Ceramics

Fundamental Engineering Materials (MA1002)

Associate Professor Sandy Chian School of Mechanical & Aerospace Engineering

MA1002-‐Fundamental Engineering-‐On Line Course Materials 1

Text Book •  William D. Callister, David G.Rethwisch “Materials Science and Engineering – An IntroducMon” 8th EdiMon, John Wiley and Sons, 2011


Course Learning ObjecBves •  To understand the Materials around us:

– Understand the fundamental building blocks of Materials [(Chapters 1 & 2)]

–  The inter-‐relaBonship between •  these building blocks (atoms), •  their arrangements (structures and processes) and •  their impact on properBes (applicaBons) [(Chapters 3 – 9)]


Topics to be Introduced Ceramics (Chapter 12)

Polymers (Chapters 14, 15) Composites (Chapter 16)

•  What are these materials? •  What are their structures and properBes? •  What are they used for?


Review QuesBons on Bondings •  Important to recap the different types primary and secondary bonds in materials. – Refer to Professor Shearwood’s notes if needed.

•  See Ceramic Review QuesBon Set 1 MA1002-‐Fundamental Engineering-‐On Line Course Materials 5

Review QuesBon Set (1)



Ceramics

Structures & ProperBes


What are Ceramics?


Common items associated with the term Ceramics: Porcelain, chinawares, bricks, crystal vase, floor Mles, oven ware, etc.….. Materials known for their high compressive strengths, heat resistance BUT briWle

Atoms in Ceramics •  Ceramics are inorganic, non-‐metallic materials consisMng of

– Metal atoms (e.g. Iron, Aluminum, Calcium, etc )and –  non-‐metal atoms (e.g. Oxides (O), Nitrides (N), and Carbides (C)) elements

•  Refer to Periodic Table for examples of Metals and Non-‐Metals

•  These metallic and non-‐metallic elements are bonded together primarily by ionic or covalent bonds or both


Periodic Table

MA1002-‐Fundamental Engineering-‐On Line Course Materials 11 Figure 2.6: Callister & Rethwisch, 8th ediMon

Examples of Ceramics Oxide based Ceramics

– Aluminum oxides (Al2O3)

–  Silicon dioxide (SiO2)

–  Sodium Silicate (Na2SiO3)

Non-‐oxide based Ceramics – Silicon nitride (Si3N4)

– Tungsten carbide (WC)


Comparison with Metals Metals •  Crystalline •  Metallic bond •  Free electrons •  Good thermal/electrical conducMvity •  Opaque •  High tensile strength •  Low shear strength •  PlasMc flow •  High density •  Moderate hardness

Ceramics •  Crystalline/Amorphous •  Ionic/Covalent •  CapMve electrons •  Poor thermal/electrical conducMvity •  Transparent/Opaque •  Poor tensile strength •  High shear strength •  None •  IniMal low density •  High hardness


See Review QuesBon set (2) on Molecular Structures

•  The concept of Crystal and Amorphous structures were covered in previous lectures (Prof Shearwood & Prof Tan) and its Mmely to recap them at this juncture before proceeding.

•  ObjecMve is to re-‐cap what the terms “crystalline” and “amorphous” structures mean and how these properMes and bonding influence material behaviours.





Ceramic Materials Outline •  Firstly we shall introduce Ceramics in terms of their ApplicaMon classificaMons …..

•  Following that we will explore their various Structures and Morphologies

•  And finally, how these structures & morphologies affect their properMes (and applicaMons)


2 Main ClassificaBons of Ceramics in Terms of their ApplicaBons

•  TradiBonal (ConvenMonal) Ceramics –  Clay based products

•  Porcelains, tableware, pokeries, etc.

•  Fine Ceramics –  Structural Ceramics

•  Used for their mechanical and engineering properMes

–  FuncBonal Ceramics •  ApplicaMons other than mechanical strength such as electrical, opMcal and or

magneMc properMes



ConvenBonal Ceramics

versus

Fine Ceramics

TradiBonal (ConvenBonal) Ceramics •  Made from 3 Principal Components:

•  Clay: Consists of hydrated aluminum silicates with small amounts of other oxides such as TiO2, Fe2O3, MgO, CaO, Na2O and K2O

–  FuncMon is to provide workability of the materials before firing hardens it and consMtutes the major body material.

