W
e begin our exploration of the field of materials science and engineering by focusing on materials sci- ence. Chapters 2 through 10 cover a variety of funda- mental topics from physics and chemistry. A student may well have encountered many of the concepts in Chapter 2 (atomic bonding) in previous courses. Of special interest to the field of materials science is the role of atomic bonding in providing a classification scheme for materials. Metallic, ionic, and covalent bonding roughly correspond to the categories of structural materials: metals, ceramics/glasses, and polymers.Semiconductors, an important category of electronic materials, generally cor- respond to covalent bonding. Chapter 3 introduces the crystalline structures of many engineered materials and includes an introduction to x- ray diffraction, an important tool for determining crystal structure. Chapter 4 identifies various imperfections that can occur relative to the crystalline structures of Chapter 3. In Chapter 5, we see that some of these structural defects play a central role in solid- state diffusion, and, in Chapter 6, we find that other defects are responsible for some of the mechanical behavior of materials. Chapter 7 introduces the thermal behavior of materials, and, in Chapter 8, we see that certain mechanical and ther- mal processes (such as machining and welding) can lead to the failure of materi- als. In Chapter 9, we are introduced to phase diagrams that serve as useful tools for predicting the microscopic- scale structures of materials that are produced at a relatively slow rate, maintaining equilibrium along the way. In Chapter 10 on kinetics, we see the effect of more rapid heat treatments that lead to additional microstructures. Throughout Part I, we will find that fundamental principles from physics and chemistry underlie the practical behavior of engineered materials.
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A central principle of materials science is that the properties of materials that permit their engineering applications can be understood by examining the structure of those materials on a small scale. The instrument shown above is a scanning electron microscope that can provide higher magnifications with a greater depth of field than possible with traditional optical microscopes. Shown on the facing page is a micrograph produced using that instrument. The image shows particles trapped on the fibers of an air filter recovered from near the World Trade Center attack of September 11, 2001. Such analyses were used to determine the nature of particulate air pollution in the vicinity of the attack and its potential effect on human health. (Courtesy of the Department of Chemical Engineering and Materials Science, University of California, Davis.)
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atomic Bonding
C
hapter 1 introduced the basic types of materi- als available to engineers. One basis of that clas- sification system is found in the nature of atomic bonding in materials. Atomic bonding falls into two general categories. Primary bonding involves the transfer or sharing of electrons and produces a relatively strong joining of adjacent atoms. Ionic, covalent, and metallic bonds are in this category.Secondary bonding involves a relatively weak attraction between atoms in which no electron transfer or sharing occurs. Van der Waals bonds are in this category. Each of the five fundamental types of engineering materials (metals, ceramics, glasses, polymers, and semiconductors) is associated with a certain type (or types) of atomic bonding. Composites, of course, are combina- tions of fundamental types.
2.1 atomic Structure
In order to understand bonding between atoms, we must appreciate the structure within the individual atoms. For this purpose, it is sufficient to use a relatively simple planetary model of atomic structure— that is, electrons (the planets) orbit about a nucleus (the sun).
It is not necessary to consider the detailed structure of the nucleus for which physicists have catalogued a vast number of elementary particles. We need consider only the number of protons and neutrons in the nucleus as the basis of the chemical identification of a given atom. Figure 2.1 is a planetary model of a carbon atom. This illustration is schematic and definitely not to scale. In reality, the nucleus is much smaller, even though it contains nearly all the mass of the atom. Each proton and neutron has a mass of approximately 1.66 * 10-24 g. This value is referred to as an atomic mass unit (amu). It is convenient to express the mass of elemental materials in these units. For instance, the most common
2.1 atomic Structure 2.2 the Ionic Bond 2.3 the Covalent Bond 2.4 the Metallic Bond
2.5 the Secondary, or van der Waals, Bond 2.6 Materials— the Bonding Classification
Computer models of the structures of materials on the atomic scale require accurate knowledge of the bonding between adjacent atoms.
