Learning the grain boundary manifold: tools for visualizing and fitting grain boundary properties

Chesser, Ian; Francis, Toby; Graef, Marc De; Holm, Elizabeth A.

doi:10.1016/j.actamat.2020.05.024

Cited by 11 publications

(21 citation statements)

References 27 publications

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“…As the mis-orientation and the normal orientation can change during the microstructure evolution due to grain rotation or grain disappearance/appearance, the evolution of the metric could reveal important information about the structure–property relationship. Recent works by Chesser et al and Francis et al have proposed new metrics using octonions [ 70 , 71 ], revealing good predictions of GB energy of the data published by Olmsted in [ 72 ]. To the authors’ knowledge, the effect of the GB normal orientation is not clear, and more experimental, numerical, and theoretical works are needed.…”

Section: Accounting For Mis-orientation and Inclination Dependencementioning

confidence: 99%

Comparative Study and Limits of Different Level-Set Formulations for the Modeling of Anisotropic Grain Growth

et al. 2021

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In this study, four different finite element level-set (FE-LS) formulations are compared for the modeling of grain growth in the context of polycrystalline structures and, moreover, two of them are presented for the first time using anisotropic grain boundary (GB) energy and mobility. Mean values and distributions are compared using the four formulations. First, we present the strong and weak formulations for the different models and the crystallographic parameters used at the mesoscopic scale. Second, some Grim Reaper analytical cases are presented and compared with the simulation results, and the evolutions of individual multiple junctions are followed. Additionally, large-scale simulations are presented. Anisotropic GB energy and mobility are respectively defined as functions of the mis-orientation/inclination and disorientation. The evolution of the disorientation distribution function (DDF) is computed, and its evolution is in accordance with prior works. We found that the formulation called “Anisotropic” is the more physical one, but it could be replaced at the mesoscopic scale by an isotropic formulation for simple microstructures presenting an initial Mackenzie-type DDF.

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Section: Accounting For Mis-orientation and Inclination Dependencementioning

confidence: 99%

Comparative Study and Limits of Different Level-Set Formulations for the Modeling of Anisotropic Grain Growth

et al. 2021

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“…For example, Francis et al developed the octonion to compare and interpolate between GBs [122]. This was followed by a number of tools to examine the GB manifold [123]. Baird et al recently demonstrated an efficient interpolation technique in the 5D space using a Voronoi fundamental zone framework [87] as well as methods for quantitative cartography of the GB energy landscape [121].…”

Section: Gb Energy Trends In the 5d Spacementioning

confidence: 99%

Examination of computed aluminum grain boundary structures and interface energies that span the 5D space of crystallographic character

Homer,

Hart,

Owens

et al. 2022

Preprint

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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.

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“…Recently, a new GB representation, grain boundary octonions (GBOs), was reported [52] and tested [53]. The GBO representation is valuable for a number of applications.…”

Section: Prior Workmentioning

confidence: 99%

“…Laplacian kernel regression (similar to IDW) involving scaled pairwise distance matrices was later used with GBOs to predict properties of arbitrary GBs from a set of known values [53]. Using k-fold cross validation with k = 10 for 388 Ni GBE simulations [43] and an optimized scaling parameter, a RMSE of 0.0977 J m −2 was obtained compared to a constant, average model RMSE of 0.2243 J m −2 (56.4 % improvement).…”

Section: Prior Workmentioning

confidence: 99%

“…Using k-fold cross validation with k = 10 for 388 Ni GBE simulations [43] and an optimized scaling parameter, a RMSE of 0.0977 J m −2 was obtained compared to a constant, average model RMSE of 0.2243 J m −2 (56.4 % improvement). Due to computation time of pairwise distance matrices, this approach is currently "limited to datasets with several thousand or fewer" GBs [53].…”

Section: Prior Workmentioning

confidence: 99%

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Five Degree-of-Freedom Property Interpolation of Arbitrary Grain Boundaries via Voronoi Fundamental Zone Octonion Framework

Baird,

Homer,

Fullwood

et al. 2021

Preprint

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In this work we introduce the Voronoi fundamental zone octonion (VFZO) interpolation framework for grain boundary (GB) structure-property models and surrogates. The VFZO framework offers an advantage over other five degree-of-freedom (5DOF) based property interpolation methods because it is constructed as a point set in a manifold. This means that directly computed Euclidean distances approximate the original octonion distance with significantly reduced computation runtime (∼7 CPU minutes vs. 153 CPU days for a 50 000 × 50 000 pairwise-distance matrix). This increased efficiency facilitates lower interpolation error through the use of significantly more input data. We demonstrate grain boundary energy (GBE) interpolation results for a non-smooth validation function and simulated bi-crystal datasets for Fe and Ni using four interpolation methods: barycentric interpolation, Gaussian process regression (GPR) or Kriging, inverse-distance weighting (IDW), and nearest neighbor (NN) interpolation. These are evaluated for 50 000 random input GBs and 10 000 random prediction GBs. The best performance was achieved with GPR, which resulted in a reduction of the root mean square error (RMSE) by 83.0% relative to RMSE of a constant, average model. Likewise, interpolation on a large, noisy, molecular statics (MS) Fe simulation dataset improves performance by 34.4 % compared to 21.2 % in prior work. Interpolation on a small, low-noise MS Ni simulation dataset is similar to interpolation results for the original octonion metric (57.6 % vs. 56.4 %). A vectorized, parallelized, MATLAB interpolation function (interp5DOF.m) and related routines are available in our VFZO repository (gi thub.com/sgbaird-5dof/interp) which can be applied to other crystallographic point groups. The VFZO framework offers advantages for computing distances between GBs, estimating property values for arbitrary GBs, and modeling surrogates of computationally expensive 5DOF functions and simulations.

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Learning the grain boundary manifold: tools for visualizing and fitting grain boundary properties

Cited by 11 publications

References 27 publications

Comparative Study and Limits of Different Level-Set Formulations for the Modeling of Anisotropic Grain Growth

Comparative Study and Limits of Different Level-Set Formulations for the Modeling of Anisotropic Grain Growth

Examination of computed aluminum grain boundary structures and interface energies that span the 5D space of crystallographic character

Five Degree-of-Freedom Property Interpolation of Arbitrary Grain Boundaries via Voronoi Fundamental Zone Octonion Framework

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