Pith. sign in

REVIEW 2 major objections 4 minor 37 references

Accurate grain boundary plane distributions for textured microstructures from stereological analysis of orthogonal two-dimensional electron backscatter diffraction orientation maps

T0 review · 2 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read This paper shows that pooling stereological data from three orthogonal EBSD sections produces qualitatively correct grain boundary plane distributions for heavily textured materials.

desk verdict Useful, honestly hedged benchmark showing three orthogonal sections fix the worst single-section bias in textured microstructures, but the 'texture strength' test never varies crystallographic texture, so the core claim is only supported at an unrealistic 50 MRD extreme. read the letter →

arxiv 2505.24798 v1 pith:NKQBF7EK submitted 2025-05-30 cond-mat.mtrl-sci

Martin Folwarczny , Ao Li , Rushvi Shah , Aaron Chote , Alexandra C. Austin , Yimin Zhu , Gregory S. Rohrer , Michael A. Jackson
show 2 more authors
Souhardh Kotakadi Katharina Marquardt
This is my paper
classification cond-mat.mtrl-sci
keywords grainboundaryplanedistributionstereologyEBSDcrystallographictexturecharacterfive-parametersyntheticmicrostructureanisotropy
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Grain boundary plane distributions (GBPDs) measure how often each crystallographic plane appears on grain boundaries, and they control many material properties. Measuring them from a single two-dimensional EBSD map is fast but fails for textured materials, because one section views different boundary types with different biases. This paper argues that combining EBSD maps from three mutually perpendicular sections removes part of that bias: the resulting GBPDs match the true distributions in pattern, identifying the dominant and rare boundary plane families. The method still overestimates the degree of anisotropy, so the authors recommend it for qualitative ranking of grain boundary planes rather than quantitative MRD values. It also requires the three sections to be aligned with the principal axes of the crystallographic texture.

What carries the argument

The load-bearing object is the grain boundary plane distribution plotted on a stereographic projection in units of multiples of a random distribution (MRD), computed by stereology from the orientations of grain boundary traces visible in 2D sections. The standard stereological estimator assumes that the observed traces sample boundary plane normals with uniform geometric probability; a single planar section of a textured material violates that assumption by viewing some boundary types nearly edge-on and omitting others. Pooling traces from three mutually perpendicular sections supplies the estimator with boundary orientations from three complementary viewing directions, partially restoring uniform sampling. The reference standard used to judge success is the GBPD computed from a triangular mesh of the full 3D grain boundary network, which contains all five macroscopic grain boundary parameters.

What would settle it

Take a real textured sample with texture intensity below 10 MRD, record EBSD maps from three orthogonal sections aligned with the texture axes, and compare the stereological GBPD to a ground truth from serial sectioning or synchrotron 3D mapping; if the dominant plane families do not match, or if a misaligned set still reproduces the pattern, the paper's central qualitative claim is refuted.

Watch

Extended reading notes

Core claim

The central claim is that stereological GBPD analysis, which normally assumes random observation perspectives, can be applied to heavily textured microstructures if the boundary trace data are pooled from three orthogonal two-dimensional EBSD sections. On synthetic hexagonal and tetragonal microstructures with known 3D ground truth, the pooled sections reproduced the qualitative GBPD pattern, showing the same dominant plane families and the same under-represented families, whereas individual sections often missed the most and least frequent planes entirely. Two caveats are part of the claim: the stereological GBPD overestimates the anisotropy, so maximum MRD values run too high, and the orthogonal sections must be aligned with the texture's principal axes, because a deliberately misaligned set produced a false maximum tilted by the misalignment angle.

Load-bearing premise

The synthetic microstructures—with textures up to 50 MRD, perfectly aligned grain shapes and crystal orientations, and no grain boundary energy—are a sufficient proxy for real textured materials to judge whether the three-section method gives qualitatively correct GBPDs.