In this model of a molecule that plays an important role in organic photovoltaic materials, atoms are shown as spheres joined by covalent bonds. (Courtesy of Roland Faller, Adam Moule, and Varuni Dantanarayana, University of California, Davis.)
isotope of carbon, 12C (shown in Figure 2.1), contains in its nucleus six protons and six neutrons, for an atomic mass of 12 amu. It is also convenient to note that there are 0.6023 * 1024 amu per gram. This large value, known as Avogadro’s* number, represents the number of protons or neutrons necessary to produce a mass of 1 g. Avogadro’s number of atoms of a given element is termed a gram- atom. For a compound, the corresponding term is mole; that is, one mole of NaCl contains Avogadro’s number of Na atoms and Avogadro’s number of Cl atoms.
Avogadro’s number of 12C atoms would have a mass of 12.00 g. Naturally occurring carbon actually has an atomic mass of 12.011 amu because not all carbon atoms contain six neutrons in their nuclei. Instead, some contain seven.
Different numbers of neutrons (six or seven) identify different isotopes— various forms of an element that differ in the number of neutrons in the nucleus. In nature, 1.1% of the carbon atoms are the isotope 13C. However, the nuclei of all carbon atoms contain six protons. In general, the number of protons in the nucleus is known as the atomic number of the element. The well- known period- icity of chemical elements is based on this system of elemental atomic numbers and atomic masses arranged in chemically similar groups (vertical columns) in a periodic table (Figure 2.2).
While chemical identification is done relative to the nucleus, atomic bonding involves electrons and electron orbitals. The electron, with a mass of
1 H 1.008
3 Li 6.941
4 Be 9.012 I A
II A III A IV A V A VI A VII A
VIII
III B IV B V B VI B VII B I B
11 Na 22.99
12 Mg 24.31
13 Al 26.98
14 Si 28.09
15 P 30.97
16 S 32.06
17 Cl 35.45
18 Ar 39.95 5
B 10.81
6 C 12.01
7 N 14.01
8 O 16.00
9 F 19.00
10 Ne 20.18
2 He 4.003
0
19 K 39.10
20 Ca 40.08
21 Sc 44.96
22 Ti 47.90
23 V 50.94
24 Cr 52.00
25 Mn 54.94
26 Fe 55.85
27 Co 58.93
28 Ni 58.71
29 Cu 63.55
30 Zn 65.38
31 Ga 69.72
32 Ge 72.59
33 As 74.92
34 Se 78.96
35 Br 79.90
36 Kr 83.80 37
Rb 85.47
38 Sr 87.62
39 Y 88.91
40 Zr 91.22
41 Nb 92.91
42 Mo 95.94
43 Tc 98.91
44 Ru 101.07
45 Rh 102.91
46 Pd 106.4
47 Ag 107.87
48 Cd 112.4
49 In 114.82
50 Sn 118.69
51 Sb 121.75
52 Te 127.60
53 I 126.90
54 Xe 131.30 55
Cs 132.91
56 Ba 137.33
57 La 138.91 87
Fr (223)
88 Ra 226.03
89 Ac (227)
104 Rf (261)
105 Db (262)
106 Sg (266) 72
Hf 178.49
73 Ta 180.95
74 W 183.85
75 Re 186.2
76 Os 190.2
77 Ir 192.22
78 Pt 195.09
79 Au 196.97
80 Hg 200.59
81 Tl 204.37
82 Pb 207.2
83 Bi 208.98
84 Po (210)
58 Ce 140.12
59 Pr 140.91
60 Nd 144.24
61 Pm (145)
62 Sm 150.4
63 Eu 151.96
64 Gd 157.25
65 Tb 158.93
66 Dy 162.50
67 Ho 164.93
68 Er 167.26
69 Tm 168.93
70 Yb 173.04
71 Lu 174.97 90
Th 232.04
91 Pa 231.04
92 U 238.03
93 Np 237.05
94 Pu (244)
95 Am (243)
96 Cm (247)
97 Bk (247)
98 Cf (251)
99 Es (254)
100 Fm (257)
101 Md (258)
102 No (259)
103 Lw (260)
85 At (210)
86 Rn (222) II B
Outer orbital (with four sp3 hybrid bonding electrons)
Inner orbital (with two 1s electrons)
Nucleus (with six protons and six neutrons)
Figure 2.1 Schematic of the planetary model of a 12C atom.
