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A study of 346 computed [1 0 0] disorientation axis grain boundaries provides insight into grain boundary energy structure-property relationships. The grain boundaries come from 6 coincidence site lattice misorientations at regularly spaced disorientation angles, and cover the full range of boundary plane orientations. The computed energy has clear trends in disorientation angle and boundary plane orientation. The data are used to reexamine the ‘special’ attribute frequently applied to low Σ coincidence site lattice misorientations and low-angle boundaries and to assess the accuracy of a face-centered cubic grain boundary energy function developed by Bulatov, Reed, and Kumar (Acta Mater. 65 (2014) 161-175).

Efforts to construct predictive grain boundary (GB) structure–property models have historically relied on property measurements or calculations made on bicrystals. Experimental bicrystals can be difficult or expensive to fabricate, and computational constraints limit atomistic bicrystal simulations to high-symmetry GBs (i.e., those with small enough GB periodicity). Although the use of bicrystal property data to construct GB structure–property models is more direct, in many experimental situations the only type of data available may be measurements of the effective properties of polycrystals. In this work, we investigate the possibility of inferring GB structure–property models from measurements of the homogenized effective properties of polycrystals when the form of the structure–property model is unknown. We present an idealized case study in which GB structure–property models for diffusivity are inferred from noisy simulation results of two-dimensional microstructures, under the assumption that the number of polycrystal measurements available is larger than the number of parameters in the inferred model. We also demonstrate how uncertainty quantification for the inferred structure–property models is easily performed within this framework.

High-throughput simulations can be a powerful tool in the discovery of new materials and behaviors. As part of a special issue on Rising Stars in Computational Materials Science, this article uses the work of the author to show how high-throughput simulations have had an impact in grain boundary structure-property relationships and other complex microstructural phenomena. The work demonstrates how new tools designed to analyze large datasets produced by high-throughput simulations are enabling comprehensive grain boundary structure-property relationships to be obtained. High-throughput simulations are also used to demonstrate the impact descriptive and inferential statistics has had in extracting key aspects of deformation in metallic glasses. Finally, several different examples are used to show a balanced approach between simulations designed to survey and simulations designed for detailed analysis. Together, the two approaches provide a comprehensive picture of the variety of behaviors that exist, while ensuring that the physics underlying the behaviors are thoroughly understood.

Shear strain profiles along slip bands in a modified Rolls-Royce nickel superalloy (RR1000) were analyzed for a tensile sample deformed by 2%. The strain increased with distance away from a grain boundary (GB), with maximum shear strain towards the center of the grain, indicating that dislocation nucleation generally occurred in the grain interior. The strain gradients in the neighborhood of the GBs were quantified and generally correlated with rotation about the active slip system line direction. This leads to an ability to determine the active slip system in these regions. The dislocation spacing and pileup stresses were inferred. The dislocation spacing closely follows an Eshelby analytical solution for a single ended pileup of dislocations under an applied stress. The distribution of pileup stress values for GBs of a given misorientation angle follows a log-normal distribution, with no correlation between the pileup stress and the GB misorientation angle. Furthermore, there is no observed correlation between various transmissivity factors and slip band pileup stress. Hence it appears that the obstacle strength of any of the observed GBs is adequate to facilitate the dislocation pileups present in the slip bands. However, slip band transmission does correlate with transmissivity factors, with the current study focusing on the Luster and Morris m’-factor. Observation of strain profiles of transmitted bands indicate dislocation nucleation locations.

