CeramicsCeramics

keramikos - burnt stuff in Greek - desirable properties of ceramics are normally achieved through a high temperature heat treatment process (firing).

Usually a compound between metallic and nonmetallic elementsAlways composed of more than one element (e.g., Al2O3, NaCl,

SiC, SiO2)Bonds are partially or totally ionic, can have combination of ionic

and covalent bonding (electronegativity)Generally hard, brittle and electrical and thermal insulatorsCan be optically opaque, semi-transparent, or transparentTraditional ceramics – based on clay (china, bricks, tiles,

porcelain), glasses.“New ceramics” for electronic, computer, aerospace industries.

Types of Ceramics

Ceramics are divided into two general groups: Traditional (e.g. pottery, clays, rocks) and engineering ceramics.• Rocks and minerals• Glasses

- SiO2 based- attributes: transparent to light, easy to form- applications: windows, containers, lenses, etc.

• Clays- composed of Al2O3, SiO2 and chemically bound water- attributes: easy to form with water addition- applications: bricks, tiles, porcelain, pottery, etc.

• Cements- consisting of CaO, SiO2 and AL2O3- attributes: form paste with water and then harden- applications: construction, roads, concrete

• Engineering Ceramics (advanced, high-performance) - e.g. Al2O3, SiC, Si3N4, ZrO2- attributes: excellent physical, chemical or mechanical properties- applications: heat engines, cutting tools, die materials, superconductors

The crystal structure of an ionically bonded material is determined by the number of atoms of each element required for charge neutrality and the optimum packing based on the relative sizes of the ions.The building criteria for the ceramic crystal structure are:- maintain neutrality (zero net electric charge)- charge balance dictates chemical formula- achieve closest packing (most stable structure)The condition for minimum energy implies maximum attraction and minimum repulsion of the atomsThis leads to atomic contact (hard sphere model), configurationswhere anions (-) have the highest number of cation (+) neighbors and vice versa.Structure types: AX, AmXp, AmBnXp... based on chemistry and charge balance.(BCC, FCC and HCP structures involved only one type of atom)

IONIC BONDING and STRUCTURE

Charge Neutrality:--Net charge in the structure should be zero.

The structure maximizes the number of nearest oppositely chargedneighbors.Since cations are usually smaller than anions, the crystal structure is usually determined by the maximum number of anions that it ispossible to pack around the cations, which, for a given anion size will increase as the size of the cation, increases.To achieve the state of lowest energy, the cations and anions will tend to maximize attractions and minimize repulsions. Attractions are maximized when each cation surrounds itself with as many anions as possible, but without touching.

Crystal Structures in Ceramics with predominantly ionic bonding

Crystal structure is defined byThe electric charge: The crystal must remain electrically

neutral. Charge balance dictates chemical formula (Ca2+ and F-

form CaF2).Relative size of the cation and anion. The ratio of the atomic

radii (rcation/ranion) dictates the atomic arrangement. Stable structures have cation/anion contact.

Coordination Number: the number of anions nearest neighbors for a cation.

As the ratio gets larger (that is as rcation/ranion ~ 1) the coordination number gets larger and larger.

Holes in sphere packing

Triangular Tetrahedral Octahedral

Calculating minimum radius ratiofor a triangle:

1550

2330

21

21

.

cos

)30=( cos

=

==+

°=

+=

=

a

c

ca

a

ca

a

rr

rrrAO

AB

rrAO

rAB

αα

A C

BO

AC

B

O

4140

2245

21

21

.

cos

)45=( cos

=

==+

°=

+=

=

a

c

o

ca

a

ca

a

rr

rrrAO

AB

rrAO

rAB

αα

for an octahedral hole

C.N. = 2 rC/rA < 0.155

C.N. = 3 0.155 < rC/rA < 0.225

C.N. = 4 0.225 < rC/rA < 0.414

C.N. = 6 0.414 < rC/rA < 0.732

C.N. = 8 0.732 < rC/rA < 1.0

Ionic (and other) structures may be derived from the occupation of interstitial sites in close-packed arrangements.