•  Silica: (Also known as flint or quartz) has a high melBng component and its funcMon is to provide high temperature properMes

•  Potash feldspar: Basic composiMon K2O/Al2O3.6SiO2 –  has a low melBng temperature and makes a glass when the

ceramic mix is fired and bonds the refractory components together.


PlasBcity of clay allows shaping of tradiBonal ceramic product

21

hkps://www.youtube.com/watch?v=aCkIgAcj644


Fine Ceramics

Structural (Engineering) Ceramics •  Refers mainly to ceramics with excepBonal mechanical properBes (i.e.

high tensile load, compressive strength, wear resistance, etc.)

•  Mainly pure compounds or nearly pure compounds of predominantly oxides, carbides or nitrides.

•  Examples of important engineering ceramics: –  Alumina (Al2O3) –  Silicon nitride (Si3N4) –  Silicon carbide (SiC) –  Zirconia (ZrO2)


FuncBonal Ceramics •  Refers to ceramics that have special properBes such as electrical, magneMc, dielectrical, opMcal, etc.

•  Examples include: –  Barium Mtanate: mechanical transducer, ceramic capacitors

–  Bismuth stronMum calcium copper oxide: High temperature super conductors

–  Lead zirconate Mtanate (PZT): Ultrasonic transducer


FuncBonal Ceramics


Ni-‐LaNbO4 La-‐(Sr)MnO3 Fibre opMcs

Advanced Ceramics


HydroxyapaMte for bone implants

Space shukle shield

Ceramics in Space Engineering


Ceramic Review QuesBon Set (3)



Structure & Morphology


4 ClassificaBons of Ceramics Morphology •  Polycrystalline ceramics

–  Alumina, Silicon carbide, silica

•  Glass –  Amorphous

•  non-‐crystalline

–  Glass Ceramics •  Small crystalline precipitates in glass matrix •  (Schok’s Ceran™ ceramic cooktop panels)

–  Porcelain •  Large crystals in glass matrix •  Heterogeneous microstructures


General ProperBes of Ceramics •  Hard and brikle with low toughness and ducMlity

•  Low thermal and electrical conducMvity

•  High melMng point and chemical resistance

•  Low thermal coefficient of thermal expansion


ProperBes (Density)


Lower than metals

ProperBes (Mechanical)


Similar to metals

ProperBes ( Toughness)


Lower than metals

ProperBes (Electrical)


insulators

Lower conducBvity than metals

What Determines Ceramic ProperBes? •  Chemical composiBons

–  Types of atoms and bondings

•  Micro-‐ and Nano-‐ Structures

•  Defects –  Point, line, or planar defects –  Refer to Prof. Shearwood’s notes on defects


Bonding in Ceramics •  Can be ionic and/or covalent.

– Many ceramics exhibit both bonds

–  Ionic character of the bond depends on the electronegaMviMes of the atoms present


Percentage Ionic Character •  Greater the difference in electronegaBvity of the atoms, the more ionic the bond.

•  Percentage Ionic Character:

where XA and XB are the electronegaBviBes for the respecMve elements


% Ionic character = {1- exp[- (0.25)(XA - XB )2 ]} *100

42

Adapted from Fig. 2.7, Callister & Rethwisch 8e. (Fig. 2.7 is adapted from Linus Pauling, The Nature of the Chemical Bond, 3rd ediMon, Copyright 1939 and 1940, 3rd ediMon. Copyright 1960 by Cornell University.)

• Degree of ionic character may be large or small:

Ionic Characteristics in Ceramics

SiC: small

CaF2: large

MA1002-‐Fundamental Engineering-‐On Line Course Materials

Is Si-‐C bond Ionic or Covalent? •  ElectronegaMvity values of Si and C are 1.8 and 2.5 respecMvely

•  Si-‐C bond is 88.5% covalent in character MA1002-‐Fundamental Engineering-‐On Line Course Materials 43

% ionic character = 100 {1-exp[-0.25(XSi − XC )2 ]} =11.5%

Review QuesBon Set (4) •  Sample calculaMons for the students to try ….



