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engineering
materials science engineering

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

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.
(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 accept or impurity atom.
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 aresubstitutional.
(a) The room-temperature electrical conductivity of a silicon specimen is 5.93 x 10???3 (?-m)???1. The hole concentration is known to be 7.0 x 1017 m???3. Using the electron and hole mobilities for silicon in Table 18.3, compute the electron concentration. (b) On the basis of the result in part
Germanium to which 5 ( 1022 m-3 Sb atoms have been added is an extrinsic semiconductor at room temperature, and virtually all the Sb atoms may be thought of as being ionized (i.e., one charge carrier exists for each Sb atom).(a) Is this material n-type or p-type?(b) Calculate the electrical
The following electrical characteristics have been determined for both intrinsic and p-type extrinsic indium phosphide (InP) at room temperature: Calculate electron and holemobilities.
Calculate the conductivity of intrinsic silicon at 100°C.
At temperatures near room temperature, the temperature dependence of the conductivity for intrinsic germanium is found to equal where C is a temperature-independent constant and T is in Kelvins. Using Equation 18.36, calculate the intrinsic electrical conductivity of germanium at150°C.
Using Equation 18.36 and the results of Problem 18.33, determine the temperature at which the electrical conductivity of intrinsic germanium is 22.8 (?-m)???1.
Estimate the temperature at which GaAs has an electrical conductivity of 3.7 3 1023 (V-m)21 assuming the temperature dependence for of Equation 18.36. The data shown in Table 18.3 might prove helpful.
Compare the temperature dependence of the conductivity for metals and intrinsic semiconductors. Briefly explain the difference in behavior.
Calculate the room-temperature electrical conductivity of silicon that has been doped with 5 ( 1022 m–3 of boron atoms.
Calculate the room-temperature electrical conductivity of silicon that has been doped with 2 × 1023 m–3 of arsenic atoms.
Estimate the electrical conductivity, at 125°C, of silicon that has been doped with 1023 m–3 of aluminum atoms.
Estimate the electrical conductivity, at 85°C, of silicon that has been doped with 1020 m–3 of phosphorus atoms.
Some hypothetical metal is known to have an electrical resistivity of 4 x 10-8 (-m). Through a specimen of this metal that is 25 mm thick is passed a current of 30 A; when a magnetic field of 0.75 tesla is simultaneously imposed in a direction perpendicular to that of the current, a Hall voltage of
Some metal alloy is known to have electrical conductivity and electron mobility values of 1.5 x 107 (ohm-m)-1 and 0.0020 m2/V-s, respectively. Through a specimen of this alloy that is 35 mm thick is passed a current of 45 A. What magnetic field would need to be imposed to yield a Hall voltage of
How is the energy in the reaction described by Equation 18.21 dissipated?
What are the two functions that a transistor may perform in an electronic circuit?
We noted in Section 12.5 (Figure) that in FeO (wüstite), the iron ions can exist in both Fe2+ and Fe3+ states. The number of each of these ion types depends on temperature and the ambient oxygen pressure. Furthermore, we also noted that in order to retain electroneutrality, one Fe2+ vacancy will
At temperatures between 775°C (1048 K) and 1100°C (1373 K), the activation energy and preexponential for the diffusion coefficient 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 1000°C (1273 K).
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?
A parallel-plate capacitor with dimensions of 100 mm by 25 mm and a plate separation of 3 mm must have a minimum capacitance of 38 pF (3.8 ( 10-11 F) when an ac potential of 500 V is applied at a frequency of 1 MHz. Which of those materials listed in Table 18.5 are possible candidates? Why?
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 8.0 ( 10-9 C to be stored
For NaCl, the ionic radii for Na+ and Cl- ions are 0.102 and 0.181 nm, respectively. If an externally applied electric field produces a 5% expansion of the lattice, compute the dipole moment for each Na+–Cl- pair. Assume that this material is completely unpolarized in the absence of an electric
The polarization P of a dielectric material positioned within a parallel-plate capacitor is to be 1.0 × 10-6 C/m2.(a) What must be the dielectric constant if an electric field of 5 × 104 V/m is applied?(b) What will be the dielectric displacement D?
A charge of 3.5 ( 10-11 C is to be stored on each plate of a parallel-plate capacitor having an area of 160 mm2 (0.25 in.2) and a plate separation of 3.5 mm (0.14 in.).(a) What voltage is required if a material having a dielectric constant of 5.0 is positioned within the plates?(b) What voltage
(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)
(a) Compute the magnitude of the dipole moment associated with each unit cell of BaTiO3, as illustrated in Figure. (b) Compute the maximum polarization that is possible for thismaterial.