A2X

AX-TYPE anion - cation charges are the same (equal + and -)-Rock Salt Structure -NaCl, MgO, MnS, LiF, FeO-Cesium Chloride Structure (CsCl)-Zinc Blende Structure (ZnS, ZnTe, SiC)

AmXp -TYPE - cation charges are NOT the same-AX2 (CaF2,UO2, PuO2 and ThO2)

AmBnXp -TYPE - more than one cation charges-ABO3 (BaTiO3, CoTiO3, SrTiO3)

CRYSTAL STRUCTURE TYPES

o/t fcc(ccp) hcpall oct. NaCl NiAsall tetr. A2X (ReB2)o/t (all) (Li3Bi) (Na3As)½ t sphalerite (ZnS) wurtzite (ZnS)(½ o CdCl2 CdI2)

Comparison between structures with filled octahedral and tetrahedral holes

Location and number of tetrahedral holes in a fcc (ccp) unit cell

- Z = 4 (number of atoms in the unit cell)

- N = 8 (number of tetrahedral holes in the unit cell)

AX-TYPE anion - cation charges are the same-Rock Salt Structure -NaCl, MgO, MnS, LiF, FeO-Cesium Chloride Structure (CsCl)-Zinc Blende Structure (ZnS, ZnTe, SiC)

Note: Cesium chloride structure is NOT BCC as the structure has two different atoms (if there was only one type of atom, it would be BCC)

Crystals having filled Interstitial Sites

NaCl structure has Na+ ions at all 4 octahedral sites

Octahedral, Oh, Sites

Na+ ions

Cl- ions

Ionic Crystals prefer the NaClStructure:

• Large interatomic distance• LiH, MgO, MnO, AgBr, PbS, KCl, KBr

Crystals having filled Interstitial Sites

Both the diamond cubic structureAnd the Zinc sulfide structures have 4 tetrahedral sites occupied and 4 tetrahedral sited empty.

Tetrahedral, Th, Sites

Zn atoms

S atoms

Covalently Bonded Crystals Prefer this Structure• Shorter Interatomic Distances than ionic • Group IV Crystals (C, Si, Ge, Sn)• Group III--Group V Crystals (AlP, GaP, GaAs, AlAs, InSb)• Zn, Cd – Group VI Crystals (ZnS, ZnSe, CdS)• Cu, Ag – Group VII Crystals (AgI, CuCl, CuF)

Rock Salt Structure (NaCl)

Cl NaCoordination = 6

NaCl, MgO, LiF, FeO, CoO

NaCl structure: rC = rNa = 0.102 nm,

rA = rCl = 0.181 nm rC/rA = 0.56

AX Type Crystal Structures

Cesium Chloride Structure (CsCl)

CsClCoordination = 8Is this a body centered cubic structure?

CsCl Structure: rC = rCs = 0.170 nm, rA = rCl = 0.181 nm → rC/rA = 0.94

Zinc Blende Structure (ZnS)

ZnSCoordination = 4radius ratio = 0.402

ZnS, ZnTe, SiC have this crystal structure

AmXp-Type Crystal StructuresIf the charges on the cations and anions are not the same, a compound can exist with the chemical formula AmXp , where m and/or p ≠ 1. An example would be AX2 , for which a common crystal structure is found in fluorite (CaF2).AmXp -TYPE - cation charges are NOT the same-AX2 (CaF2,UO2, PuO2 and ThO2)

Fluorite CaF2Fluorite (CaF2): rC = rCa = 0.100 nm, rA= rF = 0.133 nm ⇒ rC/rA = 0.75From the table for stable geometries we see that C.N. = 8Other compounds that have this crystal structure include UO2 , PuO2 , and ThO2.

