MS3001 Ceramics 02 Crystal(6)

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Metallic and Ceramic Materials (MS3001)(MS3001)

Kong Ling Bing

School of Materials Science and EngineeringNanyang Technological Universityy g g y

N4.1-01-25, Tel: 67905032Email: [email protected]

Outline Introduction 1 h Crystal Structure of Ceramics 2 hy Defects in Ceramics 2 h Phase Diagram of Ceramics 2 h Phase Diagram of Ceramics 2 h Ceramic Processing 4 h El t i l P ti f C i 4 h Electrical Properties of Ceramics 4 hMagnetic Properties of Ceramics 4 h

Four Tutorials

CA (mid) + Final Exam( )

Metallic and Ceramic MaterialsMetallic and Ceramic Materials (MS3001)( )

2. Crystal Structure of Ceramics

Objectives Understand chemical bonds in ceramics.

Understand the concept of crystal structures in ceramics. Understand the concept of crystal structures in ceramics.

Calculate the minimum cation-to-anion radius ratio for the coordination number 3 4 6 and 8coordination number 3, 4, 6, and 8.

Understand the crystal structure of perovskite.

Understand the crystal structure of spinel.

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Structures at Different Levels

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Structures at Different Levels

Subatomic level – electronic structure of individual atoms that defines interaction among atoms (bonding).

Atomic level – arrangement of atoms in Atomic level arrangement of atoms in materials (same atoms can have different properties, e.g. graphite and diamond).

Microscopic structure – arrangement of small grains of materials that can be gidentified by microscopy.

Macroscopic structure – structural pelements that may be viewed with the naked eye.

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Review – Electron ConfigurationsL shell with two subshells

Nucleus

2s

1s

K 2s2p

KL

1s22s22p2 or [He]2s22p21s22s22p2 or [He]2s22p2p [ ] p

The shell model of atom in which the electrons are confined to stay

p [ ] p

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within certain shells and in subshells within shells.

Review – Electron Configurations

I 1sIncreasi

2s 2p3s 3p 3ding ener

p4s 4p 4d 4f5s 5p 5d 5frgy 5s 5p 5d 5f6s 6p 6d7 77s 7p

Electron configurations of the neutral gaseous atoms in the ground state.

9Order: 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p 7s 5f 6d 7p

Chemical Bonds in Ceramics Underlying many of the properties found in ceramics are the strong

primary bonds that hold the atoms together and form the ceramic i lmaterials.

These chemical bonds are of two types:

ionic in character, involving a transfer of bonding electrons from electropositive atoms (cations) to electronegative atoms e ect opos t ve ato s (cat o s) to e ect o egat ve ato s(anions), and

covalent in character involving orbital sharing of electrons covalent in character, involving orbital sharing of electrons between the constituent atoms or ions.

% i i h [1 ( 0 25{X X