The dielectric constant for a soda–lime glass measured at very high frequencies (on the order of 1015 Hz) is approximately 2.3. What fraction of the dielectric constant at relatively low frequencies (1 MHz) is attributed to ionic polarization? Neglect any orientation polarization contributions.
Briefly explain why the ferroelectric behavior of BaTiO3 ceases above its ferroelectric Curie temperature.
Using information contained in Figures 18.8, determine the electrical conductivity of an 80 wt% Cu-20 wt% Zn alloy at -150oC (-240oF).
Is it possible to alloy copper with nickel to achieve a minimum tensile strength of 375MPa (54,400psi) and yet maintain an electrical conductivity of 2.5 x 106 (ohm-m)-1? If not, why? If so, what concentration of nickel is required? You may want to consult Figure a.
Specify an acceptor impurity type and concentration (in weight percent) that will produce a p-type silicon material having a room temperature electrical conductivity of 50 (ohm-m)-1.
One integrated circuit design calls for diffusing boron into very high purity silicon at an elevated temperature. It is necessary that at a distance 0.2 ?m from the surface of the silicon wafer, the room-temperature electrical conductivity be 1.2 x 103 (ohm-m)-1. The concentration of B at the
Problem 18.47 noted that FeO (wustite) may behave as a semiconductor by virtue of the transformation of Fe2+ to Fe3+ and the creation of Fe2+ vacancies; the maintenance of electro neutrality requires that for every two Fe3+ ions, one vacancy is formed. The existence of these vacancies is reflected
One of the procedures in the production of integrated circuits is the formation of a thin insulating layer of SiO2 on the surface of chips (see Figure 18.26). This is accomplished by oxidizing the surface of the silicon by subjecting it to an oxidizing atmosphere (i.e., gaseous oxygen or water
The base semiconducting material used in virtually all of our modern integrated circuits is silicon. However, silicon has some limitations and restrictions. Write an essay comparing the properties and applications (and/or potential applications) of silicon and gallium arsenide.
Estimate the energy required to raise the temperature of 2 kg (4.42lbm) of the following materials from 20 to 100°C (68 to 212°F): aluminum, steel, soda–lime glass, and high-density polyethylene.
To what temperature would 25lbm of a 1025 steel specimen at 25oC (77oF) be raised if 125 Btu of heat is supplied?
(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?
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.
The constant A in Equation 19.2 is 12?4R/5 , where R is the gas constant and ?D is the Debye temperature (K). Estimate ?D for copper, given that the specific heat is 0.78 J/kg-K at 10 K.
(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.
An aluminum wire 10 m (32.8 ft) long is cooled from 38 to -1°C (100 to 30°F). How much change in length will it experience?
A 0.1 m (3.9 in.) rod of a metal elongates 0.2 mm (0.0079 in.) on heating from 20 to 100°C (68 to 212°F). Determine the value of the linear coefficient of thermal expansion for this material.
Compute the density for nickel at 500°C, given that its room-temperature density is 8.902 g/cm3. Assume that the volume coefficient of thermal expansion, αv, is equal to 3αl.
When a metal is heated its density decreases. There are two sources that give rise to this diminishment of ρ: (1) the thermal expansion of the solid, and (2) the formation of vacancies (Section 4.2). Consider a specimen of copper at room temperature (20°C) that has a density of 8.940 g/cm3.(a)
The difference between the specific heats at constant pressure and volume is described by the expression where ?v is the volume coefficient of thermal expansion, v0 is the specific volume (i.e., volume per unit mass, or the reciprocal of density), ? is the compressibility, and T is the absolute
(a) Calculate the heat flux through a sheet of steel 10 mm (0.39 in.) thick if the temperatures at the two faces are 300 and 100°C (572 and 212°F); assume steady-state heat flow. (b) What is the heat loss per hour if the area of the sheet is 0.25 m2 (2.7 ft2)? (c) What will be the heat loss per
(a) Would you expect Equation 19.7 to be valid for ceramic and polymeric materials? Why or why not?(b) Estimate the value for the Wiedemann??Franz constant L [in ?-W/(K)2] at room temperature (293 K) for the following nonmetals: silicon (intrinsic), glass-ceramic (Pyroceram), fused silica,
Briefly explain why the thermal conductivities are higher for crystalline than noncrystalline ceramics.
Briefly explain why metals are typically better thermal conductors than ceramic materials.
(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.
