《材料科学与工程基础》英文影印版习题及思考题及答案

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《材料科学与工程基础》英文习题及思考题及答案

第二章 习题和思考题

Questions and Problems

2.6 Allowed values for the quantum numbers ofelectrons are as follows:

The relationships between n and the shell designationsare noted in Table 2.1.

Relative tothe subshells,

l ＝0 corresponds to an s subshell

l ＝1 corresponds to a p subshell

l ＝2 corresponds to a d subshell

l ＝3 corresponds to an f subshell

For the K shell, the four quantum numbersfor each of the two electrons in the 1s state, inthe order of nlmlms , are 100(1/2 ) and 100(-1/2 ).Write the four quantum numbers for allof the electrons intheLandMshells, and notewhich correspond to the s, p, and d subshells.

2.7 Give the electron configurations for the followingions: Fe2+, Fe3+, Cu+, Ba2+,

Br-, andS2-.

2.17 (a) Briefly cite the main differences betweenionic, covalent, and metallic

bonding.

(b) State the Pauli exclusion principle.

2.18 Offer an explanation as to why covalently bonded materials are generally less

dense than ionically or metallically bonded ones.

2.19 Compute the percents ionic character of the interatomic bonds for the following

compounds: TiO2 , ZnTe, CsCl, InSb, and MgCl2 .

2.21 Using Table 2.2, determine the number of covalent bonds that are possible for

atoms of the following elements: germanium, phosphorus, selenium, and chlorine.

2.24 On the basis of the hydrogen bond, explain the anomalous behavior of water

when it freezes. That is, why is there volume expansion upon solidification?

3.1 What is the difference between atomic structure and crystal structure?

3.2 What is the difference between a crystal structure and a crystal system?

3.4 Show for the body-centered cubic crystal structure that the unit cell edge length

a and the atomic radius R are related through a =4R/√3.

3.6 Show that the atomic packing factor for BCC is 0.68. .

3.27* Show that the minimum cation-to-anion radius ratio for a coordination

number of 6 is 0.414. Hint: Use the NaCl crystal structure (Figure 3.5), and assume that anions and cations are just touching along cube edges and across face diagonals.

3.48 Draw an orthorhombic unit cell, and within that cell a [121] direction and a

(210) plane.

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3.50 Here are unit cells for two hypothetical metals:

(a) What are the indices for the directions

indicated by the two

vectors

in sketch (a)?

(b) What are the indices for the two planes drawn in

sketch (b)?

3.51* Within a cubic unit cell, sketch the

following directions:

.

3.53 Determine the indices for the directions shown in the following cubic unit cell:

3.57 Determine the Miller indices for the planes

shown in the following unit cell:

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3.58

Determine the Miller indices for the planes shown in the following unit cell:

3.61* Sketch within a cubic unit cell the following planes:

3.62 Sketch the atomic packing of (a) the (100)

plane for the FCC crystal structure, and (b) the (111) plane for the BCC crystal structure (similar to Figures 3.24b and 3.25b).

3.77 Explain why the properties of polycrystalline materials are most often

isotropic.

5.1 Calculate the fraction of atom sites that are vacant for lead at its melting

temperature of 327_C. Assume an energy for vacancy formation of 0.55

eV/atom.

5.7 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 of each defect?

5.8 Below, atomic radius, crystal structure, electronegativity, and the most common

valence are tabulated, for several elements; for those that are nonmetals, only

atomic radii are indicated.

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Which of these elements would you expect to form the following with copper:

(a) A substitutional solid solution having complete solubility?

(b) A substitutional solid solution of incomplete solubility?

(c) An interstitial solid solution?

5.9 For both FCC and BCC crystal structures, there are two different types of

interstitial sites. In each case, one site is larger than the other, which site is

normally occupied by impurity atoms. For FCC, this larger one is located at the center of each edge of the unit cell; it is termed an octahedral interstitial site. On the other hand, with BCC the larger site type is found at 0, __, __ positions—that is, lying on _100_ faces, and situated midway between two unit cell edges on this face and one-quarter of the distance between the other two unit cell edges; it is termed a tetrahedral interstitial site. For both FCC and BCC crystal

structures, compute the radius r of an impurity atom that will just fit into one of these sites in terms of the atomic radius R of the host atom.

5.10 (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 vacancies would you expect to form? How many of the

vacancies are created for every Cl_ added?

5.28 Copper and platinum both have the FCC crystal structure and Cu forms a

substitutional solid solution for concentrations up to approximately 6 wt% Cu at room temperature. Compute the unit cell edge length for a 95 wt% Pt-5 wt% Cu alloy.

5.29 Cite the relative Burgers vector–dislocation line orientations for edge, screw, and

mixed dislocations.

6.1 Briefly explain the difference between selfdiffusion and interdiffusion.

6.3 (a) Compare interstitial and vacancy atomic mechanisms for diffusion.

(b) Cite two reasons why interstitial diffusion is normally more rapid than

vacancy diffusion.

6.4 Briefly explain the concept of steady state as it applies to diffusion.

6.5 (a) Briefly explain the concept of a driving force.

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(b) What is the driving force for steadystate diffusion?

6.6 Compute the number of kilograms of hydrogen that pass per hour through a

5-mm thick sheet of palladium having an area of 0.20 m2 at 500℃. Assume a diffusion coefficient of 1.0×10- 8 m2/s, that the concentrations at the high- and low-pressure sides of the plate are 2.4 and 0.6 kg of hydrogen per cubic meter of palladium, and that steady-state conditions have been attained.

