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

## Aug 8, 2015 Dissemination: MAX phases Results

New publication appearing on line in *Philosophical Magazine* with Antoine Guitton, Anne Joulain, Ludovic Thilly and Christophe Tromas (Poitiers, France).

The MAX phases represent a novel category of materials which have a lamellar structure (figure 1) and high lattice anisotropy. Little is known yet about the elementary deformation mechanisms of these phases. Microstructural observations on deformed samples suggest the prominence of dislocation activity in the basal plane (figure 2).

*Figure 1: Ti _{2}AlN lamellar structure, Ti atoms are in cyan, Al atoms in blue and N in grey.*

*Figure 2: TEM observation of long straight dislocation segments lying in the basal plane in Ti _{2}AlN. Dislocations exhibit strong orientation dependence with segments having strong edge (in black on the right panel) and 30° (in grey on the right panel) characters with a Burgers vector b =1/3[2-1-10]*

In this paper, we use the techniques developed in the RheoMan project to model core structure of dislocations in the basal plane for one of those MAX phase: Ti_{2}AlN. We use the numerical approach, called Peierls-Nabarro-Galerkin model (PNG) coupled with first-principles calculations of generalized stacking fault (figure 3).

*Figure 3: γ-surfaces (in J/m²) in (0001) plane between Ti and Al on which dissociation path (in grey line and obtained with PNG calculation) of the 1/3[2-1-10] dislocations has been superimposed. The hexagonal base (a_{1}, a_{2}, a_{3}) is represented, γ_{s} is the stable stacking fault with γs = 0.72 J/m². The 1/3[2-1-10] Burgers vector is in a_{1}.*

We highlight the easiness of glide of *1/3[2-1-10]* dislocations in the basal plane, due to the dissociation into two partials dislocations, whatever the dislocation character (screw in figure 4, mixed or edge). This easiness of glide in the basal plane is confirmed by calculation of the Peierls stress. This study illustrates the importance in associating numerical models and experimental data, in order to understand the deformation mechanism of complex materials.

*Figure 4: Core structure of screw dislocation. Disregistry function f(x) and associated Burgers vector density ρ = df(x)/dx (dotted line) are plotted in (0001) plane.*

See the paper just published by our group:

K. Gouriet, Ph. Carrez, P. Cordier, Antoine Guitton, Anne Joulain, Ludovic Thilly and Christophe Tromas (2015) "Dislocation modelling in Ti_{2}AlN MAX phase based on the Peierls-Nabarro model". *Philosophical Magazine*, doi: http://dx.doi.org/10.1080/14786435.2015.1066938