Editorial extensions

If this is right

  • Single-section EBSD GBPDs in textured materials can be misleading, sometimes failing to show the most and least common boundary planes at all.
  • Three orthogonal sections are sufficient for qualitative identification of dominant grain boundary plane families in heavily textured hexagonal and tetragonal microstructures.
  • Quantitative MRD intensities from the combined-section method are not reliable because anisotropy is systematically overestimated.
  • Sections must be cut along the texture's principal axes; misaligned sections produce a GBPD with peaks shifted by the misalignment angle.
  • The ratio of stereological to true maximum intensity follows a linear trend with grain aspect ratio when only one ellipsoid axis is varied, suggesting a path toward a correction factor.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial inference: on real materials with weaker textures, the bias removed by three sections may be smaller, but the qualitative success could degrade because energy-driven boundary selection is absent from these geometric simulations.
  • Editorial inference: the linear overestimation ratio suggests an aspect-ratio-based correction is feasible, but the broken trend when the B axis changes indicates the correction may need more than a single scalar.
  • Editorial inference: a decisive experiment is to compare three-section stereology against serial-section ground truth on the same sample; the paper's own conclusion calls for exactly this verification.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 4 minor

Summary. The manuscript presents a stereological method for estimating grain boundary plane distributions (GBPDs) from EBSD data collected on three orthogonal sections of a textured polycrystal. The authors generate synthetic textured microstructures with hexagonal and tetragonal crystal symmetries using DREAM.3D, compute reference GBPDs from triangle meshes of the full 3D grain boundary network, and compare these to stereological GBPDs obtained from the exported 2D sections. They find that a single section often gives misleading dominant planes, whereas the combined three-section analysis reproduces the qualitative pattern of the ground-truth GBPD in their aligned cases, although the anisotropy (maximum MRD) is overestimated. They also show that when the orthogonal sections are not aligned with the texture principal axes the method fails, and they conclude that the sections must be aligned with those axes. The paper recommends the three-section approach for qualitative identification of dominant boundary planes in heavily textured samples and calls for a future correction algorithm.

Significance. The paper addresses a real practical problem: fast, cheap GBPD characterization of textured engineering materials from 2D EBSD data. The validation design is transparent and rigorous in several respects: ground-truth GBPDs are computed from independent 3D triangle-mesh data; the stereology code is a pre-existing, externally developed method; no free parameters are fitted; and synthetic microstructures allow direct comparison. The result that three orthogonal sections improve on single sections is useful and plausible. However, the demonstrated regime is narrow: the simulated ODF maxima (~50 MRD) are deliberately far above realistic values (<10 MRD), grain boundary energy is ignored, and the method requires exact alignment of the sectioning planes with the texture principal axes. The 'texture strength test' does not vary the crystallographic texture strength, only the morphological grain elongation, so the central claim of qualitative accuracy for textured microstructures is not shown to transfer to the texture-intensity range of real materials.

major comments (2)
  1. [§2.3, Table 2, Figures 10–11] The test described as a 'texture strength test' varies only the ellipsoid axis ratios (A:B:C), while the crystallographic ODF components (φ1 = 0°–80°, Φ = 0°, φ2 = 0°) and the associated distribution widths are identical to the original tetragonal dataset; the horizontal axis of Figure 11 is the ellipsoid aspect ratio A:C, not the ODF maximum intensity. Consequently, the test does not probe the dependence of the method on crystallographic texture strength. The only crystallographic texture intensity examined is the deliberately extreme approximately 50 MRD case, and Section 2.1 explains that this extreme was chosen to reduce the grain-shape/crystal-orientation mismatch. At realistic texture intensities (typically <10 MRD), that mismatch returns, and no measurement reported in the paper shows that the combined three-section stereology still reproduces the ground truth. Since the paper's central recommendation is for textured materials in general, this is a load-bearing gap; the authors' own Section 4 statement that 'it is not clear whether the same behaviour would be observed in real materials' is an explicit admission of this limitation.
  2. [§3 and §5] The agreement between the combined stereological GBPD and the ground truth is assessed only visually, with statements such as 'patterns corresponded well' (Section 5) and 'qualitatively correct' (abstract). No quantitative measure of agreement is provided, such as a correlation coefficient between the MRD values on a common grid, the mean absolute difference in MRD, or a metric of whether the top-ranked boundary planes are correctly identified. Because the paper's claim is that the method is 'qualitatively accurate,' a reproducible, quantitative metric would allow an objective assessment and would also permit a direct comparison of the three-section method against single-section results. Without such a metric, the central claim is difficult to falsify or to compare with future methods.
minor comments (4)
  1. [§3, Figure 12] There are several typographical errors, including 'GPBDs' for 'GBPDs' in the text near Figure 11, 'Mul ples of random distri u on' in the label near Figure 12, and 'expect ed' in Section 2.1; these should be corrected.
  2. [§2.2] The number of exported sections per direction and the spacing between them are not specified in Table 2 or in the text, despite being described as important for statistics and for avoiding sampling artefacts; please provide these values for reproducibility.
  3. [Figure 9 discussion] The text states that the combined GBPD is 'an averaged plot' of the individual section GBPDs; if this is meant literally, it is inaccurate because the stereological calculation is applied to the combined set of boundary segments, not to the separately computed GBPDs. Please clarify the wording.
  4. [§2.3] The phrase 'texture strength test' is misleading because the test varies grain elongation, not the crystallographic texture strength; consider renaming it to 'grain elongation test' or 'morphology test' to avoid confusion with the ODF intensity issue raised in the major comments.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the three-section stereology claim is benchmarked against an independently meshed 3D ground truth with no fitted parameters.

