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physics
thermodynamics

Materials Science and Engineering An Introduction 8th edition William D. Callister Jr., David G. Rethwisch - Solutions

Calculate the density of FeO, given that it has the rock salt crystal structure.
Magnesium oxide has the rock salt crystal structure and a density of 3.58 g/cm3. (a) Determine the unit cell edge length. (b) How does this result compare with the edge length as determined from the radii in Table 12.3, assuming that the Mg2+ and O2- ions just touch each other along the edges?
Compute the theoretical density of diamond given that the C-C distance and bond angle are 0.154 nm and 109.5°, respectively. How does this value compare with the measured density?
Compute the theoretical density of ZnS given that the Zn-S distance and bond angle are 0.234 nm and 109.5°, respectively. How does this value compare with the measured density?
Cadmium sulfide (CdS) has a cubic unit cell, and from x-ray diffraction data it is known that the cell edge length is 0.582 nm. If the measured density is 4.82 g/cm3, how many Cd2+ and S2- ions are there per unit cell?
(a) Using the ionic radii in Table 12.3, compute the theoretical density of CsCl. (Hint: Use a modification of the result of Problem 3.3.) (b) The measured density is 3.99 g/cm3. How do you explain the slight discrepancy between your calculated value and the measured one?
From the data in Table 12.3, compute the theoretical density of CaF2, which has the fluorite structure.
Show that the minimum cation-to-anion radius ratio for a coordination number of 4 is 0.225.
A hypothetical AX type of ceramic material is known to have a density of 2.65 g/cm3 and a unit cell of cubic symmetry with a cell edge length of 0.43 nm. The atomic weights of the A and X elements are 86.6 and 40.3 g/mol, respectively. On the basis of this information, which of the following
The unit cell for MgFe2O4 (MgO-Fe2O3) has cubic symmetry with a unit cell edge length of 0.836 nm. If the density of this material is 4.52 g/cm3, compute its atomic packing factor. For this computation, you will need to use ionic radii listed in Table 12.3.
The unit cell for Cr2O3 has hexagonal symmetry with lattice parameters a = 0.4961 nm and c = 1.360 nm. If the density of this material is 5.22 g/cm3, calculate its atomic packing factor. For this computation assume ionic radii of 0.062 nm and 0.140 nm, respectively for Cr3+ and O2-.
Compute the atomic packing factor for the diamond cubic crystal structure (Figure 12.15). Assume that bonding atoms touch one another, that the angle between adjacent bonds is 109.5°, and that each atom internal to the unit cell is positioned a/4 of the distance away from the two nearest cell
Compute the atomic packing factor for cesium chloride using the ionic radii in Table 12.3 and assuming that the ions touch along the cube diagonals.
For each of the following crystal structures, represent the indicated plane in the manner of Figures 3.11 and 3.12, showing both anions and cations:(a) (100) plane for the rock salt crystal structure,(b) (110) plane for the cesium chloride crystal structure,(c) (111) plane for the zinc blende
In terms of bonding, explain why silicate materials have relatively low densities.
Determine the angle between covalent bonds in an SiO44− tetrahedron.
Calculate the fraction of lattice sites that are Schottky defects for sodium chloride at its melting temperature (801°C). Assume an energy for defect formation of 2.3 eV.
Show that the minimum cation-to-anion radius ratio for a coordination number of 6 is 0.414. [Use the NaCl crystal structure, and assume that anions and cations are just touching along cube edges and across face diagonals.]
Calculate the number of Frenkel defects per cubic meter in zinc oxide at 1000°C. The energy for defect formation is 2.51 eV, while the density for ZnO is 5.55 g/cm3 at (1000°C).
