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

GTBL042-03 GTBL042-Callister-v3 September 24, 2007 19:46

3rd Revise Page

52 • Chapter 3 / Structures of Metals and Ceramics

EXAMPLE PROBLEM 3.5

Ceramic Crystal Structure Prediction

On the basis of ionic radii (Table 3.4), what crystal structure would you predict

for FeO?

Solution

First, note that FeO is an AX-type compound. Next, determine the cation–anion

radius ratio, which from Table 3.4 is

rFe 2 +

rO 2 −

=

0 .077 nm

0 .140 nm

= 0. 550

This value lies between 0.414 and 0.732, and, therefore, from Table 3.3 the

coordination number for the Fe^2 +ion is 6; this is also the coordination number

of O^2 −, since there are equal numbers of cations and anions. The predicted

crystal structure will be rock salt, which is the AX crystal structure having a

coordination number of 6, as given in Table 3.5.

Concept Check 3.1

Table 3.4 gives the ionic radii for K+and O^2 −as 0.138 and 0.140 nm, respectively.

(a)What would be the coordination number for each O^2 −ion?

(b)Briefly describe the resulting crystal structure for K 2 O.

(c)Explain why this is called the antifluorite structure.

[The answer may be found at http://www.wiley.com/college/callister (Student Companion Site).]

3.7 DENSITY COMPUTATIONS—CERAMICS

It is possible to compute the theoretical density of a crystalline ceramic material

from unit cell data in a manner similar to that described in Section 3.5 for metals. In

this case the densityρmay be determined using a modified form of Equation 3.5, as

follows:

ρ=

n′(

∑

AC+

∑

AA)

VCNA

(3.6)

Theoretical density

for ceramic materials

where

n′=the number of formula units^2 within the unit cell

AC=the sum of the atomic weights of all cations in the formula unit

AA=the sum of the atomic weights of all anions in the formula unit

VC=the unit cell volume

NA=Avogadro’s number, 6.02× 1023 formula units/mol

(^2) By “formula unit” we mean all the ions that are included in the chemical formula unit. For
example, for BaTiO 3 , a formula unit consists of one barium ion, a titanium ion, and three
oxygen ions.