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Continuous description of grain boundaries using crystal defectfields: the example of a {3 1 0}/[0 0 1] tilt boundary in MgO

Abstract : Continuum dislocation/generalized-disclination modelling of a MgO {310}/[001] tilt boundary is proposed by using an atomistic-to-continuum crossover method. Using the relaxed and un-relaxed atomic positions obtained from first-principles simulations, calculation of the displacement, distortion (strain and rotation), curvature and second order distortion fields is performed in the boundary area. The dislocation and disclination density fields are used to smoothly describe the discontinuities in the displacement and rotation fields across the boundary. In addition, a generalized-disclination density tensor field is introduced to reflect shear and stretch discontinuities across the boundary. This continuous model provides new mechanical insights into the structure of MgO grain boundary, as well as a basis for coarse-grained representations of the polycrystalline structure. 1. Introduction The Earth's lower mantle is mainly composed of silicates with perovskite structure and of ferropericlase (Mg, Fe)O. The structure of crystal defects such as grain boundaries in these compounds is of primary importance for their rheology. The structure of grain boundaries (GBs) in MgO has been studied mainly at the atomic scale, on the basis of first-principles methods and molecular dynamics (MD) simulations. For instance, a number of MgO tilt boundaries were constructed at atomistic level to investigate the effects of pressure and temperature on their structure and stability (Harris et al., 1996), the related vacancy migration (Harris et al., 1997), the pressure-induced structural transition (Harris et al., 1999), and the impurity-induced structural transformation (Saito et al., 2014; Yan et al., 1998). The structure and stability of oxygen vacancies on the terraces, sub-surface and low-coordinated surface sites of MgO were studied by performing ab initio Hartree-Fock cluster model calculations (Pacchioni and Pescarmona, 1998). The electronic properties of oxygen vacancies, proton impurities, and their stable combinations at a MgO boundary were calculated by employing the embedded cluster method (McKenna and Shluger, 2009). The atomic and electronic structures of three {n10}/[001] MgO tilt GBs (n=2, 3, and 4) were explored as a function of pressure from first principles within the density functional theory (Verma and Karki, 2010). Atomistic studies are useful to provide information on fundamental material properties at GBs such as defect migration, diffusion and stability of vacancies. However, the size of the systems investigated and the time scale over which simulations can be conducted are limited for computational reasons. Further, they do not give direct insight into the role played by GBs in the dissipative mechanical behaviour of the material during plastic yielding (mediated by shear, sliding or migration), because describing the latter essentially needs the stress, strain and strain-rate fields, and their relationships in the body, particularly in the GB area. Continuous modeling of the structure of GBs using smooth distortion (strain and rotation) fields at inter-atomic scale is attractive because it provides a basis for a mechanical description of the latter. In such a framework, it is understood that work density is defined and stress transmitted by matter at this scale (Nielsen and Martin, 1985). The attractiveness of such continuous modeling of the GB structure further derives from its ability to serve as a basis for coarse-grained representations of polycrystalline media (Fressengeas et al., 2014) to be used in more macroscopic engineering studies. Within the recent elasto-plastic framework proposed by Fressengeas et al. (2011), it was found that dislocation/disclination density fields were appropriate objects for a consistent continuous description of the atomic structure of GBs (Cordier et al., 2014; Fressengeas et al., 2014). Based on this work, an atomistic-to-continuum crossover method has been proposed to construct the dislocation/disclination density fields and the associated elastic distortion (strain and rotation), curvature and second-distortion fields in the GB area, starting from the relaxed and unrelaxed atomic configurations of GBs (Sun et al., 2016). In the present paper, we apply this method to build a continuous model of a symmetric grain boundary in MgO, the atomistic structure of which is calculated from first-principles simulations. The strong variations of the displacement, strain and rotation tensor fields across GBs are discussed in details, and crystal defect density fields smoothly describing the structure of the GB are introduced accordingly. The outline of the paper is as follows. In Section 2, atomic scale modelling of a {310}/[001] GB of MgO, and details of the calculation techniques bridging atomic and continuum representations are briefly recalled. In Section 3, the continuous displacement, distortion, curvature and second-order distortion fields of the GB are calculated from discrete atomic positions. In Section 4, the strong variations of the displacement and rotation fields in the GB area are discussed, and dislocation and disclination density fields are introduced. In Section 5, generalized disclinations are presented to further describe the strong variations in the strain field. Discussion and conclusions follow in Section 6.
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Xiao-Yu Sun, Patrick Cordier, Vincent Taupin, Claude Fressengeas, Bijaya Karki. Continuous description of grain boundaries using crystal defectfields: the example of a {3 1 0}/[0 0 1] tilt boundary in MgO. European Journal of Mineralogy, Copernicus, 2017, 29 (2), pp.155-165. ⟨10.1127/ejm/2017/0029-2609⟩. ⟨hal-02938037⟩



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