Page 114 - Materials Science and Engineering An Introduction

86 • Chapter 3 / The Structure of Crystalline Solids

crystals or nuclei form at various positions. These have random crystallographic
orientations, as indicated by the square grids. The small grains grow by the succes-
sive addition from the surrounding liquid of atoms to the structure of each. The
extremities of adjacent grains impinge on one another as the solidification process
approaches completion. As indicated in Figure 3.20, the crystallographic orientation
varies from grain to grain. Also, there exists some atomic mismatch within the region
grain boundary where two grains meet; this area, called a grain boundary, is discussed in more detail
in Section 4.6.

3.15 ANISOTROPY
The physical properties of single crystals of some substances depend on the crystallo-
graphic direction in which measurements are taken. For example, the elastic modulus,
the electrical conductivity, and the index of refraction may have different values in the
anisotropy [100] and [111] directions. This directionality of properties is termed anisotropy, and it
is associated with the variance of atomic or ionic spacing with crystallographic direction.
Substances in which measured properties are independent of the direction of measure-
isotropic ment are isotropic. The extent and magnitude of anisotropic effects in crystalline ma-
terials are functions of the symmetry of the crystal structure; the degree of anisotropy
increases with decreasing structural symmetry—triclinic structures normally are highly
anisotropic. The modulus of elasticity values at [100], [110], and [111] orientations for
several metals are presented in Table 3.4.
For many polycrystalline materials, the crystallographic orientations of the indi-
vidual grains are totally random. Under these circumstances, even though each grain
may be anisotropic, a specimen composed of the grain aggregate behaves isotropically.
Also, the magnitude of a measured property represents some average of the directional
values. Sometimes the grains in polycrystalline materials have a preferential crystallo-
graphic orientation, in which case the material is said to have a “texture.”
The magnetic properties of some iron alloys used in transformer cores are
anisotropic—that is, grains (or single crystals) magnetize in a 100 -type direction
easier than any other crystallographic direction. Energy losses in transformer cores
are minimized by utilizing polycrystalline sheets of these alloys into which have been
introduced a magnetic texture: most of the grains in each sheet have a 100 -type
crystallographic direction that is aligned (or almost aligned) in the same direction,
which is oriented parallel to the direction of the applied magnetic field. Magnetic
textures for iron alloys are discussed in detail in the Material of Importance box in
Chapter 20 following Section 20.9.

Table 3.4
Modulus of Elasticity (GPa)
Modulus of Elasticity
Values for Several Metal [100] [110] [111]
Metals at Various Aluminum 63.7 72.6 76.1
Crystallographic Copper 66.7 130.3 191.1
Orientations
Iron 125.0 210.5 272.7
Tungsten 384.6 384.6 384.6
Source: R. W. Hertzberg, Deformation and Fracture
Mechanics of Engineering Materials, 3rd edition.
Copyright © 1989 by John Wiley & Sons, New York.
Reprinted by permission of John Wiley & Sons, Inc.