Antithermal grain boundary migration is an interesting phenomenon that has been recently discovered. These grain boundaries behave opposite to what is expected of thermally activated grain boundary migration; the antithermal grain boundaries exhibit mobility that decreases with increasing temperature. Two recent studies have provided insight into important behaviors correlated with antithermal migration. O'Brien and Foiles (J Mater. Sci. Vol. 51, p. 6607–6623, 2016) demonstrated that the high mobility exhibited by an antithermal Σ7 grain boundary is enabled by ordered atomic motions. Ulomek and Mohles (Acta Mater. Vol. 103, p. 424–432, 2016) demonstrated that the thermal migration of a different Σ7 grain boundary exhibited a two-step migration process. In this work, we demonstrate that the antithermal temperature dependence exhibited by these types of grain boundaries is caused by a combination of these two discoveries. Specifically, ordered atomic motions about Coincidence Site Lattice atoms (atoms common to the lattices on either side of the grain boundary), seen by O'Brien and Foiles, are interrupted by additional thermal energy at higher temperature. This is the source of the two-step process seen by Ulomek and Mohles. This two-step process is akin to stick-slip behaviors observed in shear coupled grain boundary migration. As temperature is increased, the duration of the stagnant portion increases and the mobility decreases. This behavior is demonstrated through molecular dynamics simulations in nickel bicrystals over temperatures ranging from 100 to 1400 K for Σ7 and Σ9 grain boundaries. For these Σ7 and Σ9 grain boundaries, those that have ordered atomic mechanisms are almost exclusively antithermal, while those that do not have ordered atomic mechanisms are thermally activated.

In this work we present a non-parametric Bayesian approach for developing structure-property models for grain boundaries (GBs) with built-in uncertainty quantification (UQ). Using this method we infer a structure-property model for H diffusivity in [100] tilt GBs in Ni at 700 K based on molecular dynamics (MD) data. Once a GB structure-property model is developed, it can be used as an input to mesoscale simulations of the effective properties of polycrystals, microstructure evolution, etc. A significant advantage of the Bayesian approach presented here is that it facilitates propagation of uncertainties from the underlying structure-property model to the output predictions from mesoscale modeling. Leveraging this capability, we perform mesoscale simulations of the effective diffusivity of polycrystals to investigate the interaction between structure-property model uncertainties and GB network structure. We observe a fundamental interaction between crystallographic correlations and spatial correlations in GB networks that causes certain types of microstructures (those with large populations of J 2 - and J 3 -type triple junctions) to exhibit intrinsically larger uncertainty in their effective properties. Data and code are provided in supplementary materials.

With twin grain boundaries playing an important role in numerous materials, it is important to understand their behavior across the full range of possible boundary plane orientations. This work examines the migration of 41 computed ∑3 nickel grain boundaries over a range of temperatures. The boundary plane orientation appears to play the determining role in the nature of the migration observed, which is evident when the data are plotted in the fundamental zone of possible boundary plane orientations. GBs whose boundary plane lie between ( 1 1 1 ) and ( 2 1 ¯ 1 ¯ ) exhibit thermally activated migration and the atoms do not move in a coordinated fashion. The remaining GBs, including the ( 1 0 1 ¯ ) GB, exhibit some form of thermally damped migration. The thermally damped migration is characterized by inverse temperature dependence where the GBs migrate faster at lower temperatures and move in a coordinated fashion involving Shockley partial dislocations. The inverse temperature dependence, which is confirmed by random walk simulations, appears to be consistent with dislocation drag, which could be related to the Shockley partial dislocations. At least one GB exhibits mixed mobility trends due to the presence of both thermally activated and thermally damped migration characteristics.

Grain boundary dislocation nucleation is simulated in a Nickel bicrystal with Σ21b (211)/(211) grain boundaries. Using molecular dynamics, 386 different triaxial stress states are examined for their effect on dislocation nucleation on different slip systems. The approach leads to dislocation nucleation on six of the twelve partial slip systems, enabling a study of conditions leading to nucleation. The criteria for nucleation on each of the slip systems is shown to have a linear dependence on the resolved shear, normal, and co-slip stresses, though the constants for this linear dependence are unique for each slip system. The combined nucleation criteria are used to construct a theoretical nucleation surface. The surface is reminiscent of a Mohr-Coulomb yield surface, except that in the present case the facets of the surface correspond to nucleation on different slip systems.

