O 3 5.30 Computer Problems

Fe-Fe 2 O 3 5.30 Computer Problems

Ce-Ce 2 O 3 6.86

Nb-Nb 2 O 5 4.47 23-41 Write a computer program that will W-WO 3 7.30 calculate the thickness of a coating using different inputs provided by the user

Problems 887

(e.g., density and valence of the metal, different temperatures. Explain the mecha- area or dimensions of the part being plated,

nism for this change. desired time of plating, and current).

K23-3 Five grams of zirconium are dissolved in 1000 g of water producing an electrolyte of Zr 4+ ions. Calculate the electrode

Problems

potential of the copper half-cell in this electrolyte at standard temperature and

K23-1 Describe the mechanism of stray current pressure using the Nernst equation. corrosion. K23-2 Describe how the corrosion rate of copper changes with increasing solution velocity at

Appendix A: Selected Physical Properties of Metals

Melting Atomic

Lattice

Atomic

Density Temperature Metal

g/mol

(g/cm 3 ) (°C)

2.699 660.4 Antimony

Aluminum Al

Arsenic As

Bismuth Bi

b = 6.117 c = 3.304

Boron

B 5 rhomb

Cesium Cs

Copper Cu

Ga 31 ortho

a = 4.5258

b = 4.5186 c = 7.6570

72.59 5.324 937.4 Gold

Germanium

Ge 32 DC 5.6575

19.302 1064.4 Hafnium

Au

79 FCC

Hf 72 HCP

a = 3.1883

c = 5.0422

Appendix A 889

Density Temperature Metal

g/mol

(g/cm 3 ) (°C)

Indium In

Iridium Ir

Lanthanum La

Manganese Mn

13.546 -38.9 Molybdenum

Hg 80 rhomb

Rhodium Rh

Selenium Se

b = 9.083 c = 11.60 ! = 90.8°

Silicon Si

4.84 (#557°C) Tantalum

Tellurium Te

Thorium Th

c = 3.182 DC 6.4912

Titanium Ti

3.32 (#882°C) (Continued)

890 APPENDIX A

Selected Physical Properties of Metals

Melting Atomic

Lattice

Atomic

Density Temperature Metal

g/mol

(g/cm 3 ) (°C)

Tungsten W

b = 5.869 c = 4.955

Zinc Zn

Zirconium Zr

40 HCP

a = 3.2312

91.22 6.505 1852

c = 5.1477

BCC

3.6090

(#862°C)

Appendix B: The Atomic and Ionic Radii of Selected Elements

Element

Valence

0.6 - 1 1.33 Gallium

1.35 - 1 2.20 Iron

Mercury 1.55 + 2 1.10 Molybdenum

+ 4 0.70 (Continued)

892 APPENDIX B

The Atomic and Ionic Radii of Selected Elements

Element

Valence

1.15 - 2 1.91 Silicon

1.06 - 2 1.84 Tantalum

1.43 + 5 0.68 Tellurium

1.40 - 2 2.11 Thorium

Note that 1 Å = 10 - 8 cm = 0.1 nanometer (nm)

CHAPTER 2 2-6

(i) 3.30 10 2 2 atoms/cm 3 . (ii) 4.63 * 10 22 atoms/cm * 3

2-7

(a) 9.78 10 27 atoms/ton. (b) 4.7 cm * 3

2-8

(a) 5.99 * 10 23 atoms. (b) 0.994 mol

2-24 MgO, MgO has ionic bonds. 2-25 Si, Si has covalent bonds.

CHAPTER 3

3-13 (a) 1.426 10 - 8 cm. (b) 1.4447 10 - * 8 * cm.

3-15 (a) 5.3349 . (b) 2.3101 . A ° A °

3-17 FCC. 3-19 BCT. 3-21 (a) 8 atoms/cell. (b) 0.387. 3-31 0.6% contraction.

3-41 A: C001D . B: C120D . C: C111D . D: C21 1D 3-43 A: 111 12 B: 10302 . C: 1102 2 . 3-45 A: C110D or C1100D . B: C111D or C112 3D . C: C011D or C1213D . 3-47 A: 111 012 . B: 100032 . C: 111 002 .

3-53 C110D , C110D , C101D , C101D , C011D , C011D . 3-55 Tetragonal—4; orthorhombic—2; cubic—12. 3-57 (a) (111). (b) (210). (c) 10122 . (d) (218). 3-59 [100]: 0.35089 nm, 2.85 nm –1 , 0.866. [110]: 0.496 nm, 2.015 nm –1 ,

0.612. [111]: 0.3039 nm –1 , 3.291 nm –1 , 1. The [111] is close packed. 3-61 (100): 1.617 10 15 /cm 2 , packing fraction 0.7854. (110): 1.144 10 15 * 2 * /cm , packing fraction 0.555.

