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materials science engineering

Fundamentals of Materials Science and Engineering An Integrated Approach 4th Edition David G. Rethwisch - Solutions

What is the composition, in atom percent, of an alloy that contains 99.7 lbm copper, 102 lbm zinc, and 2.1 lbm lead?
What is the composition, in atom percent, of an alloy that consists of 97 wt% Fe and 3 wt% Si?
Convert the atom percent composition in Problem 4.11 to weight percent.
Calculate the number of atoms per cubic meter in aluminum.
The concentration of carbon in an iron-carbon alloy is 0.15 wt%. What is the concentration in kilograms of carbon per cubic meter of alloy?
Determine the approximate density of a high-leaded brass that has a composition of 64.5 wt% Cu, 33.5 wt% Zn, and 2.0 wt% Pb.
Calculate the unit cell edge length for an 85 wt% Fe-15 wt% V alloy. All of the vanadium is in solid solution, and, at room temperature the crystal structure for this alloy is BCC.
Some hypothetical alloy is composed of 12.5 wt% of metal A and 87.5 wt% of metal B. If the densities of metals A and B are 4.27 and 6.35 g/cm3, respectively, whereas their respective atomic weights are 61.4 and 125.7 g/mol, determine whether the crystal structure for this alloy is simple cubic,
For a solid solution consisting of two elements (designated as 1 and 2), sometimes it is desirable to determine the number of atoms per cubic centimeter of one element in a solid solution, N1, given the concentration of that element specified in weight percent, C1. This computation is possible
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/cm3, respectively.
Germanium forms a substitutional solid solution with silicon. Compute the number of germanium atoms per cubic centimeter for a germanium-silicon alloy that contains 15 wt% Ge and 85 wt% Si. The densities of pure germanium and silicon are 5.32 and 2.33 g/cm3, respectively.
Sometimes it is desirable to be able to determine the weight percent of one element, C1 that will produce a specified concentration in terms of the number of atoms per cubic centimeter, N1, for an alloy composed of two types of atoms. This computation is possible using the following
Molybdenum forms a substitutional solid solution with tungsten. Compute the weight percent of molybdenum that must be added to tungsten to yield an alloy that contains 1.0 × 1022 Mo atoms per cubic centimeter. The densities of pure Mo and W are 10.22 and 19.30 g/cm3, respectively.
Niobium forms a substitutional solid solution with vanadium. Compute the weight percent of niobium that must be added to vanadium to yield an alloy that contains 1.55 × 1022 Nb atoms per cubic centimeter. The densities of pure Nb and V are 8.57 and 6.10 g/cm3, respectively.
Silver and palladium both have the FCC crystal structure and Pd forms a substitutional solid solution for all concentrations at room temperature. Compute the unit cell edge length for a 75 wt% Ag–25 wt% Pd alloy. The room-temperature density of Pd is 12.02 g/cm3, and its atomic weight and atomic
For an FCC single crystal, would you expect the surface energy for a (100) plane to be greater or less than that for a (111) plane? Why?
For a BCC single crystal, would you expect the surface energy for a (100) plane to be greater or less than that for a (110) plane? Why?
(a) For a given material, would you expect the surface energy to be greater than, the same as, or less than the grain boundary energy? Why?(b) The grain boundary energy of a small-angle grain boundary is less than for a high-angle one. Why is this so?
(a) Briefly describe a twin and a twin boundary.(b) Cite the difference between mechanical and annealing twins.
For each of the following stacking sequences found in FCC metals, cite the type of planar defect that exists:(a) . . . A B C A B C B A C B A . . .(b) . . . A B C A B C B C A B C . . .Now, copy the stacking sequences and indicate the position(s) of planar defect(s) with a vertical dashed line.
(a) Using the intercept method, determine the average grain size, in millimeters, of the specimen whose microstructure is shown in Figure (b); use at least seven straight-line segments. (b) Estimate the ASTM grain size number for this material.
(a) Employing the intercept technique, determine the average grain size for the steel specimen whose microstructure is shown in Figure (a); use at least seven straight-line segments. (b) Estimate the ASTM grain size number for this material.
For an ASTM grain size of 8, approximately how many grains would there be per square inch at(a) A magnification of 100,(b) Without any magnification?
Determine the ASTM grain size number if 25 grains per square inch are measured at a magnification of 600.
