Please cite this article as: Metsue, A., Carrez, P., Mainprice, D., Cordier, P., Numerical modelling of dislocations and deformation mechanisms in CaIrO 3 and MgGeO 3 postperovskites -Comparison with MgSiO 3 post-perovskite, Physics of the Earth and Planetary Interiors (2007), doi:10.1016/j.pepi.2008 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. A c c e p t e d M a n u s c r i p t 2 Abstract:In this study, we propose a theoretical approach to test the validity of the isomechanical analogues for post-perovskite structures. Intrinsic plastic properties are evaluated for three materials exhibiting a post-perovskite phase: MgSiO 3 , MgGeO 3 and CaIrO 3 .Dislocation properties of each structure are determined using the Peierls-Nabarro model based on first principles calculations of generalised stacking fault and the plastic properties are extended to crystal preferred orientations using a visco-plastic selfconsistent method. This study provides intrinsic parameters of plastic deformation such as dislocation structures and Peierls stresses that can be directly compared between the three materials. It appears that it is very difficult to draw any simple conclusions on polycrystalline deformation simply by comparing single crystal properties. In particular, contrasting single crystal properties of MgSiO 3 and CaIrO 3 lead to similar crystal preferred orientation of the polycrystal aggregates.

SUMMARY The thermodynamic properties of (Mg0.9375Fe2+0.0625)SiO3 perovskite have been investigated at the pressure and temperature conditions of the lower mantle by first‐principles calculations where iron is incorporated in the high and low‐spin states for the first time. The electronic structure of ferrous Fe‐bearing perovskite is modelled within the internally consistent local spin density approximation with a Hubbard correction U. The thermodynamic properties are derived from the calculation of the Helmholtz free energy within the quasi‐harmonic approximation, which requires the phonon frequencies determined by direct calculations of the dynamic matrices. Incorporation of iron, irrespective of its spin states, decreases the acoustic phonon mode frequencies, but less affects high‐energy optic modes, leading to decreasing of the acoustic wave velocities in Fe‐bearing MgSiO3 perovskite, consistent with previous studies on the elasticity of this phase. This study suggests that the thermodynamic properties of silicate perovskite, such as the equation of state and isothermal bulk modulus, are not largely modified by the incorporation of 6.25 per cent of ferrous iron. Calculations of the static enthalpy of the iron‐bearing perovskite in the 0–150‐GPa‐pressure range demonstrate that low‐spin ferrous iron is unstable at the pressure conditions of the lower mantle. Finally, we clarify the perovskite‐to‐post‐perovskite phase transition boundary in an (Mg0.9375Fe0.0625)SiO3 composition. Ferrous iron is found to decrease the transition pressure between the two phases with a small binary phase loop of 3–4 GPa at the lowermost mantle conditions from 111 to 115 GPa at 2500 K and from 116 to 119 GPa at 3000 K.

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[1] Phonon dispersion relations and vibrational density of states of (Mg 0.9375 Fe 0.0625 )SiO 3 postperovskite have been determined by direct first-principles calculations of the dynamical matrix up to 150 GPa. Incorporation of iron in the postperovskite phase, irrespective of the two investigated configurations and the spin state, was found to decrease the acoustic phonon frequencies but to have a minor effect on the optic modes at high frequencies. The phonon dispersion curves exhibit negative phonon frequencies below 10 GPa when iron is incorporated in the high or low spin state and indicate unstable dynamic structures. Then, the calculated phonon frequencies of dynamically stable structures are used to determine vibrational contributions to the Helmholtz free energy within the quasi-harmonic approximation. The high temperature equation of state and several thermodynamic properties are then derived for (Mg 0.9375 Fe 0.0625 )SiO 3 postperovskite and compared with those of pure MgSiO 3 postperovskite. The results show that a low concentration of iron, irrespective of high spin or low spin, in MgSiO 3 postperovskite has a minor effect on the thermodynamic properties at pressure-temperature conditions of the lowermost part of the Earth's mantle.

Hydrogen diffusion has an important role in solute-dependent hydrogen embrittlement in metals and metallic alloys. In spite of extensive studies, the complexity of hydrogen diffusion in solids remains a phenomenon that needs to be clarified. In this paper, we investigate the anisotropy of hydrogen diffusion in pure nickel single crystals using both an experimental approach and a thermodynamic development. As a first approximation, experimental data from electrochemical permeation and thermal desorption spectroscopy are described using the classical Fick’s laws and an apparent diffusion tensor. Within a thermodynamic framework, the diffusion equation can be derived from Fick’s laws with an apparent diffusion coefficient which contains an added solute content dependent term β. This term is due to the elastic strain field associated with the insertion of solute atoms. For nickel crystals, the dependence of β on the crystallographic orientation arises from the elastic anisotropy. Additionally, our results elucidate the discrepancies between the thermodynamic model and experimental observations of the effect of the solute concentration on the diffusion process. Moreover, this highlights the importance of the impact of hydrogen on vacancy formation and the subsequent consequences on the anisotropy of the apparent diffusion coefficient.

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