Using the data given below that relate to the formation of Schottky defects in some oxide ceramic (having the chemical formula MO), determine the following:(a) The energy for defect formation (in eV),(b) The equilibrium number of Schottky defects per cubic meter at 1000°C, and(c) The identity
If cupric oxide (CuO) is exposed to reducing atmospheres at elevated temperatures, some of the Cu2+ ions will become Cu+. (a) Under these conditions, name one crystalline defect that you would expect to form in order to maintain charge neutrality. (b) How many Cu+ ions are required for the creation
(a) Suppose that Li2O is added as an impurity to CaO. If the Li+ substitutes for Ca2+, what kind of vacancies would you expect to form? How many of these vacancies are created for every Li+ added? (b) Suppose that CaCl2 is added as an impurity to CaO. If the Cl- substitutes for O2-, what kind of
What point defects are possible for Al2O3 as an impurity in MgO? How many Al3+ ions must be added to form each of these defects?
For the ZrO2-CaO system (Figure 12.26), write all eutectic and eutectoid reactions for cooling.
From Figure 12.25, the phase diagram for the MgO-Al2O3 system, it may be noted that the spinel solid solution exists over a range of compositions, which means that it is non stoichiometric at compositions other than 50 mol% MgO-50 mol% Al2O3.(a) The maximum non stoichiometry on the Al2O3-rich side
When kaolinite clay [Al2(Si2O5)(OH)4] is heated to a sufficiently high temperature, chemical water is driven off. (a) Under these circumstances, what is the composition of the remaining product (in weight percent Al2O3)? (b) What are the liquidus and solidus temperatures of this material
(a) Why there may be significant scatter in the fracture strength for some given ceramic material, and (b) Why fracture strength increases with decreasing specimen size.
Demonstrate that the minimum cation-to-anion radius ratio for a coordination number of 8 is 0.732.
The tensile strength of brittle materials may be determined using a variation of Equation 8.1. Compute the critical crack tip radius for an Al2O3 specimen that experiences tensile fracture at an applied stress of 275 MPa (40,000 psi). Assume a critical surface crack length of 2 × 10-3 mm and a
The fracture strength of glass may be increased by etching away a thin surface layer. It is believed that the etching may alter surface crack geometry (i.e., reduce crack length and increase the tip radius). Compute the ratio of the original and etched crack tip radii for an eightfold increase in
A three-point bending test is performed on a glass specimen having a rectangular cross section of height d = 5 mm (0.2 in.) and width b = 10 mm (0.4 in.); the distance between support points is 45 mm (1.75 in.).(a) Compute the flexural strength if the load at fracture is 290 N (65 lbf).(b) The
A circular specimen of MgO is loaded using a three-point bending mode. Compute the minimum possible radius of the specimen without fracture, given that the applied load is 425 N (95.5 lbf), the flexural strength is 105 MPa (15,000 psi), and the separation between load points is 50 mm (2.0 in.).
A three-point bending test was performed on an aluminum oxide specimen having a circular cross section of radius 3.5 mm (0.14 in.); the specimen fractured at a load of 950 N (215 lbf) when the distance between the support points was 50 mm (2.0 in.). Another test is to be performed on a specimen of
(a) A three-point transverse bending test is conducted on a cylindrical specimen of aluminum oxide having a reported flexural strength of 390 MPa (56,600 psi). If the specimen radius is 2.5 mm (0.10 in.) and the support point separation distance is 30 mm (1.2 in.), predict whether or not you would
The modulus of elasticity for beryllium oxide (BeO) having 5 vol% porosity is 310 GPa (45 × 106 psi). (a) Compute the modulus of elasticity for the nonporous material. (b) Compute the modulus of elasticity for 10 vol% porosity.
The modulus of elasticity for boron carbide (B4C) having 5 vol% porosity is 290 GPa (42 × 106 psi).(a) Compute the modulus of elasticity for the nonporous material.(b) At what volume percent porosity will the modulus of elasticity be 235 GPa (34 × 106 psi)?
Using the data in Table 12.5, do the following: (a) Determine the flexural strength for nonporous MgO assuming a value of 3.75 for n in Equation 12.10. (b) Compute the volume fraction porosity at which the flexural strength for MgO is 62 MPa (9000 psi).
On the basis of ionic charge and ionic radii given in Table 12.3, predict crystal structures for the following materials: (a) CsI, (b) NiO, (c) KI, and (d) NiS. Justify your selections.