(111): 1.867 * 10 15 /cm 2 , 0.907. The (111) is close packed.

3-63 4,563,000.

3-66 (a) 0.2978 . (b) 0.6290 . A ° A °

3-69 (a) 6. (c) 8. (e) 4. (h) 6.

3-72 Fluorite. (a) 5.2885 . (b) 12.13 g/cm A ° 3 . (c) 0.624. 3-74 Cesium chloride. (a) 4.1916 . (b) 4.8 g/cm A ° 3 . (c) 0.693.

3-76 (111): 1.473 10 15 /cm 2 * 2 , 0.202 (Mg + 2 ). (222): 1.473 15 * 10 /cm , 0.806 (O - 2 ). 3-81 0.40497 nm. 3-83 (a) BCC. (c) 0.2327 nm.

CHAPTER 4 4-2

4.98 * 10 19 vacancies/cm 3 .

4-4

(a) 0.00204. (b) 1.39 * 10 20 vacancies/cm 3 .

4-6

(a) 1.157 * 10 20 vacancies/cm 3 . (b) 0.532 g/cm 3 .

4-9

0.344. 4-11 8.262 g/cm 3 . 4-13 (a) 0.0449. (b) one H atom per 22.3 unit cells. 4-15 (a) 0.0522 defects/unit cell. (b) 2.47

20 * 3 10 defects/cm .

4-19 (a) C011D , C011D , C110D , C110D , C101D , C101D . (b) C111D , C111D , C111D , C111D .

4-21 11102 , 11102 , 10112 , 10112 , 11012 , 11012 . 4-23 11112 C110D :b

= 2.863 , d A = 2.338 . A ° 11102 C111D :

b = 7.014 , d A °

2.863 . Ratio A = ° = 0.44.

4-42 (a) K =

19.4 psi 1 m, s 0 = 60, 290 psi. (b) 103,670 psi.

4-44 (a) 128 grains/in 2 . (b) 1,280,000 grains/in 2 .

4-46 3.6. 4-52 284 . A °

CHAPTER 5 5-9

1.08 * 9 10 jumps/s. 5-16 D –4 cm H 2 = 1.07 * 10 /s versus D N = 3.9 * 10 –9 cm 2 /s. Smaller H atoms diffuse more rapidly.

5-18 (a) 59,390 cal/mol. (b) 0.057 cm 2 /s.

5-24 (a) 0.02495 at% Sb/cm. (b) 1.246 10 19 - 3 - * Sb/(cm # cm).

5-26 (a) 1.969 - * 10 11 H atoms/(cm 3 # cm). (b) 3.3 * 10 7 H atoms/(cm 2 # s).

5-28 1.25 10 * –3 g/h. 5-30 - 198 C. °

5-42 D 0 = 3.47 * 10 –16 cm 2 /s versus D A1 = 2.48 * 10 –13 cm 2 /s. It is easier

for the smaller Al ions to diffuse.

5-43

0.01 cm: 0.87% C. 0.05 cm: 0.43% C. 0.10 cm: 0.16% C. 5-45 907 C. ° 5-47 0.53% C. 5-49 190 s. 5-51 1184 s. 5-53 667 C. ° 5-61 50,488 cal/mol; yes.

CHAPTER 6

6-21 (a) Deforms. (b) Does not neck. 6-22 (b) 10 lb or 4891 N. 6-24 20,000 lb. 6-26 50.0543 ft. 6-32 (a) 11,600 psi. (b) 13,210 psi. (c) 603,000 psi. (d) 4.5%. (e) 3.5%. (f) 11,300 psi. (g) 11,706 psi.

(h) 76.4 psi. 6-34 (a) 274 MPa. (b) 417 MPa. (c) 172 GPa. (d) 18.55%. (e) 15.8%. (f) 397.9 MPa. (g) 473 MPa.

(h) 0.17 MPa.

6-35 (a) l f = 12.00298 in., d f = 0.39997 in.

6-40 (a) 76,800 psi. (b) 22.14

* 6 10 psi.

6-42 (a) 41 mm; will not fracture.

6-50

29.8 kg/mm 2 .

6-61 Not notch-sensitive; poor toughness.

CHAPTER 7 7-4

0.99 MPa 1 m .

7-5

No; test will not be sensitive enough.

7-22

15.35 lb. 7-24 d = 1.634 in.

7-26

22 MPa; max =+ 22 MPa, min =- 22 MPa, mean = 0 MPa; a higher frequency will reduce fatigue strength due to heating.

7-28 (a) 2.5 mm. (b) 0.0039 mm.