AmBnXp-Type Crystal StructuresIt is also possible for ceramic compounds to have more than one type of cation; for two types of cations (represented by A and B), their chemical formula may be designated as AmBnXp . Barium titanate(BaTiO3), having both Ba2+ and Ti4+ cations, falls into this classification. This material has a perovskite crystal structure and rather interesting electromechanical properties.AmBnXp -TYPE - more than one cation charges-BaTiO3, CoTiO3, SrTiO3

Perovskite -an Inorganic Chameleon

ABX3 - three compositional variables, A, B and X

• CaTiO3 - dielectric• BaTiO3 - ferroelectric• Pb(Mg1/3Nb2/3)O3 - relaxor

ferroelectric• Pb(Zr1-xTix)O3 - piezoelectric• (Ba1-xLax)TiO3 – semiconductor

• (Y1/3Ba2/3)CuO3-x -superconductor

• NaxWO3 - mixed conductor; electrochromic

• SrCeO3 - H - protonic conductor• RECoO3-x - mixed conductor• (Li0.5-3xLa0.5+x)TiO3 - lithium ion

conductor• LaMnO3-x - Giant magneto-

resistance

The perovskite structure CaTiO3

- TiO6 – octahedra

- CaO12 – cuboctahedra

(Ca2+ and O2- form a cubic close packing)

→ preferred basis structure of piezoelectric, ferroelectric and superconducting materials

Density Calculations in Ceramic Structures

Ac

AC

NVAAn

×+×

= ∑ ∑ )('ρ

n’: number of formula units in unit cell (all ions that are included in the chemical formula of the compound = formula unit)ΣAC: sum of atomic weights of cations in the formula unitΣAA: sum of atomic weights of anions in the formula unitVc: volume of the unit cellNA: Avogadro’s number, 6.023x1023 (formula units)/mol

Example: NaCln’ = 4 in FCC latticeΣAC = ANa = 22.99 g/molΣAA = ACl = 35.45 g/mol

rNa=0.102x10-7 rCl=0.181x10-7 cmVc = a3 = (2rNa+2rCl)3

Vc = (2×0.102×10-7 + 2×0.181×10-7)3 cm3

( )[ ]

3

23377142

10023610181021010202453599224 −

−−=

××××+××

+×= cmg..

.....ρ

Composed mainly of silicon and oxygen, two most abundant elements in earth’s crust (rocks, soils, clays, sand)Basic building block: SiO4

4- tetrahedronSi-O bonding is largely covalent, but overall SiO4 block has charge of –4Various silicate structures – different ways to arrange SiO4

-4

blocks

Silicate Ceramics

SiO

OO O

4-

Every oxygen atom is shared by adjacent tetrahedraSilica can be crystalline (e.g., quartz) or amorphous, as in glass (fused or vitreous silica)

3D network of SiO4tetrahedra in cristobalite

High melting temperature of 1710 °C

Silica = silicon dioxide = SiO2

Most window glasses produced by adding other oxides (e.g. CaO, Na2O) whose cations are incorporated within SiO4 network. The cations break the tetrahedral network so glasses melt at lower temperature than pure amorphous SiO2. Lower melting point: easier to mold (e.g., bottles). Other oxides (e.g., TiO2, Al2O3) substitute for silicon and becomepart of network

Window glasses

CarbonCarbon is not a ceramicCarbon exists in various polymorphic forms: sp3 diamond, and amorphous carbon, sp2 graphite and fullerenes/nanotubes.

Carbon DiamondHas diamond-cubic structure (like Si, Ge)One of the strongest/hardest material knownHigh thermal conductivity Transparent in the visible and infrared, with high index of refraction. Semiconductor (can be doped to make electronic devices)Metastable (transforms to carbon when heated)

Carbon: GraphiteLayered structure with strong bonding within the planar layers and weak (van der Waals) between layersEasy interplanar cleavage (lubricant and for writing pencils)Good electrical conductorChemically stable even at high temperaturesApplications include furnaces, rocket nozzles, welding electrodes.

Carbon

Carbon: buckyballs and nanotubesBuckminsterfullerenes (buckyballs) and carbon nanotubes are expected to play an important role in future nanotechnology applications (nanoscale materials, sensors, machines, and computers).

Carbon nanotube T-junction

Nanotube holepunching

/etching

Nanotubes as reinforcing fibers in nano-composites

Nano-gear

Figures from http://www.nas.nasa.gov/Groups/SciTech/nano/

Made from tiny tubes of carbon standing on end, this material is almost 30 times darker than a carbon substance used by the National Institute of Standards and Technology as the current benchmark of blackness. It is composed of carbon nanotubes, standing on end. This arrangement traps light in the tiny gapsbetween the "blades.“ The substance has a total reflective index of 0.045 percent - which is more than three times darker than the nickel-phosphorus alloy that now holds the record as the world's darkest material(0.16 to 0.18 percent reflectance).Basic black paint, by comparison, has a reflective index of 5 percent to 10 percent.

