Dr. Pierre Hirel

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Properties of Grain Boundaries in MgO
Post-doc UMET, Lille (France), since Nov. 2012

Introduction

Magnesium oxide MgO is a ceramic material often used in electronics, sensors, and photovoltaics. In these applications, MgO often exists in a polycrystalline form, and grain boundaries have a major impact on the functional properties of the material.

Deep inside the Earth, ferropericlase (Mg,Fe)O is one of the major phases of the lower mantle, between 700 and 2880 km depth. There again, this mineral takes the form of polycrystals, and grain boundaries contribute to plastic deformation and creep. In the framework of the RheoMan project, we used atomic-scale simulations to study the properties of grain boundaries in MgO, and their evolution when they are submitted to the high pressures of the Earth's lower mantle, up to 120 GPa.

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Fig. 1 - The structure of the Earth's interior, and some examples of minerals found in the mantle.

Properties at ambient pressure

To begin, we focused our study on one peculiar type of grain boundaries, that are called symmetric tilt grain boundaries (STGB). Two MgO single crystals which [001] axes are aligned, are rotated by opposite angles ±α/2 around that axis, cut, and then stacked. They meet with equivalent crystallographic planes {hk0}, where Miller indices h and k depend on the chosen misorientation angle α.

At low angles (0°<α<20°), the crystals accomodate the misorientation by forming [010] dislocations, which are regularly spaced. This situation is well described by the elastic model by Read and Shockley, and the energies obtained in atomistic simulations fit quite well with those predicted by this model (Fig. 2). At higher angles, this description is not suited any longer: the atomic structure cannot be described solely in terms of dislocations anymore, and the Read-Shockley model fails to predict the energies. Atomistic simulations indicate that for such high misorientations (20°<α<67.4°), grain boundaries have similar energies about 1,7 J/m2.

GB energy vs misorientation

Fig. 2 - Minimum energies of symmetric tilt grain boundaries in MgO. Our results (black circles) are compared with ab initio calculations (red squares and diamonds), other atomistic simulations (blue crosses and stars), and the Read-Shockley model (dashed lines).

The specific misorientation α=67.4° marks a discontinuity in the GB energies, and also in their atomic structure. Beyond this misorientation angle, it becomes more favorable to shift one crystal with respect to the other along the grain boundary. The reason for this is the following: for the misorientation α=90°, the two crystals are both rotated by ±45° and form a simple stacking fault; shifting one crystal with respect to the other allows to restore the perfect crystal. For angles close to the right angle (67.4°<α<90°), it is therefore more favorable to shift one crystal in order to maximize the volume of perfect crystal, the small remaining misorientation being accomodated by dislocations with a ½[110] Burgers vector. Those grain boundaries are then well described by the Read-Shockley model, which predicts their energies with a good accuracy (Fig. 2).

Influence of pressure

We submitted the previous grain boundaries to pressures in the range 30-120 GPa, typical of the Earth's lower mantle. We found that pressure has several effects, which are non-linear. First, grain boundaries all change their atomic structure at the pressure 30 GPa. Atoms tend to fill the gaps inside the grain boundaries, thus increasing their compaction (Fig. 3).

{310} GB at 0 and 30 GPa

Fig. 3 - Most favourable atomic structure of the {310}[001] grain boundary, at 0 GPa (left) and 30 GPa (right).

As pressure is increased, some grain boundaries keep their new atomic structures up to 120 GPa, while others change it one or several times again. Similarly, the energy of grain boundaries changes in a non-linear way with pressure, although globally, it always increases with pressure, reaching up to 5 to 6 J/m2 at 120 GPa [1].

These results indicate that the grain growth rate may increase with pressure, while impurity segregation may be impeded. However, it will be necessary to address these topics explicitely in order to test these hypotheses.

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