7-32 C = 2.061 * 10 –3 ;n = 3.01.

7-43 101,329 h. 7-45 n =

6.82. m =- 5.7.

0.52 in. 7-51 2000 lb.

CHAPTER 8 8-5

(a) 1 – the slope is steeper. (b) 1 – it is stronger. (c) 2 – it is more ductile and less strong.

8-7

n ! 0.12; BCC. 8-11 n ! 0.15. 8-12 0.56. 8-22 0.152 in. 8-24 25,000 psi tensile, 21,000 psi yield, 6% elongation. 8-26 First step: 36% CW giving 25,000 psi tensile, 21,000 psi yield, 6% elongation. Second step: 64% CW

giving 28,000 psi tensile, 25,000 psi yield, 4% elongation. Third step: 84% CW giving 30,000 psi ten- sile, 28,000 psi yield, 3% elongation.

0.76 to 0.96 in. 8-30 48% CW, 26,000 psi tensile, 23,000 psi yield, 4% elongation. 8-45 (a) 1414 lb. (b) Will not break. 8-58 (a) 550°C, 750°C, 950°C. (b) 700°C. (c) 900°C. (d) 2285°C. 8-68 Slope ! 0.4. Yes.

8-28

CHAPTER 9

9-11 (a) 6.65 Å. (b) 109 atoms.

9-13 1.136 " 10 6 atoms.

9-30 (a) 0.0333. (b) 0.333. (c) All. 9-31 1265°C.

B ! 300 s/cm 2 , n ! 1.6.

9-40 (a) ~4.16 " 10 #3 cm. (b) 90 s.

9-42

c ! 0.003 s, m ! 0.35.

9-44

0.03 s. 9-50 (a) 900°C. (b) 430°C. (c) 470°C. (d) ~250°C/min. (e) 9.7 min.

(f) 8.1 min. (g) 60°C. (h) Zinc. (i) 87.3 min/in 2 .

9-60 V/A (riser) ! 0.68, V/A (thick) ! 1.13, V/A (thin) ! 0.89; not effective. 9-62 D Cu !

1.48 in. D Fe !

1.30 in.

9-64 (a) 46 cm 3 . (b) 4.1%.

9-69

23.04 cm. 9-72 0.046 cm 3 /100 g Al.

CHAPTER 10

10-23 (a) Yes. (c) No. (e) No. (g) No. 10-26 Cd should give the smallest decrease in conductivity; none should give unlimited solid solubility. 10-33 (a) 2330°C, 2150°C, 180°C. (c) 2570°C, 2380°C, 190°C. 10-35 (a) 100% L containing 30% MgO. (b) 70.8% L containing 38% MgO, 29.2% S containing 62%

MgO. (c) 8.3% L containing 38% MgO, 91.7% S containing 62% MgO. (d) 100% S containing 85% MgO.

10-38 (a) L: 15 mol% MgO or 8.69 wt% MgO. S: 38 mol% MgO or 24.85 wt% MgO. (b) L: 78.26 mol% or 80.1 wt%; S: 21.74 mol% or 19.9 wt% MgO. (c) 78.1 vol% L, 21.9 vol% S.

10-40 750 g Ni, Ni/Cu ! 1.62. 10-42 331 g MgO.

10-44

64.1 wt% FeO. 10-46 (a) 49 wt% W in L, 70 wt% W in \$. (b) Not possible. 10-48 212 lb W; 1200 lb W. 10-50 Ni dissolves; when the liquid reaches 10 wt% Ni, the bath begins to freeze. 10-54 (a) 2900°C, 2690°C, 210°C. (b) 60% L containing 49% W, 40% \$ containing 70% W. 10-56 (a) 55% W. (b) 18% W. 10-60 (a) 2900°C. (b) 2710°C. (c) 190°C. (d) 2990°C. (e) 90°C. (f) 300 s. (g) 340 s. (h) 60% W. 10-63 (a) 2000°C. (b) 1450°C. (c) 550°C. (d) 40% FeO. (e) 92% FeO.

(f) 65.5% L containing 75% FeO, 34.5% S containing 46% FeO. (g) 30.3% L containing 88% FeO, 69.7% S containing 55% FeO.

10-64 (a) 3100°C. (b) 2720°C. (c) 380°C. (d) 90% W. (e) 40% W. (f) 44.4% L containing 70% W, 55.6% \$ containing 88% W. (g) 9.1% L containing 50% W, 90.9% \$ containing 83% W.

