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

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3.6 Ceramic Crystal Structures • 45

atomic weightACuis given as 63.5 g/mol. The unit cell volumeVCfor FCC was

determined in Example Problem 3.1 as 16R^3

√

2, whereR, the atomic radius, is

0.128 nm.

Substitution for the various parameters into Equation 3.5 yields

ρ=

nACu

VCNA

=

nACu

(16R^3

√

2)NA

=

(4 atoms/unit cell)(63.5g/mol)

[16

√

2(1. 28 × 10 −^8 cm)

3

/unit cell](6. 02 × 1023 atoms/mol)

= 8 .89 g/cm^3

The literature value for the density of copper is 8.94 g/cm^3 , which is in very

close agreement with the foregoing result.

3.6 CERAMIC CRYSTAL STRUCTURES

Because ceramics are composed of at least two elements and often more, their crystal

structures are generally more complex than those of metals. The atomic bonding in

these materials ranges from purely ionic to totally covalent; many ceramics exhibit

a combination of these two bonding types, the degree of ionic character being de-

pendent on the electronegativities of the atoms. Table 3.2 presents the percent ionic

character for several common ceramic materials; these values were determined using

Equation 2.10 and the electronegativities in Figure 2.7.

For those ceramic materials for which the atomic bonding is predominantly ionic,

the crystal structures may be thought of as being composed of electrically charged

cation ions instead of atoms. The metallic ions, orcations,are positively charged, because

anion they have given up their valence electrons to the nonmetallic ions, oranions,which are

negatively charged. Two characteristics of the component ions in crystalline ceramic

materials influence the crystal structure: the magnitude of the electrical charge on

each of the component ions, and the relative sizes of the cations and anions. With

regard to the first characteristic, the crystal must be electrically neutral; that is, all

the cation positive charges must be balanced by an equal number of anion negative

charges. The chemical formula of a compound indicates the ratio of cations to anions,

or the composition that achieves this charge balance. For example, in calcium fluoride,

Table 3.2 For Several Ceramic Materials,

Percent Ionic Character of

the Interatomic Bonds

Percent Ionic

Material Character

CaF 2 89

MgO 73

NaCl 67

Al 2 O 3 63

SiO 2 51

Si 3 N 4 30

ZnS 18

SiC 12