ENGR 151 Materials of Engineering LECTURE 18 · • Equilibrium concentration of defects POINT DEFECTS IN CERAMICS (II) Shottky Defect: Frenkel ... At point of loading, top surface

LECTURE 18

ENGR 151

Materials of Engineering

2

COORDINATION NUMBER AND IONIC RADII

2

r cation r anion

Coord.

Number

< 0.155

0.155 - 0.225

0.225 - 0.414

0.414 - 0.732

0.732 - 1.0

3

4

6

8

linear

triangular

tetrahedral

octahedral

cubic

3

ROCK SALT STRUCTURE Same concepts can be applied to ionic solids in general.

Example: NaCl (rock salt) structure

rNa = 0.102 nm

rNa/rCl = 0.564

cations (Na+) prefer octahedral sites

Adapted from Fig. 12.2,

Callister & Rethwisch 9e.

rCl = 0.181 nm

• Structure is similar to two intermeshed

FCC lattices

4

MGO AND FEO

O2- rO = 0.140 nm

Mg2+ rMg = 0.072 nm

rMg/rO = 0.514

cations prefer octahedral sites

So each Mg2+ (or Fe2+) has 6 neighbor oxygen atoms



MgO and FeO also have the NaCl structure

5

AX CRYSTAL STRUCTURES

Fig. 12.3, Callister & Rethwisch 9e.

Cesium Chloride structure:

Since 0.732 < 0.939 < 1.0,

cubic sites preferred

So each Cs+ has 8 neighbor Cl-

AX–Type Crystal Structures include NaCl, CsCl, and zinc blende

6

AX2 CRYSTAL STRUCTURES

• Calcium Fluorite (CaF2)

• Cations in cubic sites

• UO2, ThO2, ZrO2, CeO2

• Antifluorite structure –

positions of cations and

anions reversed

• Fluorite is used to

construct elements in high

performance optics

Fig. 12.5, Callister & Rethwisch 9e.

Fluorite structure

7

ABX3 CRYSTAL STRUCTURES

Fig. 12.6, Callister &

Rethwisch 9e.

• Perovskite structure

Ex: complex oxide

BaTiO3

8

• On the basis of ionic radii, what crystal structure

would you predict for FeO?

• Answer:

5500

1400

0770

anion

cation

.

.

.

r

r

=

=

based on this ratio,

-- coord # = 6 because

0.414 < 0.550 < 0.732

-- crystal structure is similar

to NaCl Data from Table 12.3,


EXAMPLE PROBLEM: PREDICTING THE

CRYSTAL STRUCTURE OF FEO

Ionic radius (nm)

0.053

0.077

0.069

0.100

0.140

0.181

0.133

Cation

Anion

Al 3+

Fe 2 +

Fe 3+

Ca 2+

O 2-

Cl -

F -

9

DENSITY COMPUTATIONS FOR

CERAMICS

Number of formula units/unit cell

Volume of unit cell

Avogadro’s number

= sum of atomic weights of all anions in formula unit

= sum of atomic weights of all cations in formula unit

10


CERAMICS – EXAMPLE PROBLEM

11


CERAMICS – EXAMPLE PROBLEM

Most common elements on earth are Si & O

SiO2 (silica) polymorphic forms are quartz,

crystobalite, & tridymite

The strong Si-O bonds lead to a high melting

temperature (1710ºC) for this material

12

SILICATE CERAMICS

Si4+

O2-

Figs. 12.9 & 12.10, Callister &

Rethwisch 9e crystobalite

13

SILICATE CERAMICS

Rather than attempting to characterize silicate

ceramics in terms of crystal structures, we use the

SiO44- tetrahedron.

Negatively-charged entity is characterized by strong

covalent Si-O bonds.

Various silicate structures generated by 1-, 2- and 3-

dimensional arrangements of silicate structures.

Si4+

O2-

14

SILICATE CERAMICS

15

SILICATE CERAMICS

16

Bonding of adjacent SiO44- accomplished by the

sharing of common corners, edges, or faces

SIMPLE SILICATES

Mg2SiO4 Ca2MgSi2O7

Adapted from Fig.

