# RheoMan: a five-year, ERC-funded (Advanced Grant), project to model the rheology of the Earth's mantle

## Oct 22, 2015 Dislocation glide in ringwoodite Results

Physics of the Earth and Planetary Interiors publishes the last paper from Sebastian Ritterbex et al. on the multiscale modeling of dislocation glide in ringwoodite

In this paper, we model plastic deformation of Mg_{2}SiO_{4} ringwoodite by pure dislocation glide under experimental and natural strain rates. Our parameter-less, bottom up, multiscale approach yields a quantitative assessment of the critical resolved shear stress of ringwoodite at 20 GPa as function of temperature. Results suggest that deformation by pure dislocation glide would result into a high viscosity lower transition zone

The model is based on the glide mobility of the rate controlling dislocations that belong to the easiest slip systems: ½‹110›(110) and ½‹110›(111). They involve screw dislocations that are collinearly dissociated into ¼‹110› partials.

*Dislocation core structures of the ½‹110› screw dislocations in the a) (110) plane and b) (111) plane. The spread of the core structures are shown in form of the disregistry (red continuous line) and its derivative, the local density of the Burgers vectors (green dotted line)*

Dislocation glide at finite temperatures is governed by thermally activated nucleation of kink-pairs on dislocations that lead to the activation of single slip, when the critical resolved shear stress (CRSS) is temperature dependent. As such, our modeling approach is capable in determining the temperature threshold bove which dislocation-dislocation interactions take over the controll of the average dislocation mobility.

The kinematics of thermally actived plastic slip is strongly dependent on the specific atomic arrangements that build the dislocation core structures. These core structures are calculated by the use of the on the element-free method based Peierls-Nabarro-Galerkin model and parametrized by generalized stacking fault surfaces of the potentials slip planes. These so called γ-surfaces are obtained by density functional theory calculations. This allows to take accurately into account the effect of pressure on atomic bonding (*i.e.* on the dislocation core structures).

*γ-Surfaces provided by density functional theory calculations of the following planes: a) (001) plane, b) (110) plane and c) (111) plane. d) shows the γ-lines in the ½ ‹110› Burgers vector direction for the (001) ,(110) and (111) planes.*

The former results enable us to quantify the intrinsic lattice resistance dislocations have to overcome to become mobile. Finally, an elastic interaction model is presented that allows to calculate the critical configurations that trigger the elementary displacements of collinear dissociated dislocations. The model is based on the results previously calculated.

* Schematic illustration of kink-pair nucleation on collinear dissociated dislocations with equilibrium stacking fault width d. At low stress, coherently correlated nucleation of kink-pairs at both partials drives the dislocation mobility. At high stress, dislocations motion is mainly driven by the less energetically successive independent nucleation of kink-pairs on the partials*

Dislocation mobilities are established by the relation between the stress dependent enthalpy associated to a critical dislocation bow out and the rate of kink-pair nucleation.

*Glide velocity of the ½‹110›(110) and ½‹110›(111) screw dislocations as a function of the resolved shear stress at 1800 K.*

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Constitutive relations corresponding the activation of single slip are deduced from Orowan's equation in order to describe the average plasticity at the grain scale. The results are in good agreement with experimental data on plastic deformation performed at around 20 GPa and typical laboratory strain rates.

*Critical resolved shear stress CRSS versus temperature at a fixed laboratory strain rate for thermally actived glide of the ½‹110›(110) and ½‹110›(111) screw dislocations. The experimental effective flow stresses are divided by two to be converted into apparent resolved shear stresses since deformation experiments were performed on polycrystalline samples.*

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After validating our model, we were able to calculate the constitutive equations related to dislocation glide under typical conditions of the lower transition zone. We show that under these conditions, lattice friction is high and that dislocation glide is governed by the interaction between the dislocations and the crystal lattice.

A viscosity between 8x10^{23} – 5x10^{24 }Pas can be attributed to the rate limiting dislocations in ringwoodite. These viscosity values can be seen as lower bounds since they are related to the intrinsic glide resistence of single slip systems. Deformation by pure dislocation glide would therefore result into a high viscosity lower transition zone. This may explain why the transition zone seems to be "stiff" at some places, which is in line with seismic observations of stagnating slabs, where subducting lithosphere is inhibited to penetrate into the lower mantle. However, contributions of other deformation mechanisms will be necessary to explain softer behaviour.

For more information, see the paper just published:

S.Ritterbex, Ph. Carrez, K. Gouriet, P. Cordier (2015) "Modeling dislocation glide in Mg_{2}SiO_{4} ringwoodite: Towards rheology under transition zone conditions". Physics of Earth and Planetary Interiors,248, 20-29 doi:10.1016/j.pepi.2015.09.001