mtex-grain-size

Functions for ASTM (and ISO) grain size characterization from electron backscatter diffraction (EBSD) data using the MTEX toolbox for MATLAB ¹

This software package provides the following functions:

• Measurement of $\bar{A}$ following the ASTM E 112 standard for the following planimetric methods
  • Jeffries
  • Saltikov
• Measurement of $\bar{l}$ following the ASTM E 112 standard for the following intercept methods
  • Heyn
  • Abrams
• Measurement of $N_A$ following the ASTM E 112 standard for the Hilliard method
• Measurement of $\bar{A}$ following the ASTM E 2627 (EBSD-specific) standard (with 100 px minimum grain size) ²
• Measurement of the as-large-as (ALA) grain size following ASTM E 930
• Measurement of the grain size using the Triple Point Count method described by Van der Voort ³
• Calculation of the field statistics following the reporting format described in ASTM E 112, Section 15
• Conversion of $\bar{A}$, $\bar{l}$, and $N_A$ measured in microns, as obtained from the included functions, into ASTM $G$

Requirements

The code in this repository has been developed and tested on:

• MTEX Toolbox: Version 5.11.2
• MATLAB: R2024a

Modifications may be required to make it function for other versions of MATLAB or the MTEX Toolbox.

Installation

Download the mtex-grain-size repository, unzip it, move the contents to a folder of your choosing, and add that directory and its subfolders to your MATLAB path.

Then, within MATLAB, navigate to the "Home" tab >> "Environment" section of the toolbar. Click on the "Set Path" icon. Select "Add with Subfolders...", then select the location where you unzipped the repository. Then click save to store your updated MATLAB search path.

Usage

This repository provides a collection of MATLAB scripts for grain size analysis and statistical evaluation of EBSD. The scripts are organized by function and naming convention for clarity.

Function taxonomy

The naming convention for the functions in this repository is as follows:

• Functions that begin with G_ calculate the ASTM $G$ value from the parameter described after the underscore, with meanbarA referring to $\bar{A}$, meanintl referring to $\bar{l}$, and numgrain referring to $N_A$.
• Functions that begin with GrainSize_ determine $\bar{A}$, $\bar{l}$, or $N_A$ (whichever is appropriate) according to the standard (when applicable) after the first underscore and then the method. Standards and method include:
  • ASTM E 112
    • Abrams (GrainSize_E112_Abrams)
    • Heyn, returning mean lineal intercept, $\bar{l}$ (GrainSize_E112_HeynRandomLineMLI)
    • Heyn, returning number of intercepts per line length, $P_L$ (GrainSize_E112_HeynRandomLinePL)
    • Hilliard [GrainSize_E112_Hilliard]
    • Jeffries (GrainSize_E112_JeffriesPlanimetric)
    • Saltikov (GrainSize_E112_SaltikovPlanimetric)
  • ASTM E 930 (GrainSize_E930_ALA)
  • ASTM E 2627
    • As written in the standard (GrainSize_E2627_AsWritten)
    • With an adjustable minimum grain size (GrainSize_E2627_CustomMinGS)²
  • Triple Point Count (GrainSize_TriplePointCount)³
• The function FieldStats follows Section 15 in ASTM E112 to calculate the mean values and standard errors on the mean for $\bar{A}$, $\bar{l}$, or $N_A$.

Quick start

Assuming a user already has their EBSD data loaded into MTEX, the user selects their desired grain size measurement function (for options, see Function taxonomy). The grain segmentation is performed within the function. Each GrainSize function returns the ASTM grain size and relevant constituent calculations.

[G_TPC, A_T, N_A] = GrainSize_TriplePointCount(ebsd('face centered cubic'), 'PlotResults');

Error reporting

To obtain the standard deviation, 95% confidence interval, and percent relative accuracy for measurements on multiple fields, an array of the appropriate output values is sent to the FieldStats function as a parameter. The mean value that is returned can then be passed to an appropriate G_ function to obtain the ASTM grain size number $G$.

[~, ~, N_A_1] = GrainSize_TriplePointCount(ebsd_field1('face centered cubic'));
[~, ~, N_A_2] = GrainSize_TriplePointCount(ebsd_field2('face centered cubic'));
[~, ~, N_A_3] = GrainSize_TriplePointCount(ebsd_field3('face centered cubic'));
[~, ~, N_A_4] = GrainSize_TriplePointCount(ebsd_field4('face centered cubic'));
[~, ~, N_A_5] = GrainSize_TriplePointCount(ebsd_field5('face centered cubic'));

N_A_list = [N_A_1, N_A_2, N_A_3, N_A_4, N_A_5]

[N_A_bar, s, CI95, RApct] = FieldStats(N_A_list)

G = G_numgrain(N_A_bar)

Grain size function I/O

The following functions take as inputs just the EBSD data and a variable argument structure varargin:

Method	Returns	$G$ function	Input
Abrams	G_PL, abramsIntCount, abrams_lbar, abramsCircumference_tot	G_meanintl(u)	abrams_lbar
Heyn MLI	G_L, lbar, n, intercept_lengths	G_meanintl(u)	lbar
Heyn PL	G_PL, MIC, intersection_count, nlines, total_line_length	G_meanintl(u)	MIC
Hilliard	G_PL, hilliardIntCount, hilliard_lbar, circumference	G_meanintl(u)	hilliard_lbar
Jeffries	G_N, N_A, N	G_numgrain(u)	N_A
Saltikov	G_N, N_A, N	G_numgrain(u)	N_A
E 2627	G_A, Abar, n, N_A_measured, avg_px_per_grain_before_threshold, areas	G_meanbarA(u)	Abar
TriplePointCount	G, A_T, N_A	G_numgrain(u)	N_A

