Grain Boundary Atoms Research Articles

Disruptive atomic jumps induce grain boundary stagnation

Grain growth in polycrystalline materials can be impeded by grain boundary (GB) stagnation. Using atomistic simulations, we observed that during GB migration, the disruptive jumps of a few GB atoms can disturb the original ordered collective movement of GB atoms, leading to the stagnation of the entire GB. These disruptive atomic jumps can be activated by both high driving forces and high temperatures, with even jumps of a few atoms capable of causing the stagnation of an entire GB. This mechanism also explains the non-Arrhenius behavior observed in some GBs. Additionally, a large model size could increase the rate of disruptive atomic jumps, and a clear transition in thermal behavior is observed with the increase of the GB size in GBs exhibiting clear thermally activated stagnation. Our further investigation shows that the disruptive atoms involved in these jumps do not differ from other GB atoms in terms of atomic energy, volume, density, local entropy, or Voronoi tessellation, and no “jam transition” was observed in the energy barrier spectra. This fact makes those disruptive jumps challenging to detect. To address this issue, we propose a displacement vector analysis method that effectively identifies these subtle disruptive jumps.

Spatial distribution of local elastic moduli in nanocrystalline metals

Elastoplastic properties of nanocrystalline metals are nonuniform on the scale of the grain size, and this nonuniformity affects macroscopic quantities as, in these systems, a significant part of the material is at or adjacent to a grain boundary. We use molecular dynamics simulations to study the spatial distributions of local elastic moduli in nanograined pure metals and analyze their dependence on grain size. Calculations are performed for copper and tantalum with grain sizes ranging from 5 to 20 nm. Shear-modulus distributions for grain and grain-boundary atoms were calculated. It is shown that the noncrystalline grain boundary has a wide shear-modulus distribution, which is grain-size independent, while grains have a peaked distribution, which becomes sharper with increasing grain size. Average elastic moduli of the bulk, grains, and grain boundary are calculated as a function of grain size. The atomistic simulations show that the reduction of total elastic moduli with decreasing grain size is mainly due to a resulting larger grain-boundary atoms fraction, and that the total elastic moduli can be approximated by a simple weighted average of larger grain elastic moduli and a lower grain-boundary elastic moduli. Published by the American Physical Society 2024

Implication of site-specific segregation on grain boundary structural transition and deformation response in nanocrystalline Ni-Nb alloy

In this study, atomistic simulation technique is utilized to examine the impact of grain boundary (GB) character (disorientation angle), structure (boundary-free volume) and energy (boundary excess energy) on site-specific Nb solute segregation behaviour and structural transition in nanocrystalline (NC) Ni. Further, the role of site-specific solute segregation on deformation response in NC Ni is also studied. Towards this, hybrid Monte Carlo/molecular dynamics simulations is performed to obtain the equilibrium structure in a Ni-Nb binary alloy at 500 K and 1200 K. The spectral nature of GB atoms is explored in NC Ni, and found that the GBs have a skew-normal distribution for excess atomic volume and excess atomic energy. Furthermore, comprehensive segregation energy calculations are performed for each GB site, revealing the preferential affinity of Nb towards GB sites in NC Ni. The study also examined interfacial solute excess for each boundary as a function of GB energy and Voronoi volume. The findings indicate that the GB energy decreased as the solute excess increased, whereas the Voronoi volume demonstrated an increment in response to the solute excess. Moreover, simulations conducted at 1200 K reveal that not all GBs within the microstructure are transformed to amorphous complexions; rather some GBs remain ordered. The simulated tensile tests conducted at 500 K and 1200 K reveal that the strengthening in Ni-Nb enhances with the increase in dopant concentration. Additionally, the simulated shear test conducted at 1200 K shows that the deformation in Ni-5Nb occurs more uniformly than pure NC Ni due to formation of thicker amorphous GBs in the former one.