For some ceramic materials, why does the thermal conductivity first decrease and then increase with rising temperature?
For each of the following pairs of materials, decide which has the larger thermal conductivity. Justify your choices.(a) Pure copper; aluminum bronze (95 wt% Cu-5 wt% Al).(b) Fused silica; quartz.(c) Linear polyethylene; branched polyethylene.(d) Random poly(styrene-butadiene) copolymer;
We might think of a porous material as being a composite wherein one of the phases is a pore phase. Estimate upper and lower limits for the room-temperature thermal conductivity of a magnesium oxide material having a volume fraction of 0.30 of pores that are filled with still air.
Nonsteady-state heat flow may be described by the following partial differential equation:where DT is the thermal diffusivity; this expression is the thermal equivalent of Fick’s second law of diffusion (Equation 5.4b). The thermal diffusivity is defined according toIn this expression, k, ρ, and
Beginning with Equation 19.3, show that Equation 19.8 isvalid.
(a) Briefly explain why thermal stresses may be introduced into a structure by rapid heating or cooling.(b) For cooling, what is the nature of the surface stresses?(c) For heating, what is the nature of the surface stresses?
(a) If a rod of 1025 steel 0.5 m (19.7 in.) long is heated from 20 to 80°C (68 to 176°F) while its ends are maintained rigid, determine the type and magnitude of stress that develops. Assume that at 20°C the rod is stress free. (b) What will be the stress magnitude if a rod 1 m (39.4 in.) long
A copper wire is stretched with a stress of 70MPa (10,000psi) at 20°C (68°F). If the length is held constant, to what temperature must the wire be heated to reduce the stress to 35MPa (5000psi)?
If a cylindrical rod of nickel 100.00 mm long and 8.000 mm in diameter is heated from 20(C to 200(C while its ends are maintained rigid, determine its change in diameter. You may want to consult Table6.1.
The two ends of a cylindrical rod of 1025 steel 75.00 mm long and 10.000 mm in diameter are maintained rigid. If the rod is initially at 25(C, to what temperature must it be cooled to have a 0.008-mm reduction in diameter?
What measures may be taken to reduce the likelihood of thermal shock of a ceramic piece?
Railroad tracks made of 1025 steel are to be laid during the time of year when the temperature averages 10°C (50°F). If a joint space of 4.6 mm (0.180 in.) is allowed between the standard 11.9-m (39-ft) long rails, what is the hottest possible temperature that can be tolerated without the
The ends of a cylindrical rod 6.4 mm (0.25 in.) in diameter and 250 mm (10 in.) long are mounted between rigid supports. The rod is stress free at room temperature [20(C (68(F)]; and upon cooling to -40(C (-40(F), a maximum thermally induced tensile stress of 125MPa (18,125psi) is possible. Of
A coil of wire 0.20 m long and having 200 turns carries a current of 10 A. (a) What is the magnitude of the magnetic field strength H? (b) Compute the flux density B if the coil is in a vacuum. (c) Compute the flux density inside a bar of titanium that is positioned within the coil. The
Demonstrate that the relative permeability and the magnetic susceptibility are related according to Equation 20.7.
It is possible to express the magnetic susceptibility ?m in several different units. For the discussion of this chapter, ?m was used to designate the volume susceptibility in SI units, that is, the quantity that gives the magnetization per unit volume (m3) of material when multiplied by H. The mass
(a) Explain the two sources of magnetic moments for electrons.(b) Do all electrons have a net magnetic moment? Why or why not?(c) Do all atoms have a net magnetic moment? Why or why not?
The magnetic flux density within a bar of some material is 0.435 tesla at an H field of 3.44 ( 105 A/m. Compute the following for this material: (a) The magnetic permeability, and (b) The magnetic susceptibility. (c) What type(s) of magnetism would you suggest is (are) being displayed by this
The magnetization within a bar of some metal alloy is 3.2 ( 105 A/m at an H field of 50 A/m. Compute the following: (a) The magnetic susceptibility, (b) The permeability, and (c) The magnetic flux density within this material. (d) What type(s) of magnetism would you suggest as being displayed by
Compute (a) The saturation magnetization and (b) The saturation flux density for cobalt, which has a net magnetic moment per atom of 1.72 Bohr magnetons and a density of 8.90 g/cm3.
Confirm that there are 2.2 Bohr magnetons associated with each iron atom, given that the saturation magnetization is 1.70 ( 106 A/m, that iron has a BCC crystal structure, and that the unit cell edge length is 0.2866 nm.
