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1 This presentation relies on: 1)\\_en 2)\\_Gallery 3) MICROMECHANICS II: CRYSTAL PLASTICITY

2 Review of deformation styles:

3 Brittle: failure that occurs during elastic deformation and is localized along a single plane. Ductile: when the rock undergoes a large change in shape without breaking. At the grain scale, the deformation may occur by cracking and/or fracturing, or it may occur as plastic deformation. While brittle deformation is localized, ductile deformation is distributed. Cataclastic flow: refers to distributed microfractures at grain level such that at a mesoscopic level or hand specimen scale the rock appears to flow, and therefore is "ductile".

4 Pressure solution A common deformation mechanism in the upper crust, which involves the solution and re-precipitation of minerals.

5 Slide taken from: This process is accelerated in the presence of water.

6 0-Dimensional defects and diffusion creep Vacancies are missing atoms. Interstitials are atoms that are sitting not in their regular place. Micromechanics defects play a central role not only in brittle deformation (why?), but also in crystal plasticity. Diffusion and creep:

7 Vacancy diffusionInterstitial diffusion Point defects generally are mobile - at least at high temperatures. The migration of point defects in crystalline solids are referred to as creep deformation.

8 1-Dimensional defects and dislocation creep Dislocations are linear defects in lattice structure. These are the most important defects for the understanding of deformation under crustal conditions - including the rupture of earthquakes. STM (Scanning Tunneling Microscope) image of a dislocation.

9 The Burger vector and the Burger circuit All dislocations may be described by a combination of 2 end-members: 1) Edge dislocation: when the Burger vector is oriented perpendicular to the dislocation line. 2) Screw dislocation: when the Burger vector is oriented parallel to the dislocation line.

10 Dislocation creep proceeds atomic step by atomic step and finite strain is the result of this process repeated billions of times! Edge dislocation Screw dislocation Question: Is this an elastic deformation?

11 Edge dislocation is analogous to a carpet wrinkle Figure taken from:

12 The rheology of dislocation creep where: is the strain rate is a constant is the differential stress is a constant is the activation energy is the universal gas constant is the temperature (parameters in red are experimentally determined)

13 The strength of minerals Based on the above equation, it is possible to construct differential stress versus temperature for a variety of rock types. An important conclusion is that only olivine would have significant strength at the base of continental crust!

14 The brittle-ductile transition and the “jelly sandwich” model The transition between brittle and ductile deformations occurs when the ductile strain rate is fast enough to prevent the stress from becoming large enough to reach the brittle strength. Figure from Continental geothermal gradient. Composition of crust is quartz-dominated. Composition of mantle is olivine-dominated. This may explain why earthquakes are confined to shallow depths. I'm not aware of field evidence for brittle deformation below the Moho

15 The strength profile depends on the geothermal gradient and the mineralogical composition. A word of caution: This model relies entirely on the results of laboratory experiments that were conducted on tiny rock/mineral samples and were subjected to strain rates that are up to 7 orders of magnitude smaller than typical tectonic rates. Thus, the extrapolation of these results to geological scale is non-trivial!

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