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CHAPTER

9 Structure and Properties of Ceramics 8-1

INTRODUCTION • • • •

Ceramics are inorganic and nonmetallic. Bounded by ionic or covalent bonds. Good electrical and heat insulation property. Brittle, and lesser ductility and toughness than metals. • High chemical stability and high melting temperature. • Traditional Ceramics: Basic components (Clay and Silica). • Engineering Ceramics: Pure compounds (Al2O3, SiC). 8-2

Ionic and Covalent Bonding in Simple Ceramics

• Mixture of Ionic and Covalent Types.

• Depends on electronegativity difference.

CaF2: large SiC: small

Ionic Bonding Which sites will cations occupy? 1. Size of sites – does the cation fit in the site 1. Stoichiometry – if all of one type of site is full the remainder have to go into other types of sites. 1. Bond Hybridization

1. Size of Sites 1. Size - Stable structures: --maximize the # of nearest oppositely charged neighbors.

-

+

-

-

-

unstable • Charge Neutrality:

-

-

-

stable

--Net charge in the structure should be zero. --General form:

+

-

CaF 2 :

+

-

stable Ca 2+ + cation

Fanions F-

A m Xp m, p determined by charge neutrality

Coordination Number and Ionic Radii r cation • Coordination number increases with r anion

Issue: How many anions can you arrange around a cation? r cation r anion < 0.155

Coord # 2 linear

0.155 - 0.225

3

triangular

0.225 - 0.414

4

TD

0.414 - 0.732

6

OH

0.732 - 1.0

8

cubic

Adapted from Table 12.2, Callister 7e.

ZnS (zincblende) Adapted from Fig. 12.4, Callister 7e.

NaCl (sodium chloride)

Adapted from Fig. 12.2, Callister 7e.

CsCl (cesium chloride) Adapted from Fig. 12.3, Callister 7e.

Cation Site Size

• Determine minimum rcation/ranion for OH site (C.N. = 6) 2ranion + 2rcation =2a

a = 2ranion 2ranion + 2rcation = 2 2ranion ranion + rcation =2ranion

rcation = ( 2− 1)ranion

rcation = 0.414 ranion

2. Stoichiometry 1. Stoichiometry –

If all of one type of site is full the remainder have to go into other types of sites.

Ex: FCC unit cell has 4 OH and 8 TD sites. If for a specific ceramic each unit cell has 6 cations and the cations prefer OH sites 4 in OH 2 in TD

3. Bond Hybridization •

Bond Hybridization – significant covalent bonding – –

the hybrid orbitals can have impact if significant covalent bond character present For example in SiC •

XSi = 1.8 and XC = 2.5

% ionic character = 100 {1 - exp[-0.25( X Si − X C )2 ]} = 11.5% • ca. 89% covalent bonding • both Si and C prefer sp3 hybridization • Therefore in SiC get TD sites

Example: Predicting Structure of FeO • On the basis of ionic radii, what crystal structure would you predict for FeO? Cation Ionic radius (nm) Al 3+ 0.053 Fe 2+ 0.077 Fe 3+ 0.069 Ca 2+ 0.100 Anion O2Cl F-

0.140 0.181 0.133

• Answer:

Data from Table 12.3, Callister 7e.

rcation 0.077 = ranion 0.140 = 0.550 based on this ratio, --coord # = 6 --structure = NaCl

Ceramic Crystal Structure • AX Crystal Structure – E.g. NaCl, CsCl, Zinc Blende • AX2 Crystal Structure – E.g. Fluorite • ABX3 Crystal Structure – E.g. Perovskite • Silicate – E.g. Silica, Glass, Silicates • Carbon – E.g. Diamond, Graphite

SodiumAX Chloride CrystalCrystal Structure Structure •

Highly Ionically bonded with Na+ ions occupying interstitial sites between FCC and Cl- ions. • Radius ratio = 0.56, CN = 6. • MgO, CaO, NiO and FeO have similar structures.

Figure 10.7

rNa = 0.102 nm rCl = 0.181 nm rNa/rCl = 0.564 ∴ cations prefer OH sites

Cesium Chloride Crystal Structure • CsCl is ionically bonded with radius ratio

= 0.94 and CN = 8. • Eight chloride ion surround a central cesium cation at the ( ½ , ½ , ½ ) position. • CsBr, TlCl and TlBr have similar structure.

