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Chapter 11Chapter 11 in Smith & Hashemi

Ceramics: • inorganic materials that consist of metallic and nonmetallic (or two nonmetallic) elements • bonded by ionic and / or covalent bonds• has nonmetallic properties

- good electrical and thermal insulators- hard and brittle (low toughness and ductility)

Chapter 10. Ceramics

Chapter 11

Ionic Arrangements in Ionic Solids

Ionic solids – cations and anions in the unit cell

Packing of the ions is determined by:

1. The relative size of the ions

2. Electrical neutrality requirement (each cation has to be surrounded by anion)

Coordination number: the number of nearest neighbors surrounding an ion

3D solids: each cation has to be surrounded by anion

cation

Anion

But possible in some 2D materials

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Chapter 11

Size Limitations for Dense Packing

The radius ratio:

the ratio of the radius of the central cation to that of the surrounding anions

The radius ratio when the anions just start to contact each other and the central cation: critical (minimum) radius ratio

anion

cation

rr

Chapter 11

Calculate the critical (minimum) radius ratio r/R for the triangular coordination (CN = 3) of three anions of radii R surrounding a central cation of cadius r in an ionic solid

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Chapter 11

Simple Ceramic Crystal Structures (Ionic)

ABO3 perovskite

AB2O4 spinel

Al2O3 corrundum

CaF2 fluorite

ZnS zincblende

NaCl

CsCl

Anion coordination number

Cationcoordination number

# of anionsper u.cell

# of cationsper u.cell

Structure

Chapter 11

Cesium Chloride - CsCl

Cs (0, 0, 0)

Cl (1/2, 1/2, 1/2)

Layer 1

Layer 2

Layer 3 = Layer 1

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Chapter 11

Sodium Chloride – NaCl (Rocksalt)

Layer 1

Layer 2

Layer 3 = Layer 1

Chapter 11

NaCl - coordination

Solids with the NaCl-type structure:

LiCl, KCl, AgCl

MgO, TiO, TiN, BaS, TiC

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Chapter 11

Interstitial Sites in fcc Crystal LatticeOctahedral sites

Tetrahedral sites

Chapter 11

Zinc Blend (ZnS) crystal structure

Zn (0, 0, 0)

S (x+0.25, y+0.25, z+0.25)

⇐ Layer 1

⇐ Layer 2

⇐ Layer 3

⇐ Layer 4

Layer 5=1

Layer 1 Layer 2 Layer 3 Layer 4

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Chapter 11

Calcium Fluoride – CaF2

⇐ Layer 1

⇐ Layer 2

⇐ Layer 3

⇐ Layer 4

Layer 5=1

Layer 1 Layer 2 Layer 3 Layer 4

Ca (0, 0, 0)

F (+0.25, +0.25, +0.25)

(-0.25, -0.25, -0.25)

Chapter 11

CaF2 - coordination

Solids with fluorite structure: CO2, CdF2, CeO2, CoSi2, ZrO2

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Chapter 11

Corumdum – Al2O3

Interstitial sites in the hcp lattice:

Chapter 11

Perovskite – CaTiO3

Layer 1: CaO

Layer 2: TiO2

ABO3

A: M2+ (Ca, Sr, Ba, La) B: M4+ (Ti, Zr, Mn)

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Chapter 11

Coordination in perovskite

Ti – octahedral coordination by O (CN=6)

d(Ti-O)= a / 2Ca – cuboid coordination by O (CN = 12)

O – octahedral by Ti and Ca

Chapter 11

Spinel (garnet) – MgAl2O4

• O - ions forming a fcc lattice• The A cations occupy 1/8 of the tetrahedral

interstitial sites and B cations occupy 1/2 of the octahedral sites

• there are 32 O-ions in the unit cell

AB2O4 - normalA: M2+ (Fe, Mg) B: M3+ (Al, Fe, Cr)

MgAl2O4 - spinel

FeAl2O4

FeFe2O4 - magnetite

AB2O4 – inverse

A cations: octahedral sites, B cations: terahedral sitesA: M2+ (Mn, Ni) B: M3+ (Al, Fe, Cr)

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Chapter 11

Spinel structure – top view

Chapter 11

Silicon dioxide – (α) SiO2

C (diamond)

Si, Ge Cristobalite

Si C.N. = 4 SiO44-

O C.N. = 2

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Chapter 11

Quartz, tridymite and cristobalite

β-quartz: the linked tetrahedra form helices or spirals

High–T (> 1470oC) polymorph

Cristobalite

Ideal case shown

typically distorted into tetragonal structure at RT

tridymite

Triclinic crystal

870 and 1470oC

Chapter 11

Silicate Structures

Basic building block - SiO44- tetrahedron

Or Si2O76-; Si3O96-; Si6O18

12- (ring)

Corner – to - corner connection is most common (chain and rings):

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Chapter 11

Crystalline or amorphous…

The strong dependency of the bonding on crystallographic direction for covalent compounds result in a barrier to a formation of a crystalline structure

Strictly periodic arrangements cannot be easily established during solidification, and only chain molecules are formed

Chapter 11

Layered Silicates

From Callister

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Chapter 11

Definition of a Glass

Glass: an inorganic product of high temperature treatment (fusion) that has been cooled to a rigid condition without crystallization

Solidification behavior of a glass will be intrinsically different compared to the crystalline solid

Glass liquid becomes more viscous as T⇓

Transforms from soft plastic state to rigid brittle glassy state in narrow ∆T

Chapter 11

Glass Modifying Oxides

Oxides that break up glass network: network modifiers

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Chapter 11

Point Defects in Ionic Solids

Conditions of electroneutrality must be maintained:

Defects in ceramics does not occur alone (will be paired to another defect)

Frenkel defects:

Cation vacancy VM

cation interstitial

Schottky defects:

Cation vacancy

anion vacancy

Chapter 11

Nonstoichiometric compounds

If no defects present, compound is said to be stoichiometric: ratio of anions to cations is as predicted from stoichiometry

Otherwise: nonstoichiometric

Fe2+ vacancy in FeO as a result of the formation of 2 Fe3+ ions

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Chapter 11

Substitutional crystals

Na+ substitution by K+

Cl- substitution by Br-

Substitutional ions are about the same size as the “host” ions

Chapter 11

Vegard’s law

Vegard’s law is an approximate empirical ruleStates that a linear relation exists (T = const) between the crystal lattice

constant of substitutional compound (alloy) and the concentration of the constituent elements

0.0 0.2 0.4 0.6 0.8 1.05.6

5.7

5.8

5.9

6.0

6.1

6.2

6.3

6.4

KCl

Latti

ce c

onst

ant,

a [A

nstr]

% of KNaCl0.0 0.2 0.4 0.6 0.8 1.0

150

155

160

165

170

175

BO2

Vol

ume,

V [A

nstr3 ]

% of BAO2NaCl ⇒ Na1-xKxCl ⇒ KCl

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Chapter 11

Ionic Conductivity

The sequence A-D shows how cation migration can occur by series of movements of cations into crystal vacancies

Equilibrium vacancy concentrations in ionic solids:

kTE

V

V

eNN−

×=

NV - # of vacanciesN - number of lattice sitesEV – energy required to form a vacancyEV = 0.5 (E+ + E-)

k – Boltzmann constant T – absolute temperature

Chapter 11

Increasing the Ionic Conductivity

By substitutionally increasing # of vacancies beyond the equilibrium value

E.g.: KCl

K1-2x Cax Cl or K1-2xCax Vx Cl

Higher ionic conductivity as # of cation vacancies is greater than equilibrium #

From G. Gottstein

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Chapter 11

Common Engineering Ceramics

Relatively brittle

Tensile strength: 0.69-200MPa (7000 MPa for Al2O3 whiskers)

Compressive strength much higher

Hard and low impact resistant

Exception: clay (soft, easily deformable due to the secondary bonding between layers

Chapter 11

Silicon Carbide

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Chapter 11

Zirconia (Zirconium oxide)

Tetragonal structure stabilization by addition of 10mol% of CaO, MgO, Y2O3 –

fully stabilized zirconia

Stabilization by addition ~9mol% of MgO

partially stabilized zirconia

3 crystal structures:

Monoclinic RT – 1170oC

Tetragonal 1170oC – 2370oC

Cubic (fluorite) above 2370oC

T = 1170oC: tetragonal to monoclinic transition in pure ZrO2

Monoclinic – poor mechanical properties

Chapter 11

11.6 Mechanical properties of ceramics

Relatively brittle

Tensile strength: 0.69-200MPa (7000 MPa for Al2O3 whiskers)

Compressive strength much higher

Hard and low impact resistant

Exception: clay (soft, easily deformable due to the secondary bonding between layers

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Chapter 11

Mechanisms of deformation of ceramics

Will be different for ionic and covalent compounds

Covalent compounds: brittle fracture due to separation of electron-pair bonds without their subsequent reformation

Brittle in both polycrystalline and single crystal states

Ionic compounds: can show significant plastic deformation (single crystal NaCl or MgO)

Slip system: {110} <1-10>

Involve ions of the opposite charge

Chapter 11

Toughness of Ceramic Material

aYK πσ=1

K1 - Stress intensity factorσ - Applied stressa - edge crack lengthY - geometric constant

KIc - critical value of stress intensity factor (fracture toughness)

aY f πσ=

Q: The maximum-sized internal flaw in a hot-pressed SiC ceramic is 25 µm. If this material has a fracture toughness of 3.7 MPa m, what is the maximum stress that this material can support? (Use Y =π1/2)

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Chapter 11

Summary

Ceramics: inorganic materials that consist of metallic and nonmetallic (or two nonmetallic) elements

• bonded by ionic and / or covalent bonds• has nonmetallic properties (good electrical and thermal insulators; hard and brittle (low

toughness and ductility)

Describe crystal structures of simple ceramic materials (CsCl; NaCl; ZnS zincblende; CaF2fluorite; Al2O3 corundum; AB2O4 spinel; ABO3 perovskite; SiC, SiO2 in terms of number of cations and anions per unit cell; cation and anion coordination numbers

Definition of a glass, transition temperatures

Point Defects in Ionic Solids

Nonstoichiometric compounds

Ionic conductivity: what is involved?

Chapter 11

Problems:

10.1 What two main factors affect the packing of ions in ionic solids?10.2 Using Pauling’s equation (Chapter 2), compare the percent covalent

character of the following compounds: HfC, TiO2, SiC, BC, NaCl and ZnS.10.3 Predict the coordination number for (a) BaO and (b) LiF. Ionic radii are

Ba2+ = 0.143 nm, O2- = 0.132 nm, Li+ =0.078 nm, F- = 0.133 nm.10.4 Calculate the linear density in ions per nanometer in the [111] and [110]

directions for CeO2, which has the fluorite structure. Ionic radii are Ce4+ = 0.102 nm and O2- = 0.132 nm.

10.5 Calculate the planar density in ions per square nanometer in the (111) and (110) planes of ThO2, which has the fluorite structure. Ionic radii are Th4+ = 0.110 nm and O2- = 0.132 nm.

10.6 Explain the plastic deformation mechanism for some single-crystal ionic solids such as NaCl and MgO. What is the preferred slip system?

10.7 How is a glass distinguished from other ceramic materials? How does the specific volume versus temperature plot for a glass differ from that for a crystalline material when these materials are cooled from the liquid state?