# Origins of DREAM3D

## Publications That Describe Algorithms Contained In DREAM3D¶

[1] S. P. Donegan, J. C. Tucker, A. D. Rollett, K. Barmak, and M. Groeber. Extreme value analysis of tail departure from log-normality in experimental and simulated grain size distributions. Acta materialia, 61(15):5595-5604, 2013.

Grain size data were taken from four three- and two-dimensional microstructures, including simulated grain growth, thin film and superalloy data sets. Probability plots revealed approximately log-normal distributions for experimental grain size data sets, but with systematic differences in the upper tails. A simulated grain size data set obtained from Potts model growth exhibited strong deviation from log-normality. A peaks-over-threshold analysis was applied to quantify the differences in the upper tails. Potts model simulation of normal grain growth shows the shortest tail, whereas the thin film data showed the longest tail (i.e. closest to log-normal), with an intermediate tail shape in the superalloy. (C) 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

[2] J. C. Tucker, L. H. Chan, G. S. Rohrer, M. A. Groeber, and A. D. Rollett. Tail departure of log-normal grain size distributions in synthetic three-dimensional microstructures. Metallurgical And Materials Transactions A-Physical Metallurgy And Materials Science, 43A(8):2810-2822, 2012. 8th Symposium on Bulk Metallic Glasses (BMGs)/TMC Annual Meeting and Exhibition FEB 27-MAR 03, 2011 San Diego, CA TMS, ASM.

[3] J. C. Tucker, L. H. Chan, G. S. Rohrer, M. A. Groeber, and A. D. Rollett. Comparison of grain size distributions in a ni-based superalloy in three and two dimensions using the saltykov method. Scripta materialia, 66(8):554-557, 2012.

[4] S. D. Sintay and A. D. Rollett. Testing the accuracy of microstructure reconstruction in three dimensions using phantoms. Modelling and Simulation in Materials Science and Engineering, 20(7), 2012. 075005.

[5] S. Y. Wang, E. A. Holm, J. Suni, M. H. Alvi, P. N. Kalu, and A. D. Rollett. Modeling the recrystallized grain size in single phase materials. Acta materialia, 59(10):3872-3882, 2011.

[6] M. D. Uchic, M. A. Groeber, and A. D. Rollett. Automated serial sectioning methods for rapid collection of 3-d microstructure data. Jom, 63(3):25-29, 2011.

[7] I. M. Robertson, C. A. Schuh, J. S. Vetrano, N. D. Browning, D. P. Field, D. J. Jensen, M. K. Miller, I. Baker, D. C. Dunand, R. Dunin-Borkowski, B. Kabius, T. Kelly, S. Lozano-Perez, A. Misra, G. S. Rohrer, A. D. Rollett, M. L. Taheri, G. B. Thompson, M. Uchic, X. L. Wang, and G. Was. Towards an integrated materials characterization toolbox. Journal of Materials Research, 26(11):1341-1383, 2011.

The material characterization toolbox has recently experienced a number of parallel revolutionary advances, foreshadowing a time in the near future when material scientists can quantify material structure evolution across spatial and temporal space simultaneously. This will provide insight to reaction dynamics in four-dimensions, spanning multiple orders of magnitude in both temporal and spatial space. This study presents the authors' viewpoint on the material characterization field, reviewing its recent past, evaluating its present capabilities, and proposing directions for its future development. Electron microscopy; atom probe tomography; x-ray, neutron and electron tomography; serial sectioning tomography; and diffraction-based analysis methods are reviewed, and opportunities for their future development are highlighted. Advances in surface probe microscopy have been reviewed recently and, therefore, are not included [D.A. Bonnell et al.: Rev. Modern Phys. in Review]. In this study particular attention is paid to studies that have pioneered the synergetic use of multiple techniques to provide complementary views of a single structure or process; several of these studies represent the state-of-the-art in characterization and suggest a trajectory for the continued development of the field. Based on this review, a set of grand challenges for characterization science is identified, including suggestions for instrumentation advances, scientific problems in microstructure analysis, and complex structure evolution problems involving material damage. The future of microstructural characterization is proposed to be one not only where individual techniques are pushed to their limits, but where the community devises strategies of technique synergy to address complex multiscale problems in materials science and engineering.

