It is often convenient to identify a plane or direction in a crystal by its indices. Note that all parallel planes have the same indices.

Planar Indices

The rules for determining the Miller indices of planes are as follows:

1. Write the intercepts of the plane on the three axes in order (a1, a2, and a3).

2. Take the reciprocals of these.

3. Reduce to the lowest set of integers with the same ratios.

4. Enclose in parentheses (hkl).

Commas are not used except in the rare case that one of the integers is larger than one digit. (This is rare because we are normally interested only in planes with low indices.) If a plane is parallel to an axis, its intercept is taken as ∞ and its reciprocal as 0. If the plane contains one of the axes or the origin, either analyze a parallel plane or translate the axes before finding indices. This is permissible since all parallel planes have the same indices. A negative index is indicated by a bar over the index rather than a negative sign, e.g., (11). Figure A2.1 shows several examples.

Direction Indices

The indices of a direction are the translations parallel to the three axes that produce the direction under consideration. The rules for finding direction indices are as follows:

1. Write the components of the direction parallel to the three axes in order.

2. Reduce to the lowest set of integers with the same ratios.

3. Enclose in brackets [uvw].

Polymer is the technical term for what are commonly called plastics. Polymers consist of very large molecules. In fact, the word polymer comes from poly (for many) and mer (for parts). There are two main groups of polymers: thermoplastics, which are composed of linear molecules and will soften and melt when heated, and thermosetting polymers, whose molecules form three-dimensional framework structures. Thermosetting polymers will not melt or even soften appreciably when heated. The basic organic chemistry of bonding in polymers is treated in Appendix 7.

Thermoplastics

Thermoplastics consist of long chain molecules. The simplest of these have carbon-carbon backbones. The structure of polyethylene is illustrated schematically in Figure 11.1. Other linear polymers with carbon-carbon backbones are listed in Table 11.1.

Other thermoplastics have more complex backbones. Among these are nylon, polyester (PET), polycarbonate, cellulose, and poly(paraphenylene terephthalamide) or PPTA (also known as Kevlar®). Figure 11.2 illustrates the molecular structure of these.

Elastomers are rubber-like polymers. They have carbon backbones that include carbon-carbon double bonds. Figure 11.3 shows the repeating unit. The radicals, R, are listed in Table 11.2.

Silicones are polymers with -Si-O-Si-O- backbones.

Degree of Polymerization

The degree of polymerization is the average number of mer units per molecule. It is the molecular weight of the polymer divided by the molecular weight of the mer. There are two ways of describing the molecular weight: the number-average molecular weight, and the weight-average molecular weight. They are usually not very different but the weight average is always somewhat larger.

What Is a Phase?

A phase is a state of aggregation of matter that has a distinctive structure. Phases may be solid, liquid, or gaseous. A phase may be a pure material or a solution of several components. A solid phase is either amorphous or has a characteristic crystal structure and definite composition range. A physical system may contain more than one solid phase with different crystal structures, or different ranges of possible compositions – one or more mutually insoluble liquid phases (for example oil and water) and a gas phase. All gasses are mutually soluble, and therefore only one gaseous phase is possible.

Single-phase materials include brass (a solid solution of zinc in copper with zinc atoms occupying lattice sites), sodium chloride crystals, glass, and polyethylene. Most plain carbon steels are two-phase materials, consisting of an iron-rich solid solution and iron carbide. A glass of ice water consists of two phases: liquid water and ice. In a glass of tonic water there may be three phases: liquid, ice, and gas bubbles.

The composition of a single phase may vary from place to place, but composition change is always gradual and without abrupt changes. In multiple-phase systems, however, there are discontinuities of composition and structure at phase boundaries. The compositions on each side of the boundary are usually in equilibrium. For example, the oxygen concentration changes abruptly between copper with some oxygen dissolved in it and copper oxide.

Properties

One material is chosen over another for a particular application because its properties are better suited for the intended use. Among the important properties are strength, corrosion resistance, electrical conductivity, weight, material cost, processing costs, and appearance. Usually several properties are important.

In many applications, stiffness is important. Materials deform when a stress is applied to them. If the stress is low, the deformation will be elastic. In this case the deformation will disappear and the material will regain its original shape when the stress is removed. Good examples are elastic bands and paper clips. With greater stress, a material may deform plastically. In this case the deformation does not disappear when the stress is removed, so the shape change is permanent. This happens when the stress exceeds the yield strength of the material. With a still higher stress, the material may reach its tensile strength and fail. Ductility and toughness are also important. The ductility of a material is the amount of deformation a material may undergo before breaking. Toughness is a measure of how much energy a material absorbs per area before fracture.

