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physics
modern physics

Materials Science and Engineering An Introduction 9th edition William D. Callister Jr., David G. Rethwisch - Solutions

For an iron-carbon alloy of composition 3 wt% C-97 wt% Fe, make schematic sketches of the microstructure that would be observed for conditions of very slow cooling at the following temperatures: 1250°C (2280°F), 1145°C (2095°F), and 700°C (1290°F). Label the phases and indicate their
79Often, the properties of multiphase alloys may be approximated by the relationship E (alloy) = EαVα + EβVβ (9.24) Where E represents a specific property (modulus of elasticity, hardness, etc.), and V is the volume fraction. The subscripts α and β denote the existing phases or micro
How many kilograms of nickel must be added to 1.75 kg of copper to yield a liquids temperature of 1300(C?
A steel alloy contains 95.7 wt% Fe, 4.0 wt% W, and 0.3 wt% C. (a) What is the eutectoid temperature of this alloy? (b)What is the eutectoid composition? (c)What is the proeutectoid phase? Assume that there are no changes in the positions of other phase boundaries with the addition of W.
A steel alloy is known to contain 93.65 wt% Fe, 6.0 wt% Mn, and 0.35 wt% C. (a) What is the approximate eutectoid temperature of this alloy? (b) What is the proeutectoid phase when this alloy is cooled to a temperature just below the eutectoid? (c) Compute the relative amounts of the proeutectoid
How many kilograms of nickel must be added to 5.43 kg of copper to yield a solidus temperature of 1200(C?
The kinetics of the austenite-to-pearlite transformation obeys the Avrami relationship. Using the fraction transformed-time data given here, determine the total time required for 95% of the austenite to transform to pearlite:Fraction Transformed __________ Time (s)0.2
The fraction recrystallized-time data for the recrystallization at 350°C of a previously deformed aluminum are tabulated here. Assuming that the kinetics of this process obey the Avrami relationship, determine the fraction recrystallized after a total time of 116.8 min.Fraction Recrystallized
Determine values for the constants n and k (Equation 10.17) for the recrystallization of copper (Figure 10.11) at 119°C?
Suppose that a steel of eutectoid composition is cooled to 675°C (1250°F) from 760°C (1400°F) in less than 0.5 s and held at this temperature. (a) How long will it take for the austenite-to-pearlite reaction to go to 50% completion? To 100% completion? (b) Estimate the hardness of the alloy
Using the isothermal transformation diagram for an iron-carbon alloy of eutectoid composition (Figure 10.22), specify the nature of the final microstructure (in terms of micro-constituents present and approximate percentages of each) of a small specimen that has been subjected to the following
Using the isothermal transformation diagram for a 1.13 wt% C steel alloy (Figure 10.39), determine the final microstructure (in terms of just the micro-constituents present) of a small specimen that has been subjected to the following time-temperature treatments. In each case assume that the
Make a copy of the isothermal transformation diagram for a 1.13 wt% C iron-carbon alloy (Figure 10.39), and then on this diagram sketch and label time-temperature paths to produce the following microstructures: (a) 6.2% proeutectoid cementite and 93.8% coarse pearlite (b) 50% fine pearlite and 50%
Name the micro-structural products of eutectoid iron-carbon alloy (0.76 wt% C) specimens that are first completely transformed to austenite, then cooled to room temperature at the following rates: (a) 1°C/s (b) 20°C/s (c) 50°C/s (d) 175°C/s
Figure 10.40 shows the continuous-cooling transformation diagram for a 0.35 wt% C iron-carbon alloy. Make a copy of this figure, and then sketch and label continuous-cooling curves to yield the following microstructures:(a) Fine pearlite and proeutectoid ferrite(b) Martensite(c) Martensite and
Name the micro-structural products of 4340 alloy steel specimens that are first completely transformed to austenite, then cooled to room temperature at the following rates: (a) 0.005°C/s (b) 0.05°C/s (c) 0.5°C/s (d) 5°C/s
If ice homogeneously nucleates at -40°C, calculate the critical radius given values of -3.1 ×108 J/m3 and 25 × 10-3 J/m2, respectively, for the latent heat of fusion and the surface free energy?
