Page 164 - Materials Science and Engineering An Introduction

136 • Chapter 4 / Imperfections in Solids

4.7 Which of the following systems (i.e., pair of met- 4.16 Calculate the composition, in weight percent, of
als) would you expect to exhibit complete solid an alloy that contains 105 kg of Fe, 0.2 kg of C,
solubility? Explain your answers. and 1.0 kg of Cr.
(a) Cr-V 4.17 What is the composition, in atom percent, of an
alloy that contains 33 g of Cu and 47 g of Zn?
(b) Mg-Zn
4.18 What is the composition, in atom percent, of an
(c) Al-Zr
alloy that contains 44.5 lb m of Ag, 83.7 lb m of Au,
(d) Ag-Au and 5.3 lb m of Cu?
(e) Pb-Pt 4.19 Convert the atom percent composition in
4.8 (a) Compute the radius r of an impurity atom Problem 4.18 to weight percent.
that will just fit into an FCC octahedral site in 4.20 Calculate the number of atoms per cubic meter
terms of the atomic radius R of the host atom in Pb.
(without introducing lattice strains).
4.21 Calculate the number of atoms per cubic meter
(b) Repeat part (a) for the FCC tetrahedral site. in Cr.
(Note: You may want to consult Figure 4.3a.)
4.22 The concentration of Si in an Fe-Si alloy is
4.9 Compute the radius r of an impurity atom that 0.25 wt%. What is the concentration in kilograms
will just fit into a BCC tetrahedral site in terms of Si per cubic meter of alloy?
of the atomic radius R of the host atom (without 4.23 The concentration of P in Si is 1.0 10 at%.
7
introducing lattice strains). (Note: You may want What is the concentration in kilograms of P per
to consult Figure 4.3b.)
cubic meter?
4.10 (a) Using the result of Problem 4.8(a), compute 4.24 Determine the approximate density of a Ti-6Al-4V
the radius of an octahedral interstitial site in FCC titanium (Ti) alloy that has a composition of 90 wt%
iron.
Ti, 6 wt% Al, and 4 wt% V.
(b) On the basis of this result and the answer to 4.25 Calculate the unit cell edge length for an 80 wt% Ag-
Problem 4.9, explain why a higher concentration 20 wt% Pd alloy. All of the palladium is in solid solu-
of carbon will dissolve in FCC iron than in iron tion, the crystal structure for this alloy is FCC, and the
that has a BCC crystal structure.
3
room-temperature density of Pd is 12.02 g/cm .
4.11 (a) For BCC iron, compute the radius of a tetrahe- 4.26 Some hypothetical alloy is composed of 25 wt%
dral interstitial site. (See the result of Problem 4.9.)
of metal A and 75 wt% of metal B. If the densi-
3
(b) Lattice strains are imposed on iron atoms ties of metals A and B are 6.17 and 8.00 g/cm ,
surrounding this site when carbon atoms occupy respectively, and their respective atomic weights
it. Compute the approximate magnitude of this are 171.3 and 162.0 g/mol, determine whether the
strain by taking the difference between the carbon crystal structure for this alloy is simple cubic, face-
atom radius and the site radius and then dividing centered cubic, or body-centered cubic. Assume a
this difference by the site radius. unit cell edge length of 0.332 nm.

Specification of Composition 4.27 For a solid solution consisting of two elements
(designated 1 and 2), sometimes it is desirable to
4.12 Derive the following equations: determine the number of atoms per cubic centim-
(a) Equation 4.7a eter of one element in a solid solution, N 1 , given
the concentration of that element specified in
(b) Equation 4.9a
weight percent, C 1 . This computation is possible
(c) Equation 4.10a using the following expression:
(d) Equation 4.11b N A C 1
N 1 = (4.21)
4.13 What is the composition, in atom percent, of an C 1 A 1 A 1
alloy that consists of 92.5 wt% Ag and 7.5 wt% + (100 - C 1 )
r 1 r 2
Cu?
where N A is Avogadro’s number, r 1 and r 2 are the
4.14 What is the composition, in atom percent, of an densities of the two elements, and A 1 is the atomic
alloy that consists of 5.5 wt% Pb and 94.5 wt% Sn?
weight of element 1.
4.15 What is the composition, in weight percent, of Derive Equation 4.21 using Equation 4.2 and
an alloy that consists of 5 at% Cu and 95 at% Pt? expressions contained in Section 4.4.