Page 157 - Materials Science and Engineering An Introduction

4.11 Grain-Size Determination • 129

For photomicrographs taken at magnifications other than 100 , use of the following
modified form of Equation 4.17 is necessary:
100 2
n M a b = 2 G-1 (4.18)
M
In this expression, n M is the number of grains per square inch at magnification M. In ad-
2
M
dition, the inclusion of the ( ) term makes use of the fact that, whereas magnification
100
is a length parameter, area is expressed in terms of units of length squared. As a conse-
quence, the number of grains per unit area increases with the square of the increase in
magnification.
Relationships have been developed that relate mean intercept length to ASTM
grain-size number; these are as follows:
G = -6.6457 log / - 3.298 (for / in mm) (4.19a)
G = -6.6353 log / - 12.6 (for / in in.) (4.19b)
At this point, it is worthwhile to discuss the representation of magnification
(i.e., linear magnification) for a micrograph. Sometimes magnification is specified
in the micrograph legend (e.g., “60 ” for Figure 4.14b); this means the micrograph
represents a 60 times enlargement of the specimen in real space. Scale bars are also
used to express degree of magnification. A scale bar is a straight line (typically hori-
zontal), either superimposed on or located near the micrograph image. Associated
with the bar is a length, typically expressed in microns; this value represents the
distance in magnified space corresponding to the scale line length. For example,
in Figure 4.15b, a scale bar is located below the bottom right-hand corner of the
micrograph; its “100
m” notation indicates that 100
m correlates with the scale
bar length.
To compute magnification from a scale bar, the following procedure may be used:
1. Measure the length of the scale bar in millimeters using a ruler.
2. Convert this length into microns [i.e., multiply the value in step (1) by 1000
because there are 1000 microns in a millimeter].
3. Magnification M is equal to

measured scale length (converted to microns)
M = (4.20)
the number appearing by the scale bar (in microns)
For example, for Figure 4.15b, the measured scale length is approximately 10 mm,
which is equivalent to (10 mm)(1000
m/mm) 10,000
m. Inasmuch as the scale bar
length is 100
m, the magnification is equal to

10,000
m
M = = 100*
100
m
This is the value given in the figure legend.

Concept Check 4.4 Does the grain-size number (G of Equation 4.17) increase or decrease
with decreasing grain size? Why?
[The answer may be found at www.wiley.com/college/callister (Student Companion Site).]