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Electron Backscatter Diffraction (EBSD) is a widely used approach for characterising the microstructure of various materials. However, it is difficult to accurately distinguish similar (body centred cubic and body centred tetragonal, with small tetragonality) phases in steels using standard EBSD software. One method to tackle the problem of phase distinction is to measure the tetragonality of the phases, which can be done using simulated patterns and cross-correlation techniques to detect distortion away from a perfectly cubic crystal lattice. However, small errors in the determination of microscope geometry (the so-called pattern or projection centre) can cause significant errors in tetragonality measurement and lead to erroneous results. This paper utilises a new approach for accurate pattern centre determination via a strain minimisation routine across a large number of grains in dual phase steels. Tetragonality maps are then produced and used to identify phase and estimate local carbon content. The technique is implemented using both kinetically simulated and dynamically simulated patterns to determine their relative accuracy. Tetragonality maps, and subsequent phase maps, based on dynamically simulated patterns in a point-by-point and grain average comparison are found to consistently produce more precise and accurate results, with close to 90% accuracy for grain phase identification, when compared with an image-quality identification method. The error in tetragonality measurements appears to be of the order of 1%, thus producing a commensurate ∼0.2% error in carbon content estimation. Such an error makes the technique unsuitable for estimation of total carbon content of most commercial steels, which often have carbon levels below 0.1%. However, even in the DP steel for this study (0.1 wt.% carbon) it can be used to map carbon in regions with higher accumulation (such as in martensite with nonhomogeneous carbon content). LAY DESCRIPTION: Electron Backscatter Diffraction (EBSD) is a widely used approach for characterising the microstructure of various materials. However, it is difficult to accurately distinguish similar (BCC and BCT) phases in steels using standard EBSD software due to the small difference in crystal structure. One method to tackle the problem of phase distinction is to measure the tetragonality, or apparent 'strain' in the crystal lattice, of the phases. This can be done by comparing experimental EBSD patterns with simulated patterns via cross-correlation techniques, to detect distortion away from a perfectly cubic crystal lattice. However, small errors in the determination of microscope geometry (the so-called pattern or projection centre) can cause significant errors in tetragonality measurement and lead to erroneous results. This paper utilises a new approach for accurate pattern centre determination via a strain minimisation routine across a large number of grains in dual phase steels. Tetragonality maps are then produced and used to identify phase and estimate local carbon content. The technique is implemented using both simple kinetically simulated and more complex dynamically simulated patterns to determine their relative accuracy. Tetragonality maps, and subsequent phase maps, based on dynamically simulated patterns in a point-by-point and grain average comparison are found to consistently produce more precise and accurate results, with close to 90% accuracy for grain phase identification, when compared with an image-quality identification method. The error in tetragonality measurements appears to be of the order of 1%, thus producing a commensurate error in carbon content estimation. Such an error makes an estimate of total carbon content particularly unsuitable for low carbon steels; although maps of local carbon content may still be revealing. Application of the method developed in this paper will lead to better understanding of the complex microstructures of steels, and the potential to design microstructures that deliver higher strength and ductility for common applications, such as vehicle components.

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).

Improved plasticity models require simultaneous experimental local strain and microstructural evolution data. Microscopy tools, such as electron backscatter diffraction (EBSD), that can monitor transformation at the relevant length-scale, are often incompatible with digital image correlation (DIC) techniques required to determine local deformation. In this paper, the viability of forescatter detector (FSD) images as the basis for the DIC study is investigated. Standard FSD and an integrated EBSD/FSD approach (Pattern Region of Interest Analysis System: PRIAS™) are analyzed. Simultaneous strain and microstructure maps are obtained for tensile deformation of Q&P 1180 steel up to ~14% strain. Tests on an undeformed sample that is simply shifted indicate a standard deviation of error in strain of around 0.4% without additional complications from a deformed surface. The method resolves strain bands at ~2 μm spacing but does not provide significant sub-grain strain resolution. Similar resolution was obtained for mechanically polished and electropolished samples, despite electropolished surfaces presenting a smoother, simpler topography. While the resolution of the PRIAS approach depends upon the EBSD step size, the 80 nm step size used provides seemingly similar resolution as 8,000× (22.7 nm) FSD images. Surface feature evolution prevents DIC analysis across large strain steps (>6% strain), but restarting DIC, using an FSD reference image from an interim strain step, allows reasonable DIC across the stress–strain curve. Furthermore, the data are obtained easily and provide complementary information for EBSD analysis.

