EBSD · Grain size
Measuring grain size: why one sample gives three different numbers
The page makes one grain structure and measures it three ways at once. Start by ticking Count twin boundaries in the first box and watch the ASTM number jump.
- 1. Line intercept (ASTM E112)
- 2. Jeffries grain count
- 3. EBSD reconstruction
- Side by side
- 4. 2D slice vs 3D size
How does the line intercept method measure grain size?
test linecounted crossingtwin crossing (skipped unless counted)Field 400 x 250 µm
Test line length L-
Crossings P-
Mean intercept l = L/P-
ASTM grain size G-
l along x (horizontal)-
l along y (vertical)-
95% relative accuracy-
Twin crossings found-
ECD of mean area / l-
Try it: set twins to 1.5 per grain, then tick Count twin boundaries. More crossings means a smaller l and a larger G. ASTM E112 says to skip twins.
How does the Jeffries planimetric method count grains?
whole grain inside (counts 1)cut by the circle (counts 1/2)Click the picture to move the circle.
Inside-
Cut by circle-
Equivalent grains-
Test area-
NA grains per mm²-
ASTM G-
True NA (all grains)-
True G-
Error in NA-
Try it: shrink the circle to 60 µm and press Move circle a few times. With only a few grains inside, G jumps around. E112 asks for at least 50 grains inside.
How does EBSD measure grain size, and why do step size and threshold matter?
grain boundary (above threshold)twin boundary merged awayremoved: smaller than minimum sizeBars: EBSD grains. Line: true grains.
Histogram weighting
Map points-
Grains counted-
Points per grain-
Mean ECD, by number-
Mean ECD, by area-
ASTM G (from mean area)-
True ECD, by number-
True ECD, by area-
Error (by number)-
Try it: set noise to 2.0° and the threshold to 1.5°. Noise alone breaks the grains into hundreds of specks. Put the threshold back to 5° and the true grains return.
Why do the three methods give different grain sizes?
| Method (current settings) | Twins | Size, µm | G |
|---|
Why does a 2D section under-estimate 3D grain size?
true ball diameter Dsection circle diameter dHistogram from 20,000 random cuts
Mean ball D-
Mean circle d-
d / D-
Mean intercept l-
D / l-
Balls cut by this plane-
A plane rarely cuts a ball through its middle, so most circles are smaller than the ball. For balls of one size, theory gives d/D = π/4 = 0.785 and D/l = 1.5 (Underwood 1970). For space-filling grains (tetrakaidecahedra, a 14-sided shape, with a lognormal size spread) Mendelson (1969) derived D = 1.56 l.
Try it: with spread 0, D/l reads 1.50 and d/D reads about 0.79. Raise the spread to 0.4 and D/l drops, because big balls are cut more often.
What should I remember about grain size numbers?
Say which method.The same sample gives l, a 2D circle diameter and a 3D diameter. They differ by factors of about 1.3 and 1.5. A number without its method is not a grain size.
Say how twins were treated.Twin bands can cut l in half. E112 ignores twin boundaries: both sides of a twin boundary belong to the same grain. Many EBSD users merge Σ3 twins. Both choices are fine if stated.
EBSD needs points per grain.ASTM E2627 asks for at least 100 points in the smallest grain counted and 500 in the average grain. Coarse steps and noise both bias the mean.
Number vs area weighting.A few small grains pull the number mean down. The area-weighted mean follows the big grains, which hold most of the volume. Report both, or the one your model needs.
More detail: equations, the model and its limits
- Intercept (E112). l = L / P, with L the total test line length and P the number of boundary crossings. On a real micrograph a line ends inside a grain; E112 counts each such end piece as half an intercept, which gives the same l = L / P. The field here is periodic, so the end pieces of one line join into one grain and no correction is needed. G = -6.6439 log10(l in mm) - 3.2877. G = 0 means l = 0.320 mm.
- Jeffries (E112). N = Ninside + Ncut/2, NA = N / area. G = 3.321928 log10(NA in mm-2) - 2.954. G = 0 means NA = 7.75 mm-2.
- The two E112 formulas agree only if the mean grain area is 1.26 l2, so the equivalent circle diameter (ECD) of the mean area is 1.27 times l. This is the rule for circles, l = πd/4 (E112 says it is exact for circles and not quite exact for real equiaxed grains; the circle rule gives 4/π = 1.273 l2, E112 rounds to 1.26). The grains on this page are polygons, so the ratio is usually above 1.27; the first box and the comparison box show the ratio for the current map. Where the ratio differs from 1.27, the intercept G and the Jeffries G differ too.
- EBSD (E2627 style). Neighbouring points join the same grain when their misorientation is below the threshold (cubic symmetry, 24 operators). Σ3 twins are found as 60° about <111> within the Brandon limit of 15°/√3 = 8.66°. ECD = √(4A/π). G uses the mean grain area.
