Elastic grain-boundary responses in copper and aluminium

We examined the grain boundary energy (GBE) and grain boundary excess free volume (BFV) by applying the first-principles calculation for six [110] symmetric tilt grain boundaries in aluminum to clarify the origin of GBE. The GBE increased linearly as BFV increased. The elastic energy associated with BFV, namely the grain boundary elastic energy, was estimated as a function of BFV and the shear modulus. The grain boundary elastic energies were close in value to the GBEs. The charge density distributions indicated that the bonding in the grain boundary region is significantly different from the bonding in the bulk. The grain boundary elastic energies were 15–32% higher than the GBEs. This overestimation of the grain boundary elastic energy is caused by the characteristics of the electronic bonding at the grain boundary, which is different from bonding in the bulk. We have concluded that GBE results mainly from the grain boundary elastic energy.

The asymptotic free energy of planar walls and boundaries is analyzed for scalar and vector spin systems. Under the hypothesis of correlation decay, various alternative definitions are found to be equivalent in the thermodynamic limit and independent of the “associated” walls. Furthermore, a torus, or box having periodic boundary conditions, is shown to have no boundary or surface free energy. For vector spin systems withn-component spins, existence of the thermodynamic limit is shown forn=2 and “positive” interactions.

A 3D phase-field model for grain growth combined with a grain boundary (GB) energy database is proposed. The phase-field model is applied to a grain growth simulation of polycrystalline bcc Fe to investigate the effect of anisotropic GB energy on the microstructural evolution and its kinetics. It is found that the anisotropy in the GB energy results in different microstructures and slower kinetics, especially when the portion of low-angle, low-energy GBs is large. We discuss the applicability of the proposed phase-field simulation technique, based on the GB or interfacial energy database to simulations for microstructural evolution, including abnormal grain growth, phase transformations, etc., in a wider range of polycrystalline materials.

The energy of symmetric and asymmetrical tilt grain boundaries in Cu is calculated by the method of computer modeling for a unified model. The misorientation axis of the neighboring grains corresponds to the [100], [110], and [111] crystallographic directions. It is demonstrated that the dependences of the energy on the misorientation angle of the symmetric boundaries have similar characters for different misorientation axes, and the energy of the majority of special boundaries does not differ from that of general boundaries. The shape of energy surfaces for the asymmetrical grain boundaries depends on the crystal misorientation axis. The energy of the symmetric boundaries is smaller than that of the asymmetrical boundaries.

Grain growth prediction with inclination dependence of 〈1 1 0〉 tilt grain boundary using multi-phase-field model with penalty for multiple junctions

It is proposed that annealing twins form during grain growth as a result of a decrease in the interfacial free energy of grain boundaries that would not be achieved in the absence of twinning. Experiments designed to permit detection of the changes in grain boundary free energy accompanying the formation of twins give results in agreement with this concept. The abundance of twins found in annealed copper depends on the texture in a manner that is consistent with the theory.

The mechanism of serrated grain boundary formation and its effect on liquation behaviour have been studied in a wrought nickel-based superalloy – Alloy 263. It was newly discovered that grain boundaries are considerably serrated in the absence of γ ′-phase or M23C6 at the grain boundaries. An electron energy-loss spectroscopy study suggests that serration is triggered by the discontinuous segregation of C and Cr atoms at grain boundaries for the purpose of relieving the excessive elastic strain energy. The grain boundaries serrate to have specific segments approaching one {111} low-index plane at a boundary so that the interfacial free energy of the grain boundary can be decreased, which may be responsible for the driving force of the serration. The serrated grain boundaries effectively suppress grain coarsening and are highly resistant to liquation due to their lower wettability resulting from a lower interfacial energy of the grain boundary.