Grain boundary character distributions (GBCD) are routinely measured from bulk microcrystalline samples by electron backscatter diffraction (EBSD) and serial sectioning can be used to reconstruct relative grain boundary energy distributions (GBED) based on the 3D geometry of triple lines, assuming that the Herring condition of force balance is satisfied. These GBEDs correlate to those predicted from molecular dynamics (MD); furthermore, the GBCD and GBED are found to be inversely correlated. For nanocrystalline thin films, orientation mapping via precession enhanced electron diffraction (PED) has proven effective in measuring the GBCD, but the GBED has not been extracted. Here, the established relative energy extraction technique is adapted to PED data from four sputter deposited samples: a 40 nm-thick tungsten film and a 100 nm aluminum film as-deposited, after 30 and after 150 minutes annealing at 400{\deg}C. These films have columnar grain structures, so serial sectioning is not required to determine boundary inclination. Excepting the most energetically anisotropic and highest population boundaries, i.e. aluminum {\Sigma}3 boundaries, the relative GBED extracted from these data do not correlate with energies calculated using MD nor do they inversely correlate with the experimentally determined GBCD for either the tungsten or aluminum films. Failure to reproduce predicted energetic trends implies that the conventional Herring equation cannot be applied to determine relative GBEDs and thus geometries at triple junctions in these films are not well described by this condition; additional geometric factors must contribute to determining triple junction geometry and boundary network structure in spatially constrained, polycrystalline materials., Comment: The document contains the manuscript, figure captions, and a short supplemental document with further details

The deformation of materials at cryogenic temperature is of interest for space, arctic, and fundamental science applications. In this work, a custom-built cooling system attached to a commercial picoindenter was used for in situ cryogenic microcompression testing of equal-channel angular-pressed copper with real-time electron backscatter diffraction. Stress-driven grain growth at cryogenic temperatures was observed during a series of elastic and plastic deformations. These results provide direct evidence for the previously predicted phenomenon, whereas previous ex situ examinations demonstrated coarsening after cryogenic loading when samples were not maintained at cryogenic temperatures between deformation and characterization.

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.

The space of possible grain boundary structures is vast, with 5 macroscopic, crystallographic degrees of freedom that define the character of a grain boundary. While numerous datasets of grain boundaries have examined this space in part or in full, we present a computed dataset of over 7304 unique aluminum grain boundaries in the 5D crystallographic space. Our sampling also includes a range of possible microscopic, atomic configurations for each unique 5D crystallographic structure, which total over 43 million structures. We present an overview of the methods used to generate this dataset, an initial examination of the energy trends that follow the Read-Shockley relationship, hints at trends throughout the 5D space, variations in GB energy when non-minimum energy structures are examined, and insights gained in machine learning of grain boundary energy structure-property relationships. This dataset, which is available for download, has great potential for insight into GB structure-property relationships., Comment: 16 pages, 10 figures

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.

