We continue our multi-part discussion of quantitative metallography. We hope this information will be usable by many in their metallurgical investigations.

Phase Proportions
One of the most common measurements – determination of the amount of phases present – can be done using three different methods. Areal analysis, developed by Delesse in 1848, says that the area percent of a phase on a 2-D plane is equal to its volumetric percent – AA = VV. However, measuring the area of a second phase is very tedious unless it is quite coarse. Lineal analysis, developed by Rosiwal in 1898, says that the lineal fraction of test lines in a phase on the 2-D plane is equal to its volumetric percent – LL = VV. This is relatively easy to determine but still rather tedious.

Starting around 1930, several people in different fields and countries showed that the percentage of points on a test grid lying in the phase of interest was equal to the volumetric percentage – PP = VV. Of the three methods, this is the most efficient technique. It gives the best accuracy for the least effort when done manually. The point-counting technique is described fully in ASTM E 562 (also ISO 9042). Image analyzers use essentially the same procedure – the amount of a phase (usually called the area fraction even if it really is a point fraction) is determined by the number of picture elements, or “pixels,” in the phase of interest divided by the total number of pixels (i.e. PP, usually expressed as a percentage).  

Grain Size
Grain size is perhaps the most commonly performed microstructural measurement, although chart ratings are more commonly done than actual measurements (this is changing). A recent ASTM inter-laboratory “round robin” showed that chart ratings of grain size are biased; that is the ASTM grain-size number is 0.5-1 unit too low (see Appendix XI of E 112-10). No bias existed when planimetric measurements were compared to intercept measurements by the same rater.  

The ASTM grain size number, G, is defined as: n = 2G-1 

where n is the number of grains per square inch at 100X. To convert n to NA (the number of grains per square mm at IX), multiply n by 15.5. The ASTM grain-size charts show graded series of grain structures of different types.

The grain size can be measured by the Planimetric Method (developed by Jeffries in 1915 based upon earlier work by Sauveur) or by the Intercept Method (developed by Heyn in 1904). In the Planimetric Method, a count is made of the number of grains completely within a circle of known area and the number of grains intersected by the circle to obtain NA. Then, NA is related to G. This method is slow when done manually because the grains must be marked when counted to obtain an accurate count.

In the Intercept Method, either straight lines, curved lines or circles are placed over the structure and a count is made of either the number of grain-boundary intersections (P) or the number of grains intercepted (N) by the line. P or N is divided by the true line length, L, to determine PL or NL, the number of intersections or interceptions per unit length (for a single-phased structure). The reciprocal of PL or NL gives the mean lineal intercept length, L, which is a measure of grain size that can be converted to a G value. The Intercept Method is more efficient than the Planimetric Method, yielding acceptable measurement precision (<10% relative accuracy) in much less time. ASTM E 112 contains a complete description of these methods.