Maestro

9
Solid Solutions and Phase Equilibrium
9–15 The unary phase diagram for SiO2 is shown in Figure 9–3(c). Locate the triple point where solid, liquid, and vapor coexist and give the temperature and the type of solid present. What do the other “triple” points indicate? Solution: (a) The solid-liquid-vapor triple point occurs at 1713 C; the solid phase present at this point is b-cristobalite. (b)The other triple points describe the equilibrium between two solids and a vapor phase. 9–34 Based on Hume-Rothery’s conditions, which of the following systems would be expected to display unlimited solid solubility? Explain. (a) Au–Ag (e) Mo–Ta Solution: (a) rAu rAg ¢r (b) rAl rCu ¢r (c) rAl rAu ¢r (d) rU rW ¢r (b) Al–Cu (f) Nb–W 1.442 1.445 0.2% v v (c) Al–Au (g) Mg–Zn 1 1 3 1 3 1 4 4 FCC FCC YesFCC FCC No FCC FCC No Ortho FCC No (d) U–W (h) Mg–Cd

1.432 v 1.278 v 10.7% 1.432 1.442 0.7% 1.38 1.371 0.7% v v v v

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The Science and Engineering of Materials (e) rMo rTa ¢r (f) rNb rW ¢r (g) rMg rZn ¢r (h) rMg rCd ¢r 1.363 v 1.43 v 4.7% 1.426 1.371 3.9% v v

Instructor’s Solution Manual 4 5 4 4 2 2 2 2 BCC BCC No BCC BCC Yes HCP HCP No HCP HCP Yes

1.604 v 1.332 v 17% 1.604v 1.490 v 7.1%

The Au–Ag, Mo–Ta, and Mg–Cd systems have the required radius ratio, the same crystal structures, and the same valences. Each of these might be expected to display complete solid solubility. [The Au–Ag and Mo–Ta do have isomorphous phase diagrams. In addition, the Mg–Cd alloys all solidify like isomorphous alloys; however a number of solid state phase transformations complicatethe diagram.] 9–35 Suppose 1 at% of the following elements is added to copper (forming a separate alloy with each element) without exceeding the solubility limit. Which one would be expected to give the higher strength alloy? Is any of the alloying elements expected to have unlimited solid solubility in copper? (a) Au (b) Mn (c) Sr 1.278 Å rAu ¢r ¢r ¢r ¢r ¢r rCu 12.4% 68.3% 8.0% 2.0% rCu 12.8% Maybe Unlimited Solubility. Different structure. Highest Strength Different structure. Different structure. (d) Si (e) Co

Solution: For copper: rCu (a) Au: r (b) Mn: r (c) Sr: r (d) Si: r (e) Co: r

1.442 1.12 2.151 1.176 1.253

The Cu–Sr alloy would be expected to be strongest (largest size difference). The Cu–Au alloy satisfies Hume-Rothery’s conditions and might be expected to displaycomplete solid solubility—in fact it freezes like an isomorphous series of alloys, but a number of solid state transformations occur at lower temperatures. 9–36 Suppose 1 at% of the following elements is added to aluminum (forming a separate alloy with each element) without exceeding the solubility limit. Which one would be expected to give the least reduction in electrical conductivity? Is any of thealloy elements expected to have unlimited solid solubility in aluminum? (a) Li (b) Ba (c) Be (d) Cd (e) Ga

CHAPTER 9 Solution: For aluminum: r (a) Li: r (b) Ba: r (c) Be: r (d) Cd: r (e) Ga: r 1.519 2.176 1.143 1.49 1.218

Solid Solutions and Phase Equilibrium

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1.432 Å (FCC structure with valence of 3) ¢r ¢r ¢r ¢r ¢r 6.1% 52.0% 20.2% 4.1% 14.9% BCC BCC HCP HCP Orthorhombic valencevalence valence valence valence 1 2 2 2 3

The cadmium would be expected to give the smallest reduction in electrical conductivity, since the Cd atoms are most similar in size to the aluminum atoms. None are expected to have unlimited solid solubility, due either to difference in valence, atomic radius or crystal structure. 9–37 Which of the following oxides is expected to have the largest solidsolubility in Al2O3? (a) Y2O3 (b) Cr2O3 (c) Fe2O3 0.51 Å 0.63 0.51 0.51 23.5% 25.5% 100 74.5%

Solution: The ionic radius of Al3 (a) rY3 (b) rCr3 (c) rFe3 0.89 0.63 0.64 ¢r ¢r ¢r

We would expect Cr2O3 to have a high solubility in Al2O3; in fact, they are completely soluble in one another. 9–41 Determine the liquidus temperature, solidus temperature, and freezing range for the following...