Grain boundary segregation behavior of Mo atoms in nanocrystalline Ni–Mo alloy

In this paper, molecular dynamics method was used to design the grain boundary (GB) segregation structure of solute atom Mo in nanocrystalline nickel, and the effect of the segregation structure on the migration and deformation mechanism of nanocrystalline Ni–Mo alloy boundaries was studied. The results indicate that the addition of solute atom Mo can cause segregation at GBs, and the yield strength and tensile strength of nanocrystalline Ni are significantly increased through solid solution strengthening. Mo atoms segregation result in an increase of the GB thickness and stability of the GB. In addition, by labeling GB atoms and tracking their diffusion trajectories, it was found that after adding Mo atoms, the probability of atomic diffusion at GBs decreased. This indicates that Mo atoms reduce GB energy and improve GB stability. Meanwhile, as the Mo content increases, the degree of atomic disorder increases, and the probability of GB migration decreases. This leads to the inability of grains to merge and inhibit their growth, effectively improving the mechanical properties of the material. As the strain increases, the number and length of dislocations increase, and a large amount of entanglement occurs at GBs. With the increase of Mo content, the number of dislocations decreases sharply, with Shockley dislocations having the highest number. Shockley dislocations interact with other dislocations and hinder their generation and movement, forming a more stable dislocation system structure and increasing the strength of the alloy. Our work focuses on observing the influence of GB segregation structure on the mechanical properties and deformation mechanism of nanocrystalline polycrystalline Ni–Mo alloys, establishing the mechanism of the influence of segregation structure on the stability and coarsening of nanocrystalline metal GBs, examining the influence of segregation structure on dislocation motion and GB migration process during deformation, and proposing positive research and development ideas and theoretical basis for designing nanocrystalline metal materials with excellent performance.

Anharmonicity in grain boundary energy for Al: Thermodynamic integration with artificial-neural-network potential

Anharmonicity in grain boundary (GB) energies for Al is elucidated by employing a thermodynamic integration method with a high-accuracy artificial-neural-network potential. Symmetric tilt GBs with the [001] and [11¯0] rotational axes are examined. It is found that anharmonic components tend to be small at low temperatures and increasingly contribute to reduction of GB free energies at elevated temperatures. The magnitude of anharmonicity is roughly correlated with excess volume at GBs. This is presumably because GB atoms tend to have longer bond lengths than the bulk atom, and hence the inclination of the potential energy surface at GBs is more moderate than in the bulk. On the other hand, the Σ13(510) GB takes non-negligible values of the anharmonic component even at intermediate temperatures. This GB contains a distinct atom around which the potential-energy curve significantly deviates from that of the harmonic approximation. Similar trends are also observed for other [001] GBs.

Screening and manipulation by segregation of dopants in grain boundary of Silicon carbide: First-principles calculations

The effect of segregation behavior of non-metallic dopants (H/He/O) and metallic dopants (Be/Al/Mg/Y) on the performance of grain boundary (GB) in SiC has been systematically investigated by first-principles calculations. Firstly, the GB energy and excess volume of different GBs have been studied to evaluate the stability of GB and the capacity to accommodate dopant atoms. The solution energies of dopant atoms greatly reduce in the GB region compared with those in the bulk, which makes the dopant atoms inside the grain tend to segregate and aggregate near the GB. The driving force of GB on dopant segregation generally decreases with the increase of distance from GB plane, and the preferential site of dopant is closely correlated with the atomic size of dopant. In addition, H and Y atom possesses the lowest segregation energy at the interstitial and substitutional site near the GB, respectively. Next, the segregation of single dopant induced the changes in the strength and stability of GB have been explored. It is found that non-metallic dopants have the significant embrittlement effects on GB strength. However, the segregation of most metallic dopants could strengthen the GB and Mg atom has the most significant strengthening effect on the GB. The stability of GB can be greatly improved by segregation of Al and Y dopants. Besides, the aggregation of H atoms has the obvious embrittlement effect on the GB. Furthermore, the co-segregation behavior of different dopants has also been explored. Be and Mg dopants have the most significant inhibition effect on the segregation of detrimental impurities H/He/O due to the repulsive interaction between dopant atoms. The present results provide a new insight into the effect of dopant segregation on GB properties and are expected to be a useful guidance for screening the chemical composition and manipulating the performance of SiC-based ceramics.

Hydrogen-promoted in-void diffusion of helium in a 3C-SiC(310) twin boundary: a first-principles study

The role of H atoms in the formation of irradiation-induced He bubbles in SiC grain boundaries (GBs) is unclear. The effects of H on the formation energies (Ef s) and diffusion behaviour of He in the 3C-SiC twin boundary (TB) were studied using the density functional theory. We observed that a He atom stabilises at three typical sites in the 3C-SiC (310) TB with Ef s = 1.95, 2.05, and 1.67 eV, which are significantly lower than those in the SiC grains. The addition of the H atom shifts the stable sites of He in the TB and increases Ef s to 4.66, 3.96, and 5.13 eV. The minimum energy pathways for He diffusion in TB were changed by the addition of H atom. Moreover, the H atom reduces the barrier from 3.69 to 1.04 eV for the He diffusion in one TB void and increases it from 1.30 to 4.08 eV for the He diffusion between adjacent TB voids. We interpreted the above results through the Bader charge, density of states, and atomic force analysis. The results indicate that H promotes the in-void diffusion but suppresses the inter-void diffusion of He atoms in SiC GBs, which favours the aggregation and nucleation of He in SiC GBs.

