《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

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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.

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:

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

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.

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

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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 _ phase of composition 92 wt% Ag–8

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