Grain Size, Grain Boundary Area
Index
Grain size in a sample can be measured by determining the mean chord length of its constituent grains. After polishing and etching to reveal the grains of the material a line of known length is projected onto the surface and the mean chord length, < L >, is determined from the reciprocal of the number of intersections, N, of the line with grain boundaries per unit line length. < L > = 1/ N.

The photograph shows a circle of 50 mm diameter projected onto a polycrystalline sample magnified x 250. The effective circumference of the circle has a length of 0.63 mm and there are 11 intersections of this with grain boundaries. The value of N is 
(11/ 0.63) = 17.5/ mm, which gives 
< L > = 0.057 mm.

The grain boundary area per unit volume, A, is given by: A = 2N. For the sample shown the grain boundary are per unit volume is 35 mm2/ mm3.

From: van Vlack, "Elements of Materials Science and Engineering," Addison Wesley (1989)