Estimate the Brinellhardnesses for specimens of a 1.13 wt% C iron-carbon alloy that have been subjected to the heat treatments described in parts (a), (b), and (c) of Problem 10.21? Refer to problem 10.21, (a) Rapidly cool to 250°C (480°F), hold for 103 s, then quench to room temperature. (b)
(a) For the solidification of nickel, calculate the critical radius r* and the activation free energy ΔG* if nucleation is homogeneous. Values for the latent heat of fusion and surface free energy are -2.53 × 109 J/m3 and 0.255 J/m2, respectively. Use the super cooling value found in Table
For some transformation having kinetics that obey the Avrami equation (Equation 10.17), the parameter n is known to have a value of 1.5. If the reaction is 25% complete after 125 s, how long (total time) will it take the transformation to go to 90% completion?
Compute the rate of some reaction that obeys Avrami kinetics, assuming that the constants n and k have values of 2.0 and 5 × 10-4, respectively, for time expressed in seconds?
It is known that the kinetics of recrystallization for some alloy obeys the Avrami equation, and that the value of n in the exponential is 5.0. If, at some temperature, the fraction recrystallized is 0.30 after 100 min, determine the rate of recrystallization at this temperature?
It is known that the kinetics of some transformation obeys the Avrami equation and that the value of k is 2.6 ( 10-6 (for time in minutes). If the fraction recrystallized is 0.65 after 120 min, determine the rate of this transformation?
Is it possible to produce an iron-carbon alloy of eutectoid composition that has a minimum hardness of 200 HB and a minimum ductility of 25%RA? If so, describe the continuous-cooling heat treatment to which the alloy would be subjected to achieve these properties. If it is not possible, then
Is it possible to produce an iron-carbon alloy of eutectoid composition that has a minimum hardness of 200 HB and a minimum ductility of 25%RA? If so, describe the continuous-cooling heat treatment to which the alloy would be subjected to achieve these properties. If it is not possible, explain why.
Is it possible to produce an oil-quenched and tempered 4340 steel that has a minimum yield strength of 1240 MPa (180,000 psi) and a ductility of at least 50%RA? If this is possible, describe the tempering heat treatment. If it is not possible, then explain why.
For a eutectoid steel, describe isothermal heat treatments that would be required to yield specimens having the following tensile strength-ductility (%RA) combinations: (a) 900 MPa and 30%RA (b) 700 MPa and 25%RA
Is it possible to produce iron-carbon alloys of eutectoid composition that, using isothermal heat treatments, have the following tensile strength-ductility (%RA) combinations? If so, for each combination describe the heat treatment required to achieve these properties. Or, if this is not possible,
For a eutectoid steel, describe continuous-cooling heat treatments that would be required to yield specimens having the following Brinell hardness-ductility (%RA) combinations: (a) 680 HB and ~0%RA (b) 260 HB and 20 %RA (c) 200 HB and 28 %RA (d) 160 HB and 67%RA
Is it possible to produce an iron-carbon alloy that has a minimum tensile strength of 620 MPa (90,000 psi) and a minimum ductility of 50% RA? If so, what will be its composition and microstructure (coarse and fine pearlites and spheroidite are alternatives)? If this is not possible, explain why.
It is desired to produce an iron-carbon alloy that has a minimum hardness of 200 HB and a minimum ductility of 35% RA. Is such an alloy possible? If so, what will be its composition and microstructure (coarse and fine pearlites and spheroidite are alternatives)? If this is not possible, explain why.
(a) For a 1080 steel that has been water quenched, estimate the tempering time at 535°C (1000°F) to achieve a hardness of 45 HRC.(b)What will be the tempering time at 425°C (800°F) necessary to attain the same hardness?
For a 4340 steel alloy, describe continuous-cooling/tempering heat treatments that would be required to yield specimens having the following yield/tensile strength-ductility property combinations: (a) Tensile strength of 1100 MPa, ductility of 50%RA (b) Yield strength of 1200 MPa, ductility of
Which of the following describes recrystallization? (A) Diffusion dependent with a change in phase composition (B) Diffusionless (C) Diffusion dependent with no change in phase composition (D) All of the above
Schematic room-temperature microstructures for four iron-carbon alloys are as follows. Rank these microstructures (by letter) from the hardest to the softest.(A) _______________ (B) _____________ (C) _______________ (D) (a) A > B > C > D (b) C > D > B > A (c) A > B > D >
On the basis of accompanying isothermal transformation diagram for a 0.45 wt% C iron-carbon alloy, which heat treatment could be used to isothermally convert a microstructure that consists of proeutectoid ferrite and fine pearlite into one that is composed of proeutectoid ferrite and martensite?
