Callister - An introduction - 8th edition

52 • Chapter 3 / The Structure of Crystalline Solids
Substitution for the various parameters into Equation 3.5 yields
nA Cu
r nA Cu
V C N A 116R 3 122N A
14 atoms/unit cell2163.5 g/mol2
[161211.28 10 8 cm2 3 /unit cell] 16.022 10 23 atoms/mol2
8.89 g/cm 3
The literature value for the density of copper is 8.94 g/cm 3 , which is in very
close agreement with the foregoing result.
3.6 POLYMORPHISM AND ALLOTROPY
polymorphism
allotropy
3.7 CRYSTAL SYSTEMS
lattice parameters
crystal system
VMSE
Crystal Systems and
Unit Cells for Metals
Some metals, as well as nonmetals, may have more than one crystal structure, a phenomenon
known as polymorphism. When found in elemental solids, the condition is
often termed allotropy. The prevailing crystal structure depends on both the temperature
and the external pressure. One familiar example is found in carbon: graphite is
the stable polymorph at ambient conditions, whereas diamond is formed at extremely
high pressures.Also, pure iron has a BCC crystal structure at room temperature, which
changes to FCC iron at 912C (1674F). Most often a modification of the density and
other physical properties accompanies a polymorphic transformation.
Because there are many different possible crystal structures, it is sometimes convenient
to divide them into groups according to unit cell configurations and/or atomic
arrangements. One such scheme is based on the unit cell geometry, that is, the shape
of the appropriate unit cell parallelepiped without regard to the atomic positions in
the cell. Within this framework, an xyz coordinate system is established with its origin
at one of the unit cell corners; each of the x, y, and z axes coincides with one of the
three parallelepiped edges that extend from this corner, as illustrated in Figure 3.4.
The unit cell geometry is completely defined in terms of six parameters: the three edge
lengths a, b, and c, and the three interaxial angles a, b, and g. These are indicated in
Figure 3.4, and are sometimes termed the lattice parameters of a crystal structure.
On this basis there are seven different possible combinations of a, b, and c, and
a, b, and g, each of which represents a distinct crystal system. These seven crystal
systems are cubic, tetragonal, hexagonal, orthorhombic, rhombohedral, 2 monoclinic,
and triclinic. The lattice parameter relationships and unit cell sketches for each are
z
Figure 3.4 A unit cell with x, y, and z coordinate axes,
showing axial lengths (a, b, and c) and interaxial angles
(, , and ).
c
a
y
x
b
2 Also called trigonal.