6.7 A sheet of steel 1.5 mm thick has nitrogen atmospheres on both sides at 1200℃

and is permitted to achieve a steady-state diffusion condition. The diffusion coefficient for nitrogen in steel at this temperature is 6×10-11 m2/s, and the diffusion flux is found to be 1.2×10- 7 kg/m2-s. Also, it is known that the concentration of nitrogen in the steel at the high-pressure surface is 4 kg/m3. How far into the sheet from this high-pressure side will the concentration be 2.0 kg/m3? Assume a linear concentration profile.

6.24. Carbon is allowed to diffuse through a steel plate 15 mm thick. The

concentrations of carbon at the two faces are 0.65 and 0.30 kg C/m3 Fe, which are maintained constant. If the preexponential and activation energy are 6.2 _

10_7 m2/s and 80,000 J/mol, respectively, compute the temperature at which the diffusion flux is 1.43 _ 10_9 kg/m2-s.

6.25 The steady-state diffusion flux through a metal plate is 5.4_10_10 kg/m2-s at a

temperature of 727_C (1000 K) and when the concentration gradient is _350

kg/m4. Calculate the diffusion flux at 1027_C (1300 K) for the same

concentration gradient and assuming an activation energy for diffusion of

125,000 J/mol.

10.2 What thermodynamic condition must be met for a state of equilibrium to exist? 10.4 What is the difference between the states of phase equilibrium and metastability? 10.5 Cite the phases that are present and the phase compositions for the following

alloys:

(a) 90 wt% Zn–10 wt% Cu at 400℃

(b) 75 wt% Sn–25wt%Pb at 175℃

(c) 55 wt% Ag–45 wt% Cu at 900℃

(d) 30 wt% Pb–70 wt% Mg at 425℃

(e) 2.12 kg Zn and 1.88 kg Cu at 500℃

(f ) 37 lbm Pb and 6.5 lbm Mg at 400℃

(g) 8.2 mol Ni and 4.3 mol Cu at 1250℃.

(h) 4.5 mol Sn and 0.45 mol Pb at 200℃

10.6 For an alloy of composition 74 wt% Zn–26 wt% Cu, cite the phases present

and their compositions at the following temperatures: 850℃, 750℃, 680℃, 600℃, and 500℃.

10.7 Determine the relative amounts (in terms of mass fractions) of the phases for

the alloys and temperatures given in Problem 10.5.

10.9 Determine the relative amounts (in

terms of volume fractions) of the phases for

the alloys and temperatures given in

Problem 10.5a, b, and c. Below are given the

approximate densities of the various metals

at the alloy temperatures:

10.18 Is it possible to have a copper–silver

alloy that, at equilibrium, consists of a _

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phase of composition 92 wt% Ag–8 wt% Cu, and also a liquid phase of

composition 76 wt% Ag–24 wt% Cu? If so, what will be the approximate

temperature of the alloy? If this is not possible, explain why.

10.20 A copper–nickel alloy of composition 70 wt% Ni–30 wt% Cu is slowly heated

from a temperature of 1300_C .

(a) At what temperature does the first liquid phase form?

(b) What is the composition of this liquid phase?

(c) At what temperature does complete melting of the alloy occur?

(d) What is the composition of the last solid remaining prior to complete

melting?

10.28 .Is it possible to have a copper–silver alloy of composition 50 wt% Ag–50 wt%

Cu, which, at equilibrium, consists of _ and _ phases having mass fractionsW_ _ 0.60 and W_ _ 0.40? If so, what will be the approximate temperature of the alloy? If such an alloy is not possible, explain why.

10.30 At 700_C , what is the maximum solubility (a) of Cu in Ag? (b) Of Ag in Cu?

第三章 习题和思考题

3.3 If the atomic radius of aluminum is 0.143nm, calculate the volume of its unit

cell in cubic meters.

3.8 Iron has a BCC crystal structure, an atomic radius of 0.124 nm, and an atomic

weight of 55.85 g/mol. Compute and compare its density with the experimental value found inside the front cover.

3.9 Calculate the radius of an iridium atom given that Ir has an FCC crystal structure,

a density of 22.4 g/cm3, and an atomic weight of 192.2 g/mol.

3.13 Using atomic weight, crystal structure, and atomic radius data tabulated inside

the front cover, compute the theoretical densities of lead, chromium, copper, and cobalt, and then compare these values with the measured densities listed in this same table. The c/a ratio for cobalt is 1.623.

3.15 Below are listed the atomic weight, density, and atomic radius for three

hypothetical alloys. For each determine whether its crystal structure is FCC,

BCC, or simple cubic and then justify your determination. A simple cubic unit cell is shown in Figure 3.40.

3.21 This is a unit cell for a hypothetical

metal:

(a) To which crystal system does

this unit cell belong?

(b) What would this crystal structure be called?

(c) Calculate the density of the material, given that its atomic weight is 141

g/mol.

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3.25 For a ceramic compound, what are the two characteristics of the component ions

that determine the crystal structure?

3.29 On the basis of ionic charge and ionic radii, predict the crystal structures for the

following materials: (a) CsI, (b) NiO, (c) KI, and (d) NiS. Justify your selections.

3.35 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 3.4, assuming that the Mg2_ and O2_ ions just touch each other along the edges?

3.36 Compute the theoretical density of diamond given that the CUC distance and

bond angle are 0.154 nm and 109.5°, respectively. How does this value compare with the measured density?

3.38 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/cm

—3 , how many Cd 2+ and S 2 ions are there per unit cell?