Electrical properties are of paramount importance in some applications. Electrical conductors should have high conductivities and insulators very low conductivities. Integrated circuits for computers require semiconductors. The dielectric constant may be important in applications involving high frequencies. Piezoelectric behavior is required for sonar transmitters and receivers.

Glasses are amorphous so they have no long-range order and no symmetry. There is, however, a great deal of short-range order. If crystallization is prevented during cooling, an amorphous glass will form with short-range order inherited from the liquid. The critical cooling rate to prevent crystallization varies greatly from one material to another. Silicate glasses cannot crystallize unless the cooling rates are extremely slow. On the other hand, extremely rapid cooling is required to prevent crystallization of metals.

Structure of Silicate Glasses

The basic structural units of silicate glasses are tetrahedra with Si4+ ions in the center bonded covalently to O2− ions at each corner. In pure silica all corner oxygen ions are shared by two tetrahedra (Figure 13.1). The result is a covalently bonded glass with a very high viscosity at elevated temperatures.

The compositions of typical commercial glasses are quite complex. Soda-lime glasses may contain 72% SiO2, 14% Na2O, 11% CaO, and 3% MgO. The Na+, Ca2+, and Mg2+ ions are bonded ionically to some of the corner O2− ions (Figure 13.2). With these alkali and alkaline earth oxides, not all of the oxygen ions are covalently bonded to two tetrahedra. This lowers the viscosity at high temperatures.

Steels

Steels are iron-base alloys usually containing carbon. Figure 7.1 shows the iron-carbon phase diagram. Below 911°C and between 1410°C and the melting point, iron has a bcc crystal structure called ferrite. Between 1410°C and 911°C it has an fcc crystal structure called austenite. Austenite dissolves much more carbon interstitially than ferrite. On slow cooling below 727°C, the austenite transforms by a eutectoid reaction into ferrite and iron carbide or cementite (which contains 6.7%C). The ferrite and cementite form alternating platelets called the eutectoid temperature. The resulting microstucture is called pearlite (see Figure 7.2).

Pearlite Formation

When a steel containing less than 0.77%C (hypo-eutectoid steel) is slowly cooled, some ferrite forms before any pearlite. A steel containing more than 0.77%C (hyper-eutectoid steel) will form some cementite before any pearlite. The formation of pearlite from austenite on cooling requires diffusion of carbon from ahead of the advancing ferrite platelets to the advancing carbide platelets as indicated in Figure 7.3. Because diffusion takes time, pearlite formation is not instantaneous. The rate at which pearlite forms depends on how much the temperature is below 717°C. The rate of diffusion increases with temperature, but the driving force for the transformation increases as the temperature is lowered. The result is that the rate of transformation is fastest between 500 and 600°C, as indicated schematically in Figure 7.4.

Aluminum

Aluminum and aluminum alloys are the most important nonferrous metals. Aluminum's density, ρ, is 2.7, which is about 1/3 of the density of iron. Its Young's modulus is 70 GPa (10 × 106 psi) which is also about 1/3 that of iron. The unique properties of aluminum that account for most of its usage are:

1. Good corrosion and oxidation resistance.

2. Good electrical and thermal conductivities.

3. Low density.

4. High reflectivity.

5. High ductility and reasonably high strength.

The uses of aluminum include foil, die castings, beverage cans, cooking and food processing, boats and canoes, and aircraft and automobile parts including sheet, engine blocks, and wheels. Aluminum's high reflectivity accounts for its use as foil for insulation and as reflective coatings on glass. Aluminum is used for power transmission lines and some wiring because of its high electrical conductivity. On an equal weight of cross section and equal cost bases, it is a better conductor than copper. Its high thermal conductivity is advantageous in its applications for radiators, air-cooled engines, and cooking utensils. The low density is important for lawn furniture, hand-held tools, and in cars, trucks, and aircraft. Aluminum's good strength and ductility is important in all structural uses where wrought products are used. Its chemical reactivity is important principally in its use in photoflash bulbs and the thermite reaction (Al + Fe2O3 → Fe + Al2O3). Its corrosion and oxidation resistance are important in packaging (foil, cans), architectural applications, and watercraft.

Composite materials have been used throughout history to achieve combinations of properties that could not be achieved with individual materials. Concrete is a composite of cement, sand, and gravel. Poured concrete is usually reinforced with steel rods. Other examples of composites include steel-belted tires; asphalt blended with gravel for roads; plywood with alternating directions of fibers, carbon, or glass fiber-reinforced polyester; or epoxy used for furniture, boats, and sporting goods. Composite materials offer combinations of properties otherwise unavailable. The reinforcing material may be in the form of particles, fibers, or sheet laminates.

