Post on 03-Apr-2018
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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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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%
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Ionic and Covalent Bonding in Simple Ceramics
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Example
Calculate the ionic percentage of SiC (XSi = 1.8 and XC = 2.5).
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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
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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.
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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.
Ionic Bonding & Structure
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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
Ionic Bonding & Structure
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Anion locations
Two sides
Corners of equilateraltriangle
Corners of tetrahedron
Corners of octahedron
Corners of cube
Crystal Structures
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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)
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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
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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
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Summary of some common ceramic crystal structures
Types of Crystal Structures
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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.
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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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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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Mechanical Properties of Ceramics
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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Mechanical Properties of Ceramics
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Mechanical Properties of Ceramics
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