The flexural strength and associated volume fraction porosity for two specimens of the same ceramic material are as follows: σfs (MPa) P 100............................. 0.05 50............................. 0.20 (a) Compute the flexural strength for a completely nonporous specimen of this
Which of the cations in Table 12.3 would you predict to form iodides having the cesium chloride crystal structure? Justify your choices.
Compute the atomic packing factor for the rock salt crystal structure in which rC/rA = 0.414.
The zinc blende crystal structure is one that may be generated from close-packed planes of anions. (a) Will the stacking sequence for this structure be FCC or HCP? Why? (b) Will cations fill tetrahedral or octahedral positions? Why? (c) What fraction of the positions will be occupied?
The corundum crystal structure, found for Al2O3, consists of an HCP arrangement of O2- ions; the Al3+ ions occupy octahedral positions. (a) What fraction of the available octahedral positions are filled with Al3+ ions?
Gallium arsenide (GaAs) and gallium phosphide (GaP) both have the zinc blende crystal structure and are soluble in one another at all concentrations. Determine the concentration in weight percent of GaP that must be added to GaAs to yield a unit cell edge length of 0.5570 nm. The densities of GaAs
It is necessary to select a ceramic material to be stressed using a three-point loading scheme (Figure 12.32). The specimen must have a circular cross section and a radius of 2.5 mm (0.10 in.), and must not experience fracture or a deflection of more than 6.2 × 10-2 mm (2.4 × 10-3 in.) at its
Some of our modern kitchen cookware is made of ceramic materials. (a) List at least three important characteristics required of a material to be used for this application. (b) Make a comparison of three ceramic materials as to their relative properties and, in addition, to cost. (c) On the basis of
What is the distinction between glass transition temperature and melting temperature?
Compare the temperatures at which soda-lime, borosilicate, 96% silica, and fused silica may be annealed.
Compare the softening points for 96% silica, borosilicate, and soda-lime glasses.
The viscosity Î· of a glass varies with temperature according to the relationshipwhere Qvis is the energy of activation for viscous flow, A is a temperature-independent constant, and R and T are, respectively, the gas constant and the absolute temperature. A plot of ln Î·
For many viscous materials, the viscosity Î· may be defined in terms of the expressionwhere Ïƒ and dÎµ/dt are, respectively, the tensile stress and the strain rate. A cylindrical specimen of a soda-lime glass of diameter 5 mm (0.2 in.) and length 100 mm (4 in.) is
(a) Explain why residual thermal stresses are introduced into a glass piece when it is cooled. (b) Are thermal stresses introduced upon heating? Why or why not?
Borosilicate glasses and fused silica are resistant to thermal shock. Why is this so?
In your own words, briefly describe what happens as a glass piece is thermally tempered.
Glass pieces may also be strengthened by chemical tempering. With this procedure, the glass surface is put in a state of compression by exchanging some of the cations near the surface with other cations having a larger diameter. Suggest one type of cation that, by replacing Na+, will induce
Cite the two desirable characteristics of clay minerals relative to fabrication processes.
(a) What is crystallization? (b) Cite two properties that may be improved by crystallization.
From a molecular perspective, briefly explain the mechanism by which clay minerals become hydroplastic when water is added.
(a) What are the three main components of a whiteware ceramic such as porcelain? (b) What role does each component play in the forming and firing procedures?
(a) Why is it so important to control the rate of drying of a ceramic body that has been hydroplastically formed or slip cast? (b) Cite three factors that influence the rate of drying, and explain how each affects the rate.
Cite one reason why drying shrinkage is greater for slip cast or hydroplastic products that have smaller clay particles.
(a) Name three factors that influence the degree to which vitrification occurs in clay-based ceramic wares. (b) Explain how density, firing distortion, strength, corrosion resistance, and thermal conductivity are affected by the extent of vitrification
Some ceramic materials are fabricated by hot isostatic pressing. Cite some of the limitations and difficulties associated with this technique.