full rationale

The derivation chain is self-contained. The paper's central claim—that combining three orthogonal EBSD sections yields qualitatively correct GBPDs for heavily textured synthetic microstructures—is tested by comparing the stereological output (computed with the Rohrer-group code applied to 2D sections) against a ground truth obtained by triangular meshing of the full 3D grain boundary network of the same DREAM.3D microstructures. These are independent computational routes to the same quantities: the 2D section data are not used to construct or fit the 3D mesh truth, and no parameters are fitted to the ground truth before the comparison. Citations to Saylor et al. and Rohrer et al. supply the stereological algorithm and the 3D analysis function, but those are established, externally used tools rather than unverified premises imported from the present authors; Gregory Rohrer's co-authorship does not make the benchmark circular because the ground-truth calculation is a direct mesh-area computation, not a fitted model. The paper's self-citations are motivational (Saylor's suggestion of multiple sections) and methodological, not load-bearing in a way that forces the reported agreement. The concern that the 'texture strength test' varies grain elongation while keeping ODF intensity fixed at 50 MRD is a limitation in the scope of validation, not a circular step; it affects how strongly the qualitative-accuracy claim transfers to realistic textures, but it does not mean the reported comparison reduces to its inputs by construction.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

The central claim rests on several domain assumptions: the validity of the established stereological inversion, the sufficiency of three aligned orthogonal sections, the representativeness of the synthetic microstructures, and the accuracy of the triangle-mesh ground truth. No parameters are fitted in this paper.

assumptions (4)
  • domain assumption The established stereological inversion from 2D sections correctly recovers the true GBPD given unbiased sampling of boundary orientations.
    The paper applies the Rohrer group code [14,17,18] without re-deriving it; the validity of this inversion is a background assumption.
  • domain assumption Three orthogonal sections aligned with the texture principal axes provide a sufficiently unbiased sample of boundary plane orientations for qualitative GBPD estimation.
    This is the premise tested in the paper; it is confirmed only for the aligned synthetic cases (Figures 8-10) and shown to fail when misaligned (Figure 12).
  • domain assumption The synthetic microstructures with texture intensities up to 50 MRD, ellipsoidal grain shapes, and no grain boundary energy represent a valid test of the method for real textured materials.
    Section 2.1 deliberately uses textures stronger than real ones (less than 10 MRD) to make results more predictable; Section 4 notes the microstructures are non-physical because DREAM.3D ignores interfacial energy.
  • domain assumption The triangle mesh produced by DREAM.3D's Quick Surface Mesh and Laplacian Smoothing accurately represents the true grain boundary network, so the computed ground truth GBPD is reliable.
    Section 2.4 and Table 3 describe the meshing; smoothing could shift plane normals, but this effect is not quantified.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Accurate grain boundary plane distributions for textured microstructures from stereological analysis of orthogonal two-dimensional electron backscatter diffraction orientation maps." pith.science (2026). https://pith.science/paper/NKQBF7EK

@misc{pith2026250524798,
  author       = {Pith},
  title        = {Pith review of: Accurate grain boundary plane distributions for textured microstructures from stereological analysis of orthogonal two-dimensional electron backscatter diffraction orientation maps},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NKQBF7EK}},
  note         = {Machine review of arXiv:2505.24798}
}
read the original abstract

