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Bruce Mayer, PE Engineering-45: Materials of Engineering

Bruce Mayer, PELicensed Electrical & Mechanical Engineer

[email protected]

Engineering 45

CeramicCeramicStructure/Structure/

PropsProps



Learning Goals – Ceramic PropsLearning Goals – Ceramic Props

How the Atomic Structure of Ceramics Differs from that of Metals

How Point Defects Operate in Ceramics Impurities

• How The Crystal Lattice Accommodates them

• How They Affect Properties

Mechanical Testing of Ceramics• Must Allow for Their Brittle Nature



CeramicsCeramics

The term CERAMIC comes from the Greek – KERAMIKOS, which means “burnt stuff”….• Ceramics are often

Processed by a high-temp heat treating process called FIRING



Ceramic Atomic BondingCeramic Atomic Bonding Ceramics are

Compounds between METAL and NONmetal IONS

Metals are the oxidANT; They GIVE UP e- to Become Positively Charged CATions

The nonmetals are the oxidIZER; They RECEIVE e- to Become Negatively Charge ANions

MetalCATion

NonMetalANion



Ceramic Atomic BondingCeramic Atomic Bonding Bonding Form

• Primarily IONIC; Secondarily COVALENT

Ionic Dominance INCREASES with INCREASING ELECTRONEGATIVITY

He -

Ne -

Ar -

Kr -

Xe -

Rn -

Cl 3.0

Br 2.8

I 2.5

At 2.2

Li 1.0

Na 0.9

K 0.8

Rb 0.8

Cs 0.7

Fr 0.7

H 2.1

Be 1.5

Mg 1.2

Sr 1.0

Ba 0.9

Ra 0.9

Ti 1.5

Cr 1.6

Fe 1.8

Ni 1.8

Zn 1.8

As 2.0

C 2.5Si

1.8

F 4.0

Ca 1.0

Table of Electronegativities

CaF2: Large

SiC: Small

Ionic

CoValent



Ceramic Crystal StructureCeramic Crystal Structure Oxide Structures

• oxygen anions are much larger than metal cations

• close packed oxygen in a lattice (usually FCC)

• Cations (usually a metal) in the holes of the oxygen lattice

Site Selection → Which sites will Cations occupy?1. Size of sites →

Does the cation fit in the site?

2. Stoichiometry if all of one type of site

is full the remainder have to go into other types of sites.

3. Bond Hybridization



Ionic Bonding & StructureIonic Bonding & Structure Charge Neutrality

Requirement• The NET Electronic

Charge on a Macroscopic Piece, or “Chunk”, of a Material MUST be ZERO

The General Ceramic Chemical Formula:

CaF2: Ca2+cation

F-

F-

anions+

pmXA

• Where– A Metal Atom

– X Nonmetal Atom

– m & p atom ratio required to satisfy CHARGE NEUTRALITY



Ceramic MicroStructural StabilityCeramic MicroStructural Stability

Two Primary Issues• Due to Coulombic Forces (Electrical

Attraction) the Solid State Ions Need OPPOSITELY Charged Nearest Neighbors

• Anion↔Cation Radial Contact Holds the Smaller Cation in Place

- -

- -+

stable

- -

- -+

stable

- -

- -+

UNstable



CoOrdination No. & Atomic RadiiCoOrdination No. & Atomic Radii The CoOrdination Number (CN) Increases

With Increasing ratio of

A

C

Anion

Cation

r

r

r

r

rcationranion

Coord #

< .155

.155-.225

.225-.414

.414-.732

.732-1.0

ZnS (zincblende)

NaCl (sodium chloride)

CsCl (cesium chloride)

2 3 4 6 8

Trends for CN vs rC/rA



Cation Site SizeCation Site Size Determine minimum rcation/ranion for OH site (C.N. = 6)

a 2ranion

2ranion 2rcation 2 2ranion

ranion rcation 2ranion

rcation ( 2 1)ranion

2ranion 2rcation 2a

4140anion

cation .r

r



Site Selection IISite Selection II

2. Stoichiometry • If all of one type of site is full the

remainder have to go into other types of sites.

