Rheology of Earth Materials :

Closing the gap between timescales in the laboratory and in the mantle

4 June 2021 - New publication in Physical Review Materials

 

Our article issued June 4th, 2021 in Physical Review Materials describes the complex relation between charged vacancies and an edge dislocation in magnesium oxide. Depending on where the vacancy is around the dislocation, the interaction can be either repulsive (up to 0.62 eV, in the dislocation core) or attractive (up to 1.35 eV, also inside the dislocation core…).

In our works we wanted to deeply understand that interaction in order to determine the pinning ability of the vacancy. If point defects are sufficiently strong pinning points they can slow the dislocation glide and thus have an impact on the plastic deformation of MgO. For that purpose, we extract the interaction energies and interaction forces between the vacancy and the dislocation.

We used two different approaches to demine these terms: atomic scale simulations with an empirical potential, and the elasticity theory. The comparison between the approaches permit us to validate our model.

For the elasticity theory, we use the elastic dipole approach. That permit us to model the impact of an elastic field (here the dislocation elastic field) on a defect that is characterized by its elastic tensor dipole (linked to the local stress tensor in vicinity of the vacancy times the volume of the cell). In such formalism, the interaction energy is nothing else that minus the elastic dipole of the vacancy times the elastic field of the dislocation. 

The elasticity theory tells us that the more space the vacancy have the better it is. Indeed, due to the strong electrostatic repulsion between first ionic neighbors of the vacancy, the vacancy takes more place than the ion missing, the relaxation volume of the vacancy is positive. It is therefore favorable for the vacancy to go inside a tensile region in which the ions have a surplus of volume.

In case of edge dislocation, there is a tensile area below the glide plane and a compressive area above it. So elasticity tells us that the vacancy would like to go below the dislocation glide plane, in the tensile zone, where the dislocation/vacancy interaction is attractive. As expected, the long-range interaction can be predicted by standard elastic developments when the vacancy is in the dislocation far field, so far from the dislocation core. We show that far corresponds to 12 atomic planes so approximately 5 Burgers vectors.

 

However, we found that even if atomistic simulations are in agreement with the theory far from the core, inside the core there is a major discrepancy between both methods. The interaction energies and interaction forces inside the dislocation core predicted by the theory are not in agreement with the simulations.

The main difference between the theory and the simulations is about the description of the dislocation core.  The theory described the dislocation as a singularity, without taking into account the dislocation core spreading. Consequently, the results given by the theory are very sharp compared to the simulation data. Furthermore the theory does take into account the local relaxation occurring inside the dislocation core that induced local ‘free zone’ where the atoms are locally in tension.

For instance, at the plane ny=1 there is a local tension zone, that explain why the interaction is strongly attractive. Because the theory is not able to describe such local relaxation, it would have predicted a compression zone for ny=1, and thus a repulsive interaction.

The pinning force of the vacancy is the maximum of the interaction forces, obtain for the plane ny=1. The force computed via our simulations are very weak compared to the theory predictions, due to the core spreading. So finally we concluded that isolated  vacancies  remain  weak pinning points which are not expected to contribute significantly  to  the  hardening  observed  experimentally  in MgO.

 

To learn more:

M. Landeiro Dos Reis, P. Carrez & P. Cordier (2021) On the interaction dislocation/vacancy in magnesium oxide: Insights from atomistic simulations and elasticity theory. Physical Review Materials, 5, 063602. https://doi.org/10.1103/PhysRevMaterials.5.063602