[8] A. Khorashadizadeh, D. Raabe, S. Zaefferer, G. S. Rohrer, A. D. Rollett, and M. Winning. Five-parameter grain boundary analysis by 3d ebsd of an ultra fine grained cuzr alloy processed by equal channel angular pressing. Advanced Engineering Materials, 13(4):237-244, 2011.

The 3D grain boundary character distribution (GBCD) of a sample subjected to equal channel angular pressing (ECAP) after eight passes and successive annealing at 650 degrees C for about 10 min is analyzed. The experiments are conducted using a dual beam system, which is a combination of a focused ion beam and a scanning electron microscope to collect a series of electron backscatter diffraction (EBSD) maps of the microstructure (3D EBSD). The data set was aligned and reconstructed to a 3D microstructure. The crystallographic character of the grain boundary planes was determined using three different methods, namely, the line segment method, the stereological method, and the triangular surface mesh method. The line segment and triangular surface mesh methods produce consistent data sets, both yielding approximately a 7% area fraction of coherent twins. These results starkly contrast that of the statistical stereological method, which produced a 44% area fraction of coherent twins.

[9] G. S. Rohrer, J. Li, S. Lee, A. D. Rollett, M. Groeber, and M. D. Uchic. Deriving grain boundary character distributions and relative grain boundary energies from three-dimensional ebsd data. Materials Science and Technology, 26(6):661-669, 2010.

Three-dimensional electron backscatter diffraction data, obtained by serial sectioning a nickel base superalloy, has been analysed to measure the geometric arrangement of grain boundary planes at triple junctions. This information has been used to calculate the grain boundary character distribution (GBCD) and the grain boundary energy distribution (GBED). The twin content from the three-dimensional GBCD calculation compares favourably with the twin content estimated by stereology. Important factors in the analysis are the alignment of the parallel layers, the ratio of the out-of-plane to in-plane spacing of the discrete orientation data and the discretisation of the domain of grain boundary types. The results show that grain boundaries comprised of (111) planes occur most frequently and that these grain boundaries have a relatively low energy. The GBCD and GBED are inversely correlated.

[10] L. Wang, S. R. Daniewicz, M. F. Horstemeyer, S. Sintay, and A. D. Rollett. Three-dimensional finite element analysis using crystal plasticity for a parameter study of fatigue crack incubation in a 7075 aluminum alloy. International Journal of Fatigue, 31(4):659-667, 2009.

Three-dimensional finite element analysis of a bicrystal using a crystal plasticity constitutive theory was performed to compute the maximum plastic shear strain range Delta gamma(p)(max) in the matrix, at the particle/matrix interface, and at the bicrystal boundary. Using the finite element analysis results, a design of experiments (DOE) technique was employed to understand and quantify the effects of seven parameters on fatigue crack incubation: applied displacement, load ratio, particle modulus, the number of initially active slip systems, the relative crystallographic misorientation at the grain boundary, the particle aspect ratio, and the normalized particle size. The simulations clearly showed that the applied displacement is the most influential parameter. In most cases, particles were found to be more significant than bicrystal boundaries for incubation. The number of initially active slip systems, the particle aspect ratio, and the normalized particle size showed some influences on fatigue incubation. The particle modulus was the least influential parameter. (C) 2008 Elsevier Ltd. All rights reserved.

[11] L. Wang, S. R. Daniewicz, M. F. Horstemeyer, S. Sintay, and A. D. Rollett. Three-dimensional finite element analysis using crystal plasticity for a parameter study of microstructurally small fatigue crack growth in a aa7075 aluminum alloy. International Journal of Fatigue, 31(4):651-658, 2009.

Three-dimensional finite element analysis using a crystal plasticity constitutive theory was performed to understand and quantify various parametric effects on microstructurally small fatigue crack growth in a AA7075 aluminum alloy. Plasticity-induced crack opening stresses (S-o/S-max) were computed, and from these results the crack propagation life N was obtained. A design of experiments (DOE) technique was used to study the influences of seven parameters (maximum load, load ratio, particle modulus, the number of initially active slip systems, misorientation angle, particle aspect ratio, and the normalized particle size) on fatigue crack growth. The simulations clearly showed that the load ratio is the most influential parameter on crack growth. The next most influential parameters are maximum load and the number of initially active slip systems. The particle modulus, misorientation angle, particle aspect ratio, and the normalized particle size showed less influence on crack growth. Another important discovery in this study revealed that the particles were more important than the grain boundaries for inducing resistance for microstructurally small fatigue crack growth. (C) 2008 Elsevier Ltd. All rights reserved.

