Page 156 - Materials Science and Engineering An Introduction

128 • Chapter 4 / Imperfections in Solids

(plus the naked eye) are presented in the bar chart of Figure 4.16b. For three of these
techniques (SPM, TEM, and SEM), an upper resolution value is not imposed by the char-
acteristics of the microscope and, therefore, is somewhat arbitrary and not well defined.
Furthermore, by comparing Figures 4.16a and 4.16b, it is possible to decide which micro-
scopic technique(s) is (are) best suited for examination of each of the structure types.

4.11 GRAIN-SIZE DETERMINATION
grain size The grain size is often determined when the properties of polycrystalline and single-
phase materials are under consideration. In this regard, it is important to realize that for
each material, the constituent grains have a variety of shapes and a distribution of sizes.
Grain size may be specified in terms of average or mean grain diameter, and a number
of techniques have been developed to measure this parameter.
Before the advent of the digital age, grain-size determinations were performed
manually using photomicrographs. However, today, most techniques are automated and
use digital images and image analyzers with the capacity to record, detect, and measure
accurately features of the grain structure (i.e., grain intercept counts, grain boundary
lengths, and grain areas).
We now briefly describe two common grain-size determination techniques: (1) linear
intercept—counting numbers of grain boundary intersections by straight test lines; and
(2) comparison—comparing grain structures with standardized charts, which are based
upon grain areas (i.e., number of grains per unit area). Discussions of these techniques is
from the manual perspective (using photomicrographs).
For the linear intercept method, lines are drawn randomly through several
photomicrographs that show the grain structure (all taken at the same magnification).
Grain boundaries intersected by all the line segments are counted. Let us represent
the sum of the total number of intersections as P and the total length of all the lines
by L T . The mean intercept length / [in real space (at 1 —i.e., not magnified)], a
measure of grain diameter, may be determined by the following expression:

/ = L T (4.16)
PM
where M is the magnification.
The comparison method of grain-size determination was devised by the American
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Society for Testing and Materials (ASTM). The ASTM has prepared several standard
comparison charts, all having different average grain sizes and referenced to photomi-
crographs taken at a magnification of 100 . To each chart is assigned a number ranging
from 1 to 10, which is termed the grain-size number. A specimen must be prepared
properly to reveal the grain structure, which is then photographed. Grain size is ex-
pressed as the grain-size number of the chart that most nearly matches the grains in the
micrograph. Thus, a relatively simple and convenient visual determination of grain-size
number is possible. Grain-size number is used extensively in the specification of steels.
The rationale behind the assignment of the grain-size number to these various
Relationship charts is as follows: Let G represent the grain-size number, and let n be the average
between ASTM number of grains per square inch at a magnification of 100 . These two parameters are
grain size number related to each other through the expression 12
and number of
grains per square G-1 (4.17)
inch (at 100 ) n = 2

11 ASTM Standard E112, “Standard Test Methods for Determining Average Grain Size.”
12 Please note that in this edition, the symbol n replaces N from previous editions; also, G in Equation 4.17 is used in
place of the previous n. Equation 4.17 is the standard notation currently used in the literature.