30079_01.pdf

PART 1

MATERIALS AND

MECHANICAL DESIGN

CHAPTER 1

STRUCTURE OF SOLIDS

Charles H. Drummond III

Department of Materials Science and Engineering

Ohio State University

Columbus, Ohio

1.1 INTRODUCTION

1.2.2 Alloys

1.1.1 Effects of Structure on

Properties

1.2.3 Noncrystalline Metals

1. .2 Atomic Structure

1.3 CERAMICS

1. .3 Bonding

1.3.1 Crystalline Ceramics

1. .4 Simple Structures

1.3.2 Noncrystalline Ceramics

1. .5 Crystallography

1.3.3 Glass-Ceramics

1. .6 States of Matter

1. .7 Polymorphism

1.4 POLYMERS

1. .8 Defects

1.5 COMPOSITES AND COATINGS

1.2 METALS

1.5.1 Fiberglass

1.2.1 Structures

1.5.2 Coatings

1.1 INTRODUCTION

1.1.1 Effects of Structure on Properties

Physical properties of metals, ceramics, and polymers, such as ductility, thermal expansion, heat

capacity, elastic modulus, electrical conductivity, and dielectric and magnetic properties, are a direct

result of the structure and bonding of the atoms and ions in the material. An understanding of the

origin of the differences in these properties is of great engineering importance.

In single crystals, a physical property such as thermal expansion varies with direction, reflecting

the crystal structure; whereas in polycrystalline and amorphous materials, a property does not vary

with direction, reflecting the average property of the individual crystals or the randomness of the

amorphous structure. Most engineering materials are polycrystalline, composed of many grains, and

thus an understanding of the properties requires not only a knowledge of the structure of the single

grains but also a knowledge of grain size and orientation, grain boundaries, and other phases present;

that is, a knowledge of the microstructure of this material.

1.1.2 Atomic Structure

Atoms consist of electrons, protons, and neutrons. The central nucleus consists of positively charged

protons and electrically neutral neutrons. Negatively charged electrons are in orbits about the nucleus

in different energy levels, occupying a much larger volume than the nucleus.

In an atom, the number of electrons equals the number of protons and, hence, an atom is neutral.

The atomic number of an element is given by the number of protons, and the atomic weight is given

by the total number of protons and neutrons. (The weight of the electrons is negligible.) Thus,

hydrogen, H, with one proton and one electron, has an atomic number of 1 and an atomic weight of

1 and is the first element in the periodic chart. Oxygen, O, with atomic number 8, has eight protons

and eight neutrons and, hence, an atomic weight of 16.

Completed electronic shells have a lower energy than partially filled orbitals when bonded to

other atoms. As a result of this energy reduction, atoms share electrons to complete the shells, or

gain or lose electrons to form completed shells. In the latter case, ions are formed in which the

Mechanical Engineers' Handbook, 2nd ed., Edited by Myer Kutz.

number of electrons is not equal to the number of protons. Thus, O by gaining two electrons, has a

charge of -2 and forms the oxygen ion O 2- .

The periodic chart arranges elements in columns of the same electronic configuration. The first

column consists of the alkalies Li, Na, K, Cs, Rb; each has one electron in the outer shell that can

be lost. Similarly, the second column of alkaline-earths can form Mg 2+ , Ca 2+ , Sr 2+ , Ba 2 + by losing

two electrons. The seventh column consists of the halogens Fl, Cl, Br, I, which by gaining one

electron become the halides, all with a charge of -1. The eighth column consists of the inert gases

He, Ne, Ar, K, Xe, with completed shells. The bonding of the elements and ions with similar elec-

tronic configurations is similar. Moving down a column increases the number of electrons and, hence,

the atom's size increases even though the outer electronic configuration remains the same.

The outer electrons that are lost, gained, or shared are called valence electrons, and the inner

electrons are called core electrons. For the most part, the valence electrons are important in deter-

mining the nature of the bonding and, hence, the structure and properties of the materials.