[12] A. Brahme, J. Fridy, H. Weiland, and A. D. Rollett. Modeling texture evolution during recrystallization in aluminum. Modelling and Simulation in Materials Science and Engineering, 17(1):015005, 2009. 015005.

The main aim of this work was to develop a model with predictive capability for microstructural evolution during recrystallization and to identify factors that exert the greatest effect on the development of texture. To achieve this aim, geometric and crystallographic observations from two orthogonal sections through a polycrystal were used as input to the computer simulations, to create a statistically representative three-dimensional model. Assignment of orientations to the grains was performed so as to optimize agreement between the orientation and misorientation distributions of assigned and observed orientations. The microstructures thus created were allowed to evolve using a Monte Carlo simulation. As a demonstration of the model the effects of anisotropy, both in energy and in mobility, stored energy and oriented nucleation (ON) on overall texture development were studied. The results were analyzed with reference to the various established competing theories of ON and oriented growth. The results suggested that all of ON, mobility anisotropy, stored energy and energy anisotropy (listed in order of their relative importance) influence texture development. It was also determined that comparison of simulated and measured textures throughout the recrystallization process is a more severe test of a model than the typical comparison of textures only at the end of the process.

[13] A. D. Rollett, S. B. Lee, R. Campman, and G. S. Rohrer. Three-dimensional characterization of microstructure by electron back-scatter diffraction. Annual Review of Materials Research, 37:627-658, 2007.

The characterization of microstructures in three dimensions is reviewed, with an emphasis on the use of automated electron back-scatter diffraction techniques. Both statistical reconstruction of polycrystalline structures from multiple cross sections and reconstruction from parallel, serial sections are discussed. In addition, statistical reconstruction of second-phase particle microstructures from multiple cross sections is reviewed.

[14] C. G. Roberts, S. L. Semiatin, and A. D. Rollett. Particle-associated misorientation distribution in a nickel-base superalloy. Scripta Materialia, 56(10):899-902, 2007. Roberts, C. G. Semiatin, S. L. Rollett, A. D.

[15] A. D. Rollett, R. Campman, and D. Saylor. Three dimensional microstructures: Statistical analysis of second phase particles in AA7075-T651, volume 519-521 of Materials Science Forum, pages 1-10. 2006.

This paper describes some aspects of reconstruction of microstructures in three dimensions. A distinction is drawn between tomographic approaches that seek to characterize specific volumes of material, either with or without diffraction, and statistical approaches that focus on particular aspects of microstructure. A specific example of the application of the statistical approach is given for an aerospace aluminum alloy in which the distributions of coarse constituent particles are modeled. Such distributions are useful for modeling fatigue crack initiation and propagation.

[16] C. S. Kim, A. D. Rollett, and G. S. Rohrer. Grain boundary planes: New dimensions in the grain boundary character distribution. Scripta materialia, 54(6):1005-1009, 2006.

The five parameter grain boundary character distribution quantifies the relative areas of different types of grain boundaries, distinguished by their lattice misorientation and grain boundary plane orientation. The viewpoint presented in this paper is that this distribution is a sensitive metric of polycrystalline structure that can be related to macroscopic properties. To demonstrate the influence of the grain boundary character distribution oil macroscopic properties, the stored elastic energy is calculated in model microstructures. (c) 2005 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

[17] Y. S. Choi, A. D. Rollett, and H. R. Piehler. Application of two-point orientation auto-correlation function (tp-oacf). Materials Transactions, 47(5):1313-1316, 2006.

A two-point orientation auto-correlation function (TP-OACF) was developed in order to quantify the spatial distribution of targeted texture components. An example of a TP-OACF was demonstrated using an idealized orientation map. Characteristics of the spatial distribution of major texture components in 6022-T4 Al sheets deformed in plane-strain tension were also quantified using a TP-OACF. The results showed that 110 < 112 > and 123 < 634 > orientations (in ND < PD > notation, where PD is the pulling direction) tend to form localized diagonal and horizontal bands through the thickness, respectively, after the plane-strain deformation. The cube orientation on the surface initially showed a relatively strong texture band along the RD, but this banding behavior was less significant after the plane-strain deformation.