3.41 A hypothetical AX type of ceramic material is known to have a density of 2.65

g/cm 3 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 crystal structures is (are) possible for this material: rock salt, cesium chloride, or zinc blende? Justify your choice(s).

3.42 The unit cell for Mg Fe2O3 (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/cm 3 , compute its atomic packing factor. For this computation, you will need to use ionic radii listed in Table 3.4.

3.44 Compute the atomic packing factor for the diamond cubic crystal structure

(Figure 3.16). 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 faces (a is the unit cell edge length).

3.45 Compute the atomic packing factor for cesium chloride using the ionic radii in

Table 3.4 and assuming that the ions touch along the cube diagonals.

3.46 In terms of bonding, explain why silicate materials have relatively low densities.

3.47 Determine the angle between covalent bonds in an SiO44— tetrahedron.

3.63 For each of the following crystal structures, represent the indicated plane in the

manner of Figures 3.24 and 3.25, showing both anions and cations: (a) (100)

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plane for the rock salt crystal structure, (b) (110) plane for the cesium chloride crystal structure, (c) (111) plane for the zinc blende crystal structure, and (d) (110) plane for the perovskite crystal structure.

3.66 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?

3.81* The metal iridium has an FCC crystal structure. If the angle of diffraction for

the (220) set of planes occurs at 69.22° (first-order reflection) when monochromatic x-radiation having a wavelength of 0.1542 nm is used, compute (a) the interplanar spacing for this set of planes, and (b) the atomic radius for an iridium atom.

4.10 What is the difference between configuration and conformation in relation to

polymer chains? vinyl chloride).

4.22 (a) Determine the ratio of butadiene to styrene mers in a copolymer having a

weight-average molecular weight of 350,000 g/mol and weight-average degree of polymerization of 4425.

(b) Which type(s) of copolymer(s) will this copolymer be, considering the following possibilities: random, alternating, graft, and block? Why?

4.23 Crosslinked 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 mer types.

4.25 (a) Compare the crystalline state in metals and polymers. (b) Compare the

noncrystalline state as it applies to polymers and ceramic glasses.

4.26 Explain briefly why the tendency of a polymer to crystallize decreases with

increasing molecular weight.

4.27* For each of the following pairs of polymers, do the following: (1) state whether

or not it is possible to determine if 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 possible to decide, then state why.

(a) Linear and syndiotactic polyvinyl chloride; linear and isotactic polystyrene. (b) Network phenol-formaldehyde; linear and heavily crosslinked cis-isoprene. (c) Linear polyethylene; lightly branched isotactic polypropylene.

(d) Alternating poly(styrene-ethylene) copolymer; random poly(vinylchloride-tetrafluoroethylene) copolymer.

4.28 Compute the density of totally crystalline polyethylene. The orthorhombic unit

cell for polyethylene is shown in Figure 4.10; also, the equivalent of two ethylene mer units is contained within each unit cell.

5.11 What point defects are possible for MgO as an impurity in Al2O3? How many

Mg 2+ ions must be added to form each of these defects?

5.13 What is the composition, in weight percent, of an alloy that consists of 6 at% Pb

and 94 at% Sn?

5.14 Calculate the composition, in weight per-cent, of an alloy that contains 218.0 kg

titanium, 14.6 kg of aluminum, and 9.7 kg of vanadium.

5.23 Gold forms a substitutional solid solution with silver. Compute the number of

gold atoms per cubic centimeter for a silver-gold alloy that contains 10 wt% Au and 90 wt% Ag. The densities of pure gold and silver are 19.32 and 10.49 g/cm

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3 , respectively.

8.53 In terms of molecular structure, explain why phenol-formaldehyde (Bakelite)

will not be an elastomer.

10.50 Compute the mass fractions of αferrite and cementite in pearlite. assuming

that pressure is held constant.

10.52 (a) What is the distinction between hypoeutectoid and hypereutectoid steels?

(b) In a hypoeutectoid steel, both eutectoid and proeutectoid ferrite exist. Explain the difference between them. What will be the carbon concentration in each? 10.56 Consider 1.0 kg of austenite containing 1.15 wt% C, cooled to below 727_C

(a) What is the proeutectoid phase?

(b) How many kilograms each of total ferrite and cementite form?

(c) How many kilograms each of pearlite and the proeutectoid phase form? (d) Schematically sketch and label the resulting microstructure.

10.60 The mass fractions of total ferrite and total cementite in an iron–carbon alloy

are 0.88 and 0.12, respectively. Is this a hypoeutectoid or hypereutectoid alloy? Why?

10.64 Is it possible to have an iron–carbon alloy for which the mass fractions of total

ferrite and proeutectoid cementite are 0.846 and 0.049, respectively? Why or why not?

第四章习题和思考题

7.3 A specimen of aluminum having a rectangular cross section 10 mm _ 12.7 mm

is pulled in tension with 35,500 N force, producing only elastic deformation.

7.5 A steel bar 100 mm long and having a square cross section 20 mm on an edge is

pulled in tension with a load of 89,000 N , and experiences an elongation of 0.10 mm . Assuming that the deformation is entirely elastic, calculate the elastic modulus of the steel.

7.7 For a bronze alloy, the stress at which plastic deformation begins is 275 MPa ,

and the modulus of elasticity is 115 Gpa .

(a) What is the maximum load that may be applied to a specimen with a

cross-sectional area of 325mm, without plastic deformation?

(b) If the original specimen length is 115 mm , what is the maximum length to which it may be stretched without causing plastic deformation?