For refractory ceramic materials, cite three characteristics that improve with and two characteristics that are adversely affected by increasing porosity.
Find the maximum temperature to which the following two magnesia-alumina refractory materials may be heated before a liquid phase will appear. (a) A spinel-bonded alumina material of composition 95 wt% Al2O3-5 wt% MgO. (b) A magnesia-alumina spinel of composition 65 wt% Al2O3-35 wt% MgO. Consult
Upon consideration of the SiO2-Al2O3 phase diagram, Figure 12.27, for each pair of the following list of compositions, which would you judge to be the more desirable refractory? Justify your choices. (a) 20 wt% Al2O3-80 wt% SiO2 and 25 wt% Al2O3-75 wt% SiO2 (b) 70 wt% Al2O3-30 wt% SiO2 and 80 wt%
Compute the mass fractions of liquid in the following refractory materials at 1600°C (2910°F): (a) 6 wt% Al2O3-94 wt% SiO2 (b) 10 wt% Al2O3-90 wt% SiO2 (c) 30 wt% Al2O3-70 wt% SiO2 (d) 80 wt% Al2O3-20 wt% SiO2
For the MgO-Al2O3 system, what is the maximum temperature that is possible without the formation of a liquid phase? At what composition or over what range of compositions will this maximum temperature be achieved?
Compare the manner in which the aggregate particles become bonded together in clay-based mixtures during firing and in cements during setting.
Soda and lime are added to a glass batch in the form of soda ash (Na2CO3) and limestone (CaCO3). During heating, these two ingredients decompose to give off carbon dioxide (CO2), the resulting products being soda and lime. Compute the weight of soda ash and limestone that must be added to 100 lbm
On the basis of the structures presented in this chapter, sketch repeat unit structures for the following polymers: (a) polychlorotrifluoroethylene, and (b) poly(vinyl alcohol).
Using the definitions for total chain molecule length, L (Equation 14.11) and average chain end-to-end distance r (Equation 14.12), for a linear polyethylene determine: (a) The number-average molecular weight for L = 2500 nm; (b) The number-average molecular weight for r = 20 nm.
Sketch portions of a linear polystyrene molecule that are (a) Syndiotactic, (b) Atactic, and (c) Isotactic. Use two-dimensional schematics per footnote 8 of this chapter.
Sketch cis and trans structures for (a) butadiene, and (b) chloroprene. Use two-dimensional schematics per footnote 11 of this chapter.
Make comparisons of thermoplastic and thermosetting polymers (a) On the basis of mechanical characteristics upon heating, and (b) According to possible molecular structures.
(a) Is it possible to grind up and reuse phenol-formaldehyde? Why or why not? (b) Is it possible to grind up and reuse polypropylene? Why or why not?
Sketch the repeat structure for each of the following alternating copolymers: (a) Poly(butadiene-chloroprene), (b) Poly(styrene-methyl methacrylate), and (c) Poly(acrylonitrile-vinyl chloride).
The number-average molecular weight of a poly(styrene-butadiene) alternating copolymer is 1,350,000 g/mol; determine the average number of styrene and butadiene repeat units per molecule.
Calculate the number-average molecular weight of a random nitrile rubber [poly(acrylonitrile-butadiene) copolymer] in which the fraction of butadiene repeat units is 0.30; assume that this concentration corresponds to a degree of polymerization of 2000.
An alternating copolymer is known to have a number-average molecular weight of 250,000 g/mol and a degree of polymerization of 3420. If one of the repeat units is styrene, which of ethylene, propylene, tetrafluoroethylene, and vinyl chloride is the other repeat unit? Why?
(a) Determine the ratio of butadiene to styrene repeat units in a copolymer having a number-average molecular weight of 350,000 g/mol and degree of polymerization of 4425. (b) Which type(s) of copolymer(s) will this copolymer be, considering the following possibilities: random, alternating, graft,
Compute repeat unit molecular weights for the following: (a) poly(vinyl chloride), (b) poly(ethylene terephthalate), (c) polycarbonate, and (d) polydimethylsiloxane.