[18] A. Brahme, M. H. Alvi, D. Saylor, J. Fridy, and A. D. Rollett. 3d reconstruction of microstructure in a commercial purity aluminum. Scripta materialia, 55(1):75-80, 2006.

[19] J. H. Cho, A. D. Rollett, and K. H. Oh. Determination of a mean orientation in electron backscatter diffraction measurements. Metallurgical And Materials Transactions A-Physical Metallurgy And Materials Science, 36A(12):3427-3438, 2005.

The average orientation of an electron backscatter diffraction (EBSD) map is calculated by the quaternion method and is compared with nonlinear solving by the Hill Climbing and Barton-Davison methods. An automated EBSD system acquires orientations on a regular grid of pixels based on indexation of Kikuchi patterns and the orientation is described by one of the crystal symmetry-related equivalents; In order to calculate the quaternion average, it is necessary to make a cloud for a set of pixels in a grain. A cloud consists of the representative orientations with small misorientation between each and every pair of points. The position criterion says that two adjacent pixels have a smaller misorientation than with all others. With this, the proper equivalent orientation, or representative orientation, for the cloud, can be selected from among all the crystal symmetry-related equivalents. The orientation average is the quaternion summation divided by its norm. The instant average or cumulative average is useful for dealing with polycrystalline grains or orientation discontinuity and is also useful for selection of the proper orientation of EBSD map with large scattering. The quaternion, Hill Climbing, and Barton-Dawson nonlinear methods are tested with a Gaussian distribution around the ideal texture component, Brass 110 < 112 >. The accuracy of the three results is similar but the nonlinear methods are associated with longer computation times than the quaternion method. The quaternion method is adapted for characterization of a partially-recrystallized interstitial-free (IF) steel and randomly distributed Brass, S, and cube texture components according to several different orientation spreads.

[20] D. M. Saylor, J. Fridy, B. S. El-Dasher, K. Y. Jung, and A. D. Rollett. Statistically representative three-dimensional microstructures based on orthogonal observation sections.

Metallurgical And Materials Transactions A-Physical Metallurgy And Materials Science, 35A(7):1969-1979, 2004. Techniques are described that have been used to create a statistically representative three-dimensional model microstructure for input into computer simulations using the geometric and crystallographic observations from two orthogonal sections through an aluminum polycrystal. Orientation maps collected on the observation planes are used to characterize the sizes, shapes, and orientations of grains. Using a voxel-based tessellation technique, a microstructure is generated with grains whose size and shape are constructed to conform to those measured experimentally. Orientations are then overlaid on the grain structure such that distribution of grain orientations and the nearest-neighbor relationships, specified by the distribution of relative misorientations across grain boundaries, match the experimentally measured distributions. The techniques are applicable to polycrystalline materials with sufficiently compact grain shapes and can also be used to controllably generate a wide variety of hypothetical microstructures for initial states in computer simulations.

[21] D. M. Saylor, B. S. El Dasher, A. D. Rollett, and G. S. Rohrer. Distribution of grain boundaries in aluminum as a function of five macroscopic parameters. Acta materialia, 52(12):3649-3655, 2004.

The grain boundary character distribution in commercially pure Al has been measured as a function of lattice misorientation and boundary plane orientation. The results demonstrate a tendency to terminate grain boundaries on low index planes with relatively low surface energies and large interplanar spacings. The most frequently observed grain boundary plane orientation is (1 1 1). However, there are also instances where boundaries terminated by higher index planes have significant populations. For example, certain twist configurations on 1 1 w planes, which correspond to symmetric [1 1 0] tilt boundaries, also have relatively high populations. The population of symirietric [1 1 0] tilt boundaries exhibits an inverse relationship with previously measured energies. (C) 2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

[22] D. M. Saylor, B. El Dasher, Y. Pang, H. M. Miller, P. Wynblatt, A. D. Rollett, and G. S. Rohrer. Habits of grains in dense polycrystalline solids. Journal of The American Ceramic Society, 87(4):724-726, 2004.