Figure 10.5

Cesium Chloride structure:

rCs + rCl−

=

0.170 = 0.939 0.181

∴ cubic sites preferred So each Cs+ has 8 neighboring ClAdapted from Fig. 12.3, Callister 7e.

Zinc Blende (ZnS) Crystal Structue • • • • • •

Four zinc and four sulfur atoms. One type (Zn or S) occupies lattice points and another occupies interstitial sites of FCC unit cell. S Atoms (0,0,0) ( ½ ,½ ,0) ( ½ , 0, ½ ) (0, ½ , ½ ) Zn Atoms ( ¾ ,¼ ,¼ ) ( ¼ ,¼ ,¾ )( ¼ ,¾,¼ ) ( ¾ ,¾ ,¾ ) Tetrahedrally covalently bonded (87% covalent character) with CN = 8. CdS, InAs, InSb and ZnSe have similar structures.

Figure 10.12

Zinc Blende structure

rZn2+ rO 2−

=

0.074 = 0.529 ⇒ OH ?? 0.140

• Size arguments predict Zn2+ in OH sites, • In observed structure Zn2+ in TD sites

• Why is Zn2+ in TD sites? – bonding hybridization of zinc favors TD sites Adapted from Fig. 12.4, Callister 7e.

Ex: ZnO, ZnS, SiC

So each Zn2+ has 4 neighboring O2-

MgO and FeO

MgO and FeO also have the NaCl structure O2-

rO = 0.140 nm

Mg2+

rMg = 0.072 nm

rMg/rO = 0.514 ∴ cations prefer OH sites Adapted from Fig. 12.2, Callister 7e.

So each oxygen has 6 neighboring Mg2+

AX2 Crystal Structure Calcium Fluorite (CaF2) Crystal Structure

•

Ca2+ ions occupy the FCC lattice sites while the Fions are located at eight tetrahedral sites. • UO2, BaF2, PbMg2 have similar structures. 10.14 allow • Large number of unoccupied octahedral sites in UO2Figure it to be used as nuclear fuel. • Fission products are accommodated in these vacant positions.

Fluorite structure • Calcium Fluorite (CaF2) • cations in cubic sites • UO2, ThO2, ZrO2, CeO2 • antifluorite structure – cations and anions reversed Adapted from Fig. 12.5, Callister 7e.

ABX3 Crystal Structures

• Perovskite (CaTiO3) : Ca2+ and O2- ions form FCC unit cell. • Ca2+ Ions occupy corners • O2- Ions occupy face centers. • Ti4+ ions are at octahedral sites.

Figure 10.16

• Perovskite Ex: complex oxide BaTiO3 Adapted from Fig. 12.6, Callister 7e.

Silicate Ceramics Most common elements on earth are Si & O

Si4+ O2Adapted from Figs. 12.9-10, Callister 7e.

crystobalite

• SiO2 (silica) structures are quartz, crystobalite, & tridymite • The strong Si-O bond leads to a strong, high melting material (1710ºC)

Amorphous Silica • Silica gels - amorphous SiO2 – Si4+ and O2- not in well-ordered lattice – Charge balanced by H+ (to form OH-) at “dangling” bonds • very high surface area > 200 m2/g

– SiO2 is quite stable, therefore unreactive • makes good catalyst support Adapted from Fig. 12.11, Callister 7e.

Silica Glass

• Dense form of amorphous silica – Charge imbalance corrected with “counter cations” such as Na+ – Borosilicate glass is the pyrex glass used in labs • better temperature stability & less brittle than sodium glass

Silicates

Simple Structure – Combine SiO44- tetrahedra by having them share corners, edges, or faces

Adapted from Fig. 12.12, Callister 7e.

Mg2SiO4

Ca2MgSi2O7

– Cations such as Ca2+, Mg2+, & Al3+ act to neutralize & provide ionic bonding

• • •

Silicate (SiO44-) is building block of silicates.