The atomic structure of grain boundaries plays a defining but poorly understood role in the properties they exhibit. Due to the complex nature of these structures, machine learning is a natural tool for extracting meaningful relationships and new physical insight. We apply a new structural representation, called the scattering transform, that uses wavelet-based convolutional neural networks to characterize the complete three-dimensional atomic structure of a grain boundary. The machine learning to predict GB energy, mobility, and shear coupling using the scattering transform representation is compared and contrasted with learning using a smooth overlap of atomic positions (SOAP) based representation. While predictions using the scattering transform are not as good as those of SOAP, other factors suggest that the scattering transform may yet play an important role in GB structure learning. These factors include the ability of the scattering transform to learn well on larger datasets, in a process similar to deep learning, as well as their ability to provide physically interpretable information about what aspects of the GB structure contribute to the learning through an inverse scattering transform.

Grain boundaries are known to act as important diffusion pathways in metals. Here we examine how hydrogen diffusion in nickel grain boundaries is affected by different grain boundary types. We simulate 26 [ 1 0 0 ] symmetric tilt grain boundaries at several temperatures and develop a modified mean squared displacement method for isolating the grain boundary diffusivity from the bulk diffusivity. We analyze the diffusivity data for the different boundaries and find the grain boundary diffusivity to be higher than the bulk diffusivity up to a temperature where the two converge. We test a model developed by Borisov et al. (Phys. Met. Metallogr. 17, 1964, 80-84) that relates grain boundary diffusion to grain boundary interfacial energy. Despite the fact that the Borisov relationship has never been used to examine solute interstitial diffusion before, it fits the simulated diffusion data well for temperatures where the grain boundary diffusivity is higher than the bulk diffusivity. Some parameters in the Borisov relationship, related to the geometry of the grain boundary and its activated states, have always taken on assumed values because they are hard to measure or acquire. The fit of the simulated data provides estimates for these values that are physically realistic and provides evidence that the use of the traditionally assumed values should be reconsidered. This work also demonstrates that while there is a need for further validation, the Borisov relationship can reasonably relate solute interstitial diffusivity of hydrogen to the interfacial energy of individual [ 1 0 0 ] symmetric tilt nickel grain boundaries, whereas in the past it has been used to relate self diffusion and interfacial energy of a grain boundary network as a whole.

Historically, attempts to correlate grain boundary (GB) structure and properties have relied on experimental measurements and computational calculations performed on bicrystals. While the resulting data can be precise, it is usually severely limited in quantity due to the cost and/or computational expense of sampling the full 5D GB character space. As a result, existing data is concentrated around highly-symmetric sub-regions. In contrast, polycrystals are ubiquitous, inexpensive, and contain a broad range of GB characters. However, extracting GB properties from the effective properties of polycrystals requires the solution of an inverse problem. In this work, we present a Bayesian framework, that we call GB property localization, to address both of these challenges by facilitating the inference of GB structure-property models from indirect polycrystal measurements and severely limited data (i.e. when the system is strongly underdetermined). The method naturally provides uncertainty quantification for the resulting inferences. We present the results of validation tests using 1DOF and 3DOF structure-property models for GB diffusivity in 2D (or columnar) microstructures, and we investigate the influence of the number of observations and the number of grains in a polycrystal on the inference quality. We identify a transition in the preferred type of data as a function of the number of observations: when data is abundant bicrystals lead to more accurate inferences; however when data is severely limited, polycrystals may provide more accurate results.

It is well known that grain boundaries (GBs) have a strong influence on mechanical properties of polycrystalline materials. Not as well-known is how different GBs interact with dislocations to influence dislocation movement. This work presents a molecular dynamics study of 33 different FCC Ni bicrystals, each subjected to four different strain states to induce incident dislocation-GB interactions for 132 unique configurations. The resulting simulations are analyzed to determine properties of the interaction that affect the likelihood of transmission of the dislocation through the GB in an effort to better inform mesoscale models of dislocation movement within polycrystals. It is found that the ability to predict the slip system of a transmitted dislocation using common geometric criteria is confirmed. Furthermore, machine learning processes are implemented revealing that geometric properties, such as the minimum potential residual Burgers vector (RBV) and the disorientation between the two grains, are stronger indicators of whether or not a dislocation would transmit than other properties, such as the resolved shear stress.

