Chapter 8 Solid Materials
8.1UNIT CELLS
Solid materials can be classified as either crystalline or amorphous.
Crystalline
solids
have very well defined and ordered repeating
patterns of the particles making up the solid.
This ordered arrangement
extends throughout the entire crystal, so there is
long-range
order
in crystalline solids
. By contrast, the ordered arrangement extends over only a short
distance in amorphous solids, so there is only
local order
in amorphous solids.
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Figure 8.1 A simple two-dimensional lattice Two different, but equivalent, unit cells are highlighted in yellow. In one, A’s are at the corners, and a B is in the center. In the other, B’s are on the corners, and an A is in the center.b
a
c
a
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The long-range order of crystalline solids resu
lts from a repeating pattern of particles.
The particles may be atoms, ions, or groups of atoms, such as polyatomic ions or molecules. The repeating pattern form
s a three-dimensional array known as the
crystalline
lattice
. Because the same pattern is repeated th
roughout the crystal, the structure of the
entire crystalline solid can be described effec
tively by describing th
e smallest repeating
unit of the crystalline lattice, known as the
unit cell
. When the unit cell is repeated in all
three directions, it generates the entire crystal. Figure 8.1 describes a two-dimensional lattice of
A’s and
B’s. A unit cell of this two-dimensional lattice can be viewed as a square
with
A’s in the corners and a
B in the center of the cell or with
B’s in the corners and an
A^
in the center. The two unit cells are highlight
ed in yellow in Figure 8.1. Translation of
either unit cell by the length of a cell edge
in any of the four directions produces an
adjacent cell. Continued operations of translation generate the complete lattice. A typical crystal might have a unit cell edge of about 10
-6mm (10 Å). This requires 10
6 (one
million) unit cells, stacked end to end, to reach
across a crystal that is only 1 mm on edge.
A three-dimensional lattice is formed by repeating a three-dimensional unit cell in three directions.
All unit cells can be uniquely characterized by the three edge lengths (a, b, and c) and
the three angles (, α
, and β
) as defined in Figure 8.2. They must be six-sided polygons γ
that completely fill space; that is, no holes are present when the unit cell polygons are packed in three-dimensions. As a result, there are only seven different types of unit cells. We limit our discussion to the simplest type of unit cell, the
cubic unit cell
. The cubic unit
cell is one in which a = b = c and
= α
= β
= 90γ
. There are three types of cubic unit °
cells: simple cubic (
sc
), body-centered cubic (
bcc
), and face-centered cubic (
fcc
).
Figure 8.2 Parameters used to define lattice types© byNorthCarolinaStateUniversity