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Register a new userAnalytical Energy Formalism and Kinetic Effects of Grain Boundary: A Case Study of Graphene
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Grain boundaries (GBs), an important constituent of polycrystalline materials, have a wide range of manifestion and significantly affect the properties of materials. Fully understanding the effects of GBs is stalemated due to lack of complete knowledge of their structures and energetics. Here, for the first time, by taking graphene as an example, we propose an analytical energy functional of GBs in angle space. We find that an arbitrary GB can be characterized by a geometric combination of symmetric GBs that follow the principle of uniform distribution of their dislocation cores in straight lines. Furthermore, we determine the elusive kinetic effects on GBs from the difference between experimental statistics and energy-dependent thermodynamic effects. This study not only presents an analytical energy functional of GBs which could also be extended to other two-dimensional materials, but also sheds light on understanding the kinetic effects of GBs in material synthesizing processes.
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Mg grain boundary (GB) segregation and GB diffusion can impact the processing and properties of Al-Mg alloys. Yet, Mg GB diffusion in Al has not been measured experimentally or predicted by simulations. We apply atomistic computer simulations to predict the amount and the free energy of Mg GB segregation, and the impact of segregation on GB diffusion of both alloy components. At low temperatures, Mg atoms segregated to a tilt GB form clusters with highly anisotropic shapes. Mg diffuses in Al GBs slower than Al itself, and both components diffuse slowly in comparison with Al GB self-diffusion. Thus, Mg segregation significantly reduces the rate of mass transport along GBs in Al-Mg alloys. The reduced atomic mobility can be responsible for the improved stability of the microstructure at elevated temperatures.
Most research on nanocrystalline alloys has been focused on planned doping of metals with other metallic elements, but nonmetallic impurities are also prevalent in the real world. In this work, we report on the combined effects of metallic dopants and nonmetallic impurities on grain boundary energy and strength using first-principles calculations, with a $Sigma$5 (310) grain boundary in Cu chosen as a model system. We find a clear correlation between the grain boundary energy and the change in excess free volume of doped grain boundaries. A combination of a larger substitutional dopant and an interstitial impurity can fill the excess free volume more efficiently and further reduce the grain boundary energy. We also find that the strengthening effects of dopants and impurities are dominated by the electronic interactions between the host Cu atoms and the two types of dopant elements. For example, the significant competing effects of metal dopants such as Zr, Nb, and Mo with impurities on the grain boundary strength are uncovered from the density of states of the d electrons. As a whole, this work deepens the fields understanding of the interaction between metallic dopants and nonmetallic impurities on grain boundary properties, providing a guide for improving the thermal stability of materials while avoiding embrittling effects.
It was recently reported that segregation of Zr to grain boundaries (GB) in nanocrystalline Cu can lead to the formation of disordered intergranular films [1,2]. In this study we employ atomistic computer simulations to study how the formation of these films affects the dislocation nucleation from the GBs. We found that full disorder of the grain boundary structure leads to the suppression of dislocation emission and significant increase of the yield stress. Depending on the solute concentration and heat-treatment, however, a partial disorder may also occur and this aids dislocation nucleation rather than suppressing it, resulting in elimination of the strengthening effect.
We have developed a method that can analyze large random grain boundary (GB) models with the accuracy of density functional theory (DFT) calculations using active learning. It is assumed that the atomic energy is represented by the linear regression of the atomic structural descriptor. The atomic energy is obtained through DFT calculations using a small cell extracted from a huge GB model, called replica DFT atomic energy. The uncertainty reduction (UR) approach in active learning is used to efficiently collect the training data for the atomic energy. In this approach, atomic energy is not required to search for candidate points; therefore, sequential DFT calculations are not required. This approach is suitable for massively parallel computers that can execute a large number of jobs simultaneously. In this study, we demonstrate the prediction of the atomic energy of a Fe random GB model containing one million atoms using the UR approach and show that the prediction error decreases more rapidly compared with random sampling. We conclude that the UR approach with replica DFT atomic energy is useful for modeling huge GBs and will be essential for modeling other structural defects.
A detailed theoretical and numerical investigation of the infinitesimal single-crystal gradient plasticity and grain-boundary theory of Gurtin (2008) A theory of grain boundaries that accounts automatically for grain misorientation and grain-boundary orientation. Journal of the Mechanics and Physics of Solids 56 (2), 640-662, is performed. The governing equations and flow laws are recast in variational form. The associated incremental problem is formulated in minimization form and provides the basis for the subsequent finite element formulation. Various choices of the kinematic measure used to characterize the ability of the grain boundary to impede the flow of dislocations are compared. An alternative measure is also suggested. A series of three-dimensional numerical examples serve to elucidate the theory.
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