Machine learning has proven to be a valuable tool to approximate functions in high-dimensional spaces. Unfortunately, analysis of these models to extract the relevant physics is never as easy as applying machine learning to a large data set in the first place. Here we present a description of atomic systems that generates machine learning representations with a direct path to physical interpretation. As an example, we demonstrate its usefulness as a universal descriptor of grain boundary systems. Grain boundaries in crystalline materials are a quintessential example of a complex, high-dimensional system with broad impact on many physical properties including strength, ductility, corrosion resistance, crack resistance, and conductivity. In addition to modeling such properties, the method also provides insight into the physical “building blocks” that influence them. This opens the way to discover the underlying physics behind behaviors by understanding which building blocks map to particular properties. Once the structures are understood, they can then be optimized for desirable behaviors.

Studies of dislocation density evolution are fundamental to improved understanding in various areas of deformation mechanics. Recent advances in cross-correlation techniques, applied to electron backscatter diffraction (EBSD) data have particularly shed light on geometrically necessary dislocation (GND) behavior. However, the framework is relatively computationally expensive—patterns are typically saved from the EBSD scan and analyzed offline. A better understanding of the impact of EBSD pattern degradation, such as binning, compression, and various forms of noise, is vital to enable optimization of rapid and low-cost GND analysis. This paper tackles the problem by setting up a set of simulated patterns that mimic real patterns corresponding to a known GND field. The patterns are subsequently degraded in terms of resolution and noise, and the GND densities calculated from the degraded patterns using cross-correlation ESBD are compared with the known values. Some confirmation of validity of the computational degradation of patterns by considering real pattern degradation is also undertaken. The results demonstrate that the EBSD technique is not particularly sensitive to lower levels of binning and image compression, but the precision is sensitive to Poisson-type noise. Some insight is also gained concerning effects of mixed patterns at a grain boundary on measured GND content.

This study explores the evolution of GNDs and their effects on back stress through experimental and computational methods. Four large-grained tantalum tensile specimens were strained in uniaxial tension, electron backscatter diffraction (EBSD) data were collected, and geometrically necessary dislocation (GND) maps of the four specimens in the unloaded state were produced. EBSD-based GND maps revealed several types of features with high GND content which caused back stress in the specimens. Correlations between five geometrically-based grain boundary (GB) transmission factors and the GB GND content were evaluated, and statistically significant correlations were found for transmission factors based on Livingston and Chalmer's N factor, Werner and Prantl's slip transfer number, and GB misorientation. The sign of individual components of the Nye tensor were used to visually and quantitatively identify clustering of GNDs of the same sign, thus giving additional evidence of increasing back stress due to deformation. Deformation of one of the specimens was simulated using multiple CPFEM based modeling approaches and predicted stress-strain responses are compared. The super dislocation model (SD model) — a crystal plasticity finite element method (CPFEM) which incorporates elastic dislocation interactions — was able to isolate impact of back stress on the overall flow stress. The SD model predicted correct stresses when compared with experimental data; however, when the elastic interactions in the SD model were turned off, stress predictions were 25% too low. Thus, demonstrating the importance of incorporating back stress into the model.

Grain boundary (GB) motion in polycrystalline materials is expected and observed to be dominated by thermally activated processes. This has important implications for properties influenced by the presence of GBs. Here, the GB motions of a catalog of 388 simulated nickel boundaries reveal a rich set of behaviors, which demonstrate that the temperature dependencies of GB mobility are far more complex than originally believed. In the set of 388 boundaries, four different general classes were observed with the following percentages: (I) ~57% exhibited traditional thermally activated mobility; (II) ~20% exhibited non-thermally activated mobility, where mobility was either independent of temperature or mobility decreased with increasing temperature (i.e., not thermally activated); (III) ~14% exhibited mixed modes of mobility, where different trends were exhibited over different temperature regimes (e.g., thermally activated at low temperature and non-thermally activated at high temperature); and (IV) ~9% exhibited unclassifiable mobility trends or were immobile over the studied temperature range. Thus, although the studied set of boundaries is not statistically representative of all GBs, it indicates that we must expand our preconceived notions to include new and interesting phenomena.