50% Ionic and 50% covalent. Many different silicate structures can be produced. • Island structure: Positive ions bond with the oxygen of SiO44•

tetrahedron. Chain/ring structure: Two corners of each SiO44- tetrahedron

Figure 10.18

bonds with corners of other tetrahedron. Figure 10.19a

Layered Silicates • Three corners of same planes of silicate tetrahedron bonded to the corners of three other silicate tetrahedra. • Each tetrahedron has one unbounded oxygen and hence chains can bond with other type of sheets. Figure 10.19b • If the bondings are weak, sheets slide over each other easily.

Figure 10.20

• Layered silicates (clay silicates) – SiO4 tetrahedra connected together to form 2-D plane

= • (Si2O5)2-

Adapted from Fig. 12.13, Callister 7e.

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

Adapted from Fig. 12.14, Callister 7e.

Note: these sheets loosely bound by van der Waal’s forces

• Can change the counterions – this changes layer spacing – the layers also allow absorption of water

• Micas KAl3Si3O10(OH)2 • Bentonite – used to seal wells – packaged dry – swells 2-3 fold in H2O – pump in to seal up well so no polluted ground water seeps in to contaminate the water supply.

Silicate Network • • •

• • •

Silica: All four corners of the SiO44- tetrahedra share oxygen atoms. Basic structures: Quartz, tridynute and cristobarlite. Important compound of many ceramic and glasses. Feldspars: Infinite 3D networks. Some Al3+ Ions replace Si4+ Ions Net negative charge. Alkaline and alkaline fit into interstitial sites.

Figure 10.22

Carbon • Carbon black – amorphous – surface area ca. 1000 m2/g • Diamond – tetrahedral carbon • hard – no good slip planes • brittle – can cut it – large diamonds – jewelry – small diamonds • often man made - used for cutting tools and polishing – diamond films • hard surface coat – tools, medical devices, etc.

Adapted from Fig. 12.15, Callister 7e.

Graphite

• layer structure – aromatic layers

Adapted from Fig. 12.17, Callister 7e.

– weak van der Waal’s forces between layers – planes slide easily, good lubricant

Fullerenes and Nanotubes

• Fullerenes or carbon nanotubes – wrap the graphite sheet by curving into ball or tube – Buckminister fullerenes • Like a soccer ball C60 - also C70 + others

Adapted from Figs. 12.18 & 12.19, Callister 7e.

Imperfections in Ceramics

• Atomic Point Defect – Schottky, Frenkel

• Impurities – Interstitial, Substitutional

Atomic Point Defect • Frenkel Defect --a cation is out of place. • Shottky Defect --a paired set of cation and anion vacancies. Shottky Defect:

Frenkel Defect

Adapted from Fig. 12.21, Callister 7e. (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.)

~e

• Equilibrium concentration of defects

−QD / kT

Impurities • Impurities must also satisfy charge balance = Electroneutrality • Ex: NaCl

Na +

Cl -

• Substitutional cation impurity

cation vacancy

Ca 2+

Na + Na + initial geometry

Ca 2+ impurity

• Substitutional anion impurity O2-

initial geometry

Cl Cl O2- impurity

Ca 2+ resulting geometry anion vacancy

resulting geometry

Interstitial Sites in FCC and HCP Crystal Lattices •

Octahedral interstitial sites: Six nearest atoms or ions equidistant from central void. • Tetrahedral Interstitial Sites: Four nearest atoms or ions equidistant from central void. • There are four octahedral sites and eight tetrahedral sites per unit cell of FCC.

Figure 10.9

Figure 10.11

Mechanical Properties • Strength of ceramics vary greatly but they are generally brittle. • Tensile strength is lower than compressive strength.

Mechanism of Deformation •

Covalently bonded ceramics: Exhibit brittle fracture due to separation of electron-pair bonds without their subsequent reformation. • Ionically bonded ceramics: Single crystal show considerable plastic deformation. Polycrystalline ceramics are brittle. • Example: NaCl crystal  Slip in {100} family of planes is rarely observed as same charges come into contact.  Cracking occurs at grain boundaries. Figure 10.44

Factors Affecting Strength

• Failure occurs mainly from surface defects. • Pores gives rise to stress concentration and cracks. • Pores reduce effective cross-sectional area. • Flaw size is related to grain size. • Finer size ceramics have smaller flaws and hence are stronger. • Composition, microstructure, surface condition, temperature and environment also determine strength.

