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Modeling defects and plasticity in MgSiO3 post-perovskite: Part 2-screw and edge [100] dislocations.

Goryaeva AM, Carrez P, Cordier P - Phys Chem Miner (2015)

Bottom Line: We show that despite a small tendency to core spreading in {011}, [100] screw dislocations glide very easily (Peierls stress of 1 GPa) in (010) where only Mg-O bonds are to be sheared.Whatever the planes, (010), (001) or {011}, edge dislocations are characterized by a wider core (of the order of 2b).The layered structure of post-perovskite results in a drastic reduction in lattice friction opposed to the easiest slip systems compared to perovskite.

View Article: PubMed Central - PubMed

Affiliation: Unité Matériaux et Transformations, UMR CNRS 8207, Université de Lille1, Bat C6, 59655 Villeneuve d'Ascq Cedex, France.

ABSTRACT

In this study, we propose a full atomistic study of [100] dislocations in MgSiO3 post-perovskite based on the pairwise potential parameterized by Oganov et al. (Phys Earth Planet Inter 122:277-288, 2000) for MgSiO3 perovskite. We model screw dislocations to identify planes where they glide easier. We show that despite a small tendency to core spreading in {011}, [100] screw dislocations glide very easily (Peierls stress of 1 GPa) in (010) where only Mg-O bonds are to be sheared. Crossing the Si-layers results in a higher lattice friction as shown by the Peierls stress of [100](001): 17.5 GPa. Glide of [100] screw dislocations in {011} appears also to be highly unfavorable. Whatever the planes, (010), (001) or {011}, edge dislocations are characterized by a wider core (of the order of 2b). Contrary to screw character, they bear negligible lattice friction (0.1 GPa) for each slip system. The layered structure of post-perovskite results in a drastic reduction in lattice friction opposed to the easiest slip systems compared to perovskite.

No MeSH data available.


Related in: MedlinePlus

Geometry of atomic systems used for modeling of screw (a) and edge (b) dislocations. Simulation cells with quadrupole arrangement of screw dislocations (a) are fully periodic; screw dislocations with positive and negative Burgers vectors are shown with “+” and “−” signs, respectively. Edge dislocations are designed in atomic systems with cluster periodicity (b) such as atoms at the top and bottom, shown as shaded areas, are kept fixed; dashed line in the middle of the cell corresponds to the glide plane
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Fig1: Geometry of atomic systems used for modeling of screw (a) and edge (b) dislocations. Simulation cells with quadrupole arrangement of screw dislocations (a) are fully periodic; screw dislocations with positive and negative Burgers vectors are shown with “+” and “−” signs, respectively. Edge dislocations are designed in atomic systems with cluster periodicity (b) such as atoms at the top and bottom, shown as shaded areas, are kept fixed; dashed line in the middle of the cell corresponds to the glide plane

Mentions: In this work, screw dislocations are modeled within a quadrupole arrangement embedded in a fully periodic atomic array (Fig. 1a). Such a cell contains two dislocations with b = [100] and two dislocations with b = []. This geometry allows to cancel the long-range displacement field produced by a single dislocation (Cai 2005). It ensures that interaction of dislocations remains only at a quadrupolar level and that the net force on each core is zero due to the periodic arrangement (Bigger et al. 1992). For such atomic configuration, the energy of a dislocation core Ec per Burgers vector b unit length can be extracted from the equation (Ismail-Beigi and Arias 2000):1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E = E_{\text{c}} + E_{\text{el}} = E_{\text{c}} \left( {r_{\text{c}} } \right) + \frac{{\mu b^{3} }}{4\pi }\left[ {\ln \left( {\frac{{d_{1} }}{{r_{\text{c}} }}} \right) + A\left( {\frac{{d_{1} }}{{d_{2} }}} \right)} \right],$$\end{document}E=Ec+Eel=Ecrc+μb34πlnd1rc+Ad1d2,where E corresponds to the energy of a straight dislocation line (defined as the total energy of the atomic system once the energy of the perfect crystal is subtracted) which includes the elastic term Eel and the energy Ec(rc) of a dislocation core with radius rc (commonly taken equal to 2b) where elastic theory breaks down; μ is an anisotropic shear modulus depending on the elastic constants; d1 and d2 are equilibrium distances between the dislocations (Fig. 1a); is a coefficient which includes all dislocation pairwise interactions and which depends only on the ratio. All simulation cells are designed in such a way that this ratio remains at the same value: 1.0071. Thus, all dislocations are equidistant, and the value is constant for all supercells. Relying on these conditions, Eq. (1) is applied to evaluate the dislocation core energy using the energies E computed for ten different simulation cells, with sizes along x and z from ~145 to ~365 Å (8640–54,000 atoms). All atomic systems are as thin as a single b along y which ensures the dislocation lines to be straight and infinite by application of periodic boundary conditions. Simulation cells are oriented in such a way that b = [100] is aligned with y (Fig. 1a) and crystallographic directions [010] and [001] are aligned either with x or z depending on the glide plane of interest. The choice of cell orientations is driven by convenience to use the same atomic configurations for dislocation glide modeling as described below.Fig. 1


Modeling defects and plasticity in MgSiO3 post-perovskite: Part 2-screw and edge [100] dislocations.

