Simple Structures
If atoms or ions are considered to be spheres, then the most efficient packing of the spheres in space
will form their most stable structure. However, the type of bonding—in particular, directional
bonding—may affect the structure formed. In two dimensions, there is only one configuration that
most efficiently fills space, the close-packed layer . If similar layers are stacked to form
a three-dimensional structure, an infinite number of configurations is possible. Two are important. In both, the first two layers are the same. In the first layer (A), the point at the center of three spheres
provides a hollow for a fourth sphere to rest. A second close-packed layer (B) then can be placed
on the first layer, with each sphere occupying the hollow. With the addition of a third layer to these
two layers, two choices are possible. A sphere in the third layer can be placed above a sphere in the
first layer in the spaces marked (•) or above a hollow not occupied by a sphere spaces
marked (x) in the second layer. If the first stacking arrangement is continued, that is, the first and
third layers in registry with each other (denoted ABABA . . .), the hexagonal close-packed (hep)
structure is generated, so called because of the hexagonal symmetry of the structure. If the second
stacking arrangement is continued, that is, the first and third layers are not on top of each other
(denoted ABCABC . . .), the cubic close-packed or face-centered cubic (fee) structure is generated,
so called because the structure formed is a face-centered cube. Both structures are shown in Fig. 1.3.
In both structures, 74% of the volume is occupied and each sphere is contacted by 12 spheres (or
12 nearest neighbors), although the arrangement is different. Another common structure is the bodycentered
cubic (bcc) structure shown in Fig. 1.3. Here, each sphere has eight nearest neighbors, with
another six at a slightly greater distance. The volume fraction occupied is 68%. In the hep and fee
structures, the stacking of a fourth sphere on top of three in any close-packed layer generates a
tetrahedral site or void, as shown in Fig. 1.4. Into such a site a smaller sphere with a coordination
number of four could fit. Three spheres from each of two layers generate an octahedral site or void,
. Into such a site a smaller sphere with a coordination number of six could fit.
In the hep and fee structures, there are two tetrahedral and one octahedral sites per packing sphere;
however, the arrangement of these sites is different.
Crystallography
All possible crystallographic structures are described in terms of 14 Bravais space lattices—only 14
different ways of periodically arranging points in space. . Each of the positions in a given space lattice is equivalent and an atom or ion or group of atoms or ions can be
centered on each position. Each of the lattices is described by a unit cell, The seven crystallographic systems
States of Matter
Matter can be divided into gases, liquids, and solids. In gases and liquids, the positions of the atoms
are not fixed with time, whereas in solids they are. Distances between atoms in gases are an order
of magnitude or greater than the size of the atoms, whereas in solids and liquids closest distances
between atoms are only approximately the size of the atoms. Almost all engineering materials are
solids, either crystalline or noncrystalline.
Crystalline Solids
In crystalline solids, the atoms or ions occupy fixed positions and vibrate about these equilibrium
positions. The arrangement of the positions is some periodic array, as discussed in Section 1.1.5. At
O0K, except for a small zero-point vibration, the oscillation of the atoms is zero. With increasing
temperature the amplitude and frequency of vibration increase up to the melting point. At the melting
point, the crystalline structure is destroyed, and the material melts to form a liquid. For a particular
single crystal the external shape is determined by the symmetry of the crystal class to which it
belongs. Most engineering materials are not single crystals but poly crystalline, consisting of many
small crystals. These crystals are often randomly oriented and may be of the same composition orof different composition or of different structures. There may be small voids between these grains.
Typical sizes of grains in such poly crystalline materials range from 0.01 to 10 mm in diameter.
Noncrystalline Solids
Noncrystalline solids (glasses) are solids in which the arrangement of atoms is periodic (random)
and lacks any long-range order. The external shape is without form and has no defined external faces
like a crystal. This is not to say that there is no structure. A local or short-range order exists in the
structure. Since the bonding between atoms or ions in a glass is similar to that of the corresponding
crystalline solid, it is not surprising that the local coordination, number of neighbors, configuration,
and distances are similar for a glass and crystal of the same composition. In fused SiO2, for example,
four O's surround each Si in a tetrahedral coordination, the same as in crystalline SiO2.
