Peierls Nabarro Galerkin Research Articles

Plasticity of the dense hydrous magnesium silicate phase A at subduction zones conditions

The plasticity of the dense hydrous magnesium silicate (DHMS) phase A, a key hydrous mineral within cold subduction zones, was investigated by two complementary approaches: high-pressure deformation experiments and computational methods. The deformation experiments were carried out at 11GPa, 400 and 580°C, with in situ measurements of stress, strain and lattice preferred orientations (LPO). Based on viscoplastic self-consistent modeling (VPSC) of the observed LPO, the deformation mechanisms at 580°C are consistent with glide on the (0001) basal and (011¯0) prismatic planes. At 400°C the deformation mechanisms involve glide on (2¯110) prismatic, (0001) basal and {112¯1} pyramidal planes. Both give flow stresses of 2.5–3GPa at strain rates of 2–4×10−5s−1. We use the Peierls–Nabarro–Galerkin (PNG) approach, relying on first-principles calculations of generalized stacking fault (γ-surface), and model the core structure of potential dislocations in basal and prismatic planes. The computations show multiple dissociations of the 13[21¯1¯0] and [011¯0] dislocations (〈a〉 and 〈b〉 dislocations) in the basal plane, which is compatible with the ubiquity of basal slip in the experiments. The γ-surface calculations also suggest 13[21¯1¯3] and [01¯11] dislocations (〈a+c〉 or 〈c−b〉 directions) in prismatic and pyramidal planes, which is also consistent with the experimental data. Phase A has a higher flow strength than olivine. When forming at depths from the dehydration of weak and highly anisotropic hydrated ultramafic rocks, phase A may not maintain the mechanical softening antigorite can provide. The seismic properties calculated for moderately deformed aggregates suggest that S-wave seismic anisotropy of phase A-bearing rocks is lower than hydrous subduction zone lithologies such as serpentinites and blueschists.

Modeling dislocation glide in Mg2SiO4 ringwoodite: Towards rheology under transition zone conditions

Deformation resulting from thermally activated plastic slip is modeled in Mg2SiO4 ringwoodite at 20GPa for a wide range of temperatures. The model relies on the structures of the rate controlling 1/2〈110〉 screw dislocations which have been modeled using the Peierls–Nabarro–Galerkin method. These calculations are parametrized by density functional theory calculations of γ-surfaces of the {001},{110} and {111} planes. At finite temperatures, dislocation mobility is controlled by kink-pair nucleation on the thermally activated 1/4〈110〉 partial screw dislocations as they occur in ringwoodite. Single slip critical resolved shear stresses (CRSS) corresponding to this mechanism are deduced from Orowan’s equation. The results are found to be in reasonably good agreement with experimental data at 20GPa which show high effective flow stresses under laboratory conditions. Finally, the CRSS’s are calculated for typical mantle strain rates of ∊̇=10-16s−1 at appropriate temperatures expected in the lower transition zone. Results show that dislocation glide remains difficult and that lattice friction is not yet negligible in ringwoodite under natural conditions.

Dislocation modelling in Ti2AlN MAX phase based on the Peierls–Nabarro model

In this study, we determined the core structure and the Peierls stress of dislocations in Ti2AlN MAX phase. We use a generalized Peierls–Nabarro model, called Peierls–Nabarro–Galerkin (PNG), coupled with first principles calculations of generalized stacking fault (GSF). The GSF calculations show that dislocation glide in the basal plane will occur preferentially between M (here Ti) and A (here Al) planes. Additionally, the results of PNG calculations demonstrate that whatever the dislocation character, dislocations are dissociated in the basal plane, with a dissociation distance below the experimental resolution of transmission electron microscopy observations. Finally, the Peierls stress calculations show that the edge and screw characters are the easiest characters to glide in the basal plane.

Numerical modeling of the core structure of [100] dislocations in Fe3C cementite

The core structure of [100] screw dislocation has been modeled in Fe3C cementite, using the Peierls–Nabarro–Galerkin model based on γ-surfaces for (010) and (001) planes. We show that γ-surfaces and core structure of the [100] screw dislocation depend of the relaxation procedure applied to the carbon atoms during γ-surface calculations. We find that [100] screw dislocations spread in (010) with a tendency toward dissociation, which is in agreement with dislocation features observed experimentally.

Modelling [1 0 0] and [0 1 0] screw dislocations in MgSiO3 perovskite based on the Peierls–Nabarro–Galerkin model

In this study, we model the core structure of screw dislocations with [1 0 0] and [0 1 0] Burgers vector in MgSiO3 perovskite, in the pressure range of Earth's lower mantle (25–130 GPa). We use a generalized Peierls–Nabarro model, called Peierls–Nabarro–Galerkin, based on generalized stacking-fault energy calculations. These stacking-fault energy calculations are performed using a pairwise potential parametrization and compared to ab initio results. The results of Peierls–Nabarro–Galerkin calculations demonstrate that [1 0 0] dislocation and [0 1 0] are, respectively, characterized by a planar core spreading in (0 1 0) and (1 0 0). Our results emphasize the role of [1 0 0](0 1 0) and [0 1 0](1 0 0) slip systems in the deformation mechanism of MgSiO3 perovskite. Furthermore, we validate the use of pairwise potential for further dislocation modelling of such minerals at the atomic scale.

