Grain boundary phases in bcc metals

A new compositional microscopic degree of freedom at grain boundaries in complex compounds: a case study in spinel

The accurate computational treatment of polycrystalline materials requires the rigorous generation of grain boundary (GB) structures as many quantities of interest depend strongly on the specifics of the macroscopic and microscopic degrees of freedom (DoFs) used in their creation. In complex materials, containing multiple sublattices and where atomic composition can vary spatially through the system, we introduce a new microscopic DoF based on this compositional variation which we find governs observable properties. In spinel - a wide class of complex oxides where this compositional variation manifests as cation inversion - we exploit this DoF to generate and analyze low-energy microstates of two GBs with three spinel chemistries (FeCr2O4, NiCr2O4 and MgAl2O4). This treatment is found to allow for the co-redistribution of cations at the GBs which acts to modify the spatial charge distribution, defect segregation energy and defect transport through these regions. Additionally, we generate low-energy metastable microstates of the GB system with an induced cation disorder, simulating those which may develop as a result of damage events. These are then analyzed to discover their composition and defect transport properties which depend strongly on the amount of induced damage. We conclude that considering this new DoF is important in describing the properties of GBs in complex materials.

Phase Pattern Formation in Grain Boundaries

In this Letter we derive conditions that predict the existence of two-phase periodic-pattern grain boundary structures that are stable against coarsening. While previous research has established that elastic effects can lead to phase pattern formation on crystal surfaces, the possibility of stable grain boundary structures composed of alternating grain boundary phases has not been previously analyzed. Our theory identifies the specific combination of grain boundary and materials properties that enable the emergence of patterned grain boundary states and shows that the dislocation content of grain boundary phase junctions, absent in surface phenomena, weakens the stability of the patterned structures. The predictions of the theory are tested using a model copper grain boundary that exhibits multiple phases and two-phase pattern formation. We discuss how, similarly to surfaces, elastic effects associated with grain boundary phase junctions have profound implications for how grain boundary phases transform.

Dual phase patterning during a congruent grain boundary phase transition in elemental copper

The phase behavior of grain boundaries can have a strong influence on interfacial properties. Little is known about the emergence of grain boundary phases in elemental metal systems and how they transform. Here, we observe the nanoscale patterning of a grain boundary by two alternating grain boundary phases with distinct atomic structures in elemental copper by atomic resolution imaging. The same grain boundary phases are found by computational grain boundary structure search indicating a first-order transformation. Finite temperature atomistic simulations reveal a congruent, diffusionless transition between these phases under ambient pressure. The patterning of the grain boundary at room temperature is dominated by the grain boundary phase junctions separating the phase segments. Our analysis suggests that the reduced mobility of the phase junctions at low temperatures kinetically limits the transformation, but repulsive elastic interactions between them and disconnections could additionally stabilize the pattern formation.

Atomistic and machine learning studies of solute segregation in metastable grain boundaries

The interaction of alloying elements with grain boundaries (GBs) influences many phenomena, such as microstructural evolution and transport. While GB solute segregation has been the subject of active research in recent years, most studies focus on ground-state GB structures, i.e., lowest energy GBs. The impact of GB metastability on solute segregation remains poorly understood. Herein, we leverage atomistic simulations to generate metastable structures for a series of [001] and [110] symmetric tilt GBs in a model Al–Mg system and quantify Mg segregation to individual sites within these boundaries. Our results show large variations in the atomic Voronoi volume due to GB metastability, which are found to influence the segregation energy. The atomistic data are then used to train a Gaussian Process machine learning model, which provides a probabilistic description of the GB segregation energy in terms of the local atomic environment. In broad terms, our approach extends existing GB segregation models by accounting for variability due to GB metastability, where the segregation energy is treated as a distribution rather than a single-valued quantity.

Direct imaging of the disconnection climb mediated point defects absorption by a grain boundary

Grain boundaries (GBs) are considered as the effective sinks for point defects, which improve the radiation resistance of materials. However, the fundamental mechanisms of how the GBs absorb and annihilate point defects under irradiation are still not well understood at atomic scale. With the aid of the atomic resolution scanning transmission electron microscope, we experimentally investigate the atomistic mechanism of point defects absorption by a ∑31 GB in α-Al₂O₃ under high energy electron beam irradiation. It is shown that a disconnection pair is formed, during which all the Al atomic columns are tracked. We demonstrate that the formation of the disconnection pair is proceeded with disappearing of atomic columns in the GB core, which suggests that the GB absorbs vacancies. Such point defect absorption is attributed to the nucleation and climb motion of disconnections. These experimental results provide an atomistic understanding of how GBs improve the radiation resistance of materials.