Describe one problem that might exist with a steel weld that was cooled very rapidly?
Give the approximate minimum temperature at which it is possible to austenitize each of the following iron-carbon alloys during a normalizing heat treatment: (a) 0.15 wt% C (b) 0.50 wt% C (c) 1.10 wt% C.
Give the approximate temperature at which it is desirable to heat each of the following iron-carbon alloys during a full anneal heat treatment: (a) 0.20 wt% C (b) 0.60 wt% C (c) 0.76 wt% C (d) 0.95 wt% C.
Name two thermal properties of a liquid medium that influence its quenching effectiveness?
What is the function of alloying elements in tool steels?
Compute the volume percent of graphite, VGr, in a 2.5 wt% C cast iron, assuming that all the carbon exists as the graphite phase. Assume densities of 7.9 and 2.3 g/cm3 for ferrite and graphite, respectively?
On the basis of microstructure, briefly explain why gray iron is brittle and weak in tension?
A cylindrical piece of 8660 steel is to be austenitized and quenched in moderately agitated oil. If the hardness at the surface of the piece must be at least 58 HRC, what is the maximum allowable diameter? Justify your answer.
Is it possible to temper an oil-quenched 4140 steel cylindrical shaft 25 mm (1 in.) in diameter so as to give a minimum yield strength of 950 MPa (140,000 psi) and a minimum ductility of 17%EL? If so, specify a tempering temperature. If this is not possible, then explain why.
Is it possible to temper an oil-quenched 4140 steel cylindrical shaft 50 mm (2 in.) in diameter so as to give a minimum tensile strength of 900 MPa (130,000 psi) and a minimum ductility of 20%EL? If so, specify a tempering temperature. If this is not possible, then explain why.
A solution heat-treated 2014 aluminum alloy is to be precipitation hardened to have a minimum yield strength of 345 MPa (50,000 psi) and a ductility of at least 12%EL. Specify a practical precipitation heat treatment in terms of temperature and time that would give these mechanical characteristics?
Is it possible to produce a precipitation hardened 2014 aluminum alloy having a minimum yield strength of 380 MPa (55,000 psi) and a ductility of at least 15%EL? If so, specify the precipitation heat treatment. If it is not possible then explain why.
Of the following alloys, pick the one(s) that may be strengthened by heat treatment, cold work, or both: 410 stainless steel, 4340 steel, F10004 cast iron, C26000 cartridge brass, 356.0 aluminum, ZK60A magnesium, R56400 titanium, 1100 aluminum, and zinc?
A structural member 250 mm (10 in.) long must be able to support a load of 44,400 N (10,000 lbf) without experiencing any plastic deformation. Given the following data for brass, steel, aluminum, and titanium, rank them from least to greatest weight in accordance with these criteria.
A cylindrical piece of steel 38 mm (1*1/2 in.) in diameter is to be quenched in moderately agitated oil. Surface and center hard-nesses must be at least 50 and 40 HRC, respectively. Which of the following alloys will satisfy these requirements: 1040, 5140, 4340, 4140, and 8640? Justify your
(a) Moderately agitated water and(b) Moderately agitated oil? Justify your choice(s)?
(a) Moderately agitated oil and(b) Moderately agitated water? Justify your choice(s).
A cylindrical piece of steel 50 mm (2 in.) in diameter is to be quenched in moderately agitated water. Surface and center hard-nesses must be at least 50 and 40 HRC, respectively. Which of the following alloys satisfy these requirements: 1040, 5140, 4340, 4140, 8620, 8630, 8640, and 8660? Justify
Which of the following elements is the primary constituent of ferrous alloys? (A) Copper (B) Carbon (C) Iron (D) Titanium
Which of the following microconstituents/phases is (are) typically found in a low-carbon steel? (A) Austenite (B) Pearlite (C) Ferrite (D) Both pearlite and ferrite
Which of the following characteristics distinguishes the stainless steels from other steel types? (A) They are more corrosion resistant. (B) They are stronger. (C) They are more wear resistant. (D) They are more ductile.
