Introduction to Engineering Materials ENGR2000 Chapter 12...

Introduction to Engineering MaterialsENGR2000

Chapter 12: Structures and Properties of CeramicsDr. Coates

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12.1 Introduction

• Ceramics– Compounds between metallic & non-metallic elements– Predominantly Ionic bonds– Some have covalent bonds– Greek word keramikos which means ‘burnt stuff’– Traditional ceramics

• china, porcelain, bricks, tiles, glasses, etc.




12.2 Crystal Structures

• Crystals composed of electrically charged ions• Cations

– Positively charged– Metallic ions

• Anions– Negatively charged– Non-metallic ions





• Concepts influencing the crystal structure– Crystal must be electrically neutral– Cations & anions are of different sizes– Cations & anions may have different magnitudes of

electrical charge





• Cations are usually smaller than anions

• Each cation prefers to have as many nearest-neighbor anions as possible.

• Each anion prefers to have as many nearest-neighbor cations as possible.

1/ AC rr




Stable ceramic crystal structures

• Anions surrounding a cation are all in contact withthat cation.




Coordination number– # of anion nearest neighbors

for a cation• The CN is related to

• For a specific CN, there is a critical or minimumradius ratio for which this contact is established.

Ac rr /




Example 12.1

• Show that the minimum cation-to-anion radiusratio for the coordination number 3 is 0.155.




155.01866.01

866.0/1

1//

/2330cos

cos

0

A

C

ACACAA

AA

CA

A

CA

A

rr

rrrrrrrr

rrr

AOAP

rrAOrAP




AX-Type Crystal Structures

• Equal number of cations & anions• AX compounds• A denotes the cation• X denotes the anion




Rock salt (NaCl) structure

• Two interpenetrating FCC lattices – one composedof cations and the other of anions

732.0/414.0

6

AC rrClCNNaCN




Rock salt (NaCl) structure

• Common ceramic materials with this crystalstructure– NaCl, MgO, MnS, LiF, FeO




Cesium Chloride Structure

• Note that this is not a BCC crystal structure(different kinds of ions)

8 ClCNCsCN




Zinc Blende (ZnS) Structure

• Common ceramic materials with this crystalstructure– ZnS, ZnTe, SiC

4 XCNACN




AmXp-Type Crystal Structures

• Consider the AX2- type CaF2 (flourite) structure

• Predicts a structure similar to the CsCl• There are ½ as many Ca ions as there are F ions.

tablefrom88.0/

CNrr AC




Flourite (CaF2) Crystal Structure

• Only ½ the center cube positions are occupied byCa ions




Example 12.2

• On the basis of ionic radii, what crystal structurewould you predict for FeO?




structure crystalsalt rock -

6:12.2 Table From

550.0140.0077.0

compound. type-AXan is FeO

2

2

XCNACN

nmnm

rr

rr

O

Fe

A

C




Example

• On the basis of ionic radii, what crystal structurewould you predict for CaF2?




4

12

Ca of #F of #

F of #21Ca of #

8:12.2 Table From

752.0133.0100.0

compound. type-AXan is CaF

2

-2

-2

2

22

2

FCNFCN

CaCN

CaCN

nmnm

rr

rr

F

Ca

A

C




Ceramic Density Computations

number. sAvogadro' theis and volumecellunit theis

unit formula in the anions all of wtsatomic of sum theis

unit formula in the cations all of wtsatomic of sum theis cellunit e within thunits formula ofnumber theis ' where

':data cellunit fromdensity lTheoretica

A

C

A

C

AC

AC

NV

A

An

NVAAn




Formula unit

• All the ions that are included in the chemicalformula.– A formula unit of BaTiO3 consists of one barium ion,

one titanium ion and three oxygen ions.