Nucleation of Grain Boundary Phases

We derive a theory that describes homogeneous nucleation of grain boundary (GB) phases. Our analysis takes account of the energy resulting from the GB phase junction, the line defect separating two different GB structures, which is necessarily a dislocation as well as an elastic line force due to the jump in GB stresses. The theory provides analytic forms for the elastic interactions and the core energy of the GB phase junction that, along with the change in GB energy, determines the nucleation barrier. We apply the resulting nucleation model to simulations of GB phase transformations in tungsten. Our theory explains why under certain conditions GBs cannot spontaneously change their structure even to a lower energy state.

Survey of Grain Boundary Energies in Tungsten and Beta-Titanium at High Temperature

Heat treatment is a necessary means to obtain desired properties for most of the materials. Thus, the grain boundary (GB) phenomena observed in experiments actually reflect the GB behaviors at relatively high temperature to some extent. In this work, 405 different GBs were systematically constructed for body-centered cubic (BCC) metals and the grain boundary energies (GBEs) of these GBs were calculated with molecular dynamics for W at 2400 K and β-Ti at 1300 K and by means of molecular statics for Mo and W at 0 K. It was found that high temperature may result in the GB complexion transitions for some GBs, such as the Σ11{332}{332} of W. Moreover, the relationships between GBEs and sin(θ) can be described by the functions of the same type for different GB sets having the same misorientation axis, where θ is the angle between the misorientation axis and the GB plane. Generally, the GBs tend to have lower GBE when sin(θ) is equal to 0. However, the GB sets with the <110> misorientation axis have the lowest GBE when sin(θ) is close to 1. Another discovery is that the local hexagonal-close packed α phase is more likely to form at the GBs with the lattice misorientations of 38.9°/<110>, 50.5°/<110>, 59.0°/<110> and 60.0°/<111> for β-Ti at 1300 K.

Accurate prediction of grain boundary structures and energetics in CdTe: a machine-learning potential approach

To accurately predict grain boundary (GB) atomic structures and their energetics in CdTe, the present study constructs an artificial-neural-network (ANN) interatomic potential. To cover a wide range of atomic environments, large amounts of density functional theory (DFT) data are used as a training dataset including point defects, surfaces and GBs. Structural relaxation combined with the trained ANN potential is applied to symmetric tilt and twist GBs, many of which are not included in the training dataset. The relative stability of the relaxed structures and their GB energies are then evaluated with the DFT level. The ANN potential is found to accurately predict low-energy structures and their energetics with reasonable accuracy with respect to DFT results, while conventional empirical potentials critically fail to find low-energy structures. The present study also provides a way to further improve the transferability of the ANN potential to more complicated GBs, using only low-Σ GBs as training datasets. Such improvement will offer a way to accurately predict atomic structures of general GBs within practical computational cost.

Direct insight into the structure-property relation of interfaces from constrained crystal structure prediction

A major issue that prevents a full understanding of heterogeneous materials is the lack of systematic first-principles methods to consistently predict energetics and electronic properties of reconstructed interfaces. In this work we address this problem with an efficient and accurate computational scheme. We extend the minima-hopping method implementing constraints crafted for two-dimensional atomic relaxation and enabling variations of the atomic density close to the interface. A combination of density-functional and accurate density-functional tight-binding calculations supply energy and forces to structure prediction. We demonstrate the power of this method by applying it to extract structure-property relations for a large and varied family of symmetric and asymmetric tilt boundaries in polycrystalline silicon. We find a rich polymorphism in the interface reconstructions, with recurring bonding patterns that we classify in increasing energetic order. Finally, a clear relation between bonding patterns and electrically active grain boundary states is unveiled and discussed.

Tensile deformation behavior of twist grain boundaries in CoCrFeMnNi high entropy alloy bicrystals

High entropy alloys (HEA) are a class of materials that consist of multiple elemental species in similar concentrations. The use of elements in far from dilute concentrations introduces a multi-dimensional composition design space by which the properties of metallic systems can be tailored. While the mechanical behavior of HEAs has been the subject of active research recently, the role of grain boundaries (GBs) in their deformation behavior remains poorly understood. Motivated by recent experiments on HEAs demonstrating that GBs act as nucleation sites for deformation twins, herein, we leverage atomistic simulations to construct a series of equiatomic CoCrFeMnNi HEA bicrystals with [Formula: see text] and [Formula: see text] symmetric twist GBs and examine their tensile behavior and underlying deformation mechanisms at 77 K. Simulation results reveal that plastic deformation proceeds by the nucleation of partial dislocations from GBs, which then grow with further loading by bowing into the bulk crystals leaving behind stacking faults. Variations in the nucleation stress exist as function of GB character, defined in this work by the twist angle. Our results provide future avenues to explore GBs as a microstructure design tool to develop HEAs with tailored properties.