- The model. A periodic 400 x 250 µm field on a 0.5 µm grid. Grains are a power (Laguerre) tessellation of seeds with lognormal weights, so the spread can be tuned. Elongation stretches the tessellation along x at constant area. Twins are straight parallel bands, 12 to 22% of the grain diameter wide, with the parent orientation turned 60° about [111]. Orientations are random (no texture).
- Limits. Real twins end inside grains and have curved ends. Real noise is not Gaussian, and real maps have unindexed points. Line intercept counting here uses exact crossings; a person with a microscope misses some. True sizes are exact for this 2D map, not for a 3D solid.
- Stereology. A ball of diameter D cut at a random height gives a circle of mean diameter π D/4. Random lines through a ball give a mean chord 2D/3, so D/l = 1.5. With a lognormal spread of sigma, D/l = 1.5 exp(-2 sigma2) for balls.
Grain size questions people ask
What is the ASTM grain size number G?
G is a log scale set by ASTM E112. Each step up in G halves the mean grain area. G = 0 means 7.75 grains per mm² in the section, or a mean intercept of 0.320 mm. G = 8 means a mean intercept of about 20 µm.Why is my EBSD grain size larger than the line intercept size?
EBSD usually reports the equivalent circle diameter. On a 2D map that is larger than the mean intercept, even when both are measured perfectly: E112 assumes 1.27 times, and the maps on this page give about 1.15 to 1.5, depending on the size spread and on the lines drawn. Merged twins and removed small grains push it higher still.Should annealing twins be counted in grain size?
E112 says to ignore twin boundaries: the metal on both sides of a twin boundary belongs to one grain. For strength, some studies count them, because twin boundaries also block slip. Pick one and state it; in widget 1 the choice can change G by more than one unit.What EBSD step size do I need for grain size?
ASTM E2627 asks for at least 100 points in the smallest grain counted and at least 500 points in the average grain. Roughly, the step should be one tenth of the mean grain diameter or finer.How do I convert mean intercept to grain diameter?
In a 2D section, circle diameter is about 4/π = 1.27 times l, as E112 assumes. For a 3D grain diameter, multiply l by about 1.5 (equal balls) to 1.56 (Mendelson, for 14-sided space-filling grains with a lognormal size spread).Which grain size goes into the Hall-Petch equation?
Most Hall-Petch data use the mean linear intercept from E112. If you use an EBSD circle diameter instead, d is roughly 1.3 times larger and the fitted slope k changes. Use the same measure as the data you compare with.How many grains or intercepts should I count?
E112 says 400 to 500 intercepts over 5 to 10 fields usually give better than 10% relative accuracy. For the Jeffries method, pick a magnification with at least 50 grains inside the test area.Is a 2D grain size the real 3D grain size?
No. A plane cuts most grains away from their widest part, so section circles are smaller than the grains. For equal balls the mean circle is 0.785 of the true diameter.Where does this connect?
- Misorientation, boundaries and Σ3 twins
- Cleaning EBSD data honestly
- KAM, GND and step size
- Hall-Petch and strengthening mechanisms
- Grain growth and Zener pinning
- SEM imaging basics
References
Show the 8 references
- ASTM E112-13 (reapproved 2021). Standard Test Methods for Determining Average Grain Size. ASTM International, West Conshohocken, PA. doi:10.1520/E0112-13R21.
- ASTM E2627-13 (reapproved 2019). Standard Practice for Determining Average Grain Size Using Electron Backscatter Diffraction (EBSD) in Fully Recrystallized Polycrystalline Materials. ASTM International. doi:10.1520/E2627-13R19.
- ASTM E1382-97 (reapproved 2015). Standard Test Methods for Determining Average Grain Size Using Semiautomatic and Automatic Image Analysis. ASTM International. doi:10.1520/E1382-97R15.
- E. E. Underwood. Quantitative Stereology. Addison-Wesley, Reading, MA, 1970.
- R. T. DeHoff and F. N. Rhines (eds.). Quantitative Microscopy. McGraw-Hill, New York, 1968.
- M. I. Mendelson. Average grain size in polycrystalline ceramics. Journal of the American Ceramic Society 52 (1969) 443-446. doi:10.1111/j.1151-2916.1969.tb11975.x.
- F. J. Humphreys. Quantitative metallography by electron backscattered diffraction. Journal of Microscopy 195 (1999) 170-185. doi:10.1046/j.1365-2818.1999.00578.x.
- D. G. Brandon. The structure of high-angle grain boundaries. Acta Metallurgica 14 (1966) 1479-1484. doi:10.1016/0001-6160(66)90168-4.
Cite this page: Tripathy, Manisha. “Measuring Grain Size: Line Intercept vs Jeffries vs EBSD.” untethered atom, 2026, https://untetheredatom.com/ebsd/measuring-grain-size.
BibTeX
@misc{tripathy2026grainsize,
author = {Tripathy, Manisha},
title = {Measuring Grain Size: Line Intercept vs Jeffries vs EBSD},
year = {2026},
howpublished = {\url{https://untetheredatom.com/ebsd/measuring-grain-size}},
note = {Interactive web tool}
}