In this exercise a line is drawn across the sample and its length is noted - to do this you will need to use the stage micrometer to determine the real length of the line, l. The number of grain boundary intercepts is then counted, n, and the grain size, d, determined.





Repeat the measurement with different line orientations on several fields of view.



The error in the measurement is


where sd is the standard deviation of all of the measurements of d that were made and N is the number of grains measured. It follows from the above equation that for a given error, s, the number of grains to be measured can be estimated. Obviously the process is iterative since sd changes as the number of measurments is increased.

Below is an example of 70/30 Brass etched in 3% FeCl3 in Methanol showing both the grain and twin boundaries - scale bar is 200µm



Care must be taken when observing grain structure to note the presence of any anisotropy in grain shape, such as might be introduced by a mechanical forming process. A numerical index of grain shape can be defined as



Where NL is the number of intercepts per unit length and NA the number of grains per unit area.

Download Mathcad Document

Grain Size - Digital Method using a circle

In this exercise, a circle is superimposed on an image of the steel and its circumference is determined once the image is calibrated using the NIH image software. A circle is used because it compensates for structural anisotropy in the sample. The number of grain boundary intercepts is counted (n) and the grain size determined by dividing the circumference of the circle (l) by the number of intercepts. We will determine the number of intercepts using two different methods ­ first by manually counting the number of intercepts you see, and then by allowing the software to determine the number of intercepts. (Then add the rest of the discussion starting with "The error in the measurementŠŠ).

EXPERIMENT You will determine the grain size of the microconstituients of your steel on 10 fields of view. Clear all images from the NIH image window, then acquire an image of your steel at an appropriate magnification with the scale bar at the far edge of the sample so the circle will not superimpose the scale bar.



Then, open the file called circlebinary.tif on the desktop.



Manually determining grain size: Combine the images by using the commands Process ­ Image Math from the NIH Image menu. The images you combine will be the image you just acquired and the image called circlebinary.tif. Use the operator "OR" in the box, and verify that the number in the miltiplier box is 1.000 and 0 is in the addition box. Call the file "result" and click OK. This will produce an image with the circle superimposed on the steel. Count the number of intersections of a microconstituient and the circle. Then calibrate the image using the known distance represented by the scale bar for the magnification you are using. To do this, refer to the handout called MY3200 "Quantitative Metallography Utilizing Digital Imaging. " (WRITE DOWN the information from the calibration box so all you will need to do for remaining calibrations will be to type in the values). Measure the diameter of the circle, and calculate the circumference.

Digitally determining grain size: Convert the same image of your steel which you used previously to a binary image. Then use process ­ binary ­ erode and follow with process ­ binary ­ dilate to remove any stray pixels from the binary.



Then Process - binary ­ skeletonize to outline the grain boundaries. Next, combine the two binary images as before, EXCEPT use "and" as the operator. The result will be a circular pattern, one pixel wide, with each pixel representing the interesction of the circle and a microconstituient grain boundary.



The image analysis unit can count how many intersections there are using analyze ­ options ­ area, then analyze- measure particles, setting the minimum size as 1 pixel, and yes to label particles. You can get the number of particles from the info window, or from analyze ­ show results. Since you have already determined the circumference of the circle, it is not necessary to recalibrate unless you need the area measurement for some reason.