Determining grain boundary energies from triple junction geometries without discretizing the five-parameter space

Shen, Yufeng; Zhong, Xiaoting; Li, He; Suter, Robert M.; Morawiec, Adam; Rohrer, Gregory S.

doi:10.1016/j.actamat.2018.12.022

Cited by 11 publications

(9 citation statements)

References 28 publications

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“…25 Simulations of the energy reconstruction process using a similar number of junctions and experimental uncertainties in the measured boundary orientation lead to the conclusion that the uncertainty of the energies is less than 0.03 relative units, and this uncertainty applies to all of the energies reported here. 25 The grain boundary character distribution, which is the relative areas of grain boundaries as a function of their five crystallographic parameters, was determined using a 3D reconstruction of the microstructure carried out in Dream.3D. 29 The pipelines used for the reconstruction are similar to the tutorial pipelines supplied with Dream.3D.…”

Section: Experimental Methodsmentioning

confidence: 62%

“…The Morawiec method has recently been improved, mainly by eliminating the need to discretize the fiveparameter space of grain boundary types, and this new method will be applied here to YSZ. 25 The purpose of this paper is to report on the relative grain boundary energies of YSZ. The microstructure of a YSZ ceramic was mapped by 3D electron backscatter diffraction (EBSD) using a dual beam-focused ion beam (DB-FIB) scanning electron microscope (SEM).…”

Section: Introductionmentioning

confidence: 99%

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Grain boundary energies in yttria‐stabilized zirconia

2021

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The three-dimensional microstructure of 8% yttria-stabilized zirconia (YSZ) was measured by electron backscatter diffraction and focused ion beam serial sectioning. The relative grain boundary energies as a function of all five crystallographic grain boundary parameters were determined based on the assumption of thermodynamic equilibrium at the internal triple junctions. Grain boundaries with (100) orientations have low energies compared to boundaries of other orientations, and all [100] twist boundaries have relatively low energies. Other classes of boundaries with lower than average energies include [100] symmetric tilt boundaries with disorientations less than 40 • and [111] twist boundaries with disorientations greater than 20 • . At fixed misorientations, the relative areas of boundaries are inversely correlated to the relative grain boundary energy. The results suggest that texturing microstructures to increase the relative areas of [100] twist boundaries might increase the oxygen ion conductivity of YSZ ceramics.

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Section: Experimental Methodsmentioning

confidence: 62%

Section: Introductionmentioning

confidence: 99%

Grain boundary energies in yttria‐stabilized zirconia

2021

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“…One such estimate for error is furnished by the work of Shen et al [74], who introduced a nondiscretizing approach to extract relative GB energies from polycrystalline samples using the locally optimal block preconditioned conjugate gradient method. Their approach utilizes regularization imposed on triple junction equilibrium equations and k-nearest neighbor distances.…”

Section: Experimental and Simulation Errormentioning

confidence: 99%

Section: Experimental and Simulation Errormentioning

confidence: 99%

“…Again comparing the relevant constant-valued control model 18 to the validation function employed by Shen et al [74], we calculate a RMSE and MAE of 0.0976 J m −2 and 0.0466 J m −2 , respectively. This implies that the validation model used by Shen et al [74] is also simpler 19 than the BRK validation model employed in the present work. 17 These errors are based on Figure 8 from Shen et al [74], which employed synthetic triple junctions with a custom validation function, rather than experimental data.…”

Section: Experimental and Simulation Errormentioning

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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Comparing Five and Lower-Dimensional Grain Boundary Character and Energy Distributions in Copper: Experiment and Molecular Statics Simulation

Korolev

Bean

Nevolin

et al. 2022

Metall Mater Trans A

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The misorientation of 515 grain boundaries has been determined using electron back scatter diffraction data from an 18 μm thick copper foil with columnar grain structure and a preferential {110} surface orientation. The energy of the grain boundaries was determined from the dihedral angles in the vicinity of grain boundary thermal grooves. The experimental grain boundary energy vs. misorientation angle shows deep minima for the low angle grain boundaries and small minima corresponding to the Σ3 and Σ9 grain boundaries. Only a small fraction of the coincidence site lattice grain boundaries demonstrate an increased occurrence frequency (compared to a random orientation distribution) and low energy. In parallel, the grain boundary energy for a subset of 400 symmetrical tilt grain boundaries was calculated using molecular statics simulations. There is a good agreement between the experiment and molecular statics modeling.

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Determining grain boundary energies from triple junction geometries without discretizing the five-parameter space

Cited by 11 publications

References 28 publications

Grain boundary energies in yttria‐stabilized zirconia

Grain boundary energies in yttria‐stabilized zirconia

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

Comparing Five and Lower-Dimensional Grain Boundary Character and Energy Distributions in Copper: Experiment and Molecular Statics Simulation

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