Shear-coupled grain boundary motion is examined for a large number of grain boundaries including 73 〈1 0 0〉, 〈1 1 0〉 and 〈1 1 1〉 symmetric tilt boundaries. In the present work, the grain boundary motion is induced by a synthetic driving force as opposed to prior studies of shear coupling induced by applied shear. For those boundaries that are observed to undergo shear-coupled motion, the results based on the two driving forces agree well, both for experiments and simulations. This agreement also confirms the generality of the shear coupling mechanism over numerous boundaries and boundary types. The examination of boundary structure provides insight into the different trends that are observed. Shear coupling according to modes not predicted by the Frank–Bilby equation are also demonstrated. The temperature dependence of shear coupling is examined, and is consistent with prior work for symmetric tilt boundaries. While prior studies have emphasized symmetric tilt boundaries, some general grain boundaries exhibit shear coupling as well. In these boundaries, it is found that the shear coupling is either temperature independent, decreases in magnitude with increasing temperature or, in some cases, changes direction with temperature.

A method for the retrieval of grain-boundary inclination parameters of the grain-boundary character distribution (GBCD) by oblique double sectioning (ODS) is proposed. In this hybrid approach, grain-boundary inclination parameters are directly measured by double sectioning, while a statistically reliable sampling of the microstructure is achieved by oblique sectioning. The solution to the fundamental equations is posed in a manner similar to the recovery of the orientation distributions from sets of incomplete pole figures, using classical Fourier representations of the distribution functions. The ODS is validated by and compared to the L A /S V stereology through simulations and experimental implementation in a sample of 439 stainless steel. Simulations show that the grain-boundary normal distributions recovered by ODS and stereology are comparable, giving errors on the order of 10−2. Experimental implementation of ODS and the L A /S V stereology in alloy 439 stainless steel demonstrate additional practical limitations of the ODS methodology when applied to materials of large or uneven grain size.

Grain boundary plane orientation is a profoundly important determinant of character in polycrystalline materials that is not well understood. This work demonstrates how boundary plane orientation fundamental zones, which capture the natural crystallographic symmetries of a grain boundary, can be used to establish structure-property relationships. Using the fundamental zone representation, trends in computed energy, excess volume at the grain boundary and temperature-dependent mobility naturally emerge and show a strong dependence on the boundary plane orientation. Analysis of common misorientation axes even suggests broader trends of grain boundary energy as a function of misorientation angle and plane orientation. Due to the strong structure-property relationships that naturally emerge from this work, boundary plane fundamental zones are expected to simplify analysis of both computational and experimental data. This standardized representation has the potential to significantly accelerate research in the topologically complex and vast five-dimensional phase space of grain boundaries.

A method for the retrieval of the complete grain boundary character distribution by oblique double-sectioning is proposed. The method, which is similar to the recovery of the orientation distribution from sets of incomplete pole-figures, is efficient and provides many advantages as compared to calibrated serial sectioning. As compared to standard stereological approaches, the new methodology retains the advantage of direct measurement of the grain boundary inclination parameters. Solutions to the fundamental equation of oblique double-sectioning are provided in the Fourier space, and some specifics in sample preparation are introduced.