Glasses do not have a definite melting point, crystals do. Instead, they gradually soften to form
a supercooled liquid at temperatures below the melting point of the corresponding crystal. Glass
formation results when a liquid is cooled sufficiently rapidly to avoid crystallization. This behavior
is summarized in Fig. 1.6, where the volume V is plotted as a function of temperature T.Crystalline materials of the same composition exhibit more than one crystalline structure called
polymorphs. Fe, for example, exists in three different structures: a, y, and 5 Fe. The a phase, ferrite,
a bcc structure, transforms at 91O0C to the y phase, austenite, an fee structure, and then at 140O0C
changes back to bcc structures 6-iron or 6-ferrite. The addition of C to Fe and the reactions and
transformations that occur are extremely important in determining the properties of steel.
SiO2 exhibits many polymorphs, including a- and /3-quartz, a- and /3-tridymite, and a- and /3-
cristobalite. The SiO4 tetrahedron is common to all the structures, but the arrangement or linking of
these tetrahedra varies, leading to different structures. The a —> /3 transitions involve only a slight
change in the Si-O-Si bond angle, are rapid, and are an example of a phase transformation called
displacive. The quartz —> tridymite —> cristobalite transformations require the reformation of the new
structure, are much slower than displacive transformations, and are called reconstructive phase transformations.
The a —> y —> 8 Fe transformations are other examples of reconstructive transformations.
A phase diagram gives the equilibrium phases a function of temperature, pressure, and composition.
More commonly, the pressure is fixed at 1 atm and only the temperature and composition are
varied.
Defects
The discussion of crystalline structures assumes that the crystal structures are perfect, with each site
occupied by the correct atoms. In real materials, at temperatures greater than O0K, defects in the
crystalline structure will exist. These defects may be formed by the substitution of atoms different
from those normally occupying the site, vacancies on the site, atoms in sites not normally occupied
(interstitials), geometrical geometrical alterations of the structure in the form of dislocations, twin boundaries, or grain boundaries.
If atoms or ions are considered to be spheres, then the most efficient packing of the spheres in space
will form their most stable structure. However, the type of bonding—in particular, directional
bonding—may affect the structure formed. In two dimensions, there is only one configuration that
most efficiently fills space, the close-packed layer . If similar layers are stacked to form
a three-dimensional structure, an infinite number of configurations is possible. Two are important. In both, the first two layers are the same. In the first layer (A), the point at the center of three spheres
provides a hollow for a fourth sphere to rest. A second close-packed layer (B) then can be placed
on the first layer, with each sphere occupying the hollow. With the addition of a third layer to these
two layers, two choices are possible. A sphere in the third layer can be placed above a sphere in the
first layer in the spaces marked (•) or above a hollow not occupied by a sphere spaces
marked (x) in the second layer. If the first stacking arrangement is continued, that is, the first and
third layers in registry with each other (denoted ABABA . . .), the hexagonal close-packed (hep)
structure is generated, so called because of the hexagonal symmetry of the structure. If the second
stacking arrangement is continued, that is, the first and third layers are not on top of each other
(denoted ABCABC . . .), the cubic close-packed or face-centered cubic (fee) structure is generated,
so called because the structure formed is a face-centered cube. Both structures are shown in Fig. 1.3.
In both structures, 74% of the volume is occupied and each sphere is contacted by 12 spheres (or
12 nearest neighbors), although the arrangement is different. Another common structure is the bodycentered
cubic (bcc) structure shown in Fig. 1.3. Here, each sphere has eight nearest neighbors, with
another six at a slightly greater distance. The volume fraction occupied is 68%. In the hep and fee
structures, the stacking of a fourth sphere on top of three in any close-packed layer generates a
tetrahedral site or void, as shown in Fig. 1.4. Into such a site a smaller sphere with a coordination
number of four could fit. Three spheres from each of two layers generate an octahedral site or void,
. Into such a site a smaller sphere with a coordination number of six could fit.
In the hep and fee structures, there are two tetrahedral and one octahedral sites per packing sphere;
however, the arrangement of these sites is different.