Ceramic Structure Stability •  Two important condiMons for ceramic crystal structure stability: – Charge Neutrality – Maximum contact between CaBons and Anions • Determined by the Co-‐OrdinaBon Number (CN)


•  Bulk ceramic must remain electrically neutral – i.e. the Net Charge must be Zero – Determined by the molecular formula (AmXp, where m and p values to achieve charge neutrality) • “m” and “p” are associated with the valencies of atoms X and A respecMvely.


Charge Neutrality

Does MgO2 exists? •  Consider the element’s electronic valence state:

– Mg: Mg2+ (divalent) – O: O2-‐ (divalent)

•  Net charge per MgO2 molecule = 1(2+) + 2(2-‐) = -‐2 –  i.e. a net negaBve charge, which is Not Allowed


Allowable Ceramic Stoichiometry •  Mn-‐O: Mn2+O2-‐; Net charge = 1(2+)+1(2-‐) = 0

•  Mn-‐F2: Mn2+F2-‐; Net charge = 1(2+)+2(1-‐) = 0

•  Ti-‐O2: Ti4+O2-‐2; Net charge = 1(4+)+2(2-‐) = 0

•  Al2-‐O3: Al3+2O2-‐3; Net charge = 2(3+)+3(2-‐) = 0


50

Significance of Cation-Anion Contact

“Stable” and “Unstable” structures

Adapted from Fig. 12.1, Callister & Rethwisch 8e.

-‐ -‐ -‐ -‐ +

unstable

-‐ -‐ -‐ -‐ +

stable

-‐ -‐

-‐ -‐ +

stable


CaBon & Anions not in contact

CaBon & Anions in contact

•  The maximum contact between caMons and anions is determined by the relaMve size of the ions.

•  Co-‐ordinaBon number (CN) & Ionic Radii –  Dependent on radius raBo of caBon to anion (rc / ra)

–  For a given co-‐ordinaMon number, there is a criBcal (minimum) radius raBo rc / ra , for which this caBon-‐anion contact is established.


Co-‐OrdinaBon Number

52

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

• Answer:

550014000770

anion

cation

...

rr

=

=

based on this raMo, -‐-‐ C.N = 6 because

0.414 < 0.550 < 0.732

-‐-‐ crystal structure is NaCl Data from Table 12.3, Callister & Rethwisch 8e.

Sample Problem: Predicting the Crystal Structure of FeO

Ionic radius (nm) 0.053 0.077 0.069 0.100

0.140 0.181 0.133

CaBon

Anion

Al 3+

Fe 2 +

Fe 3+

Ca 2+

O 2-‐

Cl -‐

F -‐


53

Ionic Radius Ratio, Coordination Number and Crystal Structure

ZnS (zinc blende)

NaCl (sodium chloride)

CsCl (cesium chloride)

Adapted from Table 12.2, Callister & Rethwisch 8e.

2

r caBon r anion

Coord No.

< 0.155

0.155 -‐ 0.225

0.225 -‐ 0.414

0.414 -‐ 0.732

0.732 -‐ 1.0

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4

6

8

linear

triangular

tetrahedral

octahedral

cubic



Types of Crystal Structures AX AX2

ABX3 (not covered)


AX-‐Type Crystal Structures •  Ceramics with equal numbers of caBons and anions.

•  Several different crystal structures possible, which are named axer a common material that assumes the parMcular structure –  Rocksalt (NaCl) :-‐ Octohedral –  Caesium Chloride (CsCl) :-‐ Cubic –  Zinc Blende (ZnS) :-‐ Tetrahedral


57

Rock Salt Structure i.e. NaCl (sodium chloride or rock salt) structure

rNa = 0.102 nm

rNa/rCl = 0.564 (bet 0.414 and 0.732) (i.e. CN = 6)

