ceramic final

7/29/2019 Ceramic Final

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Prepared by Dr. Ang Bee Chin1

Ceramic Materials

Structures and Mechanical

Properties


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Structures of ceramic materials:How do they differ from those of metals?

Point defects:

How are they different from those in metals?

Impurities:

How are they accommodated in the lattice and how

do they affect properties?

Mechanical Properties:What special provisions/tests are made for ceramic

materials?

Issues to Address


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Introduction

Ceramic materials

Inorganic, compounds between metallic and non-metallicelements

Bonded by ionic or covalent bond or combination of two

Relatively stiff and strong, very hard and extremely brittle

More resistant to high temperature and harsh environments thanmetals or polymers

Examples: aluminum oxide (Al2O3), silicon dioxide (SiO2), siliconcarbide (SiC), silicon nitride (Si3N4), clay minerals, cement, glass


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Common objects made of ceramic materials

Building

brick

Glass vaseCup

ScissorsFloor tile

Introduction


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Ceramics used for engineering applications can be divided into two

groups

Traditional ceramics: primary raw material is clay

Example: porcelain, bricks, tiles, glasses

Engineering ceramics: consist of pure or nearly pure compoundsExample: aluminum oxide (Al2O3), silicon carbide (SiC), siliconnitride (Si3N4)

Introduction


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Prepared byDr. Ang Bee Chin6

Bonding:

-- Mostly ionic, some covalent.

-- % ionic character increases with difference in

electronegativity.

Large vs small ionic bond character:

Ceramic Bonding

SiC: small

CaF2: large


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Atomic bonding ranges from purely ionic to totally covalent

Many ceramics have combination of ionic and covalent bondsThe percentage ionic character (%IC) depends on the differencein electronegativity

The greater the difference, the more ionic the bond, %ICcan be predicted using Paulings equation

XA andXB are the electronegativities for the respective elements

Ceramic Bonding

% IC = 1-e-0.25 (XA-XB)2

x 100%



Ionic and Covalent Bonding in Simple Ceramics



Example

Calculate the ionic percentage of SiC (XSi = 1.8 and XC = 2.5).



Crystal Structures

More complex than those of metals since ceramics are composedof at least two elements

Crystal structures may be thought of as being composed ofelectrically charged ions (cations and anions) instead of

atoms

Ionic solids tend to have their ions packed together as denselyas possible to lower the overall energy. Cation prefers to haveas many as possible nearest-neighbor anions and vice versa



Crystal structure is influenced by the packing of ions and

the packing of ions depends by two characteristics of ions:

1. Magnitude ofelectrical charge

The crystal must be electrically neutral

2. Relative sizes of the cations and anions

Cations (give up electron) are ordinarily smaller than anions(receive electron).


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Ionic Bonding & Structure

1.Size - Stable structures:

--maximize the # of nearest oppositely charged neighbors.- -

- -+

unstable

- -

- -+

stable

- -

- -

+

stable

If the anion does not touch the cation, then the

arrangement is unstable.



Stable ceramic crystal structures form when anions surrounding a

cation are all in contact with that cation

The number of anion nearest neighbors for a cation (coordinationnumber) is related to the cation-anion radius ratio (rC/rA)

For a specific coordination number, there is a critical or minimumratio (rC/rA)min for which this cation-anion contact is established(purely geometrical considerations)

Critical radius ratio for stability for coordination numbers 8,6 and

3 are >0.732, >0.414 and > 0.155 respectively.




2. Charge Neutrality:

--Net charge in the structure should be zero.

--General form:

CaF2:Ca 2+

cation

F-

F-

anions+

AmXp

m, p determined by charge neutrality




Anion locations

Two sides

Corners of equilateraltriangle

Corners of tetrahedron

Corners of octahedron

Corners of cube

Crystal Structures



1. Calculate the critical (minimum) cation-anion radius ratio(rC/rA)min for the coordination number 3

Example

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



Ionic radius (nm)

0.053

0.077

0.069

0.100

0.140

0.181

0.133

Cation

Anion

Al 3+

Fe 2+

Fe 3+

Ca 2+

O2-

Cl -

F-

3. On the basis of ionic radii, what crystal structure would you

predict for FeO?