U-Pu-Zr alloys are considered ideal metallic fuels for experimental breeder reactors because of their superior material properties and potential for increased burnup performance. However, significant constituent redistribution has been observed in these alloys when irradiated, or subject to a thermal gradient, resulting in inhomogeneity of both composition and phase, which, in turn, alters the fuel performance. The hybrid Potts-phase field method is reformulated for ternary alloys in a thermal gradient and utilized to simulate and predict constituent redistribution and phase transformations in the U-Pu-Zr nuclear fuel system. Simulated evolution profiles for the U-16Pu-23Zr (at. pct) alloy show concentric zones that are compared with published experimental results; discrepancies in zone size are attributed to thermal profile differences and assumptions related to the diffusivity values used. Twenty-one alloys, over the entire ternary compositional spectrum, are also simulated to investigate the effects of alloy composition on constituent redistribution and phase transformations. The U-40Pu-20Zr (at. pct) alloy shows the most potential for compositional uniformity and phase homogeneity, throughout a thermal gradient, while remaining in the compositional range of feasible alloys.

Forming limits and retained austenite (RA) transformation in Q&P 1180 steel are quantified as a function of plastic strain levels for three different strain paths. In-plane uniaxial tension testing was performed in a standard test frame, while limiting dome height tooling was employed for out-of-plane biaxial and plane strain tension experiments. Sheet specimens were tested incrementally for each strain path, and the RA content at each level of strain was measured using electron backscatter diffraction (EBSD). The biaxial tension strain path resulted in the greatest effective strain prior to necking at 0.355, compared to 0.123 for plane strain and 0.142 for uniaxial tension. EBSD measurements for various levels of plastic strain reveal a clear dependence of RA rate of transformation on strain path for the three linear strain paths that were employed in this work. Thinning strains appear to provide a slightly better correlation to RA transformation than effective strain levels, where biaxial tension achieved the greatest level just prior to necking, followed by plane-strain tension, and then uniaxial tension.

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.

A “bottom-up” representative volume element (RVE) for a dual phase steel was constructed based on measured microstructural properties (“microproperties”). This differs from the common procedure of inferring hypothetical microproperties by fitting to macroscopic behavior using an assumed micro-to-macrolaw. The bottom-up approach allows the assessment of the law itself by comparing RVE-predicted mechanical behavior with independent macroscopic measurements, thus revealing the nature of the controlling micromechanisms. An RVE for DP980 steel was constructed using actual microproperties. Finite element (FE) simulations of elastic-plastic transitions were compared with independent loading-unloading-loading and compression-tension experiments. Constitutive models of three types were utilized: 1) a standard continuum model, 2) a standard Crystal Plasticity (CP) model, and 3) a SuperDislocation (SD) model similar to CP but including the elastic interactions of discrete dislocations. These comparisons led to following conclusions: 1) While a constitutive model that ignores elastic interaction of defects can be fit to macroscopic or microscopic behavior, it cannot represent both accurately, 2) Elastic interactions among dislocations are the predominant source of nonlinearity in the nominally-elastic region (i.e. at stresses below the standard yield stress), and 3) Continuum stress inhomogeneity arising from the hard martensite / soft ferrite microstructure has a minor role in the observed transitional nonlinearity in the absence of discrete dislocation interactions.

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 effects of using a traction-free (plane-stress) assumption to obtain the full distortion tensor from high-resolution EBSD measurements are analyzed. Equations are derived which bound the traction-free error arising from angular misorientation of the sample surface; the error in recovered distortion is shown to be quadratic with respect to that misorientation, and the maximum 'safe' angular misorientation is shown to be 2.7 degrees. The effects of localized stress fields on the traction-free assumption are then examined by a numerical case study, which uses the Boussinesq formalism to model stress fields near a free surface. Except in cases where localized stress field sources occur very close to sample points, the traction-free assumption appears to be admirably robust.