A method for estimating the variance of the grain boundary character distribution from experimental recovery of the two-point correlation functions is derived. The method is illustrated in 2-D to analyze the variance of “susceptible” boundaries in alloy 304 stainless steel. Comparison of these estimates with results obtained directly from OIM measurements is presented. Introduction When the phenomena governing failure in crystalline materials by fracture or crack propagation is intergranular in nature or a mixture of intergranular and transgranular behaviors, the character of the grain boundaries in the region surrounding the point of interest will govern much of the resulting behavior. Although conditions affecting this behavior will also be governed largely by the ductility and temperature under which the fracture occurs, the intergranular interfaces will affect the ability of the material to drive or stop this fracture [1,2]. Studies regarding stress corrosion cracking (SCC) have shown the effect of special boundaries upon the propagation of cracks in experimental samples [3-7]. Boundaries of low misorientation angle along with coincident site lattice (CSL) boundaries of low value inhibited the propagation of cracks in the material whereas boundaries with large misorientation angles were prone to propagate the crack. Accordingly, all references to “susceptible” grain boundaries in this publication will be of large misorientation angle excluding low value CSLs. The connectivity or percolation of grain boundaries of certain character has also proven to be a governing factor in the fracture mechanics of materials [8]. These percolative paths were found to be largely dependent upon percolation “red bonds” which have the ability or inability to impede these percolation paths [7]. Although these two conditions are clearly related in the failure of materials, the difficulty in relating the two is that percolation theory governs the behavior for infinite lattices and failure by fracture often only occurs in a small region; therefore linking the two becomes the probability of the two effects occurring in the same place and at the point of heightened stress. Therefore these two ideas may only be related when the region of interest is large. Research Perspective. The subject of interest is to develop a model which will link the fraction of grain boundaries necessary to develop a connected path of “susceptible” boundaries across a region of interest where the connected length would pose a serious threat to the integrity of the material. Although the probability of finding a cluster of connected length in a specified area has proven difficult because of the nature of percolation, the ability to determine the fraction of “susceptible” boundaries in a given region can be extracted readily. The authors are currently studying the percolative behavior of grain boundaries in alloy 304 stainless steel in order to establish this connection, but this discussion will be presented elsewhere. The focus of this paper will be on the determination of the variance of “susceptible” boundaries as a function of window size by a new method employing a two-point correlation function. The derivation along with experimental procedures and findings for the variance will be discussed. Variance of LA The Microstructure Function ) , ( s x M . In deriving the new method for sampling the variance of the grain boundary character distribution (GBCD), SV (s) , it is illustrative to consider the 2-D function LA(s), which is the line length per unit area of boundaries of local state s. Here local state refers to any selected set of parameters defining local grain boundary character, such as lattice misorientation, boundary inclination, etc. In 2-D measurements the latter is normally inaccessible. Consider the semi-continuous grain boundary network contained in a given field of view . LA(s) for the region can be recovered in two ways; the first of which is by deconstructing the data points from an Orientation Imaging Microscopy (OIM) dataset into discrete line segments, or grain boundary traces. By adding up the length of all the grain boundary traces of state s and dividing by the area of the scan, the true value for LA(s) can be obtained for the region . The second, new method requires allowing the grain boundary traces from the OIM scan to have a finite thickness, t, and then by sampling the region of interest with the vector x . Define a new microstructure function ) , ( s x M where ± = otherwise 0 type of boundary the from 2 within lies if 1 ) , ( s t x t s x M . (1) Integrating over the region of interest, and taking the limit as the thickness goes to zero one obtains the function LA(s) Ω = → 2 ) ( ) , ( ) ( 1 lim ) ( 0 R t A x d x s x M A s L θ (2)

Zhou and Mohles [J. Zhou, and V. Mohles, Acta Materialia 59, 5997 (2011)] recently presented a molecular dynamics (MD) simulation of grain boundary motion that contradicts the results of all previous such simulations. Here we show: (i) the Zhou–Mohles (Z–M) model incorporates a fundamental error in the definition of the atomic energy and forces; (ii) because of this error, the driving force for boundary motion is unknown; (iii) the Z–M model contains an additional, unrecognized, nonlinear driving force; and (iv) these observations explain and invalidate the Z–M results.

Resolving the mechanisms associated with grain boundary migration is a difficult task. This work is focused on detailing techniques to utilize atomistic simulations to better understand the energy, structure and mobility of grain boundaries (GBs). Various techniques are detailed on how to construct different simulation cells, select boundary plane normals, and measure simulated mobility. A limited number of GBs, inspired by experimental observations, are selected for the present work. The GBs studied indicate that the structure of the theoretical set of GBs has a structure consistent with an overall minimization of energy. The mobility simulations indicate that shear coupling is the preferred migration mechanism. However, when the same GBs are constrained, as might occur in polycrystalline networks, the relative mobilities of the set of GBs are significantly altered. Finally, the influence of deformation structures, as they pertain to GB migration during recrystallization, are discussed.