Philippe Carrez

Implications for plastic flow in the deep mantle from modelling dislocations in MgSiO3 minerals.

The dynamics of the Earth’s interior is largely controlled by mantle convection, which transports radiogenic and primordial heat towards the surface. Slow stirring of the deep mantle is achieved in the solid state through high-temperature creep of rocks, which are dominated by the mineral MgSiO3 perovskite. Transformation of MgSiO3 to a ‘post-perovskite’ phase may explain the peculiarities of the lowermost mantle, such as the observed seismic anisotropy, but the mechanical properties of these mineralogical phases are largely unknown. Plastic flow of solids involves the motion of a large number of crystal defects, named dislocations. A quantitative description of flow in the Earth’s mantle requires information about dislocations in high-pressure minerals and their behaviour under stress. This property is currently out of reach of direct atomistic simulations using either empirical interatomic potentials or ab initio calculations. Here we report an alternative to direct atomistic simulations based on the framework of the Peierls–Nabarro model. Dislocation core models are proposed for MgSiO3 perovskite (at 100 GPa) and post-perovskite (at 120 GPa). We show that in perovskite, plastic deformation is strongly influenced by the orthorhombic distortions of the unit cell. In silicate post-perovskite, large dislocations are relaxed through core dissociation, with implications for the mechanical properties and seismic anisotropy of the lowermost mantle.

Modelling the rheology of MgO under Earth/'s mantle pressure, temperature and strain rates

Plate tectonics, which shapes the surface of Earth, is the result of solid-state convection in Earth’s mantle over billions of years. Simply driven by buoyancy forces, mantle convection is complicated by the nature of the convecting materials, which are not fluids but polycrystalline rocks. Crystalline materials can flow as the result of the motion of defects—point defects, dislocations, grain boundaries and so on. Reproducing in the laboratory the extreme deformation conditions of the mantle is extremely challenging. In particular, experimental strain rates are at least six orders of magnitude larger than in nature. Here we show that the rheology of MgO at the pressure, temperature and strain rates of the mantle is accessible by multiscale numerical modelling starting from first principles and with no adjustable parameters. Our results demonstrate that extremely low strain rates counteract the influence of pressure. In the mantle, MgO deforms in the athermal regime and this leads to a very weak phase. It is only in the lowermost lower mantle that the pressure effect could dominate and that, under the influence of lattice friction, a viscosity of the order of 1021–1022 pascal seconds can be defined for MgO.

Peierls–Nabarro modelling of dislocations in MgO from ambient pressure to 100 GPa

We present in this study modelling of dislocation core properties in MgO as a function of pressure from ambient conditions to 100 GPa. The calculations are based on the Peierls–Nabarro model and we use first-principles calculations of the generalized stacking fault as input parameters. Our results confirm that {1 1 0} is the dominant slip system in MgO at ambient pressure and is easier than {1 0 0} as the pressure increases. Nevertheless, the {1 1 0} slip hardens with increasing pressure leading to a decrease in the difference in the Peierls stresses between {1 1 0} and {1 0 0}.

Slip systems and plastic shear anisotropy in Mg2SiO4ringwoodite insights from numerical modelling

Novel thixotropic alkyd resins are obtained by reacting at a temperature of between about 120 DEG C. to about 150 DEG C. for at least one hour (a) at least one alkyd resin and (b) a polyamide comprising the reaction product of: (i) a polycarboxylic acid; (ii) an active hydrogen compound having the formula Xm-R-Yn, wherein R represents a group containing from 2 to 12 carbon atoms, X and Y are independently selected from primary amino, secondary amino and hydroxy, and m and n are each at least 1 and the sum of (m+n) is at least 2; and (iii) a capping agent comprised of an unsaturated and/or hydroxy functional monocarboxylic acid having from 8 to 22 carbon atom. The thixotropic alkyd resins of the present invention are particularly useful in preparing thixotropic paint and coating compositions having superior leveling and sag resistance.

Application of the Peierls-Nabarro model to dislocations in forsterite

We present a numerical model of dislocation cores in Mg 2 SiO 4 forsterite based on the Peierls-Nabarro model and using generalised stacking faults as an input. The generalised stacking faults have been calculated from ab initio density-functional theory using VASP. Core profiles, atomic models and Peierls stresses are proposed for dislocations from the following slip systems: [100](010), [100](001), [100]{021}, [001](010), [001](100) and [001]{110}. Calculations have been performed at 0 and 10 GPa, to investigate the influence of pressure. We show that [100] dislocations have narrow cores when [001] dislocations tend to spread into (100) and {110} planes. A strong softening effect is found with pressure on the [001](010) slip system. Our study emphasizes the influence of lattice friction on plastic deformation of forsterite with, beyond Peierls stresses, possible effects related to non-planar core structures.