The GrainSize_E2627_CustomMinGS function takes an additional input argument for the minimum pixels per grain:

G_A, Abar, n, N_A_measured, avg_px_per_grain_before_threshold, areas] = GrainSize_E2627_CustomMinGS(ebsd, min_px_per_grain, varargin)

ALA characterization

[G_largestGrain, volFraction] = GrainSize_E930_ALA(ebsd, G2)

Example

A more complete example analysis script is provided in the file Example.m in the repository.

Citation

If use this software in a publication, please cite whichever of the following is most appropriate:

• D.M. Timberlake, K.S. Evans, and E.J. Payton: "mtex-grain-size -- Functions for ASTM (and ISO) grain size characterization from electron backscatter diffraction (EBSD) data using the MTEX toolbox for MATLAB," 2025. doi: https://doi.org/10.5281/zenodo.16541961 [Computer software]
• K.S. Evans, D.M. Timberlake, P. Tyagi, V.M. Miller, and E.J. Payton: Metallogr. Microstruct. Anal., 2024, vol. 13, pp 966–82. https://doi.org/10.1007/s13632-024-01124-8.
• D.M. Timberlake: MS Thesis, University of Cincinnati, 2025.

Users may also find the following related publications of interest:

• Y.A. Coutinho, S.C.K. Rooney, and E.J. Payton: Metall and Mat Trans A, 2017, vol. 48, pp 2375–95. https://doi.org/10.1007/s11661-017-4031-z.
• A.R.C. Gerlt, A.K. Criner, S.L. Semiatin, K.N. Wertz, and E.J. Payton: Metall Mater Trans A, 2021, vol. 52, pp 228–41. https://doi.org/10.1007/s11661-020-06072-w.
• A.R.C. Gerlt, A.K. Criner, L. Semiatin, and E.J. Payton: J Am Ceram Soc, 2019, vol. 102, pp 37–41. https://doi.org/10.1111/jace.15950.
• A.R.C. Gerlt, R.S. Picard, A.E. Saurber, A.K. Criner, S.L. Semiatin, and E.J. Payton: Metall and Mat Trans A, 2018, vol. 49, pp 4424–8. https://doi.org/10.1007/s11661-018-4808-8.

License

Copyright (C) 2025 Eric J Payton, D Meiyan Timberlake, and Kayla S Evans.

This software is licensed under GPL-3.0-or-later (GPLv3+).

This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program. If not, see https://www.gnu.org/licenses/.

References

1. J. Friel, S. Wright, and S. Sitzman: Microsc Microanal, 2011, vol. 17, pp 838–9. https://doi.org/10.1017/S143192761100506X.
2. A.Deal: E2627-Practice for Determining Average Grain Size Using Electron Backscatter Diffraction (EBSD) in Fully Recrystallized Polycrystalline Materials, ASTM International, West Conshohocken, PA, 2013. https://www.astm.org/rr-e04-1008.html
3. E04 Committee: Test Methods for Determining Average Grain Size, ASTM International. https://doi.org/10.1520/E0112-13R21.
4. G.F. Vander Voort: Interlaboratory Study to Establish Precision Statements for ASTM E112, Tests for Determining the Average Grain Size, ASTM International, West Conshohocken, PA, 1992.
5. E04 Committee: Practice for Determining Average Grain Size Using Electron Backscatter Diffraction (EBSD) in Fully Recrystallized Polycrystalline Materials, ASTM International, 2019. https://doi.org/10.1520/E2627-13R19.
6. E04 Committee: Test Methods for Estimating the Largest Grain Observed in a Metallographic Section (ALA Grain Size), ASTM International, 2019. https://doi.org/10.1520/E0930-18.
7. F. Bachmann, R. Hielscher, and H. Schaeben: Ultramicroscopy, 2011, vol. 111, pp 1720–33. https://doi.org/10.1016/j.ultramic.2011.08.002.
8. F. Bachmann, R. Hielscher, and H. Schaeben: Solid State Phenom., 2010, vol. 160, pp 63–8. https://doi.org/10.4028/www.scientific.net/SSP.160.63.
9. G.F. Vander Voort: Practical Metallography, 2014, vol. 51, pp 201–7. https://doi.org/10.3139/147.110291.

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Footnotes

1. ISO 13067 is similar to ASTM E 2627 measurements that follow either standard can be accomplished with the functions provided in this repository. ↩

2. For a critical analysis of the use of a minimum grain size threshold in this method, see Evans et al, Metall Microsc Analysis (2024). ↩ ↩²

3. More information on this method can be found in G.F. Vander Voort: Practical Metallography, 2014, vol. 51, pp 201–7. For a comparison of this method with the more established methods in the ASTM standards, as well as an analysis of the strengths and weaknesses of triple point counts, see D.M. Timberlake, MS Thesis, University of Cincinnati, 2025. ↩ ↩²