Crystallography
All possible crystallographic structures are described in terms of 14 Bravais space lattices—only 14
different ways of periodically arranging points in space. . Each of the positions in a given space lattice is equivalent and an atom or ion or group of atoms or ions can be
centered on each position. Each of the lattices is described by a unit cell, The seven crystallographic systems
States of Matter
Matter can be divided into gases, liquids, and solids. In gases and liquids, the positions of the atoms
are not fixed with time, whereas in solids they are. Distances between atoms in gases are an order
of magnitude or greater than the size of the atoms, whereas in solids and liquids closest distances
between atoms are only approximately the size of the atoms. Almost all engineering materials are
solids, either crystalline or noncrystalline.
Crystalline Solids
In crystalline solids, the atoms or ions occupy fixed positions and vibrate about these equilibrium
positions. The arrangement of the positions is some periodic array, as discussed in Section 1.1.5. At
O0K, except for a small zero-point vibration, the oscillation of the atoms is zero. With increasing
temperature the amplitude and frequency of vibration increase up to the melting point. At the melting
point, the crystalline structure is destroyed, and the material melts to form a liquid. For a particular
single crystal the external shape is determined by the symmetry of the crystal class to which it
belongs. Most engineering materials are not single crystals but poly crystalline, consisting of many
small crystals. These crystals are often randomly oriented and may be of the same composition orof different composition or of different structures. There may be small voids between these grains.
Typical sizes of grains in such poly crystalline materials range from 0.01 to 10 mm in diameter.
Noncrystalline Solids
Noncrystalline solids (glasses) are solids in which the arrangement of atoms is periodic (random)
and lacks any long-range order. The external shape is without form and has no defined external faces
like a crystal. This is not to say that there is no structure. A local or short-range order exists in the
structure. Since the bonding between atoms or ions in a glass is similar to that of the corresponding
crystalline solid, it is not surprising that the local coordination, number of neighbors, configuration,
and distances are similar for a glass and crystal of the same composition. In fused SiO2, for example,
four O's surround each Si in a tetrahedral coordination, the same as in crystalline SiO2.
Glasses do not have a definite melting point, crystals do. Instead, they gradually soften to form
a supercooled liquid at temperatures below the melting point of the corresponding crystal. Glass
formation results when a liquid is cooled sufficiently rapidly to avoid crystallization. This behavior
is summarized in Fig. 1.6, where the volume V is plotted as a function of temperature T.Crystalline materials of the same composition exhibit more than one crystalline structure called
polymorphs. Fe, for example, exists in three different structures: a, y, and 5 Fe. The a phase, ferrite,
a bcc structure, transforms at 91O0C to the y phase, austenite, an fee structure, and then at 140O0C
changes back to bcc structures 6-iron or 6-ferrite. The addition of C to Fe and the reactions and
transformations that occur are extremely important in determining the properties of steel.
SiO2 exhibits many polymorphs, including a- and /3-quartz, a- and /3-tridymite, and a- and /3-
cristobalite. The SiO4 tetrahedron is common to all the structures, but the arrangement or linking of
these tetrahedra varies, leading to different structures. The a —> /3 transitions involve only a slight
change in the Si-O-Si bond angle, are rapid, and are an example of a phase transformation called
displacive. The quartz —> tridymite —> cristobalite transformations require the reformation of the new
structure, are much slower than displacive transformations, and are called reconstructive phase transformations.
The a —> y —> 8 Fe transformations are other examples of reconstructive transformations.
A phase diagram gives the equilibrium phases a function of temperature, pressure, and composition.
More commonly, the pressure is fixed at 1 atm and only the temperature and composition are
varied.
Defects
The discussion of crystalline structures assumes that the crystal structures are perfect, with each site
occupied by the correct atoms. In real materials, at temperatures greater than O0K, defects in the
crystalline structure will exist. These defects may be formed by the substitution of atoms different
from those normally occupying the site, vacancies on the site, atoms in sites not normally occupied
(interstitials), geometrical geometrical alterations of the structure in the form of dislocations, twin boundaries, or grain boundaries.
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