CHAPTER 11

11-7 (a) %, nonstoichiometric. (b) \$,&,',(. B is allotropic, existing in three different forms at different temperatures. (c) 1100°C: peritectic. 900°C: monotectic. 690°C: eutectic. 600°C: peritectoid. 300°C: eutectoid.

11-10 (c) SnCu 3 . 11-11 SiCu 4. 11-13 (a) 2.5% Mg. (b) 600°C, 470°C, 400°C, 130°C. (c) 74% \$ containing 7% Mg, 26% L containing 26%

Mg. (d) 100% \$ containing 12% Mg. (e) 67% \$ containing 1% Mg, 33% & containing 34% Mg. 11-15 (a) Hypereutectic. (b) 98% Sn. (c) 22.8% & containing 97.5% Sn, 77.2% L containing 61.9% Sn.

(d) 35% \$ containing 19% Sn, 65% & containing 97.5% Sn. (e) 22.8% primary & containing 97.5% Sn, 77.2% eutectic containing 61.9% Sn. (f) 30% \$ containing 2% Sn, 70% & containing 100% Sn.

11-19 (a) Hypoeutectic. (b) 1% Si. (c) 78.5% \$ containing 1.65% Si, 21.5% L containing 12.6% Si

(d) 97.6% \$ containing 1.65% Si, 2.4% & containing 99.83% Si. (e) 78.5% primary \$ containing 1.65% Si, 21.5% eutectic containing 12.6% Si. (e) 21.5% eutectic containing 12.6% Si. (f) 96% \$

containing 0% Si, 4% & containing 100% Si. 11-21 56% Sn, hypoeutectic. 11-23 52% Sn. 11-25 17.5% Li, hypereutectic. 11-27 60.5% \$, 39.5% &; 27.7% primary \$, 72.3% eutectic; 0.54. 11-29 (a) 1150°C. (b) 150°C. (c) 1000°C. (d) 577°C. (e) 423°C.

(f) 10.5 min. (g) 11.5 min. (h) 45% Si.

CHAPTER 12 12-3

c ! 8.9 " 10 #6 , n ! 2.81. 12-24 (a) For Al – 4% Mg: solution treat between 210 and 451°C, quench, and age below 210°C. For Al – 6%

Mg: solution treat between 280 and 451°C, quench, and age below 280°C. For Al – 12% Mg: solution treat between 390 and 451°C, quench, and age below 390°C. (c) The precipitates are not coherent.

12-36 (a) Solution treat between 290 and 400°C, quench, and age below 290°C. (c) Not a good candidate. (e) Not a good candidate.

12-49 (a) 795°C. (b) Primary ferrite. (c) 56.1% ferrite containing 0.0218% C and 43.9% austenite contain- ing 0.77% C. (d) 95.1% ferrite containing 0.0218% C and 4.9% cementite containing 6.67% C. (e) 56.1% primary ferrite containing 0.0218% C and 43.9% pearlite containing 0.77% C.

12-51 0.53% C, hypoeutectoid. 12-53 0.156% C, hypoeutectoid. 12-55 0.281% C. 12-57 760°C, 0.212% C. 12-61 (a) 900°C; 12% CaO in tetragonal, 3% CaO in monoclinic, 16% CaO in cubic; 30.8% monoclinic,

69.2% cubic. (c) 250°C; 47% Zn in &), 36% Zn in \$, 59% Zn in '; 52.2% \$, 47.8% '. 12-71 (a) 615°C. (b) 1.67 " 10 #5 cm. 12-73 Bainite with HRC 47. 12-75 Martensite with HRC 66. 12-84 (a) 37.2% martensite with 0.77% C and HRC 65.

(c) 84.8% martensite with 0.35% C and HRC 58. 12-86 (a) 750°C. (b) 0.455% C. 12-88 ~3% expansion. 12-90 Austenitize at 750°C, quench, and temper above 330°C.

CHAPTER 13

13-3 (a) 97.8% ferrite, 2.2% cementite, 82.9% primary ferrite, 17.1% pearlite. (c) 85.8% ferrite, 14.2% cementite, 3.1% primary cementite, 96.9% pearlite.

13-8 For 1035: A 1 ! 727°C; A 3 ! 790°C; anneal ! 820°C; normalize ! 845°C; process anneal ! 557 – 647°C; not usually spheroidized.

13-12 (a) Ferrite and pearlite. (c) Martensite. (e) Ferrite and bainite. (g) Tempered martensite.

13-14 (a) Austenitize at 820°C, hold at 600°C for 10 s, cool. (c) Austenitize at 780°C, hold at 600°C for 10 s, cool. (e) Austenitize at 900°C, hold at 320°C for 5000 s, cool.