
• But the relationships between LPO and flow geometry are poorly known for most part of Earth’s interior.

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• LPO is determined by the dominant slip systems (LPO) that are controlled by a combination of many microscopic processes (physics of LPO is complex!).

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• experimental approach: (i) systematic, well-defined lab experiments + (ii) scaling analysis
• theoretical approach: (i) key parameters (diffusion, dislocation properties) + (ii) integration of multi-scale physics of deformation

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olivine wadsleyite

[100]

[010]

[001]

~1800 K

~1700 K

~1500 K

(preliminary results)

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LPO-flow geometry relationship depends on (i) materials, and (ii) physical/chemical conditions (fabric transitions).

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Origin of plastic anisotropy (dislocation creep)�How do fabric transitions occur? What controls LPO?

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Si diffusion in olivine is nearly isotropic.

--> diffusion controlled model does not explain large plastic anisotropy

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Houlier et al. (1981) from Costa and Chakraborty (2008)

“dry”

Fabric transitions for olivine

C

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A

B

D

E

Observations for olivine

• Dominant slip direction is b=[100] (or [001])
• consistent with the role of kink/jog
• Stress-induced fabric transitions
• inconsistent with the simple diffusion-controlled model
• Larger water weakening effect for b=[001]
• cannot be explained by the simple diffusion-controlled model
• larger weakening effects for dislocations with larger Peierls stress

(or longer Burgers vector)

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• anisotropy is largely due to dislocation-related properties

(not by diffusion)

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A model of fabric transitions

• Stress/temperature-induced fabric transition (low T, high stress) [kink energy (Peierls stress)]

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• Water/temperature-induced fabric transition (high T, low stress, high water fugacity) [diffusion (point defects), jog energy]

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Testing the jog (+ diffusion) - controlled model�some speculations on post-perovskite phase

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Eshelby-Foreman theory for dislocation

energy with anisotropic elasticity

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Jog-controlled climb model is consistent

with olivine data.

• [100](010) or [100](001)

for post-perovskite?

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diffusion creep?

• large dislocation energy
• fast diffusion (Karki-Khanduja (2007))

Conclusions

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• Plastic anisotropy is caused mostly by anisotropic dislocation properties (not much by diffusion anisotropy).
• Plastic anisotropy depends on T, stress, water content etc.
• lab studies: well-defined experiments (high-T, low stress) + scaling analysis

[Direct applications of lab results without scaling analyses can lead to misleading conclusions.]

• modeling: test with well-known materials (e.g., olivine) and then apply to not-yet-studied minerals

[jog-controlled model (high-T plasticity model) works OK for olivine, and suggests [100](010) or [100](001) (or [001](100))is the easiest slip system in post-perovskite. But deformation in ppv might occur by diffusion creep.]

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Plastic anisotropy of post-perovskite ?

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Micro-physics of LPO�(reminder of ABC of LPO)

• LPO depends on macroscopic deformation geometry and microscopic deformation mechanisms.
• Deformation by dislocation creep produces LPO.
• LPO formed by dislocation creep depends activity of slip systems.
• LPO is largely controlled by easiest (+ some other) slip system(s).
• The relative easiness of slip systems is controlled by the relative rate of deformation that is controlled by (i) anisotropy of dislocation energy (kink, jog formation energy), (ii) by anisotropy of diffusion.
• These factors will change with T, P, stress, water content etc.
• Results at conditions different from Earth’s interior (e.g., low T) cannot be applied to Earth’s interior.

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How should we investigate LPO �relevant to Earth’s interior?�(micro-physics of LPO is complex)

• Experimental approach: time scales are vastly different between lab and Earth (need extrapolation)
• what kind of experiments should we conduct ?
• How should we extrapolate these results ?
• Theoretical (modeling) approach: creep processes are complex
• How should we infer the dominant slip system(s)?
• Diffusion coefficients ?
• Dislocation properties ?
• How should we integrate ?

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Strong LPO develops by deformation only through certain mechanisms

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• Classic diffusion-controlled high-T creep model: can it explain fabric transitions?

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• Peierls stress: How does it explain plastic anisotropy at high-T?

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