*Amadeo Avogadro (1776–1856), Italian physicist, who, among other contributions, coined the word molecule. Unfortunately, his hypothesis that all gases (at a given temperature and pressure) contain the same number of molecules per unit volume was not generally acknowledged as correct until after his death.
Figure 2.2 Periodic table of the elements indicating atomic number and atomic mass (in amu).
0.911 * 10-27 g, makes a negligible contribution to the atomic mass of an ele- ment. However, this particle has a negative charge of 0.16 * 10-18 coulomb (C), equal in magnitude to the +0.16 * 10-18 C charge of each proton. (The neutron is, of course, electrically neutral.)
Electrons are excellent examples of the wave- particle duality; that is, they are atomic- scale entities exhibiting both wavelike and particlelike behavior. It is beyond the scope of this book to deal with the principles of quantum mechan- ics that define the nature of electron orbitals (based on the wavelike charac- ter of electrons). However, a brief summary of the nature of electron orbitals is helpful. As shown schematically in Figure 2.1, electrons are grouped at fixed orbital positions about a nucleus. In addition, each orbital radius is characterized by an energy level, a fixed binding energy between the electron and its nucleus.
Figure 2.3 shows an energy level diagram for the electrons in a 12C atom. It is important to note that the electrons around a 12C nucleus occupy these specific energy levels, with intermediate energies forbidden. The forbidden energies cor- respond to unacceptable quantum mechanical conditions; that is, standing waves cannot be formed.
A detailed list of electronic configurations for the elements of the periodic table is given in Appendix 1, together with various useful data. The arrangement of the periodic table (Figure 2.2) is largely a manifestation of the systematic “fill- ing” of the electron orbitals with electrons, as summarized in Appendix 1. The notation for labeling electron orbitals is derived from the quantum numbers of wave mechanics. These integers relate to solutions to the appropriate wave equa- tions. We do not deal with this numbering system in detail in this book; instead, it is sufficient to appreciate the basic labeling system. For instance, Appendix 1 tells us that there are two electrons in the 1s orbital. The 1 is a principal quan- tum number, identifying this energy level as the first one which is closest to the atomic nucleus. There are also two electrons each associated with the 2s and 2p orbitals. The s, p, and so on, notation refers to an additional set of quantum num- bers. The rather cumbersome letter notation is derived from the terminology of early spectrographers. The six electrons in the 12C atom are then described as a
Energy (eV)
-283.9
-6.5 2 (sp3)
1s 0
Figure 2.3 Energy- level diagram for the orbital electrons in a 12C atom. Notice the sign convention. An attractive energy is negative. The 1s electrons are closer to the nucleus (see Figure 2.1) and more strongly bound (binding energy = -283.9 eV). The outer orbital electrons have a binding energy of only -6.5 eV. The zero level of binding energy corresponds to an electron completely removed from the attractive potential of the nucleus.
In Section 13.2, we shall see that energy level diagrams like this are central to the understanding of energy band gap structures that are, in turn, at the heart of semiconductor technology.
1s22s22p2 distribution; that is, two electrons in the 1s orbital, two in 2s, and two in 2p.
In fact, the four electrons in the outer orbital of 12C redistribute themselves in a more symmetrical fashion to produce the characteristic geometry of bonding between carbon atoms and adjacent atoms (generally described as 1s22s12p3).
This sp3 configuration in the second energy level of carbon, called hybridization, is indicated in Figures 2.1 and 2.3 and is discussed in further detail in Section 2.3.
(Note especially Figure 2.19.)
The bonding of adjacent atoms is essentially an electronic process. Strong primary bonds are formed when outer orbital electrons are transferred or shared between atoms. Weaker secondary bonds result from a more subtle attraction between positive and negative charges with no actual transfer or sharing of elec- trons. In the next section, we will look at the various possibilities of bonding in a systematic way, beginning with the ionic bond.
the Material World