Example



Types of Crystal Structures

AX-type crystal structures

Equal numbers of cations and anionsSodium chloride (NaCl) structureCesium chloride (CsCl) structureZinc blende/sulfide (ZnS) structure

AmXp-type crystal structuresCharges on cations and anions are different (m p 1)

Calcium fluoride (CaF2) structureZirconium dioxide (ZrO2) structure

AmBnXp-type crystal structuresMore than one type of cation (represented by A and B)

Barium titanite (BaTiO3) structure



Summary of some common ceramic crystal structures

Types of Crystal Structures



Sodium Chloride Crystal Structure

FCC arrangementof anions

Highly Ionically bonded with Na+ ions occupying interstitialsites between FCC and Cl- ions.

One cation at the cube center and one at the center of each of

the 12 cube edges

Radius ratio = 0.56, CN = 6. MgO, CaO, NiO and FeO

have similar structures.



MgO and FeO

MgO and FeO also have the NaCl structureO2- rO = 0.140 nm

Mg2+ rMg = 0.072 nm

rMg/rO = 0.514

cations prefer OHsites

So each oxygen has 6 neighboring Mg2+


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AX Crystal Structures

AXType Crystal Structures include NaCl, CsCl, and zinc

blende

939.0181.0

170.0

Cl

Cs

r

r

Cesium Chloride structure:

cubicsites preferred

So each Cs+ has 8 neighboring Cl-


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Cesium Chloride (CsCl) Structure

Anions located at each of the cube corners

One cation at the cube center

This is nota BCC crystal structure since ions of two different

kinds involved


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Zinc Blende (ZnS) Crystal Structue

Four zinc and four sulfur atoms.

FCC arrangement of S atom

S occupies lattice points and Zn occupies interstitial sites of

FCC unit cell.

S Atoms (0,0,0) ( , ,0) ( , 0, ) (0, , )

Zn Atoms ( , , ) ( , , )( ,, ) ( , , )

Atomic bonding is highly covalent.

(87% covalent character) with

CN = 8. CdS, InAs, InSb and ZnSe have

similar structures.

??529.0

140.0

074.0

2

2

O

ZnHO

r

r


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Mechanical Properties

We know that ceramics are more brittle thanmetals. Why?

Consider method of deformationslippage along slip planes

in ionic solids this slippage is very difficult

too much energy needed to move one anion past

another anion


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Ceramic Density Computations

Theoretical density of a crystalline ceramic material can bedetermined as follow

mass of unit cell = mass of total equivalent number of anions and cations


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Question 1:

Compute the theoretical density of sodium chloride (NaCl) on thebasis of crystal structure. Atomic weights of Na and Cl are 22.99g/mol and 35.45 g/mol respectively. The ionic radii of Na+ and Cl-are 0.102 and 0.181 nm respectively.

Example


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Compute the theoretical density of zinc blende (ZnS) on the basis of

crystal structure. Atomic weights of Zn and S are 65.37 g/mol and32.06 g/mol respectively. The ionic radii of Zn2+ and S2- are 0.06 and0.174 nm respectively.

Question 2


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Silicate Ceramics

Most common elements on earth are Si & O

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

material (1710C)

crystobalite

Si4+

O2-


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Silicate Ceramics

The structures of silicate ceramics

are generally complex: theatoms are not closely-packedtogether

Relatively low density due to non-closely-packed atoms

For the various silicate minerals, one,two or three of the corneroxygen atoms ofSi044- tetrahedra are

shared by other tetrahedra to formcomplex structures (often non-crystalline)


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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


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Combine SiO4

4-

tetrahedra by having them sharecorners, edges, or faces

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

Silicates


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Carbon and Its Allotropes

Carbon has many allotropes, i.e. exist in many crystalline forms

These allotropes have different crystal structures and

properties

Diamond

Graphite

Fullerenes

Carbon nanotubes

Carbon does not really fall within ceramic classification. Onlygraphite is often considered as ceramic materials


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Carbon and Its Allotropes

Diamond

Each carbon bonds to four other carbon (totally covalent). Its cryststructure is similar with Zinc Blende (ZnS)

Stiffest, hardest and least compressible material due to strong covabonding

Optically transparent, excellent electrical insulator and thermalconductor

Industrially, used to increase surface hardness, e.g. drills bits andcutting tools