How atoms of polycrystalline Nb20.6Mo21.7Ta15.6W21.1V21.0 refractory high-entropy alloys rearrange during the melting process

The melting mechanism of single crystal and polycrystalline Nb20.6Mo21.7Ta15.6W21.1V21.0 refractory high entropy alloys (RHEAs) were investigated by the molecular dynamics (MD) simulation using the second-nearest neighbor modified embedded-atom method (2NN MEAM) potential. For the single crystal RHEA, the density profile displays an abrupt drop from 11.25 to 11.00 g/cm3 at temperatures from 2910 to 2940 K, indicating all atoms begin significant local structural rearrangement. For polycrystalline RHEAs, a two-stage melting process is found. In the first melting stage, the melting of the grain boundary (GB) regions firstly occurs at the pre-melting temperature, which is relatively lower than the corresponding system-melting point. At the pre-melting temperature, most GB atoms have enough kinetic energies to leave their equilibrium positions, and then gradually induce the rearrangement of grain atoms close to GB. In the second melting stage at the melting point, most grain atoms have enough kinetic energies to rearrange, resulting in the chemical short-ranged order changes of all pairs.

Tracking the sliding of grain boundaries at the atomic scale.

Grain boundaries (GBs) play an important role in the mechanical behavior of polycrystalline materials. Despite decades of investigation, the atomic-scale dynamic processes of GB deformation remain elusive, particularly for the GBs in polycrystals, which are commonly of the asymmetric and general type. We conducted an in situ atomic-resolution study to reveal how sliding-dominant deformation is accomplished at general tilt GBs in platinum bicrystals. We observed either direct atomic-scale sliding along the GB or sliding with atom transfer across the boundary plane. The latter sliding process was mediated by movements of disconnections that enabled the transport of GB atoms, leading to a previously unrecognized mode of coupled GB sliding and atomic plane transfer. These results enable an atomic-scale understanding of how general GBs slide in polycrystalline materials.

High-speed mass transfer in the W–Cu pseudo-alloy

Tungsten–copper alloys are heat-resistance materials for aerospace industry. Structure stability during processing and exploitation is controlled by the diffusion processes. In particular, the microstructure evolution is determined by the diffusion of copper atoms in tungsten matrix. Several experimental studies report different diffusivity of copper, which can be associated with the discrepancy of activation energy of diffusion depending on the structure of grain boundaries in tungsten. We performed density functional theory calculations of vacancy formation energies, segregation energies, and migration barriers for copper atoms in certain high-angle grain boundaries of special type using nudged elastic band method. Based on this information we calculated the corresponding diffusion coefficients. We found that the diffusivities in the studied grain boundaries exceed the extrapolated experimental data obtained at low temperatures at least by five times. The obtained data on diffusion path help to explain the depth, from which copper is removed during the annealing of the W–Cu alloy at 1500 K.

Segregation of solute atoms in ZrC grain boundaries and their effects on grain boundary strengths

ZrC is a promising candidate for the application in ultra-high temperature regime due to its unique combination of excellent properties, such as high melting point, good chemical inertness and high temperature stability. The rapid decrease of strength at high temperatures, however, is one of the obstacles that impedes its practical services. Strengthening of grain boundaries by solute segregation is believed to be an effective way to improve its high temperature performance. Therefore, the segregation tendency of ten solid solute atoms, including Sc, Ti, V, Cr, Y, Nb, Mo, Hf, Ta, W, in ZrC grain boundaries, and the strengthening/weakening effects on grain boundaries due to segregation are investigated by first-principles calculations. The segregation tendency is found dominated by the size effect, which is confirmed by both a qualitative analysis and a quantitative approach based on support vector regression. It means that big atoms tend to segregate to grain boundary sites with local expansions, while small atoms tend to segregate to grain boundary sites with local compressions. Simulations on stress-strain responses indicate that segregation of small atoms (Ti, V, Cr, Nb, Ta, Mo, W) can usually improve grain boundary strengths by inducing compression strains to grain boundaries, even though there is also an exception. In contrast, segregation of Sc and Y will soften grain boundaries. The results reveal that strengthening of grain boundaries by solute segregation is a valuable avenue to enhance high temperature mechanical properties of ZrC, providing guidelines for further design of ZrC based materials.