7.8 A cylindrical rod of copper (E _ 110 GPa, Stress (MPa) ) having a yield strength

of 240Mpa is to be subjected to a load of 6660 N. If the length of the rod is 380 mm, what must be the diameter to allow an elongation of 0.50 mm?

7.9 Consider a cylindrical specimen of a steel alloy (Figure 7.33) 10mm in diameter

and 75 mm long that is pulled in tension. Determine its elongation when a load of 23,500 N is applied.

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7.16 A cylindrical specimen of some alloy 8 mm in diameter is stressed elastically

in tension. A force of 15,700 N produces a reduction in specimen diameter of 5 _ 10_3 mm. Compute Poisson’s ratio for this material if its modulus of elasticity is 140 GPa .

7.17 A cylindrical specimen of a hypothetical metal alloy is stressed in compression.

If its original and final diameters are 20.000 and 20.025 mm, respectively, and its final length is 74.96 mm, compute its original length if the deformation is totally elastic. The elastic and shear moduli for this alloy are 105 Gpa and 39.7 GPa, respectively.

7.19 A brass alloy is known to have a yield strength of 275 MPa, a tensile strength of

380 MPa, and an elastic modulus of 103 GPa . A cylindrical specimen of this alloy 12.7 mm in diameter and 250 mm long is stressed in tension and found to elongate 7.6 mm . On the basis of the information given, is it possible to

compute the magnitude of the load that is necessary to produce this change in length? If so, calculate the load. If not, explain why.

7.20 A cylindrical metal specimen 15.0mmin diameter and 150mm long is to be

subjected to a tensile stress of 50 Mpa; at this stress level the resulting deformation will be totally elastic.

(a) If the elongation must be less than 0.072mm,which of the metals in Tabla7.1 are suitable candidates? Why ?

(b) If, in addition, the maximum permissible diameter decrease is 2.3×10-3mm,which of the metals in Table 7.1may be used ? Why?

7.22 Cite the primary differences between elastic, anelastic, and plastic deformation

behaviors.

7.23 diameter of 10.0 mm is to be deformed using a tensile load of 27,500 N. It must

not experience either plastic deformation or a diameter reduction of more than

7.5×10-3 mm. Of the materials listed as follows, which are possible candidates? Justify your choice(s).

7.24 A cylindrical rod 380 mm long, having a diameter of 10.0 mm, is to be

subjected to a tensile load. If the rod is to experience neither plastic deformation

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nor an elongation of more than 0.9 mm when the applied load is 24,500 N,

which of the four metals or alloys listed below are possible candidates?

7.25 Figure 7.33 shows the tensile engineering stress–strain behavior for a steel alloy.

(a) What is the modulus of elasticity?

(b) What is the proportional limit?

(c) What is the yield strength at a strain offset of 0.002?

(d) What is the tensile strength?

7.27 A load of 44,500 N is applied to a cylindrical specimen of steel (displaying the

stress–strain behavior shown in Figure 7.33) that has a cross-sectional diameter of 10 mm .

(a) Will the specimen experience elastic or plastic deformation? Why?

(b) If the original specimen length is 500 mm), how much will it increase in

length when t his load is applied?

7.29 A cylindrical specimen of aluminum

having a diameter of 12.8 mm and a gauge

length of 50.800 mm is pulled in tension. Use

the load–elongation characteristics tabulated

below to complete problems a through f.

(a) Plot the data as engineering stress

versus

engineering strain.

(b) Compute the modulus of elasticity.

(c) Determine the yield strength at a

strain

offset of 0.002.

(d) Determine the tensile strength of this

alloy.

(e) What is the approximate ductility, in percent elongation?

(f ) Compute the modulus of resilience.

7.35 (a) Make a schematic plot showing the tensile true stress–strain behavior for a

typical metal alloy.

(b) Superimpose on this plot a schematic curve for the compressive true

stress–strain behavior for the same alloy. Explain any difference between this curve and the one in part a.

(c) Now superimpose a schematic curve for the compressive engineering

stress–strain behavior for this same alloy, and explain any difference between this curve and the one in part b.

7.39 A tensile test is performed on a metal specimen, and it is found that a true plastic

strain of 0.20 is produced when a true stress of 575 MPa is applied; for the same metal, the value of K in Equation 7.19 is 860 MPa. Calculate the true strain that

results from the application of a true stress of 600 Mpa.

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7.40 For some metal alloy, a true stress of 415 MPa produces a plastic true strain of

0.475. How much will a specimen of this material elongate when a true stress of 325 MPa is applied if the original length is 300 mm ? Assume a value of 0.25 for the strain-hardening exponent n.

7.43 Find the toughness (or energy to cause fracture) for a metal that experiences both

elastic and plastic deformation. Assume Equation 7.5 for elastic deformation, that the modulus of elasticity is 172 GPa , and that elastic deformation terminates at a strain of 0.01. For plastic deformation, assume that the relationship between stress and strain is described by Equation 7.19, in which the values for K and n are 6900 Mpa and 0.30, respectively. Furthermore, plastic deformation occurs between strain values of 0.01 and 0.75, at which point fracture occurs.

7.47 A steel specimen having a rectangular cross section of dimensions 19 mm×3.2

mm (0.75in×0.125in.) has the stress–strain behavior shown in Figure 7.33. If this specimen is subjected to a tensile force of 33,400 N (7,500lbf ), then

(a) Determine the elastic and plastic strain values.

(b) If its original length is 460 mm (18 in.), what will be its final length after the load in part a is applied and then released?