Determine the ASTM grain size number if 20 grains per square inch are measured at a magnification of 50.
Aluminum–lithium alloys have been developed by the aircraft industry to reduce the weight and improve the performance of its aircraft. A commercial aircraft skin material having a density of 2.55 g/cm3 is desired. Compute the concentration of Li (in wt %) that is required.
Iron and vanadium both have the BCC crystal structure and V forms a substitutional solid solution in Fe for concentrations up to approximately 20 wt% V at room temperature. Determine the concentration in weight percent of V that must be added to iron to yield a unit cell edge length of 0.289 nm.
Briefly explain the difference between self-diffusion and interdiffusion.
(a) Compare interstitial and vacancy atomic mechanisms for diffusion.(b) Cite two reasons why interstitial diffusion is normally more rapid than vacancy diffusion.
Briefly explain the concept of steady state as it applies to diffusion.
The purification of hydrogen gas by diffusion through a palladium sheet was discussed in Section 5.3. 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°C. Assume a diffusion coefficient of 1.0 × 10-8 m2/s, that
A sheet of steel 1.5 mm thick has nitrogen atmospheres on both sides at 1200°C 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
A sheet of BCC iron 1 mm thick was exposed to a carburizing gas atmosphere on one side and a decarburizing atmosphere on the other side at 725°C. After having reached steady state, the iron was quickly cooled to room temperature. The carbon concentrations at the two surfaces of the sheet were
When a-iron is subjected to an atmosphere of hydrogen gas, the concentration of hydrogen in the iron, CH (in weight percent), is a function of hydrogen pressure, PH2 (in MPa), and absolute temperature (T) according to Furthermore, the values of D0 and Qd for this diffusion system are 1.4 ? 10-7
Show that is also a solution to Equation 5.4b. The parameter B is a constant, being independent of both x and t.
Determine the carburizing time necessary to achieve a carbon concentration of 0.45 wt% at a position 2 mm into an iron?carbon alloy that initially contains 0.20 wt% C. The surface concentration is to be maintained at 1.30 wt% C, and the treatment is to be conducted at 1000?C. Use the diffusion data
An FCC iron-carbon alloy initially containing 0.35 wt% C is exposed to an oxygen-rich and virtually carbon-free atmosphere at 1400 K (1127°C). Under these circumstances the carbon diffuses from the alloy and reacts at the surface with the oxygen in the atmosphere; that is, the carbon concentration
Nitrogen from a gaseous phase is to be diffused into pure iron at 700°C. If the surface concentration is maintained at 0.1 wt% N, what will be the concentration 1 mm from the surface after 10 h? The diffusion coefficient for nitrogen in iron at 700°C is 2.5 × 10-11 m2/s.
Consider a diffusion couple composed of two semi-infinite solids of the same metal, and that each side of the diffusion couple has a different concentration of the same elemental impurity; furthermore, assume each impurity level is constant throughout its side of the diffusion couple. For this
For a steel alloy it has been determined that a carburizing heat treatment of 10-h duration will raise the carbon concentration to 0.45 wt% at a point 2.5 mm from the surface. Estimate the time necessary to achieve the same concentration at a 5.0-mm position for an identical steel and at the same
Cite the values of the diffusion coefficients for the inter-diffusion of carbon in both α-iron (BCC) and γ-iron (FCC) at 900°C. Which is larger? Explain why this is the case.
Using the data in Table 5.2, compute the value of D for the diffusion of zinc in copper at 650?C.
At what temperature will the diffusion coefficient for the diffusion of copper in nickel have a value of 6.5 ? 10-17 m2/s. Use the diffusion data in Table 5.2.
The preexponential and activation energy for the diffusion of iron in cobalt are 1.1 × 10-5 m2/s and 253,300 J/mol, respectively. At what temperature will the diffusion coefficient have a value of 2.1 × 10-14 m2/s?
The activation energy for the diffusion of carbon in chromium is 111,000 J/mol. Calculate the diffusion coefficient at 1100 K (827°C), given that D at 1400 K (1127°C) is 6.25 × 10-11 m2/s.
The diffusion coefficients for iron in nickel are given at two temperatures:(a) Determine the values of D0 and the activation energy Qd.(b) What is the magnitude of D at 1100ºC (1373 K)?