Multiscale modelling of MgO plasticity

We propose a multiscale model of plasticity of pure MgO single crystals. The core structure of the rate controlling ½〈1 1 0〉 screw dislocations has been modelled by the Peierls–Nabarro–Galerkin method. This model relies on γ-surfaces calculated ab initio for the {1 1 0}, {1 0 0} and {1 1 1} planes. The ½ 〈1 1 0〉 screw dislocations spread mostly in the {1 1 0} planes. The Peierls friction values are 150 MPa and 1.6 GPa for glide on the {1 1 0} and {1 0 0} planes, respectively. The kink pair theory is applied to model thermal activation of dislocation glide over the Peierls barrier below the athermal temperature T a and to build a velocity law for this regime. The critical resolved shear stresses are deduced below T a from the Orowan law. Above T a the athermal stress τ μ is obtained from discrete dislocation dynamics simulations to account for dislocation–dislocation interactions. This model is found to satisfactorily reproduce the critical resolved shear stresses observed experimentally, provided the contribution of impurities (unavoidable in experiments) is subtracted.

Modelling thermal activation of {1 1 0} slip at low temperature in SrTiO3

The core structure of {1 1 0} screw dislocations has been modelled in SrTiO3 with the Peierls–Nabarro–Galerkin method. This model relies on γ-surfaces calculated ab initio for the {1 0 0} and {1 1 0} planes. The {1 1 0} screw dislocation has a planar core and its Peierls friction is 350 MPa. The kink-pair theory is applied to model thermal activation of dislocation glide over the Peierls barrier. This model is found to reproduce satisfactorily the critical resolved shear stresses observed experimentally below 1000 K.

Peierls–Nabarro modelling of dislocations in diopside

The core structures of dislocations in diopside have been calculated within the Peierls model, which assumes a planar core. 1/2 dislocations can dissociate into two collinear partial dislocations. We show that [001] glide is very difficult in (010) and that a non-collinear dissociation of [001](100) (modelled within a Peierls–Nabarro–Galerkin approach) makes glide equally easy in (100) and {110}. A widely spread core structure corresponding to a low lattice friction has been found for [100](010) and [010](100) dislocations which is not supported by mechanical data and, together with TEM observations, suggests that another, probably non-planar core structure is possible for these dislocations.

Plastic deformation of wadsleyite: IV Dislocation core modelling based on the Peierls–Nabarro–Galerkin model

In this paper, we determine dislocation core structures and Peierls stresses of wadsleyite, a high-pressure mineral present in the Earth mantle. We use a Peierls–Nabarro model combined with a finite-element method in which we introduce two-dimensional generalized stacking fault energies. Several potential slip planes of wadsleyite are considered. The results show that dislocations in this mineral can exhibit complex dislocation cores with linear or non-collinear dissociation and even three-dimensional dislocation cores. The calculation of the Peierls stresses gives information on the potential activity of slip systems governing the plasticity of wadsleyite. Our study confirms experimental observations that ½〈1 1 1〉{1 0 1} is the easiest slip system in this structure at high-pressure and that [1 0 0](0 1 0) is the second easiest. Both these easily slip systems have dislocations that dissociate into collinear partial dislocations. In contrast [0 1 0] dislocations with very large Burgers vector (11.2 Å) are stabilized by complex dissociations involving four partial dislocations.

Inertial and retardation effects for dislocation interactions

A new formulation for the equation of motion of interacting dislocations is derived. From this solution it is shown that additional coupling forces, of kinetic and inertial origin, should be considered in Dislocation Dynamics (DD) simulations at high strain rates. A heuristic modification of this general equation of motion enables one to introduce retardation into inertial and elastic forces, in accordance with a progressive rearrangement of fields through wave propagation. The influence of the corresponding coupling terms and retardation effects is then illustrated in the case of the dislocation dipolar interaction and coplanar annihilation. Finally, comparison is made between the modified equation of motion and a precise numerical solution based on the Peierls–Nabarro Galerkin method. Good agreement is found between the Peierls–Nabarro Galerkin method and the equation of motion including retardation effects for a dipolar interaction. For coplanar annihilation, it is demonstrated that an unexpected mechanism, involving a complex inter-play between the core of the dislocations and kinetics energies, allows a renucleation from the completely annihilated dislocations. A description of this phenomenon that could break the most favourable reaction between dislocations is proposed.