Ex: FCC unit cell has 4 OH and 8 TD sites

• If for a specific ceramic each unit cell has 6 cations and the cations prefer OH sites

– 4 in OH → These Sites Fill First

– 2 in TD → These Sites Take the remainder



Site Selection IISite Selection II

3. Bond Hybridization – significant covalent bondingy

• the hybrid orbitals can have impact if significant covalent bond character present

• For example in SiC: XSi = 1.8 & XC = 2.5

%.)XXionic% 511]}exp[-0.25(-{1 100 character 2CSi

– ca. 89% covalent bonding– both Si and C prefer sp3 hybridization

– Therefore in SiC get TD sites



Exmpl: Predict FeExmpl: Predict Fe22OO33 Structure Structure

Using Ionic Radii Data Predict CoOrd No. and Crystal Structure for Iron Oxide

Ionic radius (nm)

0.053

0.077

0.069

0.100

0.140

0.181

0.133

Cation

Al3+

Fe2+

Fe3+

Ca2+ Anion

O2-

Cl-

F-

Check Radii Ratio

%3.49140

69

A

C

r

r

From rC:rA vs CN Table (Previous Sld) Predict:• CN = 6

• Xtal Type = NaCl



Ceramic Structure: NaClCeramic Structure: NaCl a.k.a., “Rock Salt”

Structure CN = 6

• rC/rA = 0.414-0.732

Two Interpenetrating FCC Lattices• Cations

• Anions

NOT a Simple Cubic Structure

Examples• MgO, MnS, LiF, FeO

http://www.webelements.com/webelements/index.html



Ceramic Structure: CsClCeramic Structure: CsCl CN = 8 Structure of

Interlaced Simple Cubic Structures

NOT a BCC Structure



Ceramic Structure: ZincBlendeCeramic Structure: ZincBlende CN = 4 (covalent Bonding) Basically the DIAMOND

Structure with Alternating Ions

Diamond Zinc Sulfide

Examples• SiC, GaAs



Ceramic Structure: FluoriteCeramic Structure: Fluorite Formula = AX2

rC/rA 0.8

CN • Cation → 8

• Anion → 4

Simple Cubic Structure with• “A” (e.g. Ca) at

Corners

• “X” (e.g. F) at Centers

Examples• UO2, PuO2, ThO2



Ceramic Structure: PerovskiteCeramic Structure: Perovskite

CaTiO3 – Two Types of Cations

Ca2+ CoOrdinationTi4+

CoOrdination

Chemical Formula = AmBnXp

CN • Cation-A → 12

• Cation-B → 6

• Anion → 4



Silicate CeramicsSilicate Ceramics Si and O are the

MOST abundant Elements in the Earth’s Crust

By Valence e- Ratio Si & O Form Compounds With a Si:O ratio of 1:2

Have Low Densities• About 33%-50%

That of Steel

Si-O Bond is Mostly CoValent and Quite Strong• Yields a High Melting

Temperature (1710 °C)

crystobalite



Amorphous SilicaAmorphous Silica Silica gels

amorphous SiO2

• Si4+ and O2- not in well-ordered lattice

• Charge balanced by H+ (to form OH-) at “dangling” bonds– very high surface area

> 200 m2/g

• SiO2 is quite stable, therefore unreactive– makes good catalyst support



Silica Glasses (NonCrystalline)Silica Glasses (NonCrystalline) NonXtal, or Amorphous

Structure• Called Fused-Silica or

Vitreous-Silica

SiO2 Forms a Tangled Network (Network Former)

Other Materials Added to Change Properties (e.g., Lower Melting Temp)• Network Modifiers