Metallic glass matrix (MGM) composites demonstrate impressive plasticity over monolithic metallic glasses due to their ability to delocalize strain and inhibit shear band propagation. This work investigates various microstructural factors (volume fraction, length scale and yield strength) influencing strain delocalization in a model MGM composite. Shear transformation zone dynamics is utilized to model the amorphous phase while a local Taylor dislocation model is used for the crystalline phase. An N-factorial experiment examines replicates for various macro- and microscopic measures of strain delocalization and regression analysis is used to identify statistically significant trends in the data. The experiment shows that strain delocalization and the consequent ductility are most strongly influenced by a crystalline phase with a substantially lower yield stress than that of the amorphous matrix. It also shows that increased crystalline volume fraction alone is insufficient to promote strain delocalization in the case of a crystalline phase with high relative yield stress, and that a lower yield stress for the crystalline phase implies lower maximum stresses supported by the composite. Examination of shear band–inclusion interactions indicate that the nucleation and diffuse transmission of numerous shear bands is critical to the strain delocalization. The regression analysis provides continuous functional forms for the various relationships between properties that can be exploited to optimize the microstructure of MGM composites.

A mesoscale simulation by shear transformation zone (STZ) dynamics is used to analyze the initial stages of shear localization in amorphous metals, of which many details remain unresolved due to the difficulty in accessing the appropriate time- and length-scales. Examination of a constant strain-rate tensile test of a model amorphous metal reveals four different stages in the microscopic processes that lead to formation of a shear band. These stages are identified as: (i) STZ clustering, where potential nucleation sites form as STZ activations cluster in space; (ii) growth following nucleation, where a nascent shear band exhibits a propagating front that defines the shear band path; (iii) relaxation thickening, where the shear band thickens and relaxes the system down to the flow stress; and (iv) flow thickening, where the shear band exhibits prolonged thickening at the flow stress. The results are consistent with the literature but suggest that a shear band is defined by a front that propagates very quickly with negligible accumulated strain. This propagating front likely occurs below the resolution of current methods that only observe simultaneous slip in a shear band where significant strain can be accumulated at much slower rates. Analysis of a thermodynamic model also suggests a specific critical stress that is required to nucleate a shear band, after which the shear band is allowed to grow unconstrained.

A novel method of micromechanical stereoinference is reported which yields components and gradients of Nye’s GND tensor which are inaccessible by surface EBSD. In particular, it determines the Nye’s tensor gradients going into the sample bulk. The method overcomes limitations imposed by metal’s electron opacity by combining experimentally-accessible Nye’s tensor components and measured infinitesimal elastic distortion tensors with a solution to the underlying stress equilibrium equations. The full Nye’s tensor can be transformed into a crystal coordinate frame and interpreted in the context of slip systems, a more physical sense than in the sample or experimental frame. A demonstration of the method is given for a simulated microstructure. The method is largely robust to random experimental noise but may be sensitive to pattern-center errors.

A mesoscale model, shear transformation zone dynamics (STZ dynamics), is employed to investigate the connections between the structure and deformation of metallic glasses. The present STZ dynamics model is adapted to incorporate a structure-related state variable, and evolves via two competing processes: STZ activation, which creates free volume, vs. diffusive rearrangement, which annihilates it. The dynamical competition between these two processes gives rise to an equilibrium excess free volume that can be connected to flow viscosity via the phenomenological Vogel–Fulcher–Tammann relation in relaxed structures near the glass transition temperature. On the other hand, the excess free volume allows glasses to deform at low temperatures via shear localization into shear bands, even in the presence of internal stress distributions that arise upon cooling after processing., Massachusetts Institute of Technology. Institute for Soldier Nanotechnologies, United States. Defense Threat Reduction Agency (Contract HDTRA-11-1-0062)

In this work, we introduce and demonstrate a hybrid model that combines elements of the Monte Carlo Potts Model with those of the phase field model. This hybrid model is introduced as a method to simulate microstructural evolution processes that are kinetically controlled by long-range diffusion in multi-component systems. The hybrid model uses a digitized microstructure with each site characterized by its microstructural features and its composition. The total free energy of the system is defined by bulk chemical free energy as well as interfacial energy. The coupling between the microstructure and composition is achieved by using the total free energy to drive the evolution in both fields. The kinetics are simulated by a combination of Monte Carlo methods and solution of the Cahn–Hilliard equation. This model is applied to several example problems to demonstrate its capabilities. These are diffusion in single- and two-phase diffusion couples, grain growth in a two-phase system controlled by diffusion and diffusion phase transformation by nucleation and growth of a second phase.