12.12, Callister &

Rethwisch 9e.

Presence of cations such as Ca2+, Mg2+, & Al3+

1. maintain charge neutrality, and

2. ionically bond SiO44- to one another

17

• Quartz is crystalline

SiO2:

• Basic Unit: Glass is noncrystalline (amorphous)

• Fused silica is SiO2 to which no

impurities have been added

• Other common glasses contain

impurity ions such as Na+, Ca2+,

Al3+, and B3+

(soda glass)



GLASS STRUCTURE

Si0 4 tetrahedron 4-

Si 4+

O 2 -

Si 4+

Na +

O 2 -

18

LAYERED SILICATES

Layered silicates (e.g., clays, mica, talc)

SiO4 tetrahedra connected together to form 2-D plane

A net negative charge is associated with each (Si2O5)

2- unit Oxygen ion out of the plane of the page

Negative charge balanced by adjacent plane rich in positively charged cations

Fig. 12.13, Callister

& Rethwisch 9e.

19

Kaolinite clay alternates (Si2O5)2- layer with Al2(OH)4

2+

layer

LAYERED SILICATES (CONT)

Note: Adjacent sheets of this type are loosely bound to one another by van der Waal’s forces.


Rethwisch 9e.

20

POLYMORPHIC FORMS OF CARBON

Diamond tetrahedral bonding of

carbon hardest material known

very high thermal conductivity high refractive index

large single crystals – gem stones

small crystals – used to grind/cut other materials

diamond thin films hard surface coatings – used

for cutting tools, medical devices, etc.


Rethwisch 9e.

Difficult to initiate slip – no

straightforward slip plane

structure

21

POLYMORPHIC FORMS OF CARBON (CONT)

Graphite layered structure – parallel hexagonal arrays of

carbon atoms

weak van der Waal’s forces between layers

planes slide easily over one another -- good lubricant

Fig. 12.17, Callister

& Rethwisch 9e.

22

• Vacancies

-- vacancies exist in ceramics for both cations and anions

• Interstitials -- interstitials exist for cations

-- interstitials are not normally observed for anions because anions

are large relative to the interstitial sites

Fig. 12.18, Callister & Rethwisch 9e. (From W.G. Moffatt, G.W. Pearsall, and J.

Wulff, The Structure and Properties of

Materials, Vol. 1, Structure, p.78. Copyright

©1964 by John Wiley & Sons, New York.

Reprinted by permission of John Wiley and

Sons, Inc.)

POINT DEFECTS IN CERAMICS (I)

Cation Interstitial

Cation Vacancy

Anion Vacancy

23

• Frenkel Defect -- a cation vacancy-cation interstitial pair.

• Shottky Defect -- a paired set of cation and anion vacancies.

• Equilibrium concentration of defects

POINT DEFECTS IN CERAMICS (II)

Shottky

Defect:

Frenkel

Defect

Fig. 12.19, Callister & Rethwisch 9e. (From W.G. Moffatt, G.W. Pearsall, and J.

Wulff, The Structure and Properties of

Materials, Vol. 1, Structure, p.78. Copyright

©1964 by John Wiley & Sons, New York.

Reprinted by permission of John Wiley and

Sons, Inc.)

24

• Electroneutrality (charge balance) must be maintained

when impurities are present

• Ex: NaCl

IMPERFECTIONS IN CERAMICS

Na + Cl -

• Substitutional cation impurity

without impurity Ca 2+ impurity with impurity

Ca 2+

Na +

Na +

Ca 2+

cation vacancy

• Substitutional anion impurity

without impurity O 2- impurity

O 2-

Cl -

an ion vacancy

Cl -

with impurity

25

EQUILIBRIUM CONCENTRATION OF

FRENKEL DEFECTS

26

EQUILIBRIUM CONCENTRATION OF

SCHOTTKY DEFECTS – AX-TYPE

COMPOUND

27

EXAMPLE PROBLEM

28

EXAMPLE PROBLEM

29

CERAMIC PHASE DIAGRAMS

30

CERAMIC PHASE DIAGRAMS MgO-Al2O3 diagram:


Rethwisch 9e. [Adapted from B. Hallstedt,

“Thermodynamic Assessment

of the System MgO–Al2O3,” J.

