Fundamentals of Materials Science and Engineering - An Integrated Approach

Fundamentals of Materials Science and Engineering - An Integrated Approach

(Parte 6 de 7)

Another interesting feature of these toe pads is that they are self-cleaning—that is, dirt particles don’t stick to them. Scientists are just beginning to understand the mechanism of adhesion for these tiny hairs, which may lead to the development of synthetic self-cleaning adhesives. Can you image duct tape that never looses its stickiness, or bandages that never leave a sticky residue? (Photograph courtesy of Professor Kellar Autumn, Lewis & Clark College, Portland, Oregon.)

WHY STUDY Atomic Structure and Interatomic Bonding?

An important reason to have an understanding of interatomic bonding in solids is that, in some instances, the type of bond allows us to explain a material’s properties. For example, consider carbon, which may exist as both graphite and diamond. Whereas graphite is relatively soft and has a “greasy” feel to it, diamond is the hardest known material. This dramatic disparity in properties is directly attributable to a type of interatomic bonding found in graphite that does not exist in diamond (see Section 3.9).

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Learning Objectives

After careful study of this chapter you should be able to do the following:

1. Name the two atomic models cited and note the differences between them.

2. Describe the important quantum-mechanical principle that relates to electron energies.

3. (a) Schematically plot attractive, repulsive, and net energies versus interatomic separation for two atoms or ions.

(b) Note on this plot the equilibrium separation and the bonding energy.

4. (a) Briefly describe ionic, covalent, metallic, hydrogen, and van der Waals bonds.

(b) Note which materials exhibit each of these bonding types.


Some of the important properties of solid materials depend on geometrical atomic arrangements, and also the interactions that exist among constituent atoms or molecules. This chapter, by way of preparation for subsequent discussions, considersseveralfundamentalandimportantconcepts—namely,atomicstructure,electron configurations in atoms and the periodic table, and the various types of primary and secondary interatomic bonds that hold together the atoms comprising a solid. These topicsarereviewedbriefly,undertheassumptionthatsomeofthematerialisfamiliar to the reader.

Atomic Structure


Each atom consists of a very small nucleus composed of protons and neutrons, which is encircled by moving electrons. Both electrons and protons are electrically charged, thechargemagnitudebeing1.60×10−19 C,whichisnegativeinsignforelectronsand positive for protons; neutrons are electrically neutral. Masses for these subatomic particlesareinfinitesimallysmall;protonsandneutronshaveapproximatelythesame mass, 1.67 × 10−27 kg, which is significantly larger than that of an electron, 9.1 × 10−31 kg.

Each chemical element is characterized by the number of protons in the nucleus, or the atomic number (Z).1 For an electrically neutral or complete atom, the atomicatomic number number also equals the number of electrons. This atomic number ranges in integral units from 1 for hydrogen to 92 for uranium, the highest of the naturally occurring elements.

Theatomicmass(A)ofaspecificatommaybeexpressedasthesumofthemasses of protons and neutrons within the nucleus. Although the number of protons is the same for all atoms of a given element, the number of neutrons (N) may be variable. Thus atoms of some elements have two or more different atomic masses, which are called isotopes. The atomic weight of an element corresponds to the weighted isotope atomic weight average of the atomic masses of an atom’s naturally occurring isotopes.2 The atomic mass unit(amu) may be used for computations of atomic weight. A scale has beenatomic mass unit

1 Terms appearing in boldface type are defined in the Glossary, which follows Appendix E.

2 The term “atomic mass” is really more accurate than “atomic weight” inasmuch as, in this context, we are dealing with masses and not weights. However, atomic weight is, by convention, the preferred terminology and will be used throughout this book. The reader should note that it is not necessary to divide molecular weight by the gravitational constant.

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2.3 Electrons in Atoms • 17 established whereby 1 amu is defined as 112 of the atomic mass of the most common isotope of carbon, carbon 12 (12C) (A = 12.0). Within this scheme, the masses of protons and neutrons are slightly greater than unity, and

The atomic weight of an element or the molecular weight of a compound may be specifiedonthebasisofamuperatom(molecule)ormasspermoleofmaterial.Inone moleofasubstancethereare6.0221×1023 (Avogadro’snumber)atomsormolecules.mole These two atomic weight schemes are related through the following equation:

1amu/atom(or molecule) = 1g/mol

For example, the atomic weight of iron is 5.85 amu/atom, or 5.85 g/mol. Sometimes use of amu per atom or molecule is convenient; on other occasions g (or kg)/mol is preferred. The latter is used in this book.