Cross linked copolymers consisting of 60 wt% ethylene and 40 wt% propylene may have elastic properties similar to those for natural rubber. For a copolymer of this composition, determine the fraction of both repeat unit types.
A random poly(isobutylene-isoprene) copolymer has a number-average molecular weight of 200,000 g/mol and a degree of polymerization of 3000. Compute the fraction of isobutylene and isoprene repeat units in this copolymer.
Explain briefly why the tendency of a polymer to crystallize decreases with increasing molecular weight.
For each of the following pairs of polymers, do the following: (1) state whether or not it is possible to determine whether one polymer is more likely to crystallize than the other; (2) if it is possible, note which is the more likely and then cite reason(s) for your choice; and (3) if it is not
The density of totally crystalline polypropylene at room temperature is 0.946 g/cm3. Also, at room temperature the unit cell for this material is monoclinic with lattice parameters a = 0.666 nm α = 90° b = 2.078 nm β = 99.62° c = 0.650 nm γ = 90° If the volume of a monoclinic unit cell,
The density and associated percent crystallinity for two polytetrafluoroethylene materials are as follows:(a) Compute the densities of totally crystalline and totally amorphous polytetrafluoroethylene. (b) Determine the percent crystallinity of a specimen having a density of 2.26 g/cm3.
The density and associated percent crystallinity for two nylon 6,6 materials are as follows:(a) Compute the densities of totally crystalline and totally amorphous nylon 6,6. (b) Determine the density of a specimen having 55.4% crystallinity.
Consider the diffusion of water vapor through a polypropylene (PP) sheet 2 mm thick. The pressures of H2O at the two faces are 1 kPa and 10 kPa, which are maintained constant. Assuming conditions of steady state, what is the diffusion flux [in [(cm3 STP)/cm2-s] at 298 K?
Argon diffuses through a high density polyethylene (HDPE) sheet 40 mm thick at a rate of 4.0 × 10-7 (cm3 STP)/cm2-s at 325 K. The pressures of argon at the two faces are 5000 kPa and 1500 kPa, which are maintained constant. Assuming conditions of steady state, what is the permeability coefficient
The permeability coefficient of a type of small gas molecule in a polymer is dependent on absolute temperature according to the following equation:where PM0and Qp are constants for a given gas-polymer pair. Consider the diffusion of hydrogen through a poly(dimethyl siloxane) (PDMSO) sheet 20 mm
The number-average molecular weight of a polypropylene is 1,000,000 g/mol. Compute the degree of polymerization.
(a) Compute the repeat unit molecular weight of polystyrene. (b) Compute the number-average molecular weight for a polystyrene for which the degree of polymerization is 25,000.
Below, molecular weight data for a polypropylene material are tabulated. Compute (a) the number-average molecular weight, (b) the weight-average molecular weight, and (c) the degree of polymerization.
Molecular weight data for some polymer are tabulated here. Compute (a) the number-average molecular weight, and (b) the weight-average molecular weight. (c) If it is known that this material's degree of polymerization is 710, which one of the polymers listed in Table 14.3 is this polymer? Why?
Is it possible to have a poly(methyl methacrylate) homopolymer with the following molecular weight data and a of polymerization of 527? Why or why not?
High-density polyethylene may be chlorinated by inducing the random substitution of chlorine atoms for hydrogen. (a) Determine the concentration of Cl (in wt%) that must be added if this substitution occurs for 5% of all the original hydrogen atoms. (b) In what ways does this chlorinated
For a linear polymer molecule, the total chain length L depends on the bond length between chain atoms d, the total number of bonds in the molecule N, and the angle between adjacent backbone chain atoms Î¸, as follows:Furthermore, the average end-to-end distance for a series of polymer
(a) List several advantages and disadvantages of using transparent polymeric materials for eyeglass lenses. (b) Cite four properties (in addition to being transparent) that are important for this application. (c) Note three polymers that may be candidates for eyeglass lenses, and then tabulate

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