Goryaeva AM, Carrez P, Cordier P - Phys Chem Miner (2015)

Geometry of atomic systems used for modeling of screw (a) and edge (b) dislocations. Simulation cells with quadrupole arrangement of screw dislocations (a) are fully periodic; screw dislocations with positive and negative Burgers vectors are shown with “+” and “−” signs, respectively. Edge dislocations are designed in atomic systems with cluster periodicity (b) such as atoms at the top and bottom, shown as shaded areas, are kept fixed; dashed line in the middle of the cell corresponds to the glide plane
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

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Fig1: Geometry of atomic systems used for modeling of screw (a) and edge (b) dislocations. Simulation cells with quadrupole arrangement of screw dislocations (a) are fully periodic; screw dislocations with positive and negative Burgers vectors are shown with “+” and “−” signs, respectively. Edge dislocations are designed in atomic systems with cluster periodicity (b) such as atoms at the top and bottom, shown as shaded areas, are kept fixed; dashed line in the middle of the cell corresponds to the glide plane
Mentions: In this work, screw dislocations are modeled within a quadrupole arrangement embedded in a fully periodic atomic array (Fig. 1a). Such a cell contains two dislocations with b = [100] and two dislocations with b = []. This geometry allows to cancel the long-range displacement field produced by a single dislocation (Cai 2005). It ensures that interaction of dislocations remains only at a quadrupolar level and that the net force on each core is zero due to the periodic arrangement (Bigger et al. 1992). For such atomic configuration, the energy of a dislocation core Ec per Burgers vector b unit length can be extracted from the equation (Ismail-Beigi and Arias 2000):1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E = E_{\text{c}} + E_{\text{el}} = E_{\text{c}} \left( {r_{\text{c}} } \right) + \frac{{\mu b^{3} }}{4\pi }\left[ {\ln \left( {\frac{{d_{1} }}{{r_{\text{c}} }}} \right) + A\left( {\frac{{d_{1} }}{{d_{2} }}} \right)} \right],$$\end{document}E=Ec+Eel=Ecrc+μb34πlnd1rc+Ad1d2,where E corresponds to the energy of a straight dislocation line (defined as the total energy of the atomic system once the energy of the perfect crystal is subtracted) which includes the elastic term Eel and the energy Ec(rc) of a dislocation core with radius rc (commonly taken equal to 2b) where elastic theory breaks down; μ is an anisotropic shear modulus depending on the elastic constants; d1 and d2 are equilibrium distances between the dislocations (Fig. 1a); is a coefficient which includes all dislocation pairwise interactions and which depends only on the ratio. All simulation cells are designed in such a way that this ratio remains at the same value: 1.0071. Thus, all dislocations are equidistant, and the value is constant for all supercells. Relying on these conditions, Eq. (1) is applied to evaluate the dislocation core energy using the energies E computed for ten different simulation cells, with sizes along x and z from ~145 to ~365 Å (8640–54,000 atoms). All atomic systems are as thin as a single b along y which ensures the dislocation lines to be straight and infinite by application of periodic boundary conditions. Simulation cells are oriented in such a way that b = [100] is aligned with y (Fig. 1a) and crystallographic directions [010] and [001] are aligned either with x or z depending on the glide plane of interest. The choice of cell orientations is driven by convenience to use the same atomic configurations for dislocation glide modeling as described below.Fig. 1

Bottom Line: We show that despite a small tendency to core spreading in {011}, [100] screw dislocations glide very easily (Peierls stress of 1 GPa) in (010) where only Mg-O bonds are to be sheared.Whatever the planes, (010), (001) or {011}, edge dislocations are characterized by a wider core (of the order of 2b).The layered structure of post-perovskite results in a drastic reduction in lattice friction opposed to the easiest slip systems compared to perovskite.

View Article: PubMed Central - PubMed

Affiliation: Unité Matériaux et Transformations, UMR CNRS 8207, Université de Lille1, Bat C6, 59655 Villeneuve d'Ascq Cedex, France.

ABSTRACT

In this study, we propose a full atomistic study of [100] dislocations in MgSiO3 post-perovskite based on the pairwise potential parameterized by Oganov et al. (Phys Earth Planet Inter 122:277-288, 2000) for MgSiO3 perovskite. We model screw dislocations to identify planes where they glide easier. We show that despite a small tendency to core spreading in {011}, [100] screw dislocations glide very easily (Peierls stress of 1 GPa) in (010) where only Mg-O bonds are to be sheared. Crossing the Si-layers results in a higher lattice friction as shown by the Peierls stress of [100](001): 17.5 GPa. Glide of [100] screw dislocations in {011} appears also to be highly unfavorable. Whatever the planes, (010), (001) or {011}, edge dislocations are characterized by a wider core (of the order of 2b). Contrary to screw character, they bear negligible lattice friction (0.1 GPa) for each slip system. The layered structure of post-perovskite results in a drastic reduction in lattice friction opposed to the easiest slip systems compared to perovskite.

No MeSH data available.


Related in: MedlinePlus