[23] A.D. Rollett, D.M. Saylor, J. Fridy, B.S. El-Dasher, A. Brahme, S.-B. Lee, C. Cornwell, and R. Noack. Modeling microstructures in 3d. In S. Ghosh, J.C. Castro, and J.K. Lee, editors, NUMIFORM 2004, pages 71-77. Amer. Inst. of Physics.

Many issues in forming are influenced to some degree by the internal structure of the material which is commonly referred to by the materials science community as microstructure. Although the term microstructure is commonly only thought of in the context of grain size, it more properly encompasses all relevant aspects of internal material structure. For the purposes of forming, the most relevant features are the crystallographic orientations of the grains (texture) and the locations of the grain boundaries, or, equivalently, the size, topology and shape of the grains. In order to perform realistic simulations one needs to specify the initial state of the material, e.g. on a finite element mesh, with sufficient detail that all these features are reproduced. Measuring microstructure at the scale of individual grains is possible in the synchrotron but scarcely practicable for an analyst. Cross-sections or surfaces are easily evaluated through automated diffraction in the scanning electron microscope (SEM), however. Therefore this paper describes a set of methods for generating statistically representative 3D microstructures based on microscopy input for both single-phase and two-phase materials. Examples are given of application of the technique for generating input structures for recrystallization simulation, dynamic deformation and finite element modeling. Keywords: microstructure computer simulation texture reconstruction Voronoi tessellation EBSD Al

[24] G. S. Rohrer, D. M. Saylor, B. El Dasher, B. L. Adams, A. D. Rollett, and P. Wynblatt. The distribution of internal interfaces in polycrystals. Zeitschrift Fur Metallkunde, 95(4):197-214, 2004.

[25] H. M. Miller, D. M. Saylor, B. S. El Dasher, A. D. Rollett, and G. S. Rohrer. Crystallographic distribution of internal interfaces in spinel polycrystals. Materials Science Forum, 467-470:783-788, 2004. Measurements of the grain boundary character distribution in MgAl2O4 (spinel) as a function of lattice misorientation and boundary plane orientation show that at all misorientations, grain boundaries are most frequently terminated on 111 planes. Boundaries with 111 orientations are observed 2.5 times more frequently than boundaries with 100 orientations. Furthermore, the most common boundary type is the twist boundary formed by a 60 rotation about the [111] axis. 111 planes also dominate the external form of spinel crystals found in natural settings and this suggests that they are low energy and/or slow growing planes. The mechanisms that might lead to a high population of these planes during solid state crystal growth are discussed. Keywords: Grain Boundary Character Distribution Grain Boundary Planes Stereology Spinel microstructure

[26] J. H. Cho, A. D. Rollett, and K. H. Oh. Determination of volume fractions of texture components with standard distributions in euler space. Metallurgical And Materials Transactions A-Physical Metallurgy And Materials Science, 35A(3A):1075-1086, 2004.

The intensities of texture components are modeled by Gaussian distribution functions in Euler space. The multiplicities depend on the relation between the texture component and the crystal and sample symmetry elements. Higher multiplicities are associated with higher maximum values in the orientation distribution function (ODF). The ODF generated by Gaussian function shows that the S component has a multiplicity of 1, the brass and copper components, 2, and the Goss and cube components, 4 in the cubic crystal and orthorhombic sample symmetry. Typical texture components were modeled using standard distributions in Euler space to calculate a discrete ODF, and their volume fractions were collected and verified against the volume used to generate the ODE The volume fraction of a texture component that has a standard spherical distribution can be collected using the misorientation approach. The misorientation approach means integrating the volume-weighted intensity that is located within a specified cut-off misorientation angle from the ideal orientation. The volume fraction of a sharply peaked texture component can be collected exactly with a small cut-off value, but textures with broad distributions (large full-width at half-maximum (FWHM)) need a larger cut-off value. Larger cut-off values require Euler space to be partitioned between texture components in order to avoid overlapping regions. The misorientation approach can be used for texture's volume in Euler space in a general manner. Fiber texture is also modeled with Gaussian distribution, and it is produced by rotation of a crystal located at g(0), around a sample axis. The volume of fiber texture in wire drawing or extrusion also can be calculated easily in the unit triangle with the angle distance approach.

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