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

## May 25, 2017 Continuous description of grain boundaries using crystal defect fields Results

*European Journal of Mineralogy* publishes a new article on continuum dislocation/generalized-disclination modelling of a MgO 310/[001] tilt boundary from X. Sun et al.

In this paper, we propose the continuum dislocation/generalized-disclination modelling of a MgO 310/[001] tilt boundary by using an atomistic-to-continuum crossover method.

*Figure 1. **Illustration of the displacement and transformation gradient associated with the motion of material particles from the reference state to the current state.*

Using the relaxed and un-relaxed atomic positions obtained from first-principles simulations, calculation of the displacement, distortion (strain and rotation), curvature and second order distortion fields is performed in the boundary area.

*Figure 2. **Continuity/discontinuity of displacement **and rotation fields **along the boundary. (a) Reference relaxed configuration (**blue circle**) and current un-relaxed configuration (**red cross**). (b) Close-up showing the rotation component **w*_{3}* along the boundary. (c) Values of rotat**ion compon**ent **w*_{3}* and displacement component u _{2 }*

*in the profile AC as a function of the coordinate x*

_{2}*. Note that,*

*with a small resolution (e.g., less than 1 Å), all 'discontinuities' of the displacement and rotation are smeared out as smoothness of the curves show. At larger resolution (e.g., 3 Å), the rotation jumps discontinuously from its smallest value above the boundary line to largest value below the boundary. Similarly, the displacement jumps discontinuously from its lowest to largest value in a 6 Å distance across the boundary.*

The dislocation and disclination density fields are used to smoothly describe the discontinuities in the displacement and rotation fields across the boundary.

*Figure 3. **Disclination density field θ _{33} and Burgers vector fields. The arrows represent the local Burgers vector, whose components are the edge dislocation densities (α_{13} and α_{23}) per unit surface.*

In addition, a generalized-disclination density tensor field is introduced to reflect shear and stretch discontinuities across the boundary.

*Figure 4. **Volterra'**s** distortions and examples of g-disclinations. (a) Defect line and cut surface in a reference cylinder. (b)(c) Edge and (d) screw dislocations show the discontinuities of displacement. (e)(f) Twist and (g) wedge disclinations indicate the discontinuities of rotation. (h) Shear, (i) stretch and (j) strech+rotation g-disclinations.*

This continuous model provides new mechanical insights into the structure of MgO grain boundary, as well as a basis for coarse-grained representations of the polycrystalline structure.

See the paper just published by our group:

X. Sun, P. Cordier, V. Taupin, C. Fressengeas and B.B. Karki, "Continuous description of grain boundaries using crystal defect fields: the example of a 310/[001] tilt boundary in MgO". *European Journal of Mineralogy* (2017), doi: 10.1127/ejm/2017/0029-2609