Fundamentals of Materials Science and Engineering: An Integrated Approach, 3e

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160 • Chapter 5 / Imperfections in Solids

centimeter,N 1 , for an alloy composed of two

types of atoms. This computation is possible

using the following expression:

C 1 =

100

1 +

NAρ 2

N 1 A 1

−

ρ 2

ρ 1

(5.22)

where

NA=Avogadro’s number

ρ 1 andρ 2 =densities of the two elements

A 1 andA 2 =the atomic weights of the two el-

ements

Derive Equation 5.22 using Equation 5.2 and

expressions contained in Section 5.6.

5.15Germanium forms a substitutional solid solu-

tion with silicon. Compute the weight percent

of germanium that must be added to silicon

to yield an alloy that contains 2.43× 1021 Ge

atoms per cubic centimeter. The densities of

pure Ge and Si are 5.32 and 2.33 g/cm^3 , re-

spectively.

5.16Iron and vanadium both have the BCC crys-

tal structure, and V forms a substitutional

solid solution for concentrations up to approx-

imately 20 wt% V at room temperature. Com-

pute the unit cell edge length for a 90 wt%

Fe–10 wt% V alloy.

Interfacial Defects

5.17For an FCC single crystal, would you expect

the surface energy for a (100) plane to be

greater or less than that for a (111) plane?

Why? (Note:You may want to consult the

solution to Problem W3.45, found on the

book’s Web site.)

5.18 (a)For a given material, would you expect the

surface energy to be greater than, the same

as, or less than the grain boundary energy?

Why?

(b)The grain boundary energy of a small-

angle grain boundary is less than for a

high-angle one. Why is this so?

5.19For each of the following stacking sequences

found in FCC metals, cite the type of planar

defect that exists:

(a)...ABCABCBACBA...

(b)...ABCABCBCABC...

Now, copy the stacking sequences and indicate

the position(s) of planar defect(s) with a ver-

tical dashed line.

Grain Size Determination

5.20 (a)Employing the intercept technique, de-

termine the average grain size for the

steel specimen whose microstructure is

shown in Figure 10.29(a); use at least seven

straight-line segments.

(b)Estimate the ASTM grain size number for

this material.

5.21For an ASTM grain size of 6, approximately

how many grains would there be per square

inch at

(a)a magnification of 100, and

(b)without any magnification?

5.22Determine the ASTM grain size number if 25

grains per square inch are measured at a mag-

nification of 75.

DESIGN PROBLEMS

Specification of Composition

5.D1Aluminum–lithium alloys have been devel-

oped by the aircraft industry to reduce the

weight and improve the performance of its

aircraft. A commercial aircraft skin material

having a density of 2.47 g/cm^3 is desired. Com-

pute the concentration of Li (in wt%) that is

required.

5.D2Gallium arsenide (GaAs) and indium ar-

senide (InAs) both have the zinc blende crys-

tal structure and are soluble in each other at

all concentrations. Determine the concentra-

tion in weight percent of InAs that must be

added to GaAs to yield a unit cell edge length

of 0.5820 nm. The densities of GaAs and InAs

are 5.316 and 5.668 g/cm^3 , respectively.