Fiber-reinforced Composites

Fiber composites may also be classified according to the nature of the matrix and the fiber. Examples of a number of possibilities are listed in Table 17.1.

Different geometric arrangements of the fibers are possible. In two-dimensional products, the fibers may be unidirectionally aligned at 90° to one another in a woven fabric or randomly oriented (Figure 17.1). The fibers may be very long or chopped into short segments for easy fabrication. In thick sections it is possible to randomly orient short fibers in three dimensions. Fiber reinforcement is used to impart stiffness (increased modulus) or strength to the matrix. Fiber reinforcement also increases toughness.

Corrosion of metals can be classified as either corrosion in aqueous solutions or as direct oxidation at high temperatures. Both are electrochemical in nature.

Aqueous Corrosion

An aqueous corrosion cell consists of an anode where metal ions go into solution and electrons are produced, a cathode where electrons are consumed, an aqueous solution between the anode and cathode, and an external electrical connection between the anode and cathode (Figure 23.1). The anode reaction can be written M → Mn+ + ne−, where M stands for a metal. There are several possible cathode reactions:

1. Mn+ + ne− → M (This can occur only if there is a high concentration of Mn+ ions in solution.)

2. 2H+ + 2e− → H2 (This can occur only in an acid solution.)

3. O2 + 2H2O + 4e− → 4(OH)− (This is the most common cathode reaction. Note that it requires dissolved O2.)

4. O2+ 4H+ + 4e− → 2H2O (This occurs in acidic solutions and there must be O2 in an acid solution.)

The anode and cathode reactions must occur at the same rate. The corrosion rate is often limited by the cathode reaction.

The material of the anode is more active (less noble) than the material of the cathode. The electromotive series (Table 23.1) lists the relative activity of common metals in one-molar solutions of their own salts. The most noble (least reactive) metals appear at the top and most reactive at the bottom.

Ceramics

Ceramics are compounds consisting of metal and non-metal ions bonded either covalently or ionically. Most ceramics are crystalline. They tend to have high melting points and be very hard and brittle. Their tensile strengths are limited by brittle fracture but their compressive strengths are high. Because they retain high hardnesses at elevated temperatures, they are useful as refractories such as furnace linings. Oxidation at high temperature is not a problem with refractory oxides as it is with refractory metals. Magnesia, alumina, and silica are used for furnace linings. Ceramics are also used as tools for high-speed machining of metals. The high hardness of ceramics at room temperature leads to their use as abrasives as either loose powder or bonded into grinding tools. The low ductility of ceramics limits the structural use of ceramics mainly to applications in which the loading is primarily compressive. Iron-containing ceramic are used as magnets.

The bonding strength depends on the valences of the metal and non-metal. Compounds with higher valences (e.g., SiC, Si3N4) tend to be more strongly bonded than those of lower valences (e.g., NaCl, MgO) so they have higher melting points and higher hardnesses. Appendix 9 covers the geometric principles governing the crystal structures adopted by various ceramic compounds.

Cooling

Polymerization often releases a large amount of heat. Unless the heat is removed the reactants will become too hot.

Example Problem 12–1:

1. a. How much energy is released when one mole of phenol reacts with one mole of formaldehyde?

2. b. If the process were adiabatic (no heat released to the surroundings), how much would the temperature rise? The heat capacity of phenol formaldehyde is 1.193kJ/kg°C.

Solution:

1. a. Using the data in Appendix 7, the energy to break a C-O bond and an N-H bond is 360 and 430kJ/mole, and the energy released in forming a C-N bond and an O-H bond is 305 and 500kJ/mole. The net energy release is 805 −360 = 15kJ/mole.

2. b. The molecular weight of phenol formaldehyde is 90 g/mole (2O = 32 + 2N = 28 + 2C = 24 + 6H = 6) and the molecular weight of water is 18: ΔT = 15kJ/[(0.090kg) (1.193kJ/kg°C)+ 0.018kg)(4.186kJ/kg°C)] = 82°C. This would require cooling.

Injection Molding

Injection molding is similar to die casting of metals. A molten thermoplastic is injected into a metal mold at high pressure, and the molded part is ejected after it cools sufficiently. Injection molding is used to make a wide variety of parts, from small components to entire auto body panels. The most commonly used thermoplastics are polystyrene, ABS, nylon, polypropylene, polyethylene, and PVC. Although the properties of finished products benefit from a high molecular weight, very high molecular weights are not desirable for injection molding because viscosity increases with molecular weight.