Preloaded, ready-to-use assignments and presentations www.wiley.com/college/quickstar t. 2-minute tutorials and all the resources you and your students need to get started www.wileyplus.com/firstday. As discussed in Chapter 20, some of the magnetic ceramics have this inverted spinel crystal structure.).
Preface
The fourth goal is to include features in the book that will accelerate the learning process. A series of discipline-specific modules appear on the book's website (Student Companion Site).
W ILEY PLUS
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Contents
List of Symbols
In brackets is the number of the paragraph in which a symbol is introduced or explained.
S UBSCRIPTS
- HISTORICAL PERSPECTIVE
- MATERIALS SCIENCE AND ENGINEERING
- WHY STUDY MATERIALS SCIENCE AND ENGINEERING?
- CLASSIFICATION OF MATERIALS
- Classification of Materials • 7
- Classification of Materials • 9
In addition to structure and properties, two other important components are involved in the science and engineering of materials—namely, processing and performance. Some of the common and well-known polymers are polyethylene (PE), nylon, poly(vinyl chloride) (PVC), polycarbonate (PC), polystyrene (PS) and silicone rubber. These materials typically have low densities (Figure 1.3), while their mechanical properties are generally different from the metallic and ceramic materials - they are not as stiff or as strong as these other material types (Figures 1.4 and 1.5).
MATERIALS OF IMPORTANCE Carbonated Beverage Containers
ADVANCED MATERIALS
Materials used in high-tech (or high-tech) applications are sometimes called advanced materials. For example, some of the biomaterials used in artificial hip replacements are discussed in the Biomaterials online module.
MODERN MATERIALS’ NEEDS
It is just beginning to be used in batteries for electronic devices and has promise as a power plant for cars. New materials still need to be developed for more efficient fuel cells and also for better catalysts to be used in hydrogen production.
PROCESSING/STRUCTURE/PROPERTIES/
In addition, material processing and refining methods must be improved so that they cause less environmental degradation - that is, less pollution and less destruction of the landscape through the extraction of raw materials. In some material manufacturing processes, toxic substances are also produced, and the ecological impact of their disposal must be taken into account.
PERFORMANCE CORRELATIONS
INTRODUCTION
Some important properties of solid materials depend on the geometrical arrangement of atoms and also the interactions that exist between the constituent atoms or molecules. These topics are briefly reviewed on the assumption that some of the material is familiar to the reader.
FUNDAMENTAL CONCEPTS
This chapter, in preparation for subsequent discussions, considers several basic and important concepts—namely, atomic structure, electron configurations in atoms and the periodic table, and the various types of primary and secondary interatomic bonds that hold together the atoms that make up a solid.
WHY STUDY Atomic Structure and Interatomic Bonding?
- ELECTRONS IN ATOMS
- Electrons in Atoms • 23
- THE PERIODIC TABLE
- The Periodic Table • 27
- BONDING FORCES AND ENERGIES
- Bonding Forces and Energies • 29
- PRIMARY INTERATOMIC BONDS
- Primary Interatomic Bonds • 31
- Primary Interatomic Bonds • 33
- SECONDARY BONDING OR VAN DER WAALS BONDING
- Secondary Bonding or van der Waals Bonding • 37
It is the sp3 hybrid form that defines the 109⬚ (or tetrahedral) angle often found in polymer chains (Chapter 14). The centers of the two atoms will remain separated by the equilibrium distance r0, as shown in Figure 2.8a.
MATERIALS OF IMPORTANCE
MOLECULES
The elements in each of the columns (or groups) of the periodic table have characteristic electron configurations. Based on this graph, determine (i) the equilibrium spacing r0 between the K⫹ and Cl⫺ions and (ii) the magnitude of the bond energy E0 between the two ions.
WHY STUDY The Structure of Crystalline Solids?
- INTRODUCTION
- FUNDAMENTAL CONCEPTS
- UNIT CELLS
- METALLIC CRYSTAL STRUCTURES
- Density Computations • 51
- DENSITY COMPUTATIONS
The total volume of an atom and the volume of a unit cell can be calculated from the atomic radius R. From Example Problem 3.1, the total volume of a unit cell is. Therefore, the atomic packing factor is the same.
