Computational Characterization of the Structure, Energy, Strengths, and Fracture Resistances of Symmetric Tilt Grain Boundaries in Ice

Using an interatomic potential that can capture the tetrahedral configuration of water molecules (H₂O) in ice without the need to explicitly track the motion of the O and H atoms, coarse-grained (CG) atomistic simulations are performed here to characterize the structures, energy, cohesive strengths, and fracture resistance of the grain boundaries (GBs) in polycrystalline ice resulting from water freezing. Taking the symmetric tilt grain boundaries (STGBs) with a tilting axis of ⟨0001⟩ as an example, several main findings from our simulations are (i) the GB energy, <i>E</i>_GB, exhibits a strong dependence on the GB misorientation angle, θ. The classical Read-Shockley model only predicts the <i>E</i>_GB - θ relation reasonably well when θ < 20° or θ > 45° but fails when 20° < θ < 45°; (ii) two "valleys" appear in the <i>E</i>_GB-θ landscape. One occurs at θ = 22° for Σ14(2̅31̅0) GB, and the other is at θ = 32° for Σ26(3̅41̅0) GB. These two GBs might be the most common in polycrystalline ice; (iii) all the STGB structures under consideration here are found to be a collection of edge dislocations with a Burgers vector of <b>b</b> = 1/3⟨112̅0⟩. The core structure of this edge dislocation is composed of a pentagon and a heptagon atomic ring. The separation and orientation of the structure units (SUs) at the GB exhibit a strong dependence on θ; (iv) the length of an atomic bond within the SUs, rather than <i>E</i>_GB and θ which are often used in the literature, is identified as one controlling parameter that dictates the intrinsic GB cohesive strength; (v) characterization of the fracture resistance of the GB containing an initial crack is beyond the reach of nanoscale atomistic simulations but is feasible in concurrent atomistic-continuum (CAC) simulations that can simultaneously retain the atomic GB structure together with the long-range stress field within one model. The above findings provide researchers with a stepping stone to understand the complex microstructure of polycrystalline ice and its response to external forces from the bottom up. Such knowledge may be consolidated into constitutive rules and then transferred into the higher length scale models, such as cohesive zone finite element models (CZFEMs), for predicting how polycrystalline ice fractures at laboratory and even geophysical length scales.