∴  anion (Cl-) prefers octahedral sites


rCl = 0.181 nm

4 Na+ and 4 Cl-‐ ions per unit cell


Octahedral Sites


59

CsCl Structure 939.0

181.0170.0

Cl

Cs ==−

+

r

r


∴ Since 0.732 < 0.939 < 1.0, Hence CN = 8 and cubic

sites preferred

So each Cs+ has 8 neighbor Cl-


Each unit cell of CsCl has 1-‐Cs ion and 8-‐Cl ions

Zn Blende (ZnS) Crystal Structure


All corners and faces are occupied by sulfur ions (4 per unit cell)

Zn atoms fill interior tetrahedral posiMons

Most highly covalently bonded compounds exhibit this type of crystal structure

rZn2+/rS2-‐ = 0.402, hence CN = 4

4 ZnS molecules per unit cell

Tetrahedral Sites


AmXp Type Crystal Structures •  Where charges on CaMons and Anions are not the same where “m” and/or “p” ≠ 1 –  i.e. AX2

•  Common crystal structure is found in fluorite (CaF2)

•  Other compounds include ZrO2 (cubic), UO2, PuO2 and ThO2


63

CaF2 Crystal Structure •  Molecular formula of Calcium

Fluorite (CaF2) •  No of Ca2+/unit cell = 4 •  No of F-/unit must be 8

•  Ca2+ cations in FCC (CN=8) •  F- anions in tetrahedral (CN = 4)

• i.e. Each Ca2+ co-ordin. with 8 F- Each F- co-ordin with 4 Ca2+


fluorine

calcium



66

Density Computations for Ceramics

A

AC )(NV

AAn

C

Σ+Σ"=ρ

Number of formula units/unit cell

Volume of unit cell Avogadro’s number

= sum of atomic weights of all anions in formula unit

€

ΣAA

€

ΣAC = sum of atomic weights of all caBons in formula unit

Formula unit = All the ions that are included in the chemical formula unit. For example: BaTiO3 = one Barium, one Ti, and three Oxygen.


(n’): Formula Units/Unit Cell


No. of Na+ per unit cell = 4

To maintain charge neutrality in NaCl, there must also be 4 Cl-‐

Hence there are 4 molecules of NaCl per unit cell, i.e. n’ = 4

Refer to Example problem 12.3 in Callister’s 8th EdiBon (page 463)

What about n’ for CaF2 ?


No. of Ca2+/unit cell = 4

There must be 4 molecules of CaF2 per unit cell of CaF2

n’ for CaF2 is therefore 4

Summary (1) •  Interatomic bonding in ceramics ranges from purely ionic

to totally covalent

•  Predominantly Ionic –  Metallic caMons are posiMvely charged; Non-‐metallic anions are negaMvely charged

–  Crystal structure is determined by (a) the charge magnitude on each ion, and (b) the radius of each type of ion


Summary (1) •  Many of the simpler crystal structures are described in terms of

unit cells: –  Rock Salt (AX) –  Cesium chloride (AX) –  Zinc blende (AX) –  Calcium Fluorite (AmXp)

•  Some crystal structures may be generated from the stacking of close-‐packed planes of anions; caMons fill intersMMal tetrahedral and/or octahedral posiMons that exists between adjacent planes.


Ceramics Review QuesBons 5 •  Re-‐cap on calculaMng unit cell dimensions and unit cell volumes, etc…

•  PracMce calculaMon on co-‐ordinaMon number and determinaMon of crystal structures.



Common, Abundant Ceramics


Silicates

Silicate Ceramics •  Silicate ceramics consist of silicon and oxygen atoms (ions) bonded

together in various arrangements. –  Silicon and oxygen are the two most abundant elements found in the earth’s

crust

•  Commonly found in naturally occurring minerals like clay, feldspars and micas

•  Useful engineering materials due to low cost, availability, and special properMes –  ConstrucMon materials as glass, portland cement, and brick –  Electrical insulators


Structure of Sand •  Common name is Silicon Oxide (SiO2) or silica •  In reality there is no discrete molecules of SiO2 in sand but a network of bonds: –  Each silicon atom is bonded to 4 oxygen atoms –  Each oxygen is bonded to 2 silicon atoms

•  Structure of sand is formed by bonding of structural repeaMng units of SiO4

4-‐ ions (orthosilicates)


Silicate Ceramics


Si4+

O2-

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

Tetrahedral structure (i.e. Orthosilicate Ion)

Basic building block of silicate ceramics is the Tetrahedral SiO44-‐

Each singly bonded oxygen has a single negaBve charge

Various Silicate Structures •  Different silicate structures can be formed depending on how the tetrahedra are linked together through their verBces.

