Page 160 - Materials Science and Engineering An Introduction

132 • Chapter 4 / Imperfections in Solids

• For a high-angle grain boundary, the angle of misalignment between grains is rela-
tively large; this angle is relatively small for small-angle grain boundaries.
• Across a twin boundary, atoms on one side reside in mirror-image positions of atoms
on the other side.

Microscopic • The microstructure of a material consists of defects and structural elements that are of
Techniques microscopic dimensions. Microscopy is the observation of microstructure using some
type of microscope.
• Both optical and electron microscopes are employed, usually in conjunction with
photographic equipment.
• Transmissive and reflective modes are possible for each microscope type; preference
is dictated by the nature of the specimen as well as the structural element or defect to
be examined.
• In order to observe the grain structure of a polycrystalline material using an optical
microscope, the specimen surface must be ground and polished in order to produce a
very smooth and mirror-like finish. Some type of chemical reagent (or etchant) must
then be applied in order to either reveal the grain boundaries or produce a variety of
light reflectance characteristics for the constituent grains.
• The two types of electron microscopes are transmission (TEM) and scanning (SEM).
For TEM, an image is formed from an electron beam that, although passing
through the specimen, is scattered and/or diffracted.
SEM employs an electron beam that raster-scans the specimen surface; an image
is produced from back-scattered or reflected electrons.
• A scanning probe microscope employs a small and sharp-tipped probe that raster-
scans the specimen surface. Out-of-plane deflections of the probe result from interac-
tions with surface atoms. A computer-generated and three-dimensional image of the
surface results having nanometer resolution.

Grain-Size • With the intercept method used to measure grain size, a series of straight-line seg-
Determination ments are drawn on the photomicrograph. The number of grain boundaries that are
intersected by these lines are counted, and the mean intercept length (a measure of
grain diameter) is computed using Equation 4.16.
• Comparison of a photomicrograph (taken at a magnification of 100 ) with ASTM
standard comparison charts may be used to specify grain size in terms of a grain-size
number.
• The average number of grains per square inch at a magnification of 100 is related
to grain-size number according to Equation 4.17; for magnifications other than 100 ,
Equation 4.18 is used.
• Grain-size number and mean intercept length are related per Equations 4.19a and 4.19b.

Equation Summary

Equation Page
Number Equation Solving For Number

Q y
4.1 N y = N expa - b Number of vacancies per unit volume 107
kT
N A r
4.2 N = Number of atomic sites per unit volume 108
A
(continued)