Concep t Check 2.1 Why are the atomic weights of the elements generally not integers? Cite two reasons.

[The answer may be found at (Student Companion Site).]

2.3 ELECTRONS IN ATOMS Atomic Models

Duringthelatterpartofthenineteenthcenturyitwasrealizedthatmanyphenomena involving electrons in solids could not be explained in terms of classical mechanics. What followed was the establishment of a set of principles and laws that govern sys- temsofatomicandsubatomicentitiesthatcametobeknownasquantummechanics.quantum mechanics An understanding of the behavior of electrons in atoms and crystalline solids neces- sarily involves the discussion of quantum-mechanical concepts. However, a detailed exploration of these principles is beyond the scope of this book, and only a very superficial and simplified treatment is given. One early outgrowth of quantum mechanics was the simplified Bohr atomic model, in which electrons are assumed to revolve around the atomic nucleus inBohr atomic model discrete orbitals, and the position of any particular electron is more or less well defined in terms of its orbital. This model of the atom is represented in Figure 2.1.

Anotherimportantquantum-mechanicalprinciplestipulatesthattheenergiesof electrons are quantized; that is, electrons are permitted to have only specific values of energy. An electron may change energy, but in doing so it must make a quantum jump either to an allowed higher energy (with absorption of energy) or to a lower energy (with emission of energy). Often, it is convenient to think of these allowed electron energies as being associated with energy levels or states. These states do not vary continuously with energy; that is, adjacent states are separated by finite energies. For example, allowed states for the Bohr hydrogen atom are represented in Figure 2.2a. These energies are taken to be negative, whereas the zero reference is the unbound or free electron. Of course, the single electron associated with the hydrogen atom will fill only one of these states.

Thus, the Bohr model represents an early attempt to describe electrons in atoms in terms of both position (electron orbitals) and energy (quantized energy levels).

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18 • Chapter 2 / Atomic Structure and Interatomic Bonding

Orbital electron Nucleus

Figure 2.1 Schematic representation of the Bohr atom.

This Bohr model was eventually found to have some significant limitations because of its inability to explain several phenomena involving electrons. A resolution was reached with a wave-mechanical model, in which the electron is considered towave-mechanical model exhibit both wave-like and particle-like characteristics. With this model, an electron is no longer treated as a particle moving in a discrete orbital; rather, position is considered to be the probability of an electron’s being at various locations around the nucleus. In other words, position is described by a probability distribution or electroncloud.Figure2.3comparesBohrandwave-mechanicalmodelsforthehydrogen atom. Both these models are used throughout the course of this book; the choice depends on which model allows the more simple explanation.

Quantum Number s

Usingwavemechanics,everyelectroninanatomischaracterizedbyfourparameters called quantum numbers. The size, shape, and spatial orientation of an electron’squantum number

–1 × 10–18

–2 × 10–18 (a) (b)

Energy (J)Energy (eV) n = 2 n = 3

Figure 2.2 (a)T he first three electron energy states for the Bohr hydrogen atom. (b) Electron energy states for the first three shells of the wave-mechanical hydrogen atom. (Adapted from W. G. Moffatt, G. W. Pearsall, and J. Wulff, The Structure and Properties of Materials, Vol. I, Structure, p. 10. Copyright c© 1964 by John Wiley & Sons, New York. Reprinted by permission of John Wiley & Sons, Inc.)

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2.3 Electrons in Atoms • 19 1.0

(a) (b) Orbital electron Nucleus

Probability Distance from nucleus

Figure 2.3 Comparison of the (a) Bohr and (b) wave-mechanical atom models in terms of electron distribution. (Adapted from Z. D. Jastrzebski, The Nature and Properties of Engineering Materials, 3rd edition, p. 4. Copyright c© 1987 by John Wiley & Sons, New York. Reprinted by permission of John Wiley & Sons, Inc.)

respectively, to n = 1, 2, 3, 4, 5,, as indicated in Table 2.1. Note also that this

probability density are specified by three of these quantum numbers. Furthermore, Bohr energy levels separate into electron subshells, and quantum numbers dictate the number of states within each subshell. Shells are specified by a principal quantum number n, which may take on integral values beginning with unity; sometimes these shells are designated by the letters K, L, M, N, O, and so on, which correspond, quantum number, and it only, is also associated with the Bohr model. This quantum number is related to the distance of an electron from the nucleus, or its position.