7.50 A three-point bending test was performed on an aluminum oxide specimen

having a circular cross section of radius 3.5 mm; the specimen fractured at a load of 950 N when the distance between the support points was 50 mm . Another test is to be performed on a specimen of this same material, but one that has a square cross section of 12 mm length on each edge. At what load would you expect this specimen to fracture if the support point separation is 40 mm ?

7.51 (a) A three-point transverse bending test is conducted on a cylindrical specimen

of aluminum oxide having a reported flexural strength of 390 MPa . If the speci- men radius is 2.5 mm and the support point separation distance is 30 mm ,

predict whether or not you would expect the specimen to fracture when a load of 620 N is applied. Justify your prediction.

(b) Would you be 100% certain of the prediction in part a? Why or why not?

7.57 When citing the ductility as percent elongation for semicrystalline polymers, it is

not necessary to specify the specimen gauge length, as is the case with metals. Why is this so?

7.66 Using the data represented in Figure 7.31, specify equations relating tensile

strength and Brinell hardness for brass and nodular cast iron, similar to

Equations 7.25a and 7.25b for steels.

8.4 For each of edge, screw, and mixed dislocations, cite the relationship between the

direction of the applied shear stress and the direction of dislocation line motion.

8.5 (a) Define a slip system.

(b) Do all metals have the same slip system? Why or why not?

8.7. One slip system for theBCCcrystal structure is _110__111_. In a manner similar

to Figure 8.6b sketch a _110_-type plane for the BCC structure, representing atom positions with circles. Now, using arrows, indicate two different _111_ slip directions within this plane.

8.15* List four major differences between deformation by twinning and deformation

by slip relative to mechanism, conditions of occurrence, and final result.

8.18 Describe in your own words the three strengthening mechanisms discussed in

this chapter (i.e., grain size reduction, solid solution strengthening, and strain hardening). Be sure to explain how dislocations are involved in each of the strengthening techniques.

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8.19 (a) From the plot of yield strength versus (grain diameter)_1/2 for a 70 Cu–30 Zn

cartridge brass, Figure 8.15, determine values for the constants _0 and ky in Equation 8.5.

(b) Now predict the yield strength of this alloy when the average grain diameter is 1.0 _ 10_3 mm.

8.20. The lower yield point for an iron that has an average grain diameter of 5 _ 10_2

mm is 135 MPa . At a grain diameter of 8 _ 10_3 mm, the yield point increases to 260MPa. At what grain diameter will the lower yield point be 205 Mpa ?

8.24 (a)

Show, for a tensile test, that

if there is no change in specimen volume during the deformation process (i.e., A0

l0 _Ad ld).

(b) Using the result of part a, compute the percent cold work experienced by naval brass (the stress–strain behavior of which is shown in Figure 7.12) when a stress of 400 MPa is applied.

8.25 Two previously undeformed cylindrical specimens of an alloy are to be strain

hardened by reducing their cross-sectional areas (while maintaining their circular cross sections). For one specimen, the initial and deformed radii are 16 mm and 11 mm, respectively. The second specimen, with an initial radius of 12 mm, must have the same deformed hardness as the first specimen; compute the second specimen’s radius after deformation.

8.26 Two previously undeformed specimens of the same metal are to be plastically

deformed by reducing their cross-sectional areas. One has a circular cross section, and the other is rectangular is to remain as such. Their original and deformed dimensions are as follows:

Which of these specimens will be the hardest after plastic deformation, and why?

8.27 A cylindrical specimen of cold-worked copper has a ductility (%EL) of 25%. If

its coldworked radius is 10 mm (0.40 in.), what was its radius before

deformation?

8.28 (a) What is the approximate ductility (%EL) of a brass that has a yield strength

of 275 MPa ?

(b) What is the approximate Brinell hardness of a 1040 steel having a yield strength of 690 MPa?

8.41 In your own words, describe the mechanisms by which semicrystalline polymers

(a) elasticallydeform and (b) plastically deform, and (c) by which elastomers elastically deform.

8.42 Briefly explain how each of the following influences the tensile modulus of a

semicrystallinepolymer and why:

(a) molecular weight;

(b) degree of crystallinity;

(c) deformation by drawing;

(d) annealing of an undeformed material;

(e) annealing of a drawn material.

8.43* Briefly explain how each of the following influences the tensile or yield

strength of a semicrystalline polymer and why:

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(a) molecular weight;

(b) degree of crystallinity;

(c) deformation by drawing;

(d) annealing of an undeformed material.

8.46* The tensile strength and number-average molecular weight for two

polyethylene materials are as follows:

Estimate the number-average molecular weight that is required to give a tensile

strength of 195 MPa.

8.47* For each of the following pairs of polymers, do the following: (1) state whether

or not it is possible to decide if one polymer has a higher tensile modulus than the other; (2) if this is possible, note which has the higher tensile modulus and then cite the reason(s) for your choice; and (3) if it is not possible to decide, then state why.

(a) Syndiotactic polystyrene having a number- average molecular weight of 400,000 g/ mol; isotactic polystyrene having a numberaverage molecular weight of 650,000 g/mol.

(b) Branched and atactic polyvinyl chloride with a weight-average molecular weight of 100,000 g/mol; linear and isotactic polyvinyl chloride having a

weight-average molecular weight of 75,000 g/mol.