Atomic configurations and energies of Mg symmetric tilt grain boundaries: ab initio local analysis

Mg alloys are highly expected for the wide application in the next-generation industry, while significant improvement of the plasticity of polycrystalline Mg alloys is crucial. For this purpose, it is essential to get insights into the atomic configurations, energetics, and mechanical responses of Mg grain boundaries (GBs). In this study, we investigated the overall features of atomic configurations and energies of and symmetric tilt GBs in hcp Mg by density-functional theory. We systematically constructed atomic models of coincidence-site lattice GBs by the arrangement of structural units in the full range of rotation angles. We observed that special GBs show clear cusps in both the GB-energy and excess-volume curves against the rotation angle. The reason of the stability/instability of each GB configuration was analyzed by ab initio local energy and local stress based on Bader partitioning. The features of local energies and stresses in Mg GBs are quite different from those in other materials with covalent or partial-covalent bonding nature. We observed substantial variations of local energies, local stresses and Bader charges of GB atoms, and charge inhomogeneity in a GB region, reflecting the structural disorder. Stable GBs are characterized by modest ranges of such variations and by moderate charge homogeneity. These results could be utilized in general to understand the interface stability and deformation mechanism of Mg and other simple metals.

Dislocation content of grain boundary phase junctions and its relation to grain boundary excess properties

We analyze the dislocation content of grain boundary (GB) phase junctions, i.e., line defects separating two different GB phases coexisting on the same GB plane. While regular GB disconnections have been characterized for a variety of interfaces, GB phase junctions formed by GBs with different structures and different numbers of excess atoms have not been previously studied. We apply a general Burgers circuit analysis to calculate the Burgers vectors b of junctions in two {\Sigma}5 Cu boundaries previously simulated with molecular dynamics. The Burgers vectors of these junctions cannot be described by the displacement shift complete (DSC) lattice alone. We show that, in general, the normal component of b is not equal to the difference in the GB excess volumes, but contains another contribution from the numbers of GB atoms per unit area {\Delta}N required to transform one GB phase into another. In the boundaries studied, the latter component dominates and even changes the sign of b. We derive expressions for the normal and tangential components of b in terms of the DSC lattice vectors and the non-DSC part due to {\Delta}N and additional GB excess properties, including excess volume and shears. These expressions provide a connection between GB phase transformations driven by the GB free energy difference and the motion of GB junctions under applied normal and shear stresses. The proposed analysis quantifies b and therefore makes it possible to calculate the elastic part of the energy of these defects, evaluate their contribution to the nucleation barrier during GB phase transformations, and treat elastic interactions with other defects.

Shear-coupled grain boundary migration in bicrystal Ni with metallic dopant segregation

The shear-coupled grain boundary (GB) migration in bicrystal Ni with metallic dopant segregation was investigated by the molecular dynamics simulations. Different from the approximately linear relation of the GB migration of pure bicrystal Ni with the nominal shear strain, the curve of doped bicrystal Ni can be divided into three stages. The threshold strain, saturated strain, and saturated GB migration displacement can be used to characterize them. They are considerably affected by the Cr concentration in GB, temperature, and dopant type. The higher the dopant concentration is or the lower the temperature is, the greater the resistance to GB migration is. Cu dopant induces the greatest resistance, Cr and Fe dopants have great effect on the GB migration, but Co has almost no influence. All these hindering effects can be explained from the variation of the number of pinning points induced by the dopant atoms in GB.

An origin of excess vibrational entropies at grain boundaries in Al, Si and MgO: a first-principles analysis with lattice dynamics.

First-principles lattice dynamics is applied to symmetric tilt grain boundaries (GBs) in Al, Si and MgO, with the goal of revealing critical factors in determining excess vibrational entropies at the atomic level. Excess vibrational entropies at GBs are found to vary depending on the substances. Al GBs tend to show larger excess entropies and hence larger temperature dependence of the GB free energies than those in Si and MgO. Most of the Si GBs show small excess entropies. For Al and MgO, atom-projected vibrational entropies are well correlated with bond-length changes at GB cores, and have large positive values as bond lengths increase for GB atoms. This demonstrates that a similar mechanism likely dominates excess vibrational entropies of GBs for both substances, despite their dissimilar bonding nature. For Si GBs, atoms with threefold coordination do not simply follow such a correlation, implying the importance of other factors that are different from bond-length changes. These systematic comparisons will be a foothold for understanding a physical origin of excess entropies at GBs even in more complex substances.