•  Tetrahedra are linked through a shared oxygen atom


78

Bonding of adjacent SiO44- accomplished by the sharing of

common corners, edges, or faces

Silicates


Mg2SiO4 Ca2MgSi2O7


Example of silicate

compounds: Na2Ca2Si3O9

Single Strand Silicate Structure


Single strand silicate formed by tetrahedra linked through a shared oxygen atom.

RepeaBng unit = Si2O64-‐ or as simplest formula SiO3

2-‐

Example of single strand silicate structure: enstaBte, MgSiO3 which consist of rows of single-‐strand silicate chains with Mg2+ ions between the strands to maintain charge neutrality

Other of Silicate Structures •  Ordered Structures

– 2-‐D Layered sheet – 3-‐D Crystalline (Network)

•  Disordered structured – Glass


81

2-D Layered Silicates •  Tetrahedra connected to 3 others to form

2-D sheet structure •  Repeating unit for layered silicate sheet

is (Si2O5)2-

•  Negative charge balanced by

adjacent plane rich in positively charged cations

•  Examples: Talc, mica, clay

•  Layered structure offers lubricity MA1002-‐Fundamental Engineering-‐On Line Course Materials

82

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

Layered Silicates (cont.)

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



NegaMvely charged layer

PosiMvely charged layer


Forms a Network Structure which gives SiO2 its strength and high melBng point.

i.e. similar to Diamond

3-‐D Network Crystalline Silicate Quartz (Silica) is a crystalline silicate

containing pure silicon dioxide (SiO2)

Diamond

Quartz

84

Glass is non-‐crystalline (amorphous) contains impurity ions such as Na+, Ca2+, Al3+, and B3+ (which are network disruptors)

(soda glass)


Glass Silicate

Si 4+

Na +

O 2 -‐


Network is disrupted & losing

3D regularity

Summary (2) •  Silicate structures are more conveniently represented in terms of interconnecBng SiO4

4-‐ tetrahedra.

•  Complex structures may result when other caMons (e.g Ca2+, Mg2+, Al3+) and anions (e.g. OH-‐) are added.

•  Silicate ceramics include crystalline silica (Quartz), layered silicates and non-‐crystalline silica glasses



Carbon HybridisaMon of Carbon

Graphite Diamonds


88

Structure of Carbon

•  Atomic number = 6 •  No. of proton = 6 •  No. of electrons = 6 •  Atomic mass = 12g/mole

•  Electronic configuraBon –  1s2 –  2s2 2p2

MA1002-‐Fundamental Engineering-‐On Line Course

89

Various Structural Forms of Carbon


Sheet-‐like (Graphite)

Fullerene (Ball)

Diamond (Network)

90

Methane •  Simplest organ compound of carbon.

•  Molecular structure : CH4

•  All the C-‐H bonds are the same.

•  Important QuesBon: –  How can carbon with two kinds of orbitals (2s and 2p) forms 4 idenBcal bonds with hydrogen (1s)?


Carbon-‐Hydrogen Covalent Bond


Unhybridised C: 1S2, 2S2 2P2

C H

2S1

2S1

1S1 2P1 2P1

Expect at two different bond lengths when the C forms covalent bond with 4 hydrogen

atoms to form methane

BUT all C-‐H covalent bonds are the same length

ResoluBon to QuesBon? •  Have to find a way of resolving how electrons with different orbitals in C (i.e. 2s and 2p) combine to form equivalent orbitals.

•  Need to introduce the concept of HybridisaBon.


HybridisaBon •  HybridisaMon relates to a combinaMon of atomic orbitals of a

single atom. A mathemaMcal concept introduced by Linus Pauling.

•  For Carbon, one s orbital and three p orbitals can combine or hybridise to form 4 equivalent (sp3) atomic orbitals with tetrahedral orientaBon.