(c) Random styrene-butadiene copolymer with 5% of possible sites crosslinked; block styrene-butadiene copolymer with 10% of possible sites crosslinked. (d) Branched polyethylene with a numberaverage molecular weight of 100,000 g/mol; atactic polypropylene with a number-average molecular weight of 150,000 g/mol.

8.50* For each of the following pairs of polymers, plot and label schematic

stress–strain curves on the same graph (i.e., make separate plots for parts a, b, c, and d).

(a) Isotactic and linear polypropylene having a weight-average molecular weight of 120,000 g/mol; atactic and linear polypropylene having a weight-average molecular weight of 100,000 g/mol.

(b) Branched polyvinyl chloride having a number-average degree of

polymerization of 2000; heavily crosslinked polyvinyl chloride having a

number-average degree of polymerization of 2000.

(c) Poly (styrene-butadiene) random copolymer having a number-average

molecular weight of 100,000 g/mol and 10%of the available sites crosslinked and tested at 20_C; poly(styrene-butadiene) random copolymer having a

number-average molecular weight of 120,000 g/mol and 15% of the available sites crosslinked and tested at _85_C. Hint: poly(styrene-butadiene) copolymers may exhibit elastomeric behavior.

(d) Polyisoprene, molecular weight of 100,000 g/mol having 10% of available sites crosslinked; polyisoprene, molecular weight of 100,000 g/mol having 20% of available sites crosslinked. Hint: polyisoprene is a natural rubber that may display elastomeric behavior.

8.51 List the two molecular characteristics that are essential for elastomers.

8.52 Which of the following would you expect to be elastomers and which

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thermosetting polymers at room temperature? Justify each choice.

(a) Epoxy having a network structure.

(b) Lightly crosslinked poly(styrene-butadiene) random copolymer that has a glass-transition temperature of _50_C.

(c) Lightly branched and semicrystalline polytetrafluoroethylene that has a

glasstransition temperature of _100_C.

(d) Heavily crosslinked poly(ethylene-propylene) random copolymer that has a glasstransition temperature of 0_C.

(e) Thermoplastic elastomer that has a glass-transition temperature of 75_C.

8.53 In terms of molecular structure, explain why phenol-formaldehyde (Bakelite)

will not be an elastomer.

9.4 Estimate the theoretical fracture strength of a brittle material if it is known that

fracture occurs by the propagation of an elliptically shaped surface crack of length 0.25 mm and having a tip radius of curvature of 1.2 _ 10_3 mm when a stress of 1200 Mpa is applied.

9.6 Briefly explain (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.

9.7 The tensile strength of brittle materials may be determined using a variation of

Equation 9.1b. Compute the critical crack tip radius for an Al2O3 specimen that experiences tensile fracture at an applied stress of 275 Mpa . Assume a critical surface crack length of 2 _ 10_3 mm and a theoretical fracture strength of E/10, where E is the modulus of elasticity.

9.8 If the specific surface energy for soda-lime glass is 0.30 J/m2, using data

contained in Table 7.1, compute the critical stress required for the propagation of a surface crack of length 0.05 mm.

9.9 A polystyrene component must not fail when a tensile stress of 1.25 MPa is

applied. Determine the maximum allowable surface crack length if the surface energy of polystyrene is 0.50 J/m2 . Assume a modulus of elasticity of 3.0 GPa

9.16 A specimen of a 4340 steel alloy having a plane strain fracture toughness of 45

Mpa m is exposed to a stress of 1000 MPa. Will this specimen experience fracture if it is known that the largest surface crack is 0.75 mm long? Why or why not? Assume that the parameter Y has a value of 1.0.

9.17 Some aircraft component is fabricated from an aluminum alloy that has a plane

strain fracture toughness of 35 MPa_m. It has been determined that fracture results at a stress of 250 MPa when the maximum (or critical) internal crack length is 2.0 mm. For this same component and alloy, will fracture occur at a stress level of 325 Mpa when the maximum internal crack length is 1.0 mm? Why or why not?

9.18 Suppose that a wing component on an aircraft is fabricated from an aluminum

alloy that has a plane strain fracture toughness of 40 Mpa m It has been determined that fracture results at a stress of 365 MPa when the maximum internal crack length is 2.5 mm. For this same component and alloy, compute the stress level at which fracture will occur for a critical internal crack length of 4.0 mm .

9.21. A structural component in the form of a wide plate is to be fabricated from a

steel alloy that has a plane strain fracture toughness of 77 MPa_m and a yield strength of 1400 Mpa . The flaw size resolution limit of the flaw detection

apparatus is 4.0 mm . If the design stress is one half of the yield strength and the value of Y is 1.0, determine whether or not a critical flaw for this plate is

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subject to detection.

9.25 For thermoplastic polymers, cite five factors that favor brittle fracture.

9.26 Tabulated below are data that were gathered from a series of Charpy impact tests

on a ductile cast iron:

(a) Plot the data as impact energy versus temperature.

(b) Determine a ductile-to-brittle transition temperature as that temperature corresponding to the average of the maximum and minimum impact energies. (c) Determine a ductile-to-brittle transition temperature as that temperature at which the impact energy is 80 J.

9.27 Tabulated as follows are data that were

gathered from a series of Charpy impact

tests on a tempered 4140 steel alloy:

(a) Plot the data as impact energy

versus

temperature.

(b) Determine a ductile-to-brittle transition

temperature as that temperature

corresponding to the average of the

maximum and minimum impact energies.

(c) Determine a ductile-to-brittle transition

temperature as that temperature at which the

impact energy is 70 J.

9.28 Briefly explain why BCC and HCP metal alloys may experience a

ductile-to-brittle transition with decreasing temperature, whereas FCC alloys do not experience such a transition.