Maximum volume simplex method for automatic selection and classification of atomic environments and environment descriptor compression

Fingerprint distances, which measure the similarity of atomic environments, are commonly calculated from atomic environment fingerprint vectors. In this work, we present the simplex method that can perform the inverse operation, i.e., calculating fingerprint vectors from fingerprint distances. The fingerprint vectors found in this way point to the corners of a simplex. For a large dataset of fingerprints, we can find a particular largest simplex, whose dimension gives the effective dimension of the fingerprint vector space. We show that the corners of this simplex correspond to landmark environments that can be used in a fully automatic way to analyze structures. In this way, we can, for instance, detect atoms in grain boundaries or on edges of carbon flakes without any human input about the expected environment. By projecting fingerprints on the largest simplex, we can also obtain fingerprint vectors that are considerably shorter than the original ones but whose information content is not significantly reduced.

Molecular Dynamics Studies of Hydrogen Effect on Intergranular Fracture in α-Iron.

In the current study, the effect of hydrogen atoms on the intergranular failure of α-iron is examined by a molecular dynamics (MD) simulation. The effect of hydrogen embrittlement on the grain boundary (GB) is investigated by diffusing hydrogen atoms into the grain boundaries using a bicrystal body-centered cubic (BCC) model and then deforming the model with a uniaxial tension. The Debye Waller factors are applied to illustrate the volume change of GBs, and the simulation results suggest that the trapped hydrogen atoms in GBs can therefore increase the excess volume of GBs, thus enhancing intergranular failure. When a constant displacement loading is applied to the bicrystal model, the increased strain energy can barely be released via dislocation emission when H is present. The hydrogen pinning effect occurs in the current dislocation slip system, <111>{112}. The hydrogen atoms facilitate cracking via a decrease of the free surface energy and enhance the phase transition via an increase in the local pressure. Hence, the failure mechanism is prone to intergranular failure so as to release excessive pressure and energy near GBs. This study provides a mechanistic framework of intergranular failure, and a theoretical model is then developed to predict the intergranular cracking rate.

Effect of Grain-Boundary Segregation on the Diffusion of Atoms in Grain Boundaries in Copper-Based Systems

The influence of the segregation energy on the diffusion of second-component atoms in copper is studied by molecular statics and dynamics methods. A number of modified potential is considered. The segregation energy of atoms in a grain boundary is calculated. The number of second-component atoms involved in a diffusion process is found to decrease because of desorption, which leads to a decrease in the grain-boundary diffusion coefficient.

Effect of solute segregation on diffusion induced grain boundary migration studied by molecular dynamics simulations

Diffusion-induced grain boundary migration (DIGM) is the phenomenon of normal grain boundary (GB) migration caused by the lateral diffusion of solutes along it. Despite its technological importance and the fact that DIGM has been first observed and studied since 1970, many aspects of it are still not fully understood. In this study, molecular dynamics simulations are used to investigate the physical origin of DIGM with particular focus on the effects of solute-GB interactions. For this purpose, a few binary alloy systems are deliberately selected, e.g., Al-Ti, Al-Ni, and Ni-Cu, in which strong solute-GB interactions including both solute segregation and anti-segregation occur. The simulation results showed that strong solute segregation and anti-segregation can both influence DIGM, although past experimental and theoretical studies on DIGM mostly focused on systems with segregation. Furthermore, it is shown that the direction of GB migration strongly depends on the solute-GB interaction type, e.g., segregation or anti-segregation, which causes an attraction or repulsion between the GB and solute atoms, respectively. It is thus proved that solute-GB interactions, in general, play an important role in driving DIGM. Furthermore, by combining two atomistic simulation techniques, i.e., the synthetic driving force method and interface random walk method, we are able to quantify the driving forces for DIGM. All observations made during the simulations are supported by atomic configurations and graphical analysis. It is hoped that this study sheds some light on this research area after more than a decade’s stagnation in this field.

Study of grain boundary self-diffusion in iron with different atomistic models

We studied grain boundary (GB) self-diffusion in body-centered cubic iron using ab initio calculations and molecular dynamics simulations with various interatomic potentials. A combination of different models allowed us to determine the principal characteristics of self-diffusion along different types of GBs. In particular, we found that atomic self-diffusion in symmetric tilt GBs is mostly driven by self-interstitial atoms. In contrast, in general GBs atoms diffuse predominantly via an exchange mechanism that does not involve a particular defect but is similar to diffusion in a liquid. Most observed mechanisms lead to a significant enhancement of self-diffusion along GBs as compared to diffusion in the bulk. The results of simulations are verified by comparison with available experimental data.