•  Other hybridisaMon of Carbon involving combinaMon of different

orbitals are also possible, i.e. sp2 and sp MA1002-‐Fundamental Engineering-‐On Line Course Materials 93


Other types of hybridisaBon and the resultant shapes of the orbital

95

sp3 Hybrid


S

p

sp3

4 sp3

96

Methane Structure


109.5o

97

Ethane Structure


sp3 hybridised

98

Other Carbon HybridisaBon •  One 2s-‐orbital and three 2p-‐orbitals can be hybridised into the following states:

–  Four sp3 (as in carbon in methane, C-‐H)

–  Three sp2 hybrid orbitals with one 2p-‐orbital unhybridised (e.g. alkene, -‐C=C-‐)

–  Two sp hybrid orbitals with two 2p-‐orbital unhybridised (e.g. alkyne, -‐C≡C-‐)


99

sp2 HybridisaBon


sp2

3 sp2

s

p

100

Ethylene Structure


120o

sp2 hybridised

Double Bonds

MA1002-‐Fundamental Engineering-‐On Line Course Materials 101 hkp://en.wikipedia.org/wiki/Double_bond

The double bonds in ethylene C=C is due to (1)  sp2-‐sp2 overlap (sigma bond) and (2)  overlapping of the unhybridised p-‐orbitals of both carbons (pi-‐

bond)

102

sp HybridisaBon


2 sp orbitals

s

p

103

Ethyne Structure


sp -‐ hybridised

CΞC Triple Bond •  The triple bond between the two carbon atoms are due to:

•  (1) sp – sp overlap (sigma bond) •  (2) py – py overlap (pi bond) •  (3) pz – pz overlap (pi bond)


Insert separate video on the impact of hybridisaMon on shape

of atoms and molecules



Summary 3 •  The hybridisaMon state of carbon determines the type of bond formed: –  sp3 => Single Bond (all sigma bonds) –  sp2 => Double Bond (one sigma + one pi-‐bond) –  sp => Triple Bond (one sigma + two pi-‐bonds)

–  The overlapping pi-‐orbitals to form pi-‐bonds give rise to bond sBffness and enables electrons in pi-‐orbitals to delocalise.


Allotropes of Carbon

108

a = Diamond b = Graphite c = Lonsdaleite d = Buckyball (C60) e = C540 f = C70 g = Amorphous carbon h = Single walled carbon nanotube (Buckytube)


Atoms of the element are bonded differently together.

Graphite •  A polymorphic form of Carbon

•  Although not a compound of a metal and a non-‐metal, it is someMmes considered a ceramic material.

•  Graphite has a layered structure in which the carbon atoms in the layers are strongly covalently bonded in hexagonal arrays

•  The layers are weakly bonded by secondary bonds so allowing the layers to slide past each other. Hence giving graphite its lubricaMng properMes.

109 MA1002-‐Fundamental Engineering-‐On Line Course Materials

110

Structure of Graphite –  layered structure – parallel hexagonal arrays of carbon

atoms

–  weak van der Waal’s forces between layers –  planes slide easily over one another



Line indicates VDW

forces not primary bonds

C-‐HybridisaBon in Graphite


Adapted from NTU.AC.UK Unhybridised p-‐orbital overlaps. Graphite layer is flat. Electrons are delocalised in the p-‐orbital, i.e. electron conducBve

overlappingpi-‐bond

sigma-‐bond

112

Structure of Diamond –  Tetrahedral bonding of carbon –  Network structure

•  hardest material known •  very high thermal conductivity but

electrical insulator –  large single crystals – gem

stones –  small crystals – used to grind/

cut other materials –  diamond thin films

•  hard surface coatings – used for cutting tools, medical devices, etc.



sp3-‐sp3 sigma bond

Show model of Graphite and Diamond

The impact of hybridisaMon on shape of Molecules



Diamond versus Graphite

•  Diamond –  Carbon is sp3-‐hybridised –  Pyramidal (tetrahedral) structure –  All electrons are Mghtly held by the

carbon atoms –  Non-‐electron conducMve –  OpMcally clear due to high

refracMve index –  Structure is very rigid –  Good thermal conductor (800

Mmes beker than graphite)

•  Graphite –  Carbon has 3 sp2 and one p-‐orbital –  Flat hexagonal structure –  Electrons in the p-‐orbital are delocalised

and are electron conducMve –  The p-‐orbital absorbs electrons/phonons,

hence opMcally opaque –  Sheet structure held together by weak

VDW forces. Appears as smooth and sox as layers can slide.

