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

## Mar 9, 2018 Kinks in SrTiO3 Results

New article published in Philosophical Magazine about the low-temperature glide of <110> dislocations in SrTiO_{3} perovskite

Strontium titanate SrTiO_{3} is a cubic perovskite with a very peculiar mechanical behavior. At low temperature, it is ductile thanks to the mobility of dislocations with a <110> Burgers vector, yet the flow stress does not change continuously with temperature, but undergoes a dramatic drop around 200 K. While it has been suggested in the past that this discontinuity may arise from a change in the dislocation core structure or its glide plane, no such thing was observed experimentally or in atomistic simulations.

We developped an analytical model to describe the glide of <110> dislocations in SrTiO_{3}. The model describes the motion of the dislocation by the formation of kink pairs, a mechanism where a segment of a dislocation line advances, forming kinks along the line. Since the <110> dislocations in SrTiO_{3} are dissociated into two partial dislocations separated by a stacking fault, a kink pair can form on either of the partials. One has to distinguish two scenarios: that kink pairs form on the two partial dislocations at the same time (correlated nucleation); or that only one kink pair forms on one of the two partial dislocations (uncorrelated nucleation).

**Fig. 1** - The two mechanisms accounted for by our model. (a) Simultaneous nucleation of kink pairs on both partial dislocations. (b) Nucleation of a kink pair on only one of the partials.

To parametrize this model, we used data determined from previous atomistic simulations, like the dissociation distance and the stacking fault energy. From there, the model predicts the energy cost associated with each mechanism, depending on the level of applied stress. A first important result is that the most favourable mechanism depends on the applied stress: at low applied stress, correlated nucleation is the only possible mechanism, while at high stress both correlated and uncorrelated nucleation mechanisms occur and contribute to the dislocation motion.

Finally, the energies predicted by our model were used into Orowan's equation, which allows to relate the strain rate with activation energies. This allows to determine the critical stress required to reach a target strain rate, at a given temperature. Considering the experimental strain rate έ=10^{-4} s^{-1}, we plotted the critical stress (CRSS) as a function of temperature. The excellent agreement with experimental data validates our approach. From this model, we learn that plastic flow occurs mainly via uncorrelated nucleation of kinks on individual partials at low temperature (T<200 K), and purely by correlated kink-pair nucleation at higher temperatures (200<T<1000 K). The sharp transition around T=200 K is due to the sudden loss of a glide mechanism.

**Fig. 2** - Evolution of the flow stress of SrTiO_{3} with temperature, in the low-temperature ductile regime (0-1050K). The results of our model (continuous blue and red lines) are compared with experimental data (black points).

**Reference:**

"On low-temperature glide of dissociated <110> dislocations in strontium titanate"

S. Ritterbex, P. Hirel, P. Carrez, Philos. Mag. (2018) | doi: 10.1080/14786435.2018.1438682