Examples(A)Would you expect CsBr to have the sodium chloride, zinc

blende, fluorite or cesium chloride structure? Based on your answer, determine (a) the lattice parameter, (b) the density and (c) the packing factor of CsBr.

rCs = 0.167nm ACs = 79.91 g.mol-1

rBr = 0.196nm ABr = 132.91 g.mol-1

(B) For which set of crystallographic planes will a first-order diffraction peak occur at a diffraction angle of 2θ = 44.53O

for FCC nickel (metallic atomic radius R=0.1246nm) when monochromatic radiation having a wavelength of 0.1542nmis used.

(A)8520.=

Br

Cl

rr

C.N.=8

[ ]6930

4190

167019603484

10023610419090513290979

41907260167019602223

3

33

3

12337

1

.).(

).().()(

..)..().(

.)..(.

.)..(

=+

=

=

×××+

=

==+=+=

−

−−

−

πρ

ρ

PF

cmgmolatomsxnm

molgnma

nmrra

O

BrClOLattice Parameter

Density

Packing Factor

(B)The first step to solve this problem is to compute the interplanar spacing using Bragg equation,Now, employment of equations for cubic systems, and the value of R for nickel leads to

d hklnl

2 sin θ

This means that

By trial and error, the only three integers which are all odd oreven, the sum of the squares of which equals 3.0 are 1, 1, and 1. Therefore, the set of planes responsible for this diffraction peak is the (111) set.

=(1)(0.1542 nm)

(2) sin44.53 °

2⎛

⎝⎜

⎞

⎠

= 0 .2035 nm

h 2 + k 2 + l2 =a

dhkl

=2R 2

dhkl

=(2)(0.1246 nm) 2

(0.2035 nm)= 1.732

h 2 + k 2 + l 2 = (1.732) 2 = 3.0

Molybdenum Disulfide (MoS2)

Common high tech greaseLike graphite, MoS2 has weak van der Waals forces between the basal planes. The bonds between the sulfur layers are weaker than the mbonds between the molybdenum layers. The covalent bonds of both are strong in the basal plane.Crystalline lattice structure materials,such as molybdenum disulfide, tungsten disulfide and graphite, are widely used as lubricants.Lamella lubricating powders have low shear forces between their crystalline lattice layers that minimize resistance between sliding surfaces. MoS2 occurs naturally in the form of thin solid veins within granite.

-+

Point defects in ionic crystals are charged. Coulombic forces are large and any charge imbalance wants to be balanced. Charge neutrality --> several point defects created (Charge Neutrality Defects: Frenkel defect: a cation vacancy and a cation interstitial or an anion (negative ion) vacancy and anion interstitial. (Anions are larger so it is not easy for an anion interstitial to form).Schottky defect: pair of anion and cation vacancies

Imperfections in Ceramics

Frenkel defectSchottky defect

Equilibrium concentration of defects

These defects create the electrical conductivity in ceramics.An increasing number of defects increases the conductivity.

kTQD

e−

~

Impurities must also satisfy charge balance

• Frenkel or Schottky defects: no change in cation to anion ratio →compound is stoichiometric

• Non-stoichiometry (composition deviates from the one predicted by chemical formula) may occur when one ion type can exist in two valence states, (e.g. Fe2+, Fe3+). In FeO, usual Fe valence state is 2+. If two Fe ions are in 3+ state, then a Fe vacancy is required to maintain charge neutrality → fewer Fe ions → non-stoichiometry

Imperfections in Ceramics

Impurity atoms can exist as either substitutional or interstitialsolid solutionsSubstitutional ions substitute for ions of like typeInterstitial ions are small compared to host structure (anion interstitials are unlikely).

Impurities in Ceramics

Interstitial impurity atom

Substitutional impurity ions

Solubility high if ion radii and charges match

Incorporation of ion with different charge state requires compensation by point defects.