The second quantum number, l, signifies the subshell, which is denoted by a lowercase letter—an s, p, d, or f; it is related to the shape of the electron subshell. In addition,thenumberofthesesubshellsisrestrictedbythemagnitudeofn.Allowable subshells for the several n values are also presented in Table 2.1. The number of energy states for each subshell is determined by the third quantum number, ml.F or an s subshell, there is a single energy state, whereas for p, d, and f subshells, three, five, and seven states exist, respectively (Table 2.1). In the absence of an external magnetic field, the states within each subshell have identical energies. However, when a magnetic field is applied these subshell states split, each state assuming a slightly different energy. Associated with each electron is a spin moment, which must be oriented either up or down. Related to this spin moment is the fourth quantum number, ms, for which two values are possible (+12 and −12), one for each of the spin orientations.

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20 • Chapter 2 / Atomic Structure and Interatomic Bonding

Table 2.1 The Number of Available Electron States in Some of the Electron Shells and Subshells

Number of ElectronsPrincipal Quantum Shell Number of

Number n Designation Subshells States Per Subshell Per Shell

Thus, the Bohr model was further refined by wave mechanics, in which the introduction of three new quantum numbers gives rise to electron subshells within each shell. A comparison of these two models on this basis is illustrated, for the hydrogen atom, in Figures 2.2a and 2.2b.

A complete energy level diagram for the various shells and subshells using the wave-mechanical model is shown in Figure 2.4. Several features of the diagram are worth noting. First, the smaller the principal quantum number, the lower the energy level; for example, the energy of a 1s state is less than that of a 2s state, which in turn is lower than the 3s. Second, within each shell, the energy of a subshell level increases with the value of the l quantum number. For example, the energy of a 3d state is greater than a 3p, which is larger than 3s. Finally, there may be overlap in

Principal quantum number, n

Energy s p s p s p s p df s p s p d d

Figure 2.4 Schematic representation of the relative energies of the electrons for the various shells and subshells. (From K. M. Ralls, T. H. Courtney, and J. Wulff, Introduction to Materials Science and Engineering, p. 2. Copyright c© 1976 by John Wiley & Sons, New York. Reprinted by permission of John Wiley & Sons, Inc.)

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2.3 Electrons in Atoms • 21 energy of a state in one shell with states in an adjacent shell, which is especially true of d and f states; for example, the energy of a 3d state is generally greater than that ofa4 s.

Electr on Configurations

The preceding discussion has dealt primarily with electron states —values of energyelectron state that are permitted for electrons. To determine the manner in which these states are filled with electrons, we use the Pauli exclusion principle, another quantum-Pauli exclusion principle mechanical concept. This principle stipulates that each electron state can hold no morethantwoelectrons,whichmusthaveoppositespins.Thus,s,p,d,andf subshells may each accommodate, respectively, a total of 2, 6, 10, and 14 electrons; Table 2.1 summarizesthemaximumnumberofelectronsthatmayoccupyeachofthefirstfour shells.

Of course, not all possible states in an atom are filled with electrons. For most atoms, the electrons fill up the lowest possible energy states in the electron shells and subshells, two electrons (having opposite spins) per state. The energy structure for a sodium atom is represented schematically in Figure 2.5. When all the electrons occupy the lowest possible energies in accord with the foregoing restrictions, an atom is saidtobeinitsgroundstate.However,electrontransitionstohigherenergystatesareground state possible, as discussed in Chapters 12 and 19. The electron configuration or structure electron configuration of an atom represents the manner in which these states are occupied. In the conventional notation the number of electrons in each subshell is indicated by a superscript after the shell–subshell designation. For example, the electron configurations for hydrogen, helium, and sodium are, respectively, 1s1,1 s2, and 1s22s22p63s1. Electron configurations for some of the more common elements are listed in Table 2.2.

At this point, comments regarding these electron configurations are necessary.

(Parte 6 de 7)