APF V S
POLYMORPHISM AND ALLOTROPY
Some metals, as well as non-metals, can have more than one crystal structure, a phenomenon known as polymorphism. When found in elemental solids, the condition is often called allotropy. The prevailing crystal structure depends on both the temperature and the external pressure. Also, pure iron has a BCC crystal structure at room temperature, which changes to FCC iron at 912C (1674F).
CRYSTAL SYSTEMS
A well-known example is found in carbon: graphite is the stable polymorph under ambient conditions, while diamond is formed under extremely high pressure.
Crystal Systems • 53
MATERIAL OF IMPORTANCE Tin (Its Allotropic Transformation)
POINT COORDINATES
The coordinate q (which is a fraction) corresponds to the distance qa along the x-axis, where a is the length of the edge of the unit cell. For the unit cell shown in the attached sketch (a), locate the point with coordinates 1 .14 12.
Crystallographic Directions • 57
CRYSTALLOGRAPHIC DIRECTIONS
The vector, as drawn, passes through the origin of the coordinate system and therefore no translation is needed. In the accompanying figure, the unit cell is cubic and the origin of the coordinate system, point O, is located at one of the cube corners.
Crystallographic Directions • 59
The intersections of two sets of parallel lines (eg those for a2 and a3) lie on and trisect the other axis (eg divide a1 into thirds) within the hexagonal unit cell. In addition, the z-axis of Figure 3.9 is also divided into three equal lengths (at trisection points m and n).
Crystallographic Directions • 61 Figure Reduced-scale coordinate axis
The mapping of crystallographic directions for hexagonal crystals is more complicated than for crystals belonging to the other six systems. First we start from the origin (point O), then we move one unit along the axis a1 (at point P), parallel to a2.
Crystallographic Planes • 63
Now it becomes necessary to convert these indices into an index set referred to the four-axis scheme. Multiplying the preceding indices by 3 reduces them to the lowest set, yielding values for u, v, t, and w of 2,4, 2, and 3, respectively.
CRYSTALLOGRAPHIC PLANES
An interesting and unique characteristic of cubic crystals is that planes and directions having the same indices are perpendicular to each other; however, for other crystal systems there are no simple geometric relationships between planes and directions having the same indices.
Crystallographic Planes • 65
A plane is indicated by lines representing its points of intersection with the planes that make up the planes of the unit cell or their extensions. Also, only in the cubic system, planes with the same indices, regardless of order and sign, are equivalent.
Crystallographic Planes • 67
The circles represent atoms lying in the crystallographic planes, as would be obtained from a slice taken through the centers of the full-size hard spheres. This plane intersects the a1 axis at a distance a from the origin of the a1-a2-a3-z coordinate axis system (point C).
LINEAR AND PLANAR DENSITIES
There is thus an equivalence of two atoms along the [110] direction vector in the unit cell. For example, consider the section of a (110) plane within an FCC unit cell as shown in Figures 3.11a and 3.11b.
Close-Packed Crystal Structures • 69
Linear density (LD) is defined as the number of atoms per length unit whose centers lie on the direction vector of a specific crystallographic direction; it is,. In an analogous way, planar density (PD) is taken as the number of atoms per unit of area centered on a particular crystallographic plane, or.
CLOSE-PACKED CRYSTAL STRUCTURES
The area of this planar region is therefore (4R)( ) and the planar density is determined as follows: 3.11) Linear and planar densities are important considerations regarding the process of slip, that is, the mechanism by which metals plastically deform (section 7.4).
Close-Packed Crystal Structures • 71
The significance of these FCC and HCP close-packed planes will become apparent in Chapter 7. In addition, the crystal structures of many ceramic materials can be formed by the stacking of closely packed planes of ions (Section 12.2).
SINGLE CRYSTALS
We can specify crystallographic planes and directions in terms of directionality and Miller indices; moreover, it is sometimes important to ascertain the atomic and ionic arrangements of particular crystallographic planes.
