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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?