The diffusion coefficients for silver in copper are given at two temperatures:(a) Determine the values of D0 and Qd.(b) What is the magnitude of D at 875°C?
Below is shown a plot of the logarithm (to the base 10) of the diffusion coefficient versus reciprocal of the absolute temperature, for the diffusion of iron in chromium. Determine values for the activation energy and preexponential.
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
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
At approximately what temperature would a specimen of g-iron have to be carburized for 2 h to produce the same diffusion result as at 900°C for 15 h?
(a) Calculate the diffusion coefficient for copper in aluminum at 500°C.(b) What time will be required at 600°C to produce the same diffusion result (in terms of concentration at a specific point) as for 10 h at 500°C?
A copper-nickel diffusion couple similar to that shown in Figure 5.1a is fashioned. After a 700-h heat treatment at 1100?C (1373 K) the concentration of Cu is 2.5 wt% at the 3.0-mm position within the nickel. At what temperature must the diffusion couple need to be heated to produce this same
A diffusion couple similar to that shown in Figure 5.1a is prepared using two hypothetical metals A and B. After a 30-h heat treatment at 1000 K (and subsequently cooling to room temperature) the concentration of A in B is 3.2 wt% at the 15.5-mm position within metal B. If another heat treatment is
The outer surface of a steel gear is to be hardened by increasing its carbon content. The carbon is to be supplied from an external carbon-rich atmosphere, which is maintained at an elevated temperature. A diffusion heat treatment at 850°C (1123 K) for 10 min increases the carbon concentration to
An FCC iron-carbon alloy initially containing 0.20 wt% C is carburized at an elevated temperature and in an atmosphere wherein the surface carbon concentration is maintained at 1.0 wt%. If after 49.5 h the concentration of carbon is 0.35 wt% at a position 4.0 mm below the surface, determine the
Phosphorus atoms are to be diffused into a silicon wafer using both predeposition and drive-in heat treatments; the background concentration of P in this silicon material is known to be 5 × 1019 atoms/m3. The predeposition treatment is to be conducted at 950°C for 45 minutes; the surface
Aluminum atoms are to be diffused into a silicon wafer using both predeposition and drive-in heat treatments; the background concentration of Al in this silicon material is known to be 3 × 1019 atoms/m3. The drive-in diffusion treatment is to be carried out at 1050°C for a period of 4.0 h,
It is desired to enrich the partial pressure of hydrogen in a hydrogen-nitrogen gas mixture for which the partial pressures of both gases are 0.1013MPa (1atm). It has been proposed to accomplish this by passing both gases through a thin sheet of some metal at an elevated temperature; inasmuch as
A gas mixture is found to contain two diatomic A and B species for which the partial pressures of both are 0.05065MPa (0.5atm). This mixture is to be enriched in the partial pressure of the A species by passing both gases through a thin sheet of some metal at an elevated temperature. The resulting
The wear resistance of a steel shaft is to be improved by hardening its surface. This is to be accomplished by increasing the nitrogen content within an outer surface layer as a result of nitrogen diffusion into the steel. The nitrogen is to be supplied from an external nitrogen-rich gas at an
One integrated circuit design calls for the diffusion of arsenic into silicon wafers; the background concentration of As in Si is 2.5 x 1020 atoms/m3. The predeposition heat treatment is to be conducted at 1000°C for 45 minutes, with a constant surface concentration of 8 x 1026 As atoms/m3. At a
Using mechanics of materials principles (i.e., equations of mechanical equilibrium applied to a free-body diagram), derive Equations 6.4a and6.4b.
(a) Equations 6.4a and 6.4b are expressions for normal (??) and shear (??) stresses, respectively, as a function of the applied tensile stress (?) and the inclination angle of the plane on which these stresses are taken (? of Figure 6.4). Make a plot on which is presented the orientation parameters
A specimen of aluminum having a rectangular cross section 10 mm ( 12.7 mm (0.4 in. ( 0.5 in.) is pulled in tension with 35,500 N (8000 lbf) force, producing only elastic deformation. Calculate the resulting strain.