Modelling the effect of pressure on the critical shear stress of MgO single crystals

A hierarchical multi-scale model was used to study the effect of high pressure on the critical shear stresses of MgO. The two main slip systems, ½⟨110⟩{110} and ½⟨110⟩{100}, were considered. Based on a generalised Peierls–Nabarro model, it is shown that the core structure of ½⟨110⟩ screw dislocations is strongly sensitive to pressure. Mostly planar and spread in {110} at ambient pressure, the core of screw dislocations tends to spread in {100} with increasing pressure. Subsequently, an inversion of the easiest slip systems is observed between 30 and 60 GPa. At high pressure, the plasticity of MgO single crystals is expected to be controlled by ½⟨110⟩{100} slip systems, except at high temperature where both slip systems become active. Pressure is also found to increase the critical resolved shear stresses and to shift the athermal temperature toward higher temperatures. Under high pressure, MgO is thus characterised by a significant lattice friction on both slip systems.

Atomic scale models of dislocation cores in minerals: progress and prospects

Abstract Recent advances in computer simulation at the atomic scale have made it possible to probe the structure and behaviour of the cores of dislocations in minerals. Such simulation offers the possibility to understand and predict the dislocation-mediated properties of minerals such as mechanisms of plastic deformation, pipe diffusion and crystal growth. In this review the three major methods available for the simulation of dislocation cores are described and compared. The methods are: (1) cluster-based models which combine continuum elastic theory of the extended crystal with an atomistic model of the core; (2) dipole models which seek to cancel the long-range elastic displacement caused by the dislocation by arranging for the simulation to contain several dislocations with zero net Burgers vector, thus allowing a fully periodic super-cell calculation; and (3) the Peierls-Nabarro approach which attempts to recast the problem so that it can be solved using only continuum-based methods, but parameterizes the model using results from atomic-scale calculations. The strengths of these methods are compared and illustrated by some of the recent studies of dislocations in mantle silicate minerals. Some of the unresolved problems in the field are discussed.

Electron-irradiation-induced phase transformation and fractional volatilization in (Mg, Fe)2SiO4 olivine thin films

Abstract We have performed a series of electron irradiation experiments with 300 keV electrons on thin (Mg1.8Fe0.2SiO4) olivine samples in situ in a transmission electron microscope. The irradiation-induced modifications occur in two distinct stages: firstly, stage 1 is the breakdown of olivine into small MgO crystallites and amorphous SiO2-rich phase; secondly, stage 2 is the important O loss that leads to the reduction of SiO2. The phase separation requires an electron fluence of approximately 3 × 1020 e− cm−2. This bulk dissociation process does not imply elemental diffusion over large distances. A moderate stoichiometric loss of MgO also occurs during this first stage. In stage 2, bulk diffusion of chemical species is evidenced from the inside to the outside of the irradiated area and atoms, mostly O, are desorbed from the surface, leading to a marked change in the composition. Rates of elemental loss follow first-order kinetic exponential laws, with exponential factor directly proportional to the electron fluence and inversely proportional to the sample thickness.

Effect of cation ordering and pressure on spinel elasticity by ab initio simulation

Abstract We present here a first principle computational study of the effect of cation disorder on the elasticity of spinel. Our calculated elastic moduli and structural parameters are comparable with reported experimental and theoretical results. We find that bulk modulus for MgAl2O4 spinel does not soften at pressure as high as 27 GPa, while shear modulus cS [½(c11 - c12)] decreases with pressure. Disorder increases both the bulk modulus and shear modulus in aluminate spinel, but decreases both for the silicate spinel. The elastic properties of ringwoodite are significantly affected by Si-Mg disorder; a 10% disorder decreases the seismic velocities by 3.5%. Thus, a small amount of disorder will significantly affect seismic observations.

Dislocation modeling in calcium silicate perovskite based on the Peierls-Nabarro model

Abstract In this study, we propose a study of dislocations and plasticity in CaSiO3 perovskite based on the Peierls-Nabarro modeling using the generalized stacking fault (GSF) results as a starting model. The GSF are determined from first-principle calculations using the VASP code. The dislocation properties such as planar core spreading and Peierls stresses are determined for the four possible slip systems: 〈110〉 {11̅0}, 〈100〉 {011}, 〈110〉 {001}, and 〈100〉 {001} and at 0, 30, and 100 GPa. We find that 〈110〉 {11̅0} is the easiest slip system, but more surprisingly, we show that it bears no Peierls friction, even at the higher pressure. The reasons lie in the ability of these dislocations to split into partial dislocations and in the nature of the stacking fault associated with it.