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.

Low-load nanoindentation can be used to assess not only the plastic yield point, but the distribution of yield points in a material. This paper reviews measurements of the so-called nanoscale strength distribution (NSD) on two classes of materials: crystals and metallic glasses. In each case, the yield point has a significant spread (10–50% of the mean normalized stress), but the origins of the distribution are shown to be very different in the two materials classes. In crystalline materials the NSD can arise from thermal fluctuations and is attended by significant rate and temperature dependence. In metallic glasses well below their glass-transition temperature, the NSD is reflective of fluctuations in the sampled structure and is not very sensitive to rate or temperature. Computer simulations using shear transformation zone dynamics are used to separate the effects of thermal and structural fluctuations in metallic glasses, and support the latter as dominating the NSD of those materials at low temperatures. Finally, the role of the NSD as a window on structural changes due to annealing or prior deformation is discussed as a direction for future research on metallic glasses in particular.

A combined program of experiments and simulations is used to study the problem of cyclic indentation loading on metallic glasses. The experiments use a spherical nanoindenter tip to study shear band formation in three glasses (two based on Pd and one on Fe), after subjecting the glass to cycles of load in the nominal elastic range. In all three glasses, such elastic cycles lead to significant increases in the load required to subsequently trigger the first shear band. This cyclic hardening occurs progressively over several cycles, but eventually saturates. The effect requires cycles of sufficient amplitude and is not induced by sustained loading alone. The simulations employed a new shear transformation zone (STZ) dynamics code to reveal the local STZ operations that occur beneath an indenter during cycling. These results reveal a plausible mechanism for the observed cyclic hardening: local regions of confined microplasticity can develop progressively over several cycles, without being detectable in the global load–displacement response. It is inferred that significant structural change must attend such microplasticity, leading to hardening of the glass., United States. Office of Naval Research (Grant No. N00014-08-10312), United States. Army Research Office (National Defense Science and Engineering Graduate Fellowship), King Fahd University of Petroleum and Minerals

A new mesoscale modeling technique for the thermo-mechanical behavior of metallic glasses is proposed. The modeling framework considers the shear transformation zone (STZ) as the fundamental unit of deformation, and coarse-grains an amorphous collection of atoms into an ensemble of STZs on a mesh. By employing finite element analysis and a kinetic Monte Carlo algorithm, the modeling technique is capable of simulating glass processing and deformation on time and length scales greater than those usually attainable by atomistic modeling. A thorough explanation of the framework is presented, along with a specific two-dimensional implementation for a model metallic glass. The model is shown to capture the basic behaviors of metallic glasses, including high-temperature homogeneous flow following the expected constitutive law, and low-temperature strain localization into shear bands. Details of the effects of processing and thermal history on the glass structure and properties are also discussed., United States. Office of Naval Research (contract N00014-08-1-0312)

Designers have traditionally simplified the consideration of material properties because of the diffi culty in incorporating anisotropy and non-homogeneity into design problems. Microstructure sensitive design for performance optimization (MSDPO) introduces the necessary tools to optimize both geometric design and anisotropic material properties concurrently, while also considering heterogeneous placement. In this paper a case study is presented wherein the geometry and microstructure of a micro-electro-mechanical system switch are optimized to minimize the actuation voltage, while ensuring that plastic yielding does not occur during operation. This is accomplished by varying both beam width and crystallographic texture along the length of the beam. The designed switch is predicted to reduce the actuation voltage by 90%. While this case study does not identify the manufacturing processes required to produce the optimized microstructure, such considerations can be included in MSDPO, but lie beyond the scope of this paper.

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.