POLYCRYSTALLINE MATERIALS
The concepts described in the previous four sections also apply to crystalline ceramic and polymeric materials, which are discussed in Chapters 12 and 14. The small grains grow by the successive addition of atoms from the surrounding fluid to the structure of each .
ANISOTROPY
Anisotropy • 73
In many polycrystalline materials, the crystallographic orientations of individual grains are completely random. Energy losses in the transformer cores are reduced by using polycrystalline plates of these alloys, into which a "magnetic texture" has been introduced: most of the grains in each plate have a crystallographic direction of type 81009, which is aligned (or nearly aligned) in the same direction. direction parallel to the direction of the applied magnetic field.
X-RAY DIFFRACTION: DETERMINATION OF CRYSTAL STRUCTURES
They are said to mutually reinforce (or constructively hinder) each other; and when amplitudes are added, the wave shown on the right of the figure is created. The scattered waves are out of phase, that is, corresponding amplitudes cancel or cancel each other out, or interfere destructively (that is, the resulting wave has zero amplitude), as shown on the right side of the figure.
Ray Diffraction and Bragg’s Law
- Noncrystalline Solids • 79
- NONCRYSTALLINE SOLIDS
Unit cell edge length (a) and atomic radius (R) are related according to Equation 3.1 for face-centered cubic, and. The location of a point within a unit cell is specified using coordinates that are fractional multiples of the cell edge lengths.
WHY STUDY Imperfections in Solids?
- INTRODUCTION
- VACANCIES AND SELF-INTERSTITIALS
- Impurities in Solids • 93
- IMPURITIES IN SOLIDS
- SPECIFICATION OF COMPOSITION
- Specification of Composition • 95
- Specification of Composition • 97
- Dislocations—Linear Defects • 99
- DISLOCATIONS—LINEAR DEFECTS
- INTERFACIAL DEFECTS
- Interfacial Defects • 105
Sometimes an edge dislocation is represented in Figure 4.3 by a symbol that also indicates the position of the dislocation line. For example, all positions of the curved dislocation in Figure 4.5 will have the Burgers vector displayed.
MATERIALS OF IMPORTANCE Catalysts (and Surface Defects)
- BULK OR VOLUME DEFECTS
- ATOMIC VIBRATIONS
- BASIC CONCEPTS OF MICROSCOPY
- MICROSCOPIC TECHNIQUES
- Microscopic Techniques • 111
- GRAIN SIZE DETERMINATION
- Grain Size Determination • 113
The image on the screen, which can be photographed, shows the surface features of the sample. The grain size is expressed as the grain size number of the graph that most closely matches the grains in the micrograph.
WHY Study Diffusion?
- INTRODUCTION
- DIFFUSION MECHANISMS
- STEADY-STATE DIFFUSION
- Steady-State Diffusion • 127
- NONSTEADY-STATE DIFFUSION
- Nonsteady-State Diffusion • 129
- Nonsteady-State Diffusion • 131
- FACTORS THAT INFLUENCE DIFFUSION
- Factors That Influence Diffusion • 133
- Factors That Influence Diffusion • 135
- DIFFUSION IN SEMICONDUCTING MATERIALS
- Diffusion in Semiconducting Materials • 137
- Diffusion in Semiconducting Materials • 139
The magnitude of the diffusion coefficient D is indicative of the rate at which atoms diffuse. Figure 5.8 shows a graph of the logarithm (base 10) of the diffusion coefficient versus the inverse of absolute temperature, for the diffusion of copper into gold.
MATERIALS OF IMPORTANCE Aluminum for Integrated Circuit Interconnects
Diffusion in Semiconducting Materials • 141
Since the degree of diffusion depends on the magnitude of the diffusion coefficient, so it is necessary to select a compound metal that has a small value of D in silicon. This shows that the diffusion coefficient for aluminum in silicon (2.5 x 1021 m2/s) is at least four orders of magnitude (i.e. a factor of 104) lower than the values for the other three metals.
OTHER DIFFUSION PATHS
Determine the time in which this diffusion pair must be heated to 750 C (1023 K) so that the composition is 2.5 wt. % Au at position 50 m on side with 2 wt. % Au diffusion pair. The pre-exponential and activation energies for the diffusion of Cu into Ni are given in Table 5.2.