A cylindrical specimen of a titanium alloy having an elastic modulus of 107 GPa (15.5 ( 106 psi) and an original diameter of 3.8 mm (0.15 in.) will experience only elastic deformation when a tensile load of 2000 N (450 lbf) is applied. Compute the maximum length of the specimen before deformation
A steel bar 100 mm (4.0 in.) long and having a square cross section 20 mm (0.8 in.) on an edge is pulled in tension with a load of 89,000 N (20,000 lbf), and experiences an elongation of 0.10 mm (4.0 ( 10-3 in.). Assuming that the deformation is entirely elastic, calculate the elastic modulus of
Consider a cylindrical titanium wire 3.0 mm (0.12 in.) in diameter and 2.5 × 104 mm (1000 in.) long. Calculate its elongation when a load of 500 N (112 lbf) is applied. Assume that the deformation is totally elastic.
For a bronze alloy, the stress at which plastic deformation begins is 275 MPa (40,000 psi), and the modulus of elasticity is 115 GPa (16.7 ( 106 psi).(a) What is the maximum load that may be applied to a specimen with a cross-sectional area of 325 mm2 (0.5 in.2) without plastic deformation?(b) If
A cylindrical rod of copper (E = 110GPa, 16 ( 106psi) having a yield strength of 240MPa (35,000psi) is to be subjected to a load of 6660 N (1500lbf). If the length of the rod is 380 mm (15.0 in.), what must be the diameter to allow an elongation of 0.50 mm (0.020 in.)?
Compute the elastic moduli for the following metal alloys, whose stress-strain behaviors may be observed in the "Tensile Tests" module of Virtual Materials Science and Engineering (VMSE): (a) Titanium (b) Tempered steel (c) Aluminum and (d) Tarbon steel. How do these values compare with those
Consider a cylindrical specimen of a steel alloy (Figure 6.21) 10.0 mm (0.39 in.) in diameter and 75 mm (3.0 in.) long that is pulled in tension. Determine its elongation when a load of 20,000 N (4,500lbf) isapplied.
Figure shows, for a gray cast iron, the tensile engineering stress???strain curve in the elastic region. Determine (a) The tangent modulus at 10.3MPa (1500psi), and (b) The secant modulus taken to 6.9MPa(1000psi).
As noted in Section 3.15, for single crystals of some substances, the physical properties are anisotropic; that is, they are dependent on crystallographic direction. One such property is the modulus of elasticity. For cubic single crystals, the modulus of elasticity in a general [uvw] direction,
In Section 2.6 it was noted that the net bonding energy EN between two isolated positive and negative ions is a function of interionic distance r as follows:where A, B, and n are constants for the particular ion pair. Equation 6.25 is also valid for the bonding energy between adjacent ions in solid
Using the solution to Problem 6.13, rank the magnitudes of the moduli of elasticity for the following hypothetical X, Y, and Z materials from the greatest to the least. The appropriate A, B, and n parameters (Equation 6.25) for these three materials are tabulated below; they yield EN in units of
A cylindrical specimen of aluminum having a diameter of 19 mm (0.75 in.) and length of 200 mm (8.0 in.) is deformed elastically in tension with a force of 48,800 N (11,000lbf). Using the data contained in Table 6.1, determine the following: (a) The amount by which this specimen will elongate in the
A cylindrical bar of steel 10 mm (0.4 in.) in diameter is to be deformed elastically by application of a force along the bar axis. Using the data in Table 6.1, determine the force that will produce an elastic reduction of 3 ( 10-3 mm (1.2 ( 10-4 in.) in thediameter.