9.32 A12.5mm(0.50 in.) diameter cylindrical rod fabricated from a 2014-T6 alloy

(Figure 9.46) is subjected to a repeated tension-compression load cycling along its axis. Compute the maximum and minimum loads that will be applied to yield a fatigue life of 1.0×107 cycles. Assume that the stress plotted on the vertical axis is stress amplitude, and data were taken for a mean stress of 50 MPa(7250

psi).

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9.35 The fatigue data for a ductile cast iron are given

as follows:

(a) Make an S–N plot (stress amplitude

versus logarithm cycles to failure) using the

data.

(b) What is the fatigue limit for this alloy?

(c) Determine fatigue lifetimes at stress

amplitudes of 230 MPa and 175 MPa

(d) Estimate fatigue strengths at 2_105 and

6 _ 106 cycles.

9.36 Suppose that the fatigue data for the cast iron in Problem 9.35 were taken for

bending rotating tests, and that a rod of this alloy is to be used for an automobile axle that rotates at an average rotational velocity of 750 revolutions per minute. Give maximum lifetimes of continuous driving that are allowable for the

following stress levels: (a) 250 Mpa , (b) 215 MPa , (c) 200 MPa , and (d) 150 Mpa .

9.38 (a) Compare the fatigue limits for polystyrene (Figure 9.27) and the cast iron for

which fatigue data are given in Problem 9.35.

(b) Compare the fatigue strengths at 106 cycles for polyethylene terephthalate (PET, Figure 9.27) and red brass (Figure 9.46).

9.39 Cite five factors that may lead to scatter in fatigue life data.

12.6 What is the distinction between electronic and ionic conduction?

12.7 How does the electron structure of an isolated atom differ from that of a solid

material?

12.8 In terms of electron energy band structure, discuss reasons for the difference in

electrical conductivity between metals, semiconductors, and insulators.

12.9 If a metallic material is cooled through its melting temperature at an extremely

rapid rate, it will form a noncrystalline solid (i.e., a metallic glass). Will the electrical conductivity of the noncrystalline metal be greater or less than its crystalline counterpart? Why?

12.10 Briefly tell what is meant by the drift velocity and mobility of a free electron.

12.11 (a) Calculate the drift velocity of electrons in germanium at room temperature

and when the magnitude of the electric field is 1000 V/m.

(b) Under these circumstances, how long does it take an electron to traverse a 25

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mm (1 in.) length of crystal?

12.12 An n-type semiconductor is known to have an electron concentration of 3 _

1018 m_3. If the electron drift velocity is 100 m/s in an electric field of 500 V/m, calculate the conductivity of this material.

12.13 At room temperature the electrical conductivity and the electron mobility for

copper are 6.0 _ 107 (_-m)_1 and 0.0030 m2/V-s, respectively. (a) Compute the number of free electrons per cubic meter for copper at room temperature. (b) What is the number of free electrons per copper atom? Assume a density of 8.9 g/cm3.

12.21 (a) Compute the number of free electrons and holes that exist in intrinsic

germanium at room temperature, using the data in Table12.2.

(b) Now calculate the number of free electrons per atom for germanium and silicon (Example Problem 12.1).

(c) Explain the difference. You will need the densities for Ge and Si, which are

5.32 and 2.33 g/cm3, respectively.

12.22 For intrinsic semiconductors, both electron and hole concentrations depend on

temperature as follows:

or, taking natural logarithms,

Thus, a plot of the intrinsic ln n (or ln p) versus 1/T (K)-1 should be linear and

yield a slope of -Eg/2k. Using this information and Figure 12.16, determine the band gap energy for silicon. Compare this value with the one given in Table 12.2.

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12.23 Define the following terms as they pertain to semiconducting materials:

intrinsic, extrinsic, compound, elemental. Now provide an example of each. 12.24 Is it possible for compound semiconductors to exhibit intrinsic behavior?

Explain your answer.

12.25 For each of the following pairs of semiconductors, decide which will have the

smaller band gap energy Eg and then cite the reason for your choice: (a) ZnS and CdSe, (b) Si and C (diamond), (c) Al2O3 and ZnTe, (d) InSb and ZnSe, and (e) GaAs and AlP.

12.26 (a) In your own words, explain how donor impurities in semiconductors give

rise to free electrons in numbers in excess of those generated by valence

band–conduction band excitations. (b) Also explain how acceptor impurities give rise to holes in numbers in excess of those generated by valence

band–conduction band excitations.

12.27 (a) Explain why no hole is generated by the electron excitation involving a

donor impurity atom.

(b) Explain why no free electron is generated by the

electron excitation involving an acceptor impurity atom.

12.28 Will each of the following elements act as a donor or an acceptor when added

to the indicated semiconducting material? Assume that the impurity elements are substitutional.

12.29 (a) At approximately what position is the Fermi energy for an intrinsic

semiconductor?

(b) At approximately what position is the Fermi energy for an n-type

semiconductor?

(c) Make a schematic plot of Fermi energy versus temperature for an n-type semiconductor up to a temperature at which it becomes intrinsic. Also note on this plot energy positions corresponding to

the top of the valence band and the bottom of the conduction band.

The room-temperature electrical conductivity of a silicon specimen is 103

(_- m)_1. The hole concentration is known to be 1.0 _ 1023 m_3. Using the electron and hole mobilities for silicon in Table 12.2, compute the electron concentration. (b) On the basis of the result in part a, is the specimen intrinsic,

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n-type extrinsic, or p-type extrinsic? Why?