Strength of Ceramics • 3-point bend test to measure room T strength. cross section

d b

rect.

L/2

F

L/2

Adapted from Fig. 12.32, Callister 7e.

R

d = midpoint deflection

circ. location of max tension

• Typ. values:

• Flexural strength:

σ fs = Ff

F

x

1.5Ff L bd 2

rect.

=

Ff L πR3

σfs (MPa) E(GPa) Si nitride 250-1000 304 Si carbide 100-820 345 Al oxide 275-700 393 glass (soda) 69 69 Material

Data from Table 12.5, Callister 7e.

δfs

δ

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

• 3-Point Bend Testing often used. --tensile tests are difficult for brittle materials. F cross section L/2

d b

rect.

L/2

Adapted from Fig. 12.32, Callister 7e.

R

d = midpoint deflection

circ.

• Determine elastic modulus according to:

F

x slope =

F δ

δ

linear-elastic behavior

E=

F

L3

δ 4bd 3 rect. cross section

=

F

L3

δ 12 π R4 circ. cross section

Creep • Elevated Temperature Tensile Test (T > 0.4 Tm). creep test

σ

ε

x .

slope = εss = steady-state creep rate

σ time

Toughness of Ceramic • • •

Ceramics have low strength. Research has been conducted to improve toughness. Hot pressing with additives and reaction bonding improve toughness.

•

KIC values obtained by four point bend test.

K IC = Yσ f πa σ f = fracture stress (MPa) a

= half size of target internal flaw

Y = dimensionless constant Figure 10.46

Transformation Toughening of Partially Stabilized ZrO2

• Transformation of Zirconia combined with some other refractory oxides (MgO) can produce very high toughness ceramics. • ZrO2 exists in 3 structures.  Monoclinic  Tetragonal  Cubic

Up to 11700C 1170 – 23700C above 23700C

• Adding 10% mol of MgO stabilizes cubic form so that it can exist in metastable state in room condition.

If a mixture of ZrO2 – 9 mol% MgO is sintered at about 18000C and rapidly cooled, it will be in metastable state. • If reheated to 14000C and held for sufficient time tetragonal structure precipitates. • Under action of stress, this tetragonal structure transforms to monoclinic increasing volume and hence retarding crack growth. •

Figure 10.47a

Failure •

Fatigue fracture in ceramics is rare due to absence of plastic deformation. • Straight fatigue crack in has been reported in alumina after 79,000 compression cycles. Figure 10.48

• • •

Ceramics are hard and can be used as abrasives. Examples:- Al2O3, SiC.

By combining ceramics, improved abrasives can be developed. • Example:- 25% ZrO2 + 75% Al2O3

Thermal Properties of Ceramics

• Low thermal conductivity and high heat resistance. • Many compounds are used as industrial refractories. • For insulating refractories, porosity is desirable. • Dense refractories have low porosity and high resistance to corrosion and errosion. • Aluminum oxide and MgO are expensive and difficult to form and hence not used as refractories.

Porosity

• Exist between powder particles due to forming processes. • Heat treatment will eliminate porosity but some residual porosity will remain. • Influence the elastic properties and strength. • Porosity reduce strength because: – Pores reduce cross sectional area – Act as stress concentrator

Hardness

• High hardness • Suitable for abrasive materials

Electrical Properties •

Basic properties of dielectric:  Dielectric constant:Q = CV Q = Charge V = Voltage C = Capacitance C = ε0A/d ε0 = permeability of free space

•

= 8.854 x 10-12 F/m When the medium is not free space C = Kε0A/d Where K is dielectric constant of the material between the plates

Figure 10.35

Dielectric Strength and Loss Factor •

Dielectric strength is measure of ability of material to hold energy at high voltage.  Defined as voltage gradient at which failure occurs.  Measured in volts/mil. • Dielectric loss factor: Current leads voltage by 90 degrees when a loss free dielectric is between plates of capacitor. • When real dielectric is used, current leads voltage by 900 – δ where δ is dielectric loss angle. • Dielectric loss factor = K tan δ measure of electric energy lost.