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.

Approaches to Measure the Resistivity of Grain Boundaries in Metals with High Sensitivity and Spatial Resolution: A Case Study Employing Cu

It is well-known that grain boundaries (GBs) increase the electrical resistivity of metals due to their enhanced electron scattering. The resistivity values of GBs are determined by their atomic structure; therefore, assessing the local resistivity of GBs is highly significant for understanding structure-property relationships. So far, the local electrical characterization of an individual GB has not received much attention, mainly due to the limited accuracy of the applied techniques, which were not sensitive enough to detect the subtle differences in electrical resistivity values of highly symmetric GBs. Here, we introduce a detailed methodology to probe in situ or ex situ the local resistivity of individual GBs in Cu, a metallic model system we choose due to its low resistance. Both bulk Cu samples and thin films are investigated, and different approaches to obtain reliable and accurate resistivity measurements are described, involving the van der Pauw technique for macroscopic measurements as well as two different four-point-probe techniques for local in situ measurements performed inside a scanning electron microscope. The in situ contacts are realized with needles accurately positioned by piezodriven micromanipulators. Resistivity results obtained on coincidence site lattice GBs (incoherent Σ3 and asymmetric Σ5) are reported and discussed. In addition, the key experimental details as well as pitfalls in the measurement of individual GB resistivity are addressed.

Observations of grain-boundary phase transformations in an elemental metal

The theory of grain boundary (the interface between crystallites, GB) structure has a long history¹ and the concept of GBs undergoing phase transformations was proposed 50 years ago^2,3. The underlying assumption was that multiple stable and metastable states exist for different GB orientations^4-6. The terminology 'complexion' was recently proposed to distinguish between interfacial states that differ in any equilibrium thermodynamic property⁷. Different types of complexion and transitions between complexions have been characterized, mostly in binary or multicomponent systems^8-19. Simulations have provided insight into the phase behaviour of interfaces and shown that GB transitions can occur in many material systems^20-24. However, the direct experimental observation and transformation kinetics of GBs in an elemental metal have remained elusive. Here we demonstrate atomic-scale GB phase coexistence and transformations at symmetric and asymmetric [Formula: see text] tilt GBs in elemental copper. Atomic-resolution imaging reveals the coexistence of two different structures at Σ19b GBs (where Σ19 is the density of coincident sites and b is a GB variant), in agreement with evolutionary GB structure search and clustering analysis^21,25,26. We also use finite-temperature molecular dynamics simulations to explore the coexistence and transformation kinetics of these GB phases. Our results demonstrate how GB phases can be kinetically trapped, enabling atomic-scale room-temperature observations. Our work paves the way for atomic-scale in situ studies of metallic GB phase transformations, which were previously detected only indirectly^9,15,27-29, through their influence on abnormal grain growth, non-Arrhenius-type diffusion or liquid metal embrittlement.

Local electronic descriptors for solute-defect interactions in bcc refractory metals

The interactions between solute atoms and crystalline defects such as vacancies, dislocations, and grain boundaries are essential in determining alloy properties. Here we present a general linear correlation between two descriptors of local electronic structures and the solute-defect interaction energies in binary alloys of body-centered-cubic (bcc) refractory metals (such as W and Ta) with transition-metal substitutional solutes. One electronic descriptor is the bimodality of the d-orbital local density of states for a matrix atom at the substitutional site, and the other is related to the hybridization strength between the valance sp- and d-bands for the same matrix atom. For a particular pair of solute-matrix elements, this linear correlation is valid independent of types of defects and the locations of substitutional sites. These results provide the possibility to apply local electronic descriptors for quantitative and efficient predictions on the solute-defect interactions and defect properties in alloys.

Linear Complexions: Metastable Phase Formation and Coexistence at Dislocations

The unique three-phase coexistence of metastable B2-FeNi with stable L1_{0}-FeNi and L1_{2}-FeNi_{3} is discovered near edge dislocations in body-centered cubic Fe-Ni alloys using atomistic simulations. Stable nanoscale precipitate arrays, formed along the compression side of dislocation lines and defined as linear complexions, were observed for a wide range of compositions and temperatures. By analyzing the thermodynamics associated with these phase transitions, we are able to explain the metastable phase formation and coexistence, in the process defining new research avenues for theoretical and experimental investigations.