1.1.3 Bonding

When two atoms or ions are within atomic distances of each other, distances of 0.5-3.OA, bonding

may occur between the atoms or ions. The resulting reduction in energy due to an attractive force

leads to the formation of polyatomic gas molecules, liquids, and solids. If the energy of the bonds

is large (75-275 kcal/mol), primary bonds are formed—metallic, ionic, or covalent. If the energy of

the bond is smaller (1-10 kcal/mol), secondary bonds are formed—van der Waals and hydrogen. In

addition, combinations of bond types, such as a mixture of ionic and covalent bonds, may occur.

Metallic Bonding

In a metallic crystal, an ordered arrangement of nuclei and their electrons is embedded in a cloud of

valence electrons, which are shared throughout the lattice. The resulting bonding is a nondirectional

primary bond. Since the binding energy of the valence electrons is relatively small, the mobility of

these electrons is high and creates high electrical and thermal conductivity. The atoms are approxi-

mately spherical in shape as a result of the shape of completed inner shell. Examples of metals are

Cu, Au, Ag, and Na.

Ionic Bonding

The strongest type of bonding between two oppositely charged particles is called ionic bonding. The

positively charged ions (cations) attract as many negatively charged ions (anions) as they can and

form ionic bonds. The primary bond formed is nondirectional if the bonding is purely ionic. Li + and

F~ in LiF form predominately ionic bonds. In general, since the electrons are strongly bonded,

electrical and thermal conductivities are much smaller than in metals and, thus, ionic bonded materials

are classified as insulators or dielectrics.

Covalent Bonding

Covalent bonding results from an overlap or sharing, not from gain or loss of valence electrons. A

net reduction of energy as a result of each atom's completing the other's orbital also results in a

primary bond, but it is directional. The directionality is a result of the shape of the orbitals involved

in the bonding. When C is covalently bonded to four other C's in diamond, the bonding is purely

covalent and the configuration of these four bonds is tetrahedral. When B, however, is bonded to

three other B's, a triangular configuration is formed. Organic polymers and diatomic gases such as

Cl 2 are typical examples of covalent bonding. As a result of the strong bonding of the valence

electrons, these materials, for the most part, have low electrical and thermal conductivity.

Van der Waals and Hydrogen Bonding

Van der Waals bonds are secondary bonds, the result of fluctuating dipoles, due to the fact that at an

instant of time the centers of positive and negative charge do not coincide. An example is an inert

gas such as Ar, which below -19O 0 C forms a solid as a result of these weak attractive forces. Similar

weak forces exist in molecules and solids. Hydrogen bonds are also secondary bonds, but they are

the result of permanent dipoles. For example, the water molecule, H 2 O, is nonlinear and the bonding

between H and an adjacent O in water results in H 2 O being a liquid above O 0 C a 1 ami pressure

rather than a gas, as is the case for other molecules of comparable molecular weight.

1.1.4 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 (see Fig. 1.1). If similar layers are stacked to form

a three-dimensional structure, an infinite number of configurations is possible. Two are important. In

Fig. 1.1 Close-packed layer.

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 (•) in Fig. 1.2 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 body-

centered 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,

as shown in Fig. 1.4. 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.

1.1.5 Crystallography

All possible crystallographic structures are described in terms of 14 Bravais space lattices—only 14

different ways of periodically arranging points in space. These are shown in Fig. 1.5. Each of the

Fig. 1.2 Two possible sites for sphere in fee and hep structures: x and • (from D. M. Adams,

Inorganic Solids, Wiley, New York, 1974).

Fig. 1.3 hep, fee, and bee structures (from W. G. Moffatt, G. W. Pearsall, and J. Wulff, The

Structure and Properties of Materials, Wiley, New York, 1964, Vol. I, p. 51).

Fig. 1.4 Tetrahedral and octahedral sites (from G. W. Moffatt, G. W. Pearsall, and J. Wulff, The

Structure and Properties of Materials, Wiley, New York, 1964, Vol. I, p. 58).

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