–  Bonds in each graphite sheet are very strong.

–  Good thermal conductor but less than diamond


116

Other Polymorphic Forms of Carbon 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.



MA1002-‐Fundamental Engineering-‐On Line Course Materials 118 hkp://www.youtube.com/watch?v=xVZRGcg-‐BXI

Buckyball


Carbon Nanotubes

hkp://www.youtube.com/watch?v=-‐OKyTmM_faA

Summary 4 •  The hybridisaMon state of carbon determines the nature of the bond present: – Single (sp3) – Tetrahedral (Diamond) – Double (sp2) – Planar (Graphite) – Triple (sp) -‐ Linear


Summary 4 •  Carbon may exist in several polymorphic forms: Diamond,

Graphite, Fullerenes, and Nanotubes

•  Each of these material has its own unique properMes: –  Diamond (hardness, high thermal conducMvity) –  Graphite (high-‐temperature chemical stability, good lubricity) –  Fullerenes (electrically insulaMve, conducMve or semi-‐conducMve)

–  Carbon nanotubes (extremely strong and sMff, electrically conducMve or semi-‐conducMve)





ImperfecBons in Ceramics


Causes of ImperfecBon •  Structural imperfecMon has significant impact on the properMes of the material/product

•  ImperfecMon could be due to: – Manufacturing processes giving rise to porosity, cracks, etc

–  Inherent structural defects due to atoms arrangement creaMng point defects.


Atomic Level Point Defects •  ImperfecMon at atomic level is due to the introducBon of caBons and/or anions with different charges OR size as addiMves or impuriMes in the ceramics.

– The necessity to maintain charge neutrality gives rise to several point defects in ceramics


127

• Vacancies -‐-‐ vacancies exist in ceramics for both caBons and anions • IntersBBals -‐-‐ intersMMals exist for caBons -‐-‐ intersMMals are not normally observed for anions because of their size

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

Point Defects in Ceramics (i)

CaMon IntersMMal

CaMon Vacancy

Anion Vacancy


128

• Frenkel Defect -‐ a caBon vacancy-‐caBon intersBBal pair. • ShoWky Defect -‐ a paired set of caBon and anion vacancies.

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

Point Defects in Ceramics (ii)


These defects occur in pairs to maintain charge neutrality

ShoWky Defect

Frenkel Defect

Example of Point Defect FormaBon


Case (1): SubsBtuBonal CaBon

Pure NaCl

Ca 2+

AddiMon of Ca2+ impurity

Each Ca2+ (divalent) will replace 2 Na+ (monovalent)

to maintain charge neutrality

with impurity

Ca 2+

caBon vacancy

One Ca2+ occupy the displaced Na+ caBon and to maintain charge neutrality another Na+ has to be removed, i.e. caBon vacancy

Na + Cl -‐

Case (2): SubsBtuBonal Anion


Pure NaCl

2-‐ O impurity

O

Each O2-‐ (divalent) will replace 2 Cl-‐ (monovalent) to maintain

charge neutrality

One O2-‐ occupy the displaced Cl-‐ anion and to maintain charge neutrality another Cl-‐ has to be removed, i.e. anion vacancy

Cl-‐ vacancy

NaCl with oxygen impurity

Oxygen anion

Case (3): OxidaBon of Fe2+ to Fe3+


Fe2+

O2-‐ Before Fe2+ oxidaBon

What happens when 2 Fe2+ oxidised

to form Fe3+

SoluBon


(Col A)

Original of +’ve charges (i.e. Fe2+)

(Col B)

Original –’ve charges

(O2-‐)

Col A + Col B

NeW Charge

Before OxidaBon

(Col C)

Final +’ve charges aser

Fe2+ oxidaBon

(Col D)

Final –’ve charges

Col C + Col D

NeW Charge

Aser oxidaBon

10(2+) = 20+

10(2-‐) = 20-‐

0 8(2+) + 2(3+) = 22+

10(2-‐) = 20-‐

2+

One neW 2+ charge forms for every 2 Fe2+ undergoing oxidaBon to Fe3+

To maintain charge neutrality two possible scenarios:

(a) Create a Fe2+ vacancy (b) Create a O2-‐ intersBBal OR X


Fe2+ vacancy

Fe3+

Fe2+

O2-‐

Point Defect aser Fe2+ to Fe3+ transformaBon

Porosity in Ceramics •  Ceramics are oxen processed from powder and involved

compacMon under very high pressure and temperature.