Assume there exists some hypothetical metal that exhibits ferromagnetic behavior and that has (1) a simple cubic crystal structure (Figure), (2) an atomic radius of 0.153 nm, and (3) a saturation flux density of 0.76 tesla. Determine the number of Bohr magnetons per atom for thismaterial.
There is associated with each atom in paramagnetic and ferromagnetic materials a net magnetic moment. Explain why ferromagnetic materials can be permanently magnetized whereas paramagnetic ones cannot.
Consult another reference in which Hund??s rule is outlined, and on its basis explain the net magnetic moments for each of the cations listed in Table20.4.
Estimate (a) The saturation magnetization, and (b) The saturation flux density of nickel ferrite [(NiFe2O4)8], which has a unit cell edge length of 0.8337 nm.
The chemical formula for manganese ferrite may be written as (MnFe2O4)8 because there are eight formula units per unit cell. If this material has a saturation magnetization of 5.6 ( 105 A/m and a density of 5.00 g/cm3, estimate the number of Bohr magnetons associated with each Mn2+ ion.
The formula for yttrium iron garnet (Y3Fe5O12) may be written in the form EMBED Equation.3 , where the superscripts a, c, and d represent different sites on which the Y3+ and Fe3+ ions are located. The spin magnetic moments for the Y3+ and Fe3+ ions positioned in the a and c sites are oriented
Briefly explain why the magnitude of the saturation magnetization decreases with increasing temperature for ferromagnetic materials, and why ferromagnetic behavior ceases above the Curie temperature.
A coil of wire 0.1 m long and having 15 turns carries a current of 1.0 A. (a) Compute the flux density if the coil is within a vacuum. (b) A bar of an iron???silicon alloy, the B-H behavior for which is shown in Figure, is positioned within the coil. What is the flux density within this bar? (c)
A ferromagnetic material has a remanence of 1.25 teslas and a coercivity of 50,000 A/m. Saturation is achieved at a magnetic field intensity of 100,000 A/m, at which the flux density is 1.50 teslas. Using these data, sketch the entire hysteresis curve in the range H = –100,000 to +100,000 A/m. Be
The following data are for a transformer steel: (a) Construct a graph of B versus H. (b) What are the values of the initial permeability and initial relative permeability? (c) What is the value of the maximum permeability? (d) At about what H field does this maximum permeability occur? (e) To what
An iron bar magnet having a coercivity of 4000 A/m is to be demagnetized. If the bar is inserted within a cylindrical wire coil 0.15 m long and having 100 turns, what electric current is required to generate the necessary magnetic field?
A bar of an iron???silicon alloy having the B???H behavior shown in Figure is inserted within a coil of wire 0.20 m long and having 60 turns, through which passes a current of 0.1 A. (a) What is the B field within this bar? (b) At this magnetic field, (i) What is the permeability? (ii) What is the
Estimate saturation values of H for single-crystal iron in [100], [110], and [111] directions
The energy (per unit volume) required to magnetize a ferromagnetic material to saturation (Es) is defined by the following equation: That is, Es is equal to the product of ?0 and the area under an M versus H curve, to the point of saturation referenced to the ordinate (or M) axis'for example, in
Cite the differences between hard and soft magnetic materials in terms of both hysteresis behavior and typical applications.
Assume that the commercial iron (99.95 wt% Fe) in Table 20.5 just reaches the point of saturation when inserted within the coil in Problem 20.1. Compute the saturationmagnetization.
Figure shows the B-versus-H curve for a steel alloy. (a) What is the saturation flux density? (b) What is the saturation magnetization? (c) What is the remanence? (d) What is the coercivity? (e) On the basis of data in Tables 20.5 and 20.6, would you classify this material as a soft or hard
For a superconducting material at a temperature T below the critical temperature TC, the critical field HC (T), depends on temperature according to the relationship where HC(0) is the critical field at 0 K. (a) Using the data in Table 20.7, calculate the critical magnetic fields for tin at 1.5 and
Using Equation 20.14, determine which of the superconducting elements in Table 20.7 are superconducting at 3 K and in a magnetic field of 15,000A/m.
Cite the differences between type I and type II superconductors.
Briefly describe the Meissner effect.
Cite the primary limitation of the new superconducting materials that have relatively high critical temperatures.
A cobalt–nickel alloy is desired that has a saturation magnetization of 1.3 × 106 A/m. Specify its composition in weight percent nickel. Cobalt has an HCP crystal structure with c/a ratio of 1.623, whereas the maximum solubility of Ni in Co at room temperature is approximately 35 wt%. Assume

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