An analytical model of interfacial energy based on a lattice-matching interatomic energy

Abstract

We develop an explicit model for the interfacial energy in crystals which emphasizes the geometric origin of the cusps in the energy profile. We start by formulating a general class of interatomic energies that are reference-configuration-free but explicitly incorporate the lattice geometry of the ground state. In particular, away from the interface the energy is minimized by a perfect lattice. We build these attributes into the energy by locally matching, as best as possible, a perfect lattice to the atomic positions and then quantifying the local energy in terms of the inevitable remaining mismatch, hence the term lattice-matching used to describe the resulting interatomic energy. Based on this general energy, we formulate a simpler rigid-lattice model in which the atomic positions on both sides of the interface coincide with perfect, but misoriented, lattices. In addition, we restrict the lattice-matching operation to a binary choice between the perfect lattices on both sides of the interface. Finally, we prove an L 2 -bound on the interatomic energy and use that bound as a basis for comparison with experiment. We specifically consider symmetric tilt grain boundaries (STGB), symmetric twist grain boundaries (STwGB) and asymmetric twist grain boundaries (ATwGB) in face-centered cubic (FCC) and body-centered cubic (BCC) crystals. Two or more materials are considered for each choice of crystal structure and boundary class, with the choice of materials conditioned by the availability of molecular dynamics data. Despite the approximations made, we find very good overall agreement between the predicted interfacial energy structure and that predicted by molecular dynamics. In particular, the positions of the cusps are predicted correctly, and therefore, although surface reconstruction and faceting are not included in the model, the dominant orientations of the facets are correctly predicted by our geometrical model.

Multiphase field modeling of grain boundary migration mediated by emergent disconnections

“…Over the past several decades, a multitude of GB energy calculation methods have been proposed ranging from the analytic expressions of Read and Shockley [58] to large-scale molecular statics (MS) simulations [24]. The lattice-matching model for GB energy is an analytic model that uses optimal transportation theory and lattice geometry to estimate boundary energy [59]. Lattice matching is particularly useful for bicrystal configurations in which it is difficult to obtain a periodic unit cell for MS simulations, which is often the case when calculating orientation-dependent GB energy for high Σ boundaries.…”

Intragranular nucleation of tetrahedral precipitates and discontinuous precipitation in Cu-5wt%Ag

“…The barrier for this process can be calculated using the model developed by Clemm and Fisher [27]. In their approach, they described the work of formation of a heterogeneous precipitate considering the balance between the former grain boundary interface α/α' AA  is given by the value of Cu-Cu grain boundary energy (0.8 J.m -2 [28]).…”

A three-dimensional misorientation axis- and inclination-dependent Kobayashi–Warren–Carter grain boundary model

“…Detailed constitutive information in the form of five-dimensional (5D) space of misorientation and inclination (i.e. alignment) dependent grain boundary energies has recently been produced by a number of computational studies ( Bulatov et al, 2013;Kim et al, 2014;Olmsted et al, 2009;Runnels et al, 2016;Runnels, 2016 ). This points to the need to extend the KWC framework to account for this 5D space in a manner consistent with the key features of the model, i.e.…”