Concurrent atomistic and continuum simulation of bi-crystal strontium titanate with tilt grain boundary

In this paper, we present the development of a concurrent atomistic–continuum (CAC) methodology for simulation of the grain boundary (GB) structures and their interaction with other defects in ionic materials. Simulation results show that the CAC simulation allows a smooth passage of cracks through the atomistic–continuum interface without the need for additional constitutive rules or special numerical treatment; both the atomic-scale structures and the energies of the four different [001] tilt GBs in bi-crystal strontium titanate obtained by CAC compare well with those obtained by existing experiments and density function theory calculations. Although 98.4% of the degrees of freedom of the simulated atomistic system have been eliminated in a coarsely meshed finite-element region, the CAC results, including the stress–strain responses, the GB–crack interaction mechanisms and the effect of the interaction on the fracture strength, are comparable with that of all-atom molecular dynamics simulation results. In addition, CAC simulation results show that the GB–crack interaction has a significant effect on the fracture behaviour of bi-crystal strontium titanate; not only the misorientation angle but also the atomic-level details of the GB structure influence the effect of the GB on impeding crack propagation.

[1]  J W Martin,et al.  Many-body forces in solids and the Brugger elastic constants. II. Inner elastic constants , 1975 .

[2]  H. Ohta.  Thermoelectrics based on strontium titanate , 2007 .

[3]  K. Dayal,et al.  Atomistic-to-continuum multiscale modeling with long-range electrostatic interactions in ionic solids , 2013, 1310.2500.

[4]  Y. Ikuhara,et al.  Defect energetics in SrTiO3 symmetric tilt grain boundaries , 2011 .

[5]  David L. McDowell,et al.  Coarse-grained atomistic simulation of dislocations , 2011 .

[6]  J. Kirkwood,et al.  The Statistical Mechanical Theory of Transport Processes. IV. The Equations of Hydrodynamics , 1950 .

[7]  J. D. Gezelter,et al.  Is the Ewald summation still necessary? Pairwise alternatives to the accepted standard for long-range electrostatics. , 2006, The Journal of chemical physics.

[8]  David L. McDowell,et al.  Assessment of atomistic coarse-graining methods , 2011 .

[9]  Steve Plimpton,et al.  Fast parallel algorithms for short-range molecular dynamics , 1993 .

[10]  C. Iwamoto,et al.  In situ observation of crack propagation in magnesium oxide ceramics , 2004 .

[11]  R. Ramesh,et al.  Dielectric properties in heteroepitaxial Ba0.6Sr0.4TiO3 thin films: Effect of internal stresses and dislocation-type defects , 2000 .

[12]  Youping Chen,et al.  Atomistic formulation of a multiscale field theory for nano/micro solids , 2005 .

[13]  F. Ernst,et al.  Atomistic structure of Σ = 3, (111) grain boundaries in strontium titanate , 1998 .

[14]  K. Marquardt,et al.  Atomic structures and energies of grain boundaries in Mg2SiO4 forsterite from atomistic modeling , 2012, Physics and Chemistry of Minerals.

[15]  R. Hardy,et al.  Formulas for determining local properties in molecular‐dynamics simulations: Shock waves , 1982 .

[16]  J. Hirth.  The influence of grain boundaries on mechanical properties , 1972 .

[17]  William A. Curtin,et al.  Multiscale modelling of dislocation/grain boundary interactions. II. Screw dislocations impinging on tilt boundaries in Al , 2007 .

[18]  David L. McDowell,et al.  Coarse-Grained Atomistic Simulations of Dislocations in Al Ni and Cu Crystals. , 2012 .

[19]  M. Mrovec,et al.  Theoretical investigation of {110} generalized stacking faults and their relation to dislocation behavior in perovskite oxides , 2010 .

[20]  J. Kirkwood.  The Statistical Mechanical Theory of Transport Processes I. General Theory , 1946 .

[21]  Youping Chen.  Local stress and heat flux in atomistic systems involving three-body forces. , 2006, The Journal of chemical physics.

[22]  D Mawson,et al.  Shock waves. , 1985, Nursing times.

[23]  E. B. Tadmor,et al.  Quasicontinuum models of interfacial structure and deformation , 1998 .

[24]  Michael Ortiz,et al.  Nanoindentation and incipient plasticity , 1999 .

[25]  Youping Chen,et al.  Coarse-graining atomistic dynamics of brittle fracture by finite element method , 2010 .

[26]  S. Phillpot,et al.  Exact method for the simulation of Coulombic systems by spherically truncated, pairwise r−1 summation , 1999 .

[27]  Noam Bernstein,et al.  Mixed finite element and atomistic formulation for complex crystals , 1999 .

[28]  Ellad B. Tadmor,et al.  Nucleation of dislocations beneath a plane strain indenter , 2000 .

[29]  R. Bradt,et al.  Single crystal cleavage of brittle materials , 1994 .

[30]  Horst Hahn,et al.  Interactions between non-screw lattice dislocations and coherent twin boundaries in face-centered cubic metals , 2008 .

[31]  Y. Ikuhara,et al.  Atomic structure, electronic structure, and defect energetics in [001](310)Σ5 grain boundaries of SrTiO3 and BaTiO3 , 2008 .

[32]  Y. Mishin,et al.  Atomistic modeling of interfaces and their impact on microstructure and properties , 2010 .

[33]  P. Gumbsch,et al.  Atomistic simulations of interactions between the 1 / 2⟨111⟩ edge dislocation and symmetric tilt grain boundaries in tungsten , 2008 .

[34]  Shengfeng Yang,et al.  Concurrent atomistic and continuum simulation of strontium titanate , 2013 .

[35]  N. Marks,et al.  Defects and threshold displacement energies in SrTiO3 perovskite using atomistic computer simulations , 2007 .

[36]  William A. Curtin,et al.  Multiscale modeling of dislocation/grain-boundary interactions: III. 60° dislocations impinging on Σ3, Σ9 and Σ11 tilt boundaries in Al , 2011 .

[37]  Robert E. Rudd,et al.  Coarse-grained molecular dynamics: Nonlinear finite elements and finite temperature , 2005 .

[38]  D. McDowell,et al.  Atomistic Modeling of Grain Boundaries and Dislocation Processes in Metallic Polycrystalline Materials , 2009 .

[39]  M. Mrovec,et al.  Atomistic simulation study of 〈1 1 0〉 dislocations in strontium titanate , 2012 .

[40]  William A. Curtin,et al.  Multiscale modelling of dislocation/grain-boundary interactions: I. Edge dislocations impinging on Σ11 (1 1 3) tilt boundary in Al , 2006 .

[41]  Youping Chen,et al.  Reformulation of microscopic balance equations for multiscale materials modeling. , 2009, The Journal of chemical physics.

[42]  A. Shluger,et al.  First-principles calculations of defects near a grain boundary in MgO , 2009 .

[43]  J W Martin,et al.  Many-body forces in metals and the Brugger elastic constants , 1975 .

[44]  Christian Elsässer,et al.  Interatomic potentials for strontium titanate: An assessment of their transferability and comparison with density functional theory , 2008 .

[45]  U. Gösele,et al.  Impact of misfit dislocations on the polarization instability of epitaxial nanostructured ferroelectric perovskites , 2004, Nature materials.

[46]  N. Marks,et al.  Developing pair potentials for simulating radiation damage in complex oxides , 2005 .