Example 12.3

• On the basis of crystal structure, compute thetheoretical density for NaCl. How does thiscompare with its measured density?




molgAA

molgAAn

n

n

ClA

NaC

/45.35

/99.224'

124111'

6218

81'




3

3

3

g/cm2.16density Measured

/14.2 '

:density lTheoretica

181.0

102.0:12.3 tableFrom

2

cmgNV

AAn

nmrnmr

rraaV

AC

AC

Cl

Na

ClNa

C




12.3 Silicate Ceramics

• Silicates are materials composed primarily of Siand O, the two most abundant elements in theearth’s crust.– Soils, rocks, clay & sand




31

Silicate CeramicsMost 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

Si4+

O2-

Adapted from Figs. 12.9-10, Callister & Rethwisch 8e crystobalite




32

Bonding of adjacent SiO44- accomplished by the sharing of

common corners, edges, or faces

Silicates

Mg2SiO4 Ca2MgSi2O7

Adapted from Fig. 12.12, Callister & Rethwisch 8e.

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

1. maintain charge neutrality, and2. ionically bond SiO4

4- to one another




33

Layered Silicates

• Layered silicates (e.g., clays, mica, talc)– SiO4 tetrahedra connected

together to form 2-D plane

• A net negative charge is associated witheach (Si2O5)2- unit

• Negative charge balanced byadjacent plane rich in positively chargedcations





34

• Kaolinite clay alternates (Si2O5)2- layer with Al2(OH)42+ layer

Layered Silicates (cont.)

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





35

• Quartz is crystallineSiO2:

• 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)Adapted from Fig. 12.11, Callister & Rethwisch 8e.

Glass Structure

Si0 4 tetrahedron4-

Si4+

O2-

Si4+Na +

O2-




12.4 Carbon

• Carbon exists in various polymorphic forms aswell as in the amorphous form.




37

Polymorphic Forms of Carbon

Diamond– tetrahedral bonding of

carbon• hardest material known• very high thermal conductivity

– large single crystals – gemstones

– small crystals – used togrind/cut other materials

– diamond thin films• hard surface coatings – used

for cutting tools, medicaldevices, etc.





38

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





39

Polymorphic Forms of Carbon (cont)Fullerenes and Nanotubes

• Fullerenes – spherical cluster of 60 carbon atoms, C60

– Like a soccer ball• Carbon nanotubes – sheet of graphite rolled into a tube

– Ends capped with fullerene hemispheres

Adapted from Figs. 12.18 & 12.19, Callister & Rethwisch 8e.




Carbon Nanotubes

• Tube diameters ~ 100 nm• Each nanotube is a single molecule composed of

millions of atoms• Extremely strong & stiff as well as ductile• Tensile strengths ~ 50 Gpa to 200 Gpa• Elastic modulus ~ 1000 Gpa• Low density




12.5 Imperfections in CeramicsAtomic point defects

• Vacancies– Anion vacancy– Cation vacancy

• Interstitials– Anion interstitial– Cation interstitial




42

• 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

Adapted from Fig. 12.20, Callister & Rethwisch 8e. (Fig. 12.20 is from W.G. Moffatt, G.W. Pearsall, and J. Wulff, The Structure and Properties of Materials, Vol. 1, Structure, John Wiley and Sons, Inc., p. 78.)

Point Defects in Ceramics (i)

Cation Interstitial

Cation Vacancy

Anion Vacancy




43

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

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

• Equilibrium concentration of defects

Adapted from Fig.12.21, Callister & Rethwisch 8e. (Fig. 12.21 is from W.G. Moffatt, G.W. Pearsall, and J. Wulff, The Structure and Properties of Materials, Vol. 1, Structure, John Wiley and Sons, Inc., p. 78.)

Point Defects in Ceramics (ii)

Shottky Defect:

Frenkel Defect

/kTQDe




Why are anion interstitials highly improbable?

• Anion is relatively larger• Has to fit into a small interstitial position

• No, they occur in pairs• Electro neutrality must be maintained

Can defects in ceramics occur alone?




Stoichiometry

• A state for ionic compounds wherein there is theexact ratio of cations to anions as predicted by thechemical formula.

• NaCl is stoichiometric if the ratio of Na+ ions toCl- ions is exactly 1:1




The ratio of cations to anions is not altered by the formation of a Frenkel or Schottky defect.

