Grain Boundary Formation Energy Research Articles

A tungsten deep neural-network potential for simulating mechanical property degradation under fusion service environment

Tungsten is a promising candidate material in fusion energy facilities. Molecular dynamics (MD) simulations reveal the atomistic scale mechanisms, so they are crucial for the understanding of the macroscopic property deterioration of tungsten under harsh and complex service environments. The interatomic potential used in the MD simulations is required to accurately describe a wide spectrum of relevant defect properties, which is by far challenging to the existing interatomic potentials. In this paper, we propose a new three-body embedding descriptor and hybridize it into the deep-potential (DP) framework, an end-to-end deep learning interatomic potential model. The potential model for tungsten, named DP-HYB, is trained with a database constructed by the concurrent learning method. The DP-HYB model is able to accurately predict elastic constants, stacking fault energy, the formation energies of free surfaces, and point defects, which are considered in the training dataset. It also accurately evaluates the formation energies of grain boundaries and prismatic loops, the core structure of screw dislocation, the Peierls barrier, and the transition path of the screw dislocation migration, which do not explicitly present in the training dataset. The DP-HYB is a good candidate for the atomistic simulations of tungsten property deterioration, especially those involving the mechanical property degradation under the harsh fusion service environment.

A systematic study of grain boundary segregation and grain boundary formation energy using a new copper–nickel embedded-atom potential

In this atomistic study on the copper–nickel system, a new embedded-atom alloy potential between copper and nickel is fitted to experimental data on the mixing enthalpy, taking available potentials for the pure components from literature. The resulting phase boundaries of the new potential are in very good agreement with a recent CALPHAD prediction. Using this new potential, a high angle symmetrical tilt Σ5 and a coherent Σ3 twin grain boundary (GB) are chosen for a systematic investigation of equilibrium GB segregation in the semi-grandcanonical ensemble at temperatures from 400 K to 800 K. Applying thermodynamically accurate integration techniques, the GB formation energies are calculated exactly and as an absolute value for every temperature and composition, which also enables the evaluation of GB excess entropies. The thorough thermodynamic model of GBs developed by Frolov and Mishin is excellently confirmed by the simulations quantitatively, if the impact of both segregation and GB tension on the change in GB formation energy is accounted for. In the case of the Σ3 coherent GB, it turns out that the change in GB formation energy at low temperatures is for the most part attributed to the GB tension, while segregation only has a small influence. This demonstrated effect of GB tensions should also be taken into account in the interpretation of experiments.

A Systematic Study of Grain Boundary Segregation and Grain Boundary Formation Energy Using a New Copper-Nickel Embedded-Atom Potential

Abstract In this atomistic study on the copper–nickel system, a new embedded-atom alloy potential between copper and nickel is fitted to experimental data on the mixing enthalpy, taking available potentials for the pure components from literature. The resulting phase boundaries of the new potential are in very good agreement with a recent CALPHAD prediction. Using this new potential, a high angle symmetrical tilt Σ 5 and a coherent Σ 3 twin grain boundary (GB) are chosen for a systematic investigation of equilibrium GB segregation in the semi-grandcanonical ensemble at temperatures from 400 K to 800 K. Applying thermodynamically accurate integration techniques, the GB formation energies are calculated exactly and as an absolute value for every temperature and composition, which also enables the evaluation of GB excess entropies. The thorough thermodynamic model of GBs developed by Frolov and Mishin is excellently confirmed by the simulations quantitatively, if the impact of both segregation and GB tension on the change in GB formation energy is accounted for. In the case of the Σ 3 coherent GB, it turns out that the change in GB formation energy at low temperatures is for the most part attributed to the GB tension, while segregation only has a small influence. This demonstrated effect of GB tensions should also be taken into account in the interpretation of experiments.

The formation and stability of junctions in single-wall carbon nanotubes

The structure and stability of molecular junctions, which connect two single-wall carbon nanotubes (SWCNTs) of different diameters and chiral angles, (n1, m1)-(n2, m2), are systematically investigated by density functional tight binding calculations. More than 100 junctions, which connect well-aligned SWCNTs, were constructed and calculated. For a highly stable junction between two chiral (n1, m1) and (n2, m2) SWCNTs with opposite handedness, the number of pentagon–heptagon (5/7) pairs required to build the junction can be denoted as ∣∣n2 − n1∣ − ∣m2 − m1∣∣+min{∣n2 − n1∣, ∣m2 − m1∣} with (n2, m2) rotating π/3 angle or not. While for a junction connected by two zigzag, armchair or two chiral SWCNTs with the same handedness, the number of 5/7 pairs is equal to ∣n1 − n2∣ + ∣m1 − m2∣. Similar to the formation energies of grain boundaries in graphene, the curve of the formation energies vs. chiral angle difference present an ‘M’ shape indicating the preference of ∼30 degree junctions. Moreover, the formation energies of the zigzag-type and armchair-type junctions with zero misorientation angles are largely sensitive to the diameter difference of two sub-SWCNTs.