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Carbon Forms - Graphite

Composed of layers of hexagonally

arranged carbon atoms layer structurearomatic layers

weak van der Waals forces

between layers and strong covalent

bonding within layers planes slide easily, good lubricant

Industrially, used as electrdes for

arc welding, pencils casting,

molds, high-temperaturerefractories


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Fullerenes

Exists in discrete molecular form Consists of a hollow spherical cluster of sixty carbon atoms

Single molecule is denoted by C60 and consists of 20 hexagonsand 12 pentagons arrangement such that no two pentagonsshare a common side

Has FCC structure with one C60 at each FCC lattice pointUsed in fuel cells, lubricants and semiconductors

Carbon Forms - Fullerenes


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Carbon FormsCarbon Nanotubes

Carbon nanotubes

Consists of a single sheet of graphite, rolled into a tube whereboth ends are capped with C60 hemispheres

Tube diameters are on the order ofnanometer, i.e. 100 nm or

less

Extremely strong and stiff; relatively ductile

Tensile strength of50-200 GPa; modulus of elasticity on theorder of1 TPa (Tetra-Pascal: 1TPa = 1000 GPa); fracturestrains 5-20%


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Frenkel Defect

--a cation is out of place. Shottky Defect

--a paired set of cation and anion vacancies.

Equilibrium concentration of defects

The equilibrium number of atomic defects increases with

temperature

kT/QDe~

Defects in Ceramic Structures

ShottkyDefect:

FrenkelDefect


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Defects in ceramics do not occur alone in order to maintain

electro-neutrality

Frenkel defect: Cation leaving its normal position andmoving into an interstitial site

Schottky defect: Removing one cation and one anion from

the crystal

Defects in Ceramic Structures


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Impurities must also satisfy charge balance = Electroneutrality

Ex: NaCl

Substitutional cation impurity

Impurities

Na+ Cl-

initial geometry Ca2+impurity resulting geometry

Ca2+

Na+Na+

Ca2+

cationvacancy

Substitutional anion impurity

O2-

impurity

O2-

Cl-

anion vacancy

Cl-

resulting geometryinitial geometry


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Defects in Ceramics

The equilibrium number of Frenkel and Schottky defectsincreases with temperature according to


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Prepared Dr. Ang Bee Chin42

Mechanical Properties of Ceramics

General properties

Relatively brittle, fracture occurs before any plastic deformationLarge difference between tensile and compressive strength(10 times higher in compression)

Strength depends significantly on the presence offlaws andporosity (void, decreases cross sectional area)


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Pre ared b Dr. An Bee Chin43


Stress-strain behavior

Stress-strain behavior is not usually ascertained by atensile test:

Difficulty in gripping brittle materials withoutfracturing them, ceramics fail after only 0.1% of strain

employed: three- or four-point bending test

Specimen is bent until fracture. Top surface undercompression, bottom surface under tension


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3-point bend test to measure room Tstrength.

Measuring Strength

FL/2 L/2

d= midpoint

deflection

cross section

R

b

d

rect. circ.

location of max tension

Flexural strength:

sfs

1.5FfL

bd2

FfL

pR3

(Rectangular cross sectional area)

(Circular Cross sectional area)


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Flexural strength

Defined by the stress at fracture during the bending

testComputed using the following equations


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Room Tbehavior is usually elastic, with brittle failure.

3-Point Bend Testing often used.--tensile tests are difficult for brittle materials.

Measuring Elastic Modulus

FL/2 L/2

d= midpointdeflection

cross section

R

b

d

rect. circ.

Determine elastic modulus according to:

F

x

linear-elastic behaviord

F

dslope =

E=

F

d

L3

4bd3=

F

d

L3

12 pR4

rect.crosssection

circ.crosssection


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Influence of porosity

Porosity is a measure of void spaces in materials

In ceramics, porosity is introduced during the fabrication

Porosity decreases significantly the strength of materials

Example


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Example

Question

The flexural strength and associated volume fraction porosity for twospecimens of the same ceramic material are given in the table below.

(a) Compute the flexural strength for a completely non-porousspecimen

(b) Compute the flexural strength for a 0.20 volume fraction porosity

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