Am. Ceram. Soc., 75[6], 1502

(1992). Reprinted by

permission of the American

Ceramic Society.]

31

MECHANICAL PROPERTIES

Ceramic materials are more brittle than metals.

Why is this so?

Consider mechanism of deformation

In crystalline, by dislocation motion

In highly ionic solids, dislocation motion is difficult

few slip systems

resistance to motion of ions of like charge (e.g., anions)

past one another

32

REPRESENTATION OF CRACK ORIGINS

Crack interacts with:

Microstructure of

material

Stress

Elastic waves that are

generated

33

MICROSCOPIC CRACK FEATURES

34

MICROSCOPIC CRACK FEATURES

35

STRESS-STRAIN BEHAVIOR

Cannot use tensile testing to predict stress-strain

behavior of ceramics

Difficult to prepare and test specimens with requisite

geometry

Difficult to grip brittle materials without fracturing them

Ceramics fail after only about 0.1% strain – need

precise alignment to avoid bending effects

Transverse bending test employed – flexural

loading

At point of loading, top surface of specimen is in state

of compression, bottom surface of specimen is in state

of tension

36

• Room T behavior is usually elastic, with brittle failure.

• 3-Point Bend Testing often used. -- tensile tests are difficult for brittle materials.



FLEXURAL TESTS – MEASUREMENT OF

ELASTIC MODULUS

F L/2 L/2

δ = midpoint

deflection

cross section

R

b

d

rect. circ.

• Determine elastic modulus according to:

F x

linear-elastic behavior δ

F

δ slope =

(rect. cross section)

(circ. cross section)

37

• 3-point bend test to measure room-T flexural strength.



FLEXURAL TESTS – MEASUREMENT OF

FLEXURAL STRENGTH

F L/2 L/2

δ = midpoint

deflection

cross section

R

b

d

rect. circ.

location of max tension

• Flexural strength: • Typical values:

Data from Table 12.5, Callister & Rethwisch 9e.

Si nitride

Si carbide

Al oxide

glass (soda-lime)

250-1000

100-820

275-700

69

304

345

393

69

Material σ fs (MPa) E(GPa)

(rect. cross section)

(circ. cross section)

38

PLASTIC DEFORMATION IN CERAMICS

Plastic deformation in ceramics is limited – more

of a tendency to fracture

Crystalline ceramics

Ionic structure: Limited number of slip systems for

dislocations due to electrically charged nature of

particles – attractive/repulsive forces resist motion

Covalent structure: Strong covalent bonds limit

dislocation motion, dislocation structures are complex

Noncrystalline ceramics

No dislocation motion; rather plastic deformation

occurs via viscous flow (similar to liquids)

39

SUMMARY

• Interatomic bonding in ceramics is ionic and/or covalent.

• Ceramic crystal structures are based on: -- maintaining charge neutrality

-- cation-anion radii ratios.

• Imperfections

-- Atomic point: vacancy, interstitial (cation), Frenkel, Schottky

-- Impurities: substitutional, interstitial

-- Maintenance of charge neutrality

• Room-temperature mechanical behavior – flexural tests

-- linear-elastic; measurement of elastic modulus

-- brittle fracture; measurement of flexural modulus

40

HOMEWORK

Due Monday, May 8th

12.3, 12.4, 12.5, 12.6

Quiz next Wednesday, April 26th Topic – stress, strain, and Young’s modulus and Poisson’s ratio

ENGR 151 Materials of Engineering LECTURE 18 · • Equilibrium concentration of defects POINT DEFECTS IN CERAMICS (II) Shottky Defect: Frenkel ... At point of loading, top surface

Documents