Hardness • 151
WHY STUDY The Mechanical Properties of Metals?
INTRODUCTION
The current discussion is mainly limited to the mechanical behavior of metals; polymers and ceramics are treated separately because they are mechanically very different from metals. Discussions of the microscopic aspects of deformation mechanisms and methods to strengthen and control the mechanical behavior of metals are deferred to later chapters.
CONCEPTS OF STRESS AND STRAIN
The gauge length is used in ductility calculations as explained in Section 6.6; the standard value is 50 mm (2.0 in.). The test piece is attached by its ends to the holders of the testing device (Figure 6.3).
Concepts of Stress and Strain • 153
The shear stress is defined as the tangent to the strain angle, as shown in the figure. In Figure 6.1d, shear stress is a function of the applied torque T, while shear stress is related to the angle of rotation.
Concepts of Stress and Strain • 155
Note that the state of stress is a function of the orientations of the planes on which the stresses are applied. Additionally, consider also the p-p plane oriented at some arbitrary angle to the plane of the end face of the sample.
STRESS–STRAIN BEHAVIOR
After releasing the load, the line is crossed in the opposite direction, back to the starting point. The tangent modulus is taken as the slope of the stress-strain curve at a given stress level, while the secant modulus represents the slope of the secant drawn from the origin to some given point on the curve.
Stress–Strain Behavior • 157
6.7) where G is the shear modulus, the slope of the linear elastic region of the shear stress-strain curve. The magnitude of the modulus of elasticity is proportional to the slope of each curve at the equilibrium interatomic separation r0.
ANELASTICITY
Anelasticity • 159
ELASTIC PROPERTIES OF MATERIALS
Many materials are elastically anisotropic; that is, the elastic behavior (eg, the magnitude of E) varies with crystallographic direction (see Table 3.3). Even for isotropic materials, at least two constants must be given for the full characterization of the elastic properties.
Elastic Properties Of Materials • 161
Since the grain orientation in most polycrystalline materials is random, they can be considered isotropic. When force F is applied, the specimen will elongate in the z direction and simultaneously experience a reduction in diameter d of 2.5 103 mm in the x direction.
TENSILE PROPERTIES
Consequently, a convention was established whereby a straight line is constructed parallel to the elastic portion of the stress-strain curve at a specified strain offset, typically 0.002. The stress corresponding to the intersection of this line and the stress-strain curve when it bends in the plastic region is defined as the yield strength.8 This is shown in Figure 6.10a.
Tensile Properties • 163
After yielding, the stress required to continue plastic deformation in metals increases to a maximum, point M in Figure 6.11, and then decreases to ultimate fracture, point F. The tensile strength TS (MPa or psi) is the stress at the maximum on the engineering stress- strain curve (figure 6.11).
Tensile Properties • 165
It is a measure of the degree of plastic deformation that has occurred at fracture. Since a significant part of the plastic deformation at fracture is confined to the neck region, the magnitude of %EL will depend on the length of the specimen.
Tensile Properties • 167
Thus, several important mechanical properties of metals can be determined from tensile stress-strain tests. For the static (low strain rate) situation, a measure of toughness in metals (derived from plastic deformation) can be established from the results of a tensile stress-strain test.
Tensile Properties • 169
Both joule force and inch-pound are units of energy, and so this area under the stress-strain curve represents energy absorption per unit volume (in cubic meters or cubic inches) of the material. This is demonstrated in Figure 6.13, in which stress-strain curves are plotted for both types of metals.
TRUE STRESS AND STRAIN
The answer can be found at www.wiley.com/college/callister(Student Companion Site).]. true strain Definition of true stress. For some metals and alloys, the area of the true stress-strain curve from the onset of plastic deformation to the point where constriction begins can be approximated by 6.19).
True Stress and Strain • 171
It is worth noting that the true stress necessary to sustain increasing strain continues to increase past the tensile point M. Coinciding with the formation of a neck is the introduction of a complex state of stress in the neck region (i.e. the existence of other stress components) in addition to the axial stress).