•  Pores and voids between parMcles are present during compacMon, and during heat treatments much of these pores are eliminated. Oxen some pores sMll remain.

•  Porosity in ceramics significantly reduces their elasMc property and strength.


Summary 5 •  Atomic point defects, intersMMals and vacancies for each anion and caMon type are possible.

•  Electrical charges are associated with atomic point defects in ceramic materials, defects someMmes occur in pairs (e.g. Frenkel and Schokky) in order to maintain charge neutrality.


Summary 5 •  In stoichiometric ceramic the raMo of caMons to anions is the same as predicted

by the chemical formula.

•  Non-‐stoichiometric materials are possible in cases where one of the ions may exist in more than one ionic state, e.g. Fe(1-‐x)O for Fe2+ and Fe3+

•  AddiMon of impurity atoms may result in the formaMon of subsBtuBonal or intersBBal solid soluMons. For subsMtuMonal, an impurity atom will subsMtute for that host atom to which it is most similar in an electrical sense.





Mechanical ProperBes of Ceramics

Why are Ceramics BriWle?


Crystalline Ceramics •  At room temperature (or sub-‐ambient) most ceramics fracture before the onset of plasMc deformaMon.

•  Most crystalline ceramics, which are predominantly ionic bonding, have very few slip systems along which dislocaMons may move.

•  Porous nature of ceramics MA1002-‐Fundamental Engineering-‐On Line Course Materials 140

Effect of Bonds in Ceramics on PlasBc DeformaBon

•  Crystalline (ionic) ceramics –  electrostaMc repulsion between ions when brought into close proximity of each other limits the amount slip.

•  Crystalline (covalent) ceramics –  Strong covalent bonds between atoms –  Very limited slip system –  Complex dislocaMon structure


Crystalline (Ionic) Ceramics


(a): Atoms are held by ionic bonds, i.e. each ion is surrounded by oppositely charged ions

(b): Any aWempt by the ions to slip past one another in response to the applied force is faced with strong repulsive coulombic forces. This makes slipping very difficult and the material responds by breaking. This is briWle failure.

DeformaBon in Non-‐Crystalline Ceramics

•  No plasMc deformaMon can occur by dislocaBon moBon due to absence of regular atomic structure.

•  Material deforms by viscous flow

•  In viscous flow, the material response to an applied shear stress, by sliding atoms or ions past each other by the breaking and re-‐forming of interatomic bonds.


Impact of Porosity of Tensile Strength •  Pores

– Reduces the cross-‐secMonal area across which load is applied

– Acts as stress concentrator •  For an isolated spherical pore, an applied tensile stress is amplified by a factor of 2


Effects of Porosity


σ fs =σ o exp −nP( )E = Eo 1−1.9P + 0.9P2( )

Modulus of ElasBcity Flexural Strength

Eo = Modulus of non-‐porous material σ0 and n are experimental constants; P = volume fracMon

Summary 6 •  Microcracks in ceramics are hard to control and tensile

stresses are amplified resulMng in low fracture strengths (flexural strengths)

•  Fracture strengths varies according to size of crack-‐iniBaBng flaws, and vary from sample to sample.

•  Stress amplificaMon does not occur in compression, hence ceramics are stronger in compression.


Summary 6 •  Brikleness is due to the limited operable slip systems and

dislocaBon moBon

•  PlasMc deformaMon for non-‐crystalline is by viscous flow. ViscosiMes of many non-‐crystalline ceramics are very high.

•  Many ceramics have residual pores and this reduces their modulus of elasMcity and flexural strengths.




Ceramics

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