We present a method for obtaining qualitatively accurate grain boundary plane distributions (GBPD) for textured microstructures using a stereological calculation applied to two-dimensional electron backscatter diffraction (EBSD) orientation maps. Stereology, applied to 2D EBSD orientation maps, is currently the fastest method of obtaining GBPDs. Existing stereological methods are not directly applicable to textured microstructures because of the biased viewing perspectives for different grain boundary types supplied from a single planar orientation map. The method presented in this work successfully removes part of this bias by combining data from three orthogonal EBSD orientation maps for stereology. This is shown here to produce qualitatively correct GBPDs for heavily textured synthetic microstructures with hexagonal and tetragonal crystal symmetries. Synthetic microstructures were generated to compare the stereological GBPD to a known ground truth, as the true GBPD could be obtained from a triangular mesh of the full grain boundary network in 3D. The triangle mesh data contained all five macroscopic parameters to fully describe the grain boundary structure. It was observed that our stereological method overestimated the GBPD anisotropy. However, qualitative analysis of the GBPD remains useful. Furthermore, it was found that combining data from three orthogonal sections gives reliable results when sectioning the texture's primary axes.

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

37 extracted references · 27 canonical work pages

  1. [1]

    Bhattacharya, Y.-F

    A. Bhattacharya, Y.-F. Shen, C.M. Hefferan, S.F. Li, J. Lind, R.M. Suter, C.E. Krill, G.S. Rohrer, Grain boundary velocity and curvature are not correlated in Ni polycrystals, Science 374 (2021) 189 –

    work page 2021

  2. [2]

    Cantwell, M

    P.R. Cantwell, M. Tang, S.J. Dillon, J. Luo, G.S. Rohrer, M.P. Harmer, Grain boundary complexions, Acta Mater. 62 (2014) 1–48. https://doi.org/10.1016/j.actamat.2013.07.037

    doi:10.1016/j.actamat.2013.07.037 2014

  3. [3]

    G. Dehm, J. Cairney, Implication of grain -boundary structure and chemistry on plasticity and failure, MRS Bull. 47 (2022) 800–807. https://doi.org/10.1557/s43577-022-00378-3

    work page doi:10.1557/s43577-022-00378-3 2022

  4. [4]

    Marquardt, U.H

    K. Marquardt, U.H. Faul, The structure and composition of olivine grain boundaries: 40 years of studies, status and current developments, Phys. Chem. Miner. 45 (2018) 139 –172. https://doi.org/10.1007/s00269-017-0935-9

    doi:10.1007/s00269-017-0935-9 2018

  5. [5]

    Milan, M

    E. Milan, M. Pasta, The role of grain boundaries in solid-state Li-metal batteries, Mater. Futures 2 (2023) 013501. https://doi.org/10.1088/2752-5724/aca703

    work page doi:10.1088/2752-5724/aca703 2023

  6. [6]

    Sutton, R.W

    A. Sutton, R.W. Balluffi, Mechanical properties of interfaces, in: Interfaces in Crystalline Materials, Corr. ed., Clarendon Press, Oxford, 1996: pp. 704–803

    work page 1996

  7. [7]

    Sutton, R.W

    A. Sutton, R.W. Balluffi, Electronic properties of interfaces, in: Interfaces in Crystalline Materials, Corr. ed., Clarendon Press, Oxford, 1996: pp. 657–703

    work page 1996

  8. [8]

    avies, V

    H. avies, V. andle, Single section plane assessment in grain oundary engineered rass, J. Microsc. 205 (2002) 253–258. https://doi.org/10.1046/j.1365-2818.2002.00989.x

    arXiv 2002

Show all 37 references
  1. [9]

    Toyama, T

    S. Toyama, T. Seki, B. Feng, Y. Ikuhara, N. Shibata, Direct observation of space -charge-induced electric fields at oxide grain boundaries, Nat. Commun 15 (2024) 8704. https://doi.org/10.1038/s41467-024-53014-w. 18

    2024 doi

  2. [10]

    Molodov, T

    A. Molodov, T. Gorkaya, G. Gottstein, Migration of the Σ tilt grain oundary in Al under an applied external stress, Scr. Mater. 65 (2011) 990 –993. https://doi.org/10.1016/j.scriptamat.2011.08.030

    2011 doi

  3. [11]

    Dillon, Y

    S.J. Dillon, Y. -F. Shen, G.S. Rohrer, Grain boundary energies in yttria -stabilized zirconia, J. Am. Ceram. Soc. 105 (2022) 2925–2931. https://doi.org/10.1111/jace.18283

