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.

 

 

Figure 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 (Mg2SiO4) tilt boundary provides new insights into the structure of the grain boundary.

 

 

Figure 2. Disclination density field θ11 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 (α21 and α31) 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.

 

 

Figure 3. Values of Frank vectors as a function of the height of surface.

 

 

Figure 4. Components of the Burgers vectors in the plane (e2, e3) for the three sub-lattices vs. coordinate x2 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