Grain Radius Notes

Experimental data on grain sizes often are based on measurements known as the intercept length. The intercept length can be defined as the distance between two opposed, adjacent grain boundary intersection points on a test line segment that crosses the grain at any location due to random placement of the test line. Finding these length can be done through a count of the number of grains intercepted by a test line or the number of grain boundary intersections with a test line, per unit length of test line. This then allows for the calculation of the mean lineal intercept length, $var element = document.getElementById("moose-equation-ba3efa92-3f9b-4ac4-84d2-b174f2021080");katex.render("\\bar{l}", element, {displayMode:false,throwOnError:false});$ , following Mendelson (1969),

$var element = document.getElementById("moose-equation-f17f93cb-0754-4f9c-a678-a9ffb6a16bd2");katex.render("\\bar{D}=1.56\\bar{\\ell} \\Rrightarrow \\bar{r_{gr}}=\\frac{1.56\\bar{\\ell}}{2}", element, {displayMode:true,throwOnError:false});$

A more through discussion on the intercept method can be found in ASTM ASTMI (2015).

References

ASTMI. Test Methods for Determining Average Grain Size Using Semiautomatic and Automatic Image Analysis. ASTM International, 2015.

@book{grain2015standard,
    author = "ASTMI",
    institution = "ASTM International",
    title = "Test Methods for Determining Average Grain Size Using Semiautomatic and Automatic Image Analysis",
    year = "2015",
    booktitle = "ASTM E1382",
    publisher = "ASTM International"
}

M.I. Mendelson. Average grain size in polycrystalline ceramics. Journal of the American Ceramic Society, 52:443–446, 1969.

@ARTICLE{mendelson1969,
    author = "Mendelson, M.I.",
    title = "Average Grain Size in Polycrystalline Ceramics",
    journal = "Journal of the American Ceramic Society",
    year = "1969",
    volume = "52",
    pages = "443-446"
}

References