A cylindrical specimen of some alloy 8 mm (0.31 in.) in diameter is stressed elastically in tension. A force of 15,700 N (3530 lbf) produces a reduction in specimen diameter of 5 × 10-3 mm (2 × 10-4 in.). Compute Poisson's ratio for this material if its modulus of elasticity is 140GPa (20.3 ×
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
Consider a cylindrical specimen of some hypothetical metal alloy that has a diameter of 8.0 mm (0.31 in.). A tensile force of 1000 N (225lbf) produces an elastic reduction in diameter of 2.8 × 10-4 mm (1.10 × 10-5 in.). Compute the modulus of elasticity for this alloy, given that Poisson's ratio
A brass alloy is known to have a yield strength of 275MPa (40,000psi), a tensile strength of 380MPa (55,000psi), and an elastic modulus of 103GPa (15.0 × 106 psi). A cylindrical specimen of this alloy 12.7 mm (0.50 in.) in diameter and 250 mm (10.0 in.) long is stressed in tension and found
A cylindrical metal specimen 12.7 mm (0.5 in.) in diameter and 250 mm (10 in.) long is to be subjected to a tensile stress of 28MPa (4000 psi); at this stress level the resulting deformation will be totally elastic. (a)?If the elongation must be less than 0.080 mm (3.2 ? 10-3 in.), which of the
Consider the brass alloy for which the stress-strain behavior is shown in Figure 6.12. A cylindrical specimen of this material 6 mm (0.24 in.) in diameter and 50 mm (2 in.) long is pulled in tension with a force of 5000 N (1125lbf). If it is known that this alloy has a Poisson's ratio of 0.30,
A cylindrical rod 100 mm long and having a 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
A cylindrical rod 380 mm (15.0 in.) long, having a diameter of 10.0 mm (0.40 in.), is to be subjected to a tensile load. If the rod is to experience neither plastic deformation nor an elongation of more than 0.9 mm (0.035 in.) when the applied load is 24,500 N (5500lbf), which of the four metals or
Figure 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?
A cylindrical specimen of a brass alloy having a length of 60 mm (2.36 in.) must elongate only 10.8 mm (0.425 in.) when a tensile load of 50,000 N (11,240lbf) is applied. Under these circumstances, what must be the radius of the specimen? Consider this brass alloy to have the stress-strain behavior
A load of 85,000 N (19,100lbf) is applied to a cylindrical specimen of a steel alloy (displaying the stress???strain behavior shown in Figure) that has a cross-sectional diameter of 15 mm (0.59 in.). (a) Will the specimen experience elastic and/or plastic deformation? Why? (b) If the original
A bar of a steel alloy that exhibits the stress-strain behavior shown in Figure is subjected to a tensile load; the specimen is 300 mm (12 in.) long, and of square cross section 4.5 mm (0.175 in.) on a side. (a) Compute the magnitude of the load necessary to produce an elongation of 0.45 mm (0.018
A cylindrical specimen of aluminum having a diameter of 0.505 in. (12.8 mm) and a gauge length of 2.000 in. (50.800 mm) is pulled in tension. Use the load?elongation characteristics tabulated below to complete parts (a) through (f). (a) Plot the data as engineering stress versus engineering
A specimen of ductile cast iron having a rectangular cross section of dimensions 4.8 mm ( 15.9 mm (3/16 in. ( 5/8 in.) is deformed in tension. Using the load-elongation data tabulated below, complete problems (a) through (f). (a) Plot the data as engineering stress versus engineering strain. (b)
For the titanium alloy, whose stress strain behavior may be observed in the “Tensile Tests” module of Virtual Materials Science and Engineering (VMSE), determine the following:(a) The approximate yield strength (0.002 strain offset),(b) The tensile strength, and(c) The approximate ductility, in
For the tempered steel alloy, whose stress strain behavior may be observed in the “Tensile Tests” module of Virtual Materials Science and Engineering (VMSE), determine the following:(a) The approximate yield strength (0.002 strain offset),(b) The tensile strength, and(c) The approximate
For the aluminum alloy, whose stress strain behavior may be observed in the “Tensile Tests” module of Virtual Materials Science and Engineering (VMSE), determine the following:(a) The approximate yield strength (0.002 strain offset),(b) The tensile strength, and(c) The approximate ductility, in
For the (plain) carbon steel alloy, whose stress strain behavior may be observed in the “Tensile Tests” module of Virtual Materials Science and Engineering (VMSE), determine the following:(a) The approximate yield strength,(b) The tensile strength, and(c) The approximate ductility, in percent
A cylindrical metal specimen having an original diameter of 12.8 mm (0.505 in.) and gauge length of 50.80 mm (2.000 in.) is pulled in tension until fracture occurs. The diameter at the point of fracture is 6.60 mm (0.260 in.), and the fractured gauge length is 72.14 mm (2.840 in.). Calculate the
Calculate the moduli of resilience for the materials having the stress?strain behaviors shown in Figures 6.12 and 6.21.
Determine the modulus of resilience for each of the following alloys Use modulus of elasticity values in Table 6.1.
A brass alloy to be used for a spring application must have a modulus of resilience of at least 0.75MPa (110psi). What must be its minimum yield strength?

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