- Material is stoichiometric




Non stoichiometric materials

• FeO – iron is present as Fe2+ or Fe3+




Impurities in Ceramics

• Substitutional solid solution– Substitutional impurity will substitute for the host ion

to which it is most similar in an electrical sense

Anion substitutional

Cation substitutional




Impurities in Ceramics

• Interstitial solid solution– impurity must be relatively small




12.7 Ceramic Phase DiagramsThe Al2O3 – Cr2O3 system

• Substitutional solid solution– Al3+ substitutes for Cr3+– Similarly charged ions– Similar ionic radii (0.053 nm and 0.062 nm)– Al2O3 and Cr2O3 have similar crystal structures




Isomorphous system




The MgO – Al2O3 system

• Limited solubility– Differences in charge in Mg2+ and Al3+

– Differences in radii (0.072 nm and 0.053 nm)




Eutectic points

Intermediate phase




Mechanical Properties

Brittle fracture - before any plastic deformation

Slope=elastic modulus




Elastic modulus of metals, ceramics & polymers

• Ceramics– high elastic modulus– diamond, graphite (covalent bonds)

• Metals– high elastic modulus

• Polymers– low elastic modulus– weak secondary bonds between chains

Increasing E




Plastic deformation in metals, ceramics & polymers

• Polymers– strain hardening due to chain alignment

• Metals– strain hardening

• Ceramics– almost no plastic deformation

Increasingtendency forplastic deformation




12.9 Stress-Strain Behavior




Mechanical properties of metals & ceramics

Metals• high elastic modulus• significant plastic

deformation• high fracture stress• stress-strain curves for

tension & compression arenearly identical

Ceramics• higher elastic modulus• no significant plastic

deformation• higher fracture stress• stress-strain curves depend

on the load (tension orcompression)




12.10 Mechanisms of Plastic DeformationCrystalline ceramics

• Plastic deformation occurs by motion ofdislocations

• Dislocation motion is impeded• Hence ceramics are hard & brittle




12.11 Miscellaneous Mechanical Considerations

• Porosity– Initial material is in the form of a powder for some

ceramic fabrication techniques– Residual pores or void spaces remain after the

fabrication process




material. nonporous the of modulus elastic theis

porosityfraction volume theis 9.09.11

0

20

EP

PPEE




Hardness

• Ceramics are the hardest known materials– utilized when an abrasive or grinding action is required




Resistance to environmental failure of metals, ceramics & polymers

• Ceramics– high resistance to environmental attack

• Metals• Polymers

– moisture effectsIncreasingresistance




Example

• Which material has the highest elastic modulus?• Which material has the highest ductility?• Which material has the highest toughness?• Which material does not exhibit

any significant plastic deformationprior to fracture?




66

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




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• Room T behavior is usually elastic, with brittle failure.• 3-Point Bend Testing often used.

-- tensile tests are difficult for brittle materials.Adapted from Fig. 12.32, Callister & Rethwisch 8e.

Flexural Tests – Measurement of Elastic Modulus

FL/2 L/2

d = midpoint deflection

cross section

Rb

d

rect. circ.

• Determine elastic modulus according to:F

x

linear-elastic behaviord

Fd

slope =3

3

4bdLFE

d (rect. cross section)

4

3

12 RLFEd

(circ. cross section)




68

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


Flexural Tests – Measurement of Flexural Strength

FL/2 L/2

d = midpoint deflection

cross section

Rb

d

rect. circ.

location of max tension

• Flexural strength: • Typical values:

Data from Table 12.5, Callister & Rethwisch 8e.

Si nitrideSi carbideAl oxideglass (soda-lime)

250-1000100-820275-700

69

30434539369

Material sfs (MPa) E(GPa)

223bd

LFffs s (rect. cross section)

(circ. cross section)3RLFf

fs

s




69

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




Recommended problems

• 12.5, 12.7, 12.13,12.20,12.42




Introduction to Engineering Materials ENGR2000 Chapter 12...

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