Chapter 10. Ceramics 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 11 in Smith & Hashemi

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 Anion cation

Chapter 11

But possible in some 2D materials

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Size Limitations for Dense Packing The radius ratio:

rcation ranion

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

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

Chapter 11

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Simple Ceramic Crystal Structures (Ionic) Structure

# of cations per u.cell

# of anions per u.cell

Cation coordination number

Anion coordination number

CsCl NaCl ZnS zincblende CaF2 fluorite Al2O3 corrundum AB2O4 spinel ABO3 perovskite

Chapter 11

Cesium Chloride - CsCl

Layer 1

Layer 2 Cs (0, 0, 0) Cl (1/2, 1/2, 1/2) Layer 3 = Layer 1 Chapter 11

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Sodium Chloride – NaCl (Rocksalt)

Layer 1

Layer 2

Chapter 11

Layer 3 = Layer 1

NaCl - coordination

Solids with the NaCl-type structure: LiCl, KCl, AgCl MgO, TiO, TiN, BaS, TiC

Chapter 11

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Interstitial Sites in fcc Crystal Lattice Octahedral sites

Tetrahedral sites

Chapter 11

Zinc Blend (ZnS) crystal structure Layer 5=1

Zn (0, 0, 0) S (x+0.25, y+0.25, z+0.25)

⇐ Layer 4 ⇐ Layer 3 ⇐ Layer 2 ⇐ Layer 1

Layer 1

Layer 2

Layer 3

Layer 4

Chapter 11

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Calcium Fluoride – CaF2 Layer 5=1 ⇐ Layer 4

Ca (0, 0, 0) F (+0.25, +0.25, +0.25) (-0.25, -0.25, -0.25)

⇐ Layer 3 ⇐ Layer 2 ⇐ Layer 1

Layer 1

Layer 2

Layer 3

Layer 4

Chapter 11

CaF2 - coordination

Solids with fluorite structure: CO2, CdF2, CeO2, CoSi2, ZrO2 Chapter 11

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Corumdum – Al2O3 Interstitial sites in the hcp lattice:

Chapter 11

Perovskite – CaTiO3 ABO3 A: M2+ (Ca, Sr, Ba, La)

B: M4+ (Ti, Zr, Mn)

Layer 2: TiO2

Layer 1: CaO

Chapter 11

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Coordination in perovskite

Ti – octahedral coordination by O (CN=6) d(Ti-O)= a / 2 Ca – cuboid coordination by O (CN = 12) O – octahedral by Ti and Ca Chapter 11

Spinel (garnet) – MgAl2O4 AB2O4 - normal A: M2+ (Fe, Mg) • •

•

B: M3+ (Al, Fe, Cr)

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 MgAl2O4 - spinel FeAl2O4 FeFe2O4 - magnetite

AB2O4 – inverse A cations: octahedral sites, B cations: terahedral sites A: M2+ (Mn, Ni)

B: M3+ (Al, Fe, Cr)Chapter 11

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Spinel structure – top view

Chapter 11

Silicon dioxide – (α) SiO2

C (diamond) Cristobalite

Si, Ge

Si C.N. = 4

SiO44-

O C.N. = 2 Chapter 11

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Quartz, tridymite and cristobalite tridymite Triclinic crystal 870 and 1470oC

High–T (> 1470oC) polymorph

β-quartz: the linked tetrahedra form helices or spirals

Cristobalite Ideal case shown typically distorted into tetragonal structure at RT Chapter 11

Silicate Structures Basic building block - SiO44- tetrahedron Or Si2O76-; Si3O96-; Si6O1812- (ring)

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

Chapter 11

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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 Chapter 11

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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

Chapter 11

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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

Chapter 11

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Substitutional crystals Na+ substitution by K+

Cl- substitution by Br-

Substitutional ions are about the same size as 11 the “host” ions Chapter

Vegard’s law Vegard’s law is an approximate empirical rule States that a linear relation exists (T = const) between the crystal lattice constant of substitutional compound (alloy) and the concentration of the constituent elements

6.3 6.2

175

6.1 6.0

170 3

Volume, V [Anstr ]

Lattice constant, a [Anstr]

6.4

5.9 5.8 5.7 5.6

0.0

NaCl

0.2

0.4

0.6

% of K

0.8

1.0

KCl

165 160 155 150

0.0

AO2

NaCl ⇒ Na1-xKxCl ⇒ KCl

0.2

0.4

0.6

% of B

0.8

1.0

BO2

Chapter 11

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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:

NV = N × e

−

EV kT

NV - # of vacancies N - number of lattice sites EV – energy required to form a vacancy EV = 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 #

Chapter 11

From G. Gottstein

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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

Chapter 11

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Zirconia (Zirconium oxide) 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

Tetragonal structure stabilization by addition of 10mol% of CaO, MgO, Y2O3 – fully stabilized zirconia Stabilization by addition ~9mol% of MgO partially stabilized zirconia 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 Chapter 11

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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} Involve ions of the opposite charge

Chapter 11

Toughness of Ceramic Material K 1 = Y σ πa K1 - Stress intensity factor σ - Applied stress a - edge crack length Y - geometric constant

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

= Y σ f πa

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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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; CaF2 fluorite; 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?

Chapter 11

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