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

## May 5, 2016 Disclination modeling of a grain boundary in forsterite Results

*Philosophical Magazine* publishes a new article on continuous modelling at inter-atomic scale of a high-angle symmetric tilt boundary in forsterite from X. Sun et al.

In this paper, we present a “bottom-up” procedure to build a model for a tilt boundary in olivine as a periodic array of dislocations and disclinations dipoles, starting from the atomistic structure of the boundary.

*Fig**ure 1. **Transformation gradient associated with the motion of material particles from the reference state to the current state**.*

Applying the atomistic/continuum crossover technique to the 60.8° forsterite (Mg_{2}SiO_{4}) tilt boundary provides new insights into the structure of the grain boundary.

*Fig**ure **2.** **Disclination density field θ _{11} and Burgers vector fields for (a) O, (b) Mg and (c) Si sub-lattice. The arrows represent the local Burgers vector, whose components are the edge dislocation densities (α_{21} and α_{31}) per unit surface.*

It is shown on the basis of the dislocation and disclination fields found in the three O-Si-Mg sub-lattices and their contributions to the Frank and Burgers vectors, that the lattice incompatibility associated with the tilt angle is materialized by the incompatible distortion field of the O sub-lattice in the first place.

*Fig**ure** **3**. **Values of Frank vectors as a function of the height of surface.*

*Fig**ure 4. **Components of the Burgers vectors in the plane (e _{2}, e_{3}) for the three sub-lattices*

*vs. coordinate x*

_{2}along the boundary.

The incompatible distortion field of the Si sub-lattice follows closely its O sub-lattice counterpart, as their Frank and Burgers vector components also suggest. The Mg sub-lattice behaves very differently from the other two sub-lattices. Its incompatible distortion field is very weak and is complemented by a compatible distortion field offsetting the unbalanced incompatible distortion of the O and Si fields, which allows fulfilling the balance of momentum and satisfying the periodic boundary conditions.

See the paper just published by our group:

X. Sun, P. Cordier, V. Taupin, C. Fressengeas and S. Jahn, "Continuous description of a grain boundary in forsterite from atomic scale simulations: the role of disclinations". *Philosophical Magazine* (2016), doi: 10.1080/14786435.2016.1177232