A novel thermodynamic integration (TI) scheme is presented that allows computing the free energy of grain boundaries (GBs) in crystals from atomistic computer simulation. Unlike previous approaches, the method can be applied at arbitrary temperatures and allows for a systematic extrapolation to the thermodynamic limit. It is applied to a $\Sigma11$ GB in a face centered cubic (FCC) Lennard-Jones crystal. At a constant density, the GB free energy shows a non-monotonic temperature dependence with a maximum at about half the melting temperature and the GB changes from a rigid to a rough interface with distinct finite size scaling above this temperature.

Temperature dependence of grain boundary free energy and elastic constants

The efficient and reliable computation of relative free energy changes for alchemical mutation is very important in biomolecular simulations. In this study we examine the utility of computing alchemical free energy changes using overlap perturbation techniques. These techniques include both the overlap histogram method and the overlap sampling method (a fully optimized version of the overlap sampling technique is equivalent to Bennett's method), and commonly combine sets of perturbations from both alchemical states of interest to improve a free energy calculation. In addition, we propose new variants, present generalized formulas for overlap perturbation techniques and demonstrate differences from the prevailing direct averaging approach used in alchemical free energy calculations. These overlap perturbation methods can be applied to either equilibrium or non-equilibrium free energy simulations. The alchemical transformation of an adenosine molecule in aqueous solution is used as an example for evaluating these techniques. The calculations show that the methods are capable of producing excellent free energy estimates for an extended range of perturbation magnitudes. We suggest that these overlap perturbation methods should be more widely used for the computation of alchemical free energy changes in biomolecular simulations. † woolf@groucho.med.jhmi.edu

One of the most important aims of grain boundary modeling is to predict the evolution of a large collection of grains in phenomena such as abnormal grain growth, coupled grain boundary motion, and recrystallization that occur under extreme thermomechanical loads. A unified framework to study the coevolution of grain boundaries with bulk plasticity has recently been developed by Admal et al. (2018), which is based on modeling grain boundaries as continuum dislocations governed by an energy based on the Kobayashi--Warren--Carter (KWC) model (Kobayashi et al., 1998, 2000). While the resulting unified model demonstrates coupled grain boundary motion and polygonization (seen in recrystallization), it is restricted to grain boundary energies of the Read--Shockley type, which applies only to small misorientation angles. In addition, the implementation of the unified model using finite elements inherits the computational challenges of the KWC model that originate from the singular diffusive nature of its governing equations. The main goal of this study is to generalize the KWC functional to grain boundary energies beyond the Read--Shockley-type that respect the bicrystallography of grain boundaries. The computational challenges of the KWC model are addressed by developing a thresholding method that relies on a primal dual algorithm and the fast marching method, resulting in an O(NlogN) algorithm, where N is the number of grid points. We validate the model by demonstrating the Herring angle relation, followed by a study of the grain microstructure evolution in a two-dimensional face-centered cubic copper polycrystal with crystal symmetry-invariant grain boundary energy data obtained from the lattice matching method of Runnels et al. (2016a,b).

Dislocation interactions in equilibrated boundaries

Predicting structure and energy of dislocations and grain boundaries

This investigation examines the effect of hydrogen precharging upon the fracture mode of pure nickel at 77 K. Specific attention is given to the diffusion coefficient of hydrogen along grain boundaries,D g , the critical hydrogen concentration to cause intergranular fracture, C g * , and the binding energy of grain boundaries with hydrogen,E b . Both scanning electron microscope (SEM) observations and a newly developed grain boundary diffusion model indicate that the fracture mode changes from transgranular (TG) to intergranular (IG) when the hydrogen concentration in grain boundaries reaches a critical value, in the range of 6.5 to 9.8 at. pct. The experimental results further show that the observed increment of IG cracking depth with the precharging time could be accounted for by lattice diffusion alone, thus implying that hydrogen transport in this material is not enhanced by grain boundaries. Finally, the binding energy of grain boundaries with hydrogen is found to be 11.3 to 12.3 kJ/mol.

Universal function for grain boundary energies in bcc metals