Assessment of the CSL and SU models for bcc-Fe grain boundaries from first principles

We present a systematic first principles investigation on a group of representative low-Σ (Σ⩽11) symmetric tilt grain boundaries in bcc-Fe. The grain boundary (GB) structures were constructed using both the coincident site lattice (CSL) and structural unit (SU) models. Calculations are performed to address the relation and applicability of the two models. Results suggest that on some of the GBs, the CSL and SU models may yield different atomistic structures. In these cases, their structures differ only by one vacancy, and the SU model always predicts a much lower GB formation energy than the CSL does. Further calculations on GB vacancy formation suggest that the SU model is more appropriate for describing the low-Σ bcc GBs.

Ab initio modelling of the interaction of H interstitials with grain boundaries in bcc Fe

ABSTRACTHydrogen that is accumulated within the grain boundaries can lead to a decrease of the critical strain required to fracture the material. The paper presents results of ab initio modelling of hydrogen–grain boundary interaction in ferromagnetic bcc iron. Modelling was performed using density functional theory with generalised gradient approximation (GGA’96), as implemented in WIEN2k package. Three fully relaxed tilt grain boundaries, Σ5(310), Σ5(210) and Σ3(111), were studied. The supercells contained 40–48 atoms, i.e. 20–24 atoms in each of the two ‘grains’. Calculated formation energies of grain boundaries is 1.44, 1.83 and 1.46 J/m2 and the maximum binding (trapping) energies of hydrogen to the boundaries are 0.43, 0.83 and 0.39 eV, respectively. These values are close to other researchers’ data. The higher value of trapping energy of the Σ5(210) boundary is probably due to the asymmetrical atom configurations resulting from mutual rigid shift of the two grains that was necessary to be introduced to provide optimal distances between Fe atoms, unlike the other two boundary types.

Исследование взаимодействия водорода с границами зерен в α-Fe

The article presents results of first-principles modeling of the interaction of hydrogen with grain boundaries in α-iron. The simulation was performed in the framework of density functional theory (DFT) method of the full-potential linearised augmented-plane wave (FP LAPW) with generalised gradient approximation (GGA’96) in WIEN2k package. Three tilt grain boundaries Σ3 (111), Σ5(210) and Σ5(310) were studied. The calculated tilt grain boundaries were constructed using the coincidence site lattice model. The supercells contained 40–48 atoms, i.e. 20–24 atoms in each of the two grains. Calculated formation energies of grain boundaries are 1.46, 1.83 and 1.44 J/m 2 and maximum binding energies of hydrogen to the boundaries are 0.39, 0.81 and 0.43 eV, respectively. These data are in good agreement with the results shown in other studies. The high value of trapping energy of the Σ5(210) boundary is probably due to the asymmetrical structure resulting from mutual rigid shift of the two grains, that was necessary to be introduced to provide optimum distance between Fe atoms, in contrast to the other two types of boundaries.

The favourable large misorientation angle grain boundaries in graphene.

A grain boundary (GB) in graphene is a linear defect between two specifically oriented graphene edges, whose title angles are denoted as θ1 and θ2, respectively. Here we present a systematic theoretical study on the structure and stability of GBs in graphene as a function of the misorientation angle, Φ = (θ1-θ2) and the GB orientation in multi-crystalline graphene, which is denoted by Θ = (θ1 + θ2). It is surprising that although the number of disorders of the GB, i.e., the pentagon-heptagon pairs (5|7s), reaches the maximum at Φ∼ 30°, the GB formation energy versus the Φ curve reaches a local minimum. The subsequent M-shape of the Efvs. the Φ curve is due to the strong cancellation of the local strains around 5|7 pairs by the "head-to-tail" formation. This study successfully explains many previously observed experimental puzzles, such as the multimodal distribution of GBs and the abundance of GB misorientation angles of ∼30°. Besides, this study also showed that the formation energy of GBs is less sensitive to Θ, although the twin boundaries are slightly more stable than others.

Structures and electronic properties of symmetric and nonsymmetric graphene grain boundaries

The graphene grain boundaries with periodic length up to 18Å have been studied using density functional theory. Atomic structures, thermodynamic stabilities and electronic properties of 40 grain boundaries with symmetric and nonsymmetric structures were investigated. According to the arrangements of pentagons and heptagons on the boundary, grain boundaries were cataloged into four classes. Some nonsymmetric grain boundaries constructed here have identical misorientation angles to the experimentally observed ones. The formation energies of grain boundaries can be correlated with the misorientation angle and inflection angle. Nonsymmetric grain boundaries possess comparable formation energies to their symmetric counterparts when the periodic length along the defect line is larger than 1nm. Analysis of electronic density of states shows that the existence of a grain boundary usually increases the density of states near the Fermi level, whereas some symmetric grain boundaries can open a small band gap due to local sp2-to-sp3 rehybridization.