Hot working takes place at a temperature above a metal's (A) Melting temperature (B) Recrystallization temperature (C) Eutectoid temperature (D) Glass transition temperature
Which of the following may occur during an annealing heat treatment? (A) Stresses may be relieved. (B) Ductility may increase. (C) Toughness may increase. (D) All of the above.
Which of the following influences the harden-ability of a steel? (A) Composition of the steel (B) Type of quenching medium (C) Character of the quenching medium (D) Size and shape of the specimen
Beryllium oxide (BeO) may form a crystal structure that consists of an HCP arrangement of O2-ions. If the ionic radius of Be2+ is 0.035 nm, then(a) Which type of interstitial site will the Be2+ ions occupy?(b) What fraction of these available interstitial sites will be occupied by Be2+ ions?
Iron titanate, FeTiO3, forms in the ilmenite crystal structure that consists of an HCP arrangement of O2-ions.(a) Which type of interstitial site will the Fe2+ ions occupy? Why?(b) Which type of interstitial site will the Ti4+ ions occupy? Why?(c) What fraction of the total tetrahedral sites will
The unit cell for Al2O3 has hexagonal symmetry with lattice parameters a = 0.4759 nm and c =1.2989 nm. If the density of this material is 3.99 g/cm3, calculate its atomic packing factor. For this computation use ionic radii listed in Table 12.3?
Iron oxide (FeO) has the rock salt crystal structure and a density of 5.70 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 Fe2+ and O2- ions just touch each other along the edges?
One crystalline form of silica (SiO2) has a cubic unit cell, and from x-ray diffraction data it is known that the cell edge length is 0.700 nm. If the measured density is 2.32 g/cm3, how many Si4+ and O2-ions are there per unit cell?
A hypothetical AX type of ceramic material is known to have a density of 2.10 g/cm3 and a unit cell of cubic symmetry with a cell edge length of 0.57 nm. The atomic weights of the A and X elements are 28.5 and 30.0 g/mol, respectively. On the basis of this information, which of the following
The unit cell for Fe3O4 (FeO-Fe2O3) has cubic symmetry with a unit cell edge length of 0.839 nm. If the density of this material is 5.24 g/cm3, compute its atomic packing factor. For this computation, you will need to use the ionic radii listed in Table 12.3?
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?
Would you expect Frenkel defects for anions to exist in ionic ceramics in relatively large concentrations? Why or why not?
Calculate the fraction of lattice sites that are Schottky defects for cesium chloride at its melting temperature (645°C). Assume an energy for defect formation of 1.86 eV?
Calculate the number of Frenkel defects per cubic meter in silver chloride at 350°C. The energy for defect formation is 1.1 eV, whereas the density for AgCl is 5.50 g/cm3 at 350°C?
Using the following data 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 1000Â°C(c) The identity of the
In your own words, briefly define the term stoichiometric?
Do the Hume-Rothery rules (Section 4.3) also apply to ceramic systems? Explain your answer.
Which of the following oxides would you expect to form substitutional solid solutions that have complete (i.e., 100%) solubility with MgO? Explain your answers.(a) FeO(b) BaO(c) PbO(d) CoO
The tensile strength of brittle materials may be determined using a variation of Equation 8.1. Compute the critical crack tip radius for a glass specimen that experiences tensile fracture at an applied stress of 70 MPa (10,000 psi). Assume a critical surface crack length of 10-2 mm and a
A three-point bending test is performed on a spinel (MgAl2O4) specimen having a rectangular cross section of height d = 3.8 mm (0.15 in.) and width b = 9 mm (0.35 in.); the distance between support points is 25 mm (1.0 in.).(a) Compute the flexural strength if the load at fracture is 350 N (80
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 5560 N (1250 lbf), the flexural strength is 105 MPa (15,000 psi), and the separation between load points is 45 mm (1.75 in.)?
A three-point bending test was performed on an aluminum oxide specimen having a circular cross section of radius 5.0 mm (0.20 in.); the specimen fractured at a load of 3000 N (675 lbf) when the distance between the support points was 40 mm (1.6 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 300 MPa (43,500 psi). If the specimen radius is 5.0 mm (0.20 in.) and the support point separation distance is 15.0 mm (0.61 in.), would you expect the specimen
Cite one reason why ceramic materials are, in general, harder yet more brittle than metals?
