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physics
modern physics

Questions and Answers of Modern Physics

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:
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,
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
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
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
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
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
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
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
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
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
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
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)
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
(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
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
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
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,
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
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
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
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
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
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
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
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
(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
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
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
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)
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
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
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
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,
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
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
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
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
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
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,
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
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
(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
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)
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
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
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
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
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+
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
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
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
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
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
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
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
(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
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
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
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
The flexural strength and associated volume fraction porosity for two specimens of the same ceramic material are as follows:σfs (MPa) _____________ P70 ........................... 0.1060
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
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
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
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
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
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
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
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,
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)
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

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