12.33 The following electrical characteristics have been determined for both intrinsic

and p

-type extrinsic indium phosphide (InP) at room temperature:

Calculate electron and hole mobilities.

12.34 Compare the temperature dependence of the conductivity for metals and

intrinsic semiconductors. Briefly explain the difference in behavior.

12.35 Using the data in Table 12.2, estimate the electrical conductivity of intrinsic

GaAs at 150C (423 K).

12.38 The intrinsic electrical conductivities of a semiconductor at 20 and 100C (293

and 373 K) are 1.0 and 500 (_-m)_1, respectively. Determine the approximate band gap energy for this material.

12.51 At temperatures between 775C (1048 K) and 1100C (1373 K), the activation

energy and preexponential for the diffusion coef- ficient of Fe2 in FeO are 102,000 J/mol and 7.3 _ 10_8 m2/s, respectively. Compute the mobility for an Fe2 ion at 1000C (1273 K).

12.52* A parallel-plate capacitor using a dielectric material having an r of 2.5 has a

plate spacing of 1 mm (0.04 in.). If another material having a dielectric constant of 4.0 is used and the capacitance is to be unchanged, what must be the new spacing between the plates?

12.54* Consider a parallel-plate capacitor having an area of 2500 mm2 and a plate

separation of 2 mm, and with a material of dielectric constant 4.0 positioned between the plates.

(a) What is the capacitance of this capacitor?

(b) Compute the electric field that must be applied for a charge of 8.0 _ 10_9 C to be stored on each plate.

12.55* In your own words, explain the mechanism by which charge storing capacity

is increased by the insertion of a dielectric material within the plates of a

capacitor.

12.59* (a) For each of the three types of polarization, briefly describe the mechanism

by which dipoles are induced and/or oriented by the action of an applied electric field. (b) For solid lead titanate (PbTiO3), gaseous neon, diamond, solid KCl, and liquid NH3 what kind(s) of polarization is (are) possible? Why?

17.1 Estimate the energy required to raise the temperature of 2 kg of the following

materials from 20 to 100_C aluminum, steel, soda–lime glass, and highdensity polyethylene.

17.3 (a) Determine the room temperature heat capacities at constant pressure for the

following materials: aluminum, silver, tungsten, and 70Cu-30Zn brass.

(b) How do these values compare with one another? How do you explain this? 17.4 For aluminum, the heat capacity at constant volume Cv at 30 K is 0.81 J/mol-K,

and the Debye temperature is 375 K. Estimate the specific heat (a) at 50 K and (b) at 425 K.

17.5 The constant A in Equation 17.2 is 12_4R/5 _3 D, where R is the gas constant

and_D is the Debye temperature (K). Estimate_D for copper, given that the specific heat is0.78 J/kg-K at 10 K.

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17.6 (a) Briefly explain why Cv rises with increasing temperature at temperatures

near 0 K.

(b) Briefly explain why Cv becomes virtually independent of temperature at temperatures far removed from 0 K.

17.10 A 0.1 m rod of a metal elongates 0.2 mm on heating from 20 to 100_C .

Determine the value of the linear coefficient of thermal expansion for this

material.

17.11 Briefly explain thermal expansion using the potential energy-versus-interatomic

spacing curve.

17.12 When a metal is heated its density decreases. There are two sources that give

rise to this diminishment of _: (1) the thermal expansion of the solid, and (2) the formation of vacancies (Section 5.2). Consider a specimen of copper at room temperature (20_C) that has a density of 8.940 g/cm3. (a) Determine its density upon heating to 1000_C when only thermal expansion is considered. And (b) repeat the calculation when the introduction of vacancies is taken into account. Assume that the energy of vacancy formation is 0.90 eV/atom, and that the

volume coefficient of thermal expansion, _v, is equal to 3_l .

17.16 (a) Calculate the heat flux through a sheet of steel 10mm thick if the

temperatures at the two faces are 300 and 100℃; assume steady-state heat flow (b) What is the heat loss per hour if the area of the sheet is 0.25 m2? (c) What will be the heat loss per hour if soda–lime glass instead of steel is used? (d) Calculate the heat loss per hour if steel is used and the thickness is increased to 20 mm

17.18 (a) The thermal conductivity of a single-crystal specimen is slightly greater

than a polycrystalline one of the same material. Why is this so? (b) The thermal conductivity of a plain carbon steel is greater than for a stainless steel. Why is this so?

17.19 Briefly explain why the thermal conductivities are higher for crystalline than

noncrystalline ceramics.

17.20 Briefly explain why metals are typically better thermal conductors than ceramic

materials.

17.21 (a) Briefly explain why porosity decreases the thermal conductivity of ceramic

and polymeric materials, rendering them more thermally insulative. (b) Briefly explain how the degree of crystallinity affects the thermal conductivity of

polymeric materials and why.

17.22 For some ceramic materials, why does the thermal conductivity first decrease

and then increase with rising temperature?

17.23 For each of the following pairs of materials, decide which has the larger thermal

conductivity. Justify your choices.

(a) Pure silver; sterling silver (92.5 wt%Ag– 7.5 wt% Cu).

(b) Fused silica; polycrystalline silica.

(c) Linear polyethylene (Mn _ 450,000 g/mol); lightly branched polyethylene (Mn _ 650,000 g/mol).

(d) Atactic polypropylene (Mw _ 106 g/mol); isotactic polypropylene (Mw _ 5 _ 105 g/mol).

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