The modulus of elasticity for spinel (MgAl2O4) having 5 vol% porosity is 240 GPa (35 × 106 psi).(a) Compute the modulus of elasticity for the nonporous material.(b) Compute the modulus of elasticity for 15 vol% porosity?
The modulus of elasticity for titanium carbide (TiC) having 5 vol% porosity is 310 GPa (45 × 106 psi).(a) Compute the modulus of elasticity for the nonporous material.(b) At what volume percent porosity will the modulus of elasticity be 240 GPa (35 × 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 74 MPa (10,700 psi)?
The flexural strength and associated volume fraction porosity for two specimens of the same ceramic material are as follows:σfs (MPa) _____________ P70 ........................... 0.1060 ........................... 0.15(a) Compute the flexural strength for a completely nonporous specimen of this
Using the Molecule Definition Utility found in both "Metallic Crystal Structures and Crystallography" and "Ceramic Crystal Structures" modules of VMSE, located on the book's web site [www.wiley.com/college/callister (Student Companion Site)], generate (and print out) a three-dimensional unit cell
Gallium arsenide (GaAs) and indium arsenide (InAs) both have the zinc blende crystal structure and are soluble in each other at all concentrations. Determine the concentration in weight percent of InAs that must be added to GaAs to yield a unit cell edge length of 0.5820 nm. The densities of GaAs
It is necessary to select a ceramic material to be stressed using a three-point loading scheme (Figure 12.30). The specimen must have a circular cross section, a radius of 3.8 mm (0.15 in.) and must not experience fracture or a deflection of more than 0.021 mm (8.5 × 10-4 in.) at its center when a
Which of the following are the most common coordination numbers for ceramic materials? (A) 2 and 3 (B) 6 and 12 (C) 6, 8, and 12 (D) 4, 6, and 8
An AX ceramic compound has the rock salt crystal structure. If the radii of the A and X ions are 0.137 and 0.241 nm, respectively, and the respective atomic weights are 22.7 and 91.4 g/mol, what is the density (in g/cm3) of this material?(A) 0.438 g/cm3(B) 0.571 g/cm3(C) 1.75 g/cm3(D) 3.50 g/cm3
Cite the two desirable characteristics of glasses?
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 magnesia material of composition 88.5 wt% MgO-11.5 wt% Al2O3.(b) A magnesia-alumina spinel of composition 25 wt% MgO-75 wt% Al2O3.
Upon consideration of the SiO2-Al2O3 phase diagram in Figure 12.25, for each pair of the following list of compositions, which would you judge to be the more desirable refractory? Justify your choices.(a) 99.8 wt% SiO2-0.2 wt% Al2O3 and 99.0 wt% SiO2-1.0 wt% Al2O3(b) 70 wt% Al2O3-30 wt% SiO2 and 74
Compute the mass fractions of liquid in the following fireclay refractory materials at 1600°C (2910°F):(a) 25 wt% Al2O3-75 wt% SiO2(b) 45 wt% Al2O3-55 wt% SiO2
Soda and lime are added to a glass batch in the form of soda ash (Na2CO3) and lime-stone (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 125 lbm
As the porosity of a refractory ceramic brick increases, (A) Strength decreases, chemical resistance decreases, and thermal insulation increases (B) Strength increases, chemical resistance increases, and thermal insulation decreases (C) Strength decreases, chemical resistance increases, and thermal
Which of the following are the two primary constituents of clays? (A) Alumina (Al2O3) and limestone (CaCO3) (B) Limestone (CaCO3) and cupric oxide (CuO) (C) Silica (SiO2) and limestone (CaCO3) (D) Alumina (Al2O3) and silica (SiO2)
Sketch portions of a linear polypropylene molecule that are (a) Syndiotactic, (b) Atactic, and (c) Isotactic. Use two-dimensional schematics per footnote 9 of this chapter?
The number-average molecular weight of a poly (acrylonitrile-butadiene) alternating copolymer is 1,000,000 g/mol; determine the average number of acrylonitrile and butadiene repeat units per molecule?
Calculate the number-average molecular weight of a random poly (isobutylene-isoprene) copolymer in which the fraction of isobutylene repeat units is 0.25; assume that this concentration corresponds to a degree of polymerization of 1500?

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