Na as SiO2 Network Modifier



Composition of Common GlassesComposition of Common Glasses

All Compositions in WEIGHT%



Defects In Ceramic StructuresDefects In Ceramic Structures FRENKEL Defect → Cation (the Smaller one)

has Moved to an Interstitial Location SHOTTKY Defect → Anion-Cation Pair-

Vacancy (electrical neutrality conserved)

Shottky Defect:

Frenkel Defect

• Defects Must Maintain Charge Neutrality

• Defect Density is Arrhenius

kTQDe /~



Impurities in CeramicsImpurities in Ceramics Impurities Must Also Satisfy Charge Neutrality Example: NaCl → Na+ Cl-

Ca-CATion Substitution-Defect in Rock Salt Structure

initial geometry Ca2+ impurity resulting geometry

Ca2+

Na+

Na+Ca2+

cation vacancy

• To maintain Charge Neutrality ONE Ca+2 ion Subs for TWO Na+ ions



Impurities in Ceramics cont.1Impurities in Ceramics cont.1 Impurities Must also Satisfy Charge Neutrality Example: NaCl → Na+ Cl-

O2- ANion Substitution-Defect in Rock Salt Structure

• To maintain Charge Neutrality ONE O2- ion Subs for TWO Cl- ions

initial geometry O2- impurity

O2-

Cl-

anion vacancy

Cl-

resulting geometry



Ceramic Phase DiagramsCeramic Phase Diagrams Same form and Use

as Metallic Phase Diagrams Except• Horizontal Axis is

based on Ceramic COMPOUNDS– e.g. ; Al2O3 → SiO2

• Typically Much Higher Phase-Change Temperatures Can use Lever Rule

on Compounds



Measuring Young’s ModulusMeasuring Young’s Modulus Ceramic Room Temp behavior is

Linear-Elastic with BRITTLE Fracture• Due to Brittle Failure, 3-Point Bending

Tests are used to Assess Elastic Modulus

ThenE

FL/2 L/2

= midpoint deflection

cross section

R

b

d

rect. circ.

Fx

linear-elastic behavior

F

slope =

E F

L3

4bd3 F

L3

12R4

rect. X-Section

circ. X-Section



Measuring StrengthMeasuring Strength Use the Same 3-Pt Bend Test to Measure

Room Temperature Ultimate Strength

Then the FLEXURAL Strength at Fracture

FL/2 L/2

cross section

R

b

d

rect. circ.

location of max tension

xF

Fmax

max rect.

fs mfail1.5FmaxL

bd2 Fmax L

R3circ.



Creep PerformanceCreep Performance As with Metals Characterize Creep

Performance as the Steady-State Creep Rate during Secondary-Phase Creep

time

x

slope = ss = steady-state creep rate.

Ttest >0.4Tmelt

Generally The Creep-Resistance• Ceramics > Metal >> Plastics



SummarySummary

Ceramics Exhibit Primarily IONIC Bonding• Some Ceramics; e.g., Silica. are

Covalently Bonded

Crystal Structure is a Function of• Charge Neutrality

• Maximizing of NEAREST, OPPOSITELY-Charged, Neighbors

• Cation:Anion Size-Ratio



Summary cont.1Summary cont.1

Defects• Must Preserve Charge NEUTRALITY

• Have a Concentration that Varies EXPONENTIALLY with Temperature

Room Temperature Mechanical Response is ELASTIC, but Fracture is Brittle, with negligible ductility

Elevated Temp Creep Properties are Generally Superior to those of Metals



WhiteBoard WorkWhiteBoard Work

Problem 12.21• Fe3O4 Ceramic

(LodeStone or Magnetite)– Unit Cell for Edge

Length, a = 0.839 nm

– Density, ρ = 5240 kg/m3

– Fe3O4 = FeO•Fe2O3

• Find Atomic Packing Factor, APF

[email protected] engr-45_lec-26_ceramic_structure-props.ppt 1 bruce mayer, pe...

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