    2022 doi

  4. [12]

    Faryna, M

    M. Faryna, M. Adamczyk-Habrajska, M. Lubszczyk, Influence of grain boundary plane distribution on ionic conductivity in yttria -stabilized zirconia sintered at elevated temperatures, Archiv.Civ.Mech.Eng 24 (2024) 123. https://doi.org/10.1007/s43452-024-00935-4

    2024 doi

  5. [13]

    J. Han, V. Vitek, D.J. Srolovitz, Grain -boundary metastability and its statistical properties, Acta Mater. 104 (2016) 259–273. https://doi.org/10.1016/j.actamat.2015.11.035

    2016 doi

  6. [14]

    Rohrer, The distribution of grain boundary planes in polycrystals, JOM 59 (2007) 38 –42

    G.S. Rohrer, The distribution of grain boundary planes in polycrystals, JOM 59 (2007) 38 –42. https://doi.org/10.1007/s11837-007-0114-4

    2007 doi

  7. [15]

    Vonlanthen, B

    P. Vonlanthen, B. Grobety, CSL grain boundary distribution in alumina and zirconia ceramics, Ceram. Int. 34 (2008) 1459–1472. https://doi.org/10.1016/j.ceramint.2007.04.006

    2008 doi

  8. [16]

    Randle, ed., Theoretical Aspects of Grain Boundary Geometry I: General Boundaries, in: The Measurement of Grain Boundary Geometry, 1st ed., CRC Press, 1993

    V. Randle, ed., Theoretical Aspects of Grain Boundary Geometry I: General Boundaries, in: The Measurement of Grain Boundary Geometry, 1st ed., CRC Press, 1993

    1993

  9. [17]

    Saylor, B.S

    D.M. Saylor, B.S. El -Dasher, B.L. Adams, G.S. Rohrer, Measuring the five -parameter grain - boundary distribution from observations of planar sections, Metall. Mater. Trans. A 35 (2004) 1981–1989. https://doi.org/10.1007/s11661-004-0147-z

    2004 doi

  10. [18]

    Rohrer, D.M

    G.S. Rohrer, D.M. Saylor, B.E. Dasher, B.L. Adams, A.D. Rollett, P. Wynblatt, The distribution of internal interfaces in polycrystals, MEKU 95 (2004) 197 –214. https://doi.org/10.3139/146.017934

    2004 doi

  11. [19]

    Bernier, R.M

    J.V. Bernier, R.M. Suter, A.D. Rollett, J.D. Almer, High -Energy X-Ray Diffraction Microscopy in Materials Science, Annu. Rev. Mater. Res. 50 (2020) 395–436. https://doi.org/10.1146/annurev- matsci-070616-124125

    2020 doi

  12. [20]

    Pirgazi, K

    H. Pirgazi, K. Glowinski, A. Morawiec, L.A.I. Kestens, Three-dimensional characterization of grain boundaries in pure nickel by serial sectioning via mechanical polishing, J. Appl. Crystallogr. 48 (2015) 1672–1678. https://doi.org/10.1107/S1600576715017616

    2015 doi

  13. [21]

    Spowart, H.E

    J.E. Spowart, H.E. Mullens, B.T. Puchala, Collecting and analyzing microstructures in three dimensions: A fully automated approach, JOM 55 (2003) 35 –37. https://doi.org/10.1007/s11837-003-0173-0

    2003 doi

  14. [22]

    Uchic, Serial Sectioning Methods for Generating 3D Characterization Data of Grain - and Precipitate-Scale Microstructures, in: S

    M.D. Uchic, Serial Sectioning Methods for Generating 3D Characterization Data of Grain - and Precipitate-Scale Microstructures, in: S. Ghosh, D. Dimiduk (Eds.), Computational Methods for Microstructure-Property Relationships, Springer US, Boston, MA, 2 011: pp. 31 –52. https:/...

    doi

  15. [23]

    H.H. Liu, S. Schmidt, H.F. Poulsen, A. Godfrey, Z.Q. Liu, J.A. Sharon, X. Huang, Three-Dimensional Orientation Mapping in the Transmission Electron Microscope, Science 332 (2011) 833 –834. https://doi.org/10.1126/science.1202202

    2011 doi

  16. [24]

    W. Zhu, G. Wu, A. Godfrey, S. Schmidt, Q. He, Z. Feng, T. Huang, L. Zhang, X. Huang, Five - parameter grain boundary character distribution of gold nanoparticles based on three dimensional orientation mapping in the TEM, Scr. Mater. 214 (2022) 114677. https://doi.org/10.1016/j...

    2022

  17. [25]

    Groeber, A framework for automated analysis and simulation of 3D polycrystalline microstructures

    M. Groeber, A framework for automated analysis and simulation of 3D polycrystalline microstructures. Part 2: Synthetic structure generation, Acta Mater. 56 (2008) 1274 –1287. https://doi.org/10.1016/j.actamat.2007.11.040

    2008 doi

  18. [26]

    Groeber, M.A

    M.A. Groeber, M.A. Jackson, DREAM.3D: A Digital Representation Environment for the Analysis of Microstructure in 3D, Integr. Mater. Manuf. Innov. 3 (2014) 56 –72. https://doi.org/10.1186/2193-9772-3-5

    2014 doi

  19. [27]

    Motta, A

    A.T. Motta, A. Couet, R.J. Comstock, Corrosion of Zirconium Alloys Used for Nuclear Fuel Cladding, Annu. Rev. Mater. Res. 45 (2015) 311 –343. https://doi.org/10.1146/annurev-matsci- 070214-020951. 19

    2015 doi

  20. [28]

    Tong, T.B

    V.S. Tong, T.B. Britton, Formation of very large ‘ locky alpha’ grains in Zircaloy -4, Acta Mater. 129 (2017) 510–520. https://doi.org/10.1016/j.actamat.2017.03.002

    2017 doi

  21. [29]

    Wang, J.C

    Y.N. Wang, J.C. Huang, Texture analysis in hexagonal materials, Mater. Chem. Phys. 81 (2003) 11–26. https://doi.org/10.1016/S0254-0584(03)00168-8

    2003 doi

  22. [30]

    Barberis, Zirconia powders and Zircaloy oxide films: tetragonal phase evolution during 400°C autoclave tests, J

    P. Barberis, Zirconia powders and Zircaloy oxide films: tetragonal phase evolution during 400°C autoclave tests, J. Nucl. Mater. 226 (1995) 34 –43. https://doi.org/10.1016/0022 - 3115(95)00108-5

    1995 doi

  23. [31]

    Bouvier, J

    P. Bouvier, J. Godlewski, G. Lucazeau, A Raman study of the nanocrystallite size effect on the pressure–temperature phase diagram of zirconia grown by zirconium -based alloys oxidation, J. Nucl. Mater. 300 (2002) 118–126. https://doi.org/10.1016/S0022-3115(01)00756-5

    2002 doi

  24. [32]

    Garner, P

    A. Garner, P. Frankel, J. Partezana, M. Preuss, The effect of substrate texture and oxidation temperature on oxide texture development in zirconium alloys, Journal of Nuclear Materials 484 (2017) 347–356. https://doi.org/10.1016/j.jnucmat.2016.10.037

    2017 doi

  25. [33]

    Bachmann, R

    F. Bachmann, R. Hielscher, H. Schaeben, Texture Analysis with MTEX – Free and Open Source Software Toolbox, SSP 160 (2010) 63 –68. https://doi.org/10.4028/www.scientific.net/SSP.160.63

    2010 doi

  26. [34]

    Ahrens, B

    J. Ahrens, B. Geveci, C. Law, ParaView: An End -User Tool for Large -Data Visualization, in: Visualization Handbook, Elsevier, 2005: pp. 717–731. https://doi.org/10.1016/B978-012387582- 2/50038-1

    2005 doi

  27. [35]

    Britton, J

    T.B. Britton, J. Jiang, Y. Guo, A. Vilalta -Clemente, D. Wallis, L.N. Hansen, A. Winkelmann, A.J. Wilkinson, Tutorial: Crystal orientations and EBSD — Or which way is up?, Mater. Charact. 117 (2016) 113–126. https://doi.org/10.1016/j.matchar.2016.04.008

    2016 doi

  28. [36]

    Rohrer, Grain Boundary Crystallography, (2022)

    G.S. Rohrer, Grain Boundary Crystallography, (2022). http://mimp.materials.cmu.edu/rohrer/gbXstallography/ (accessed August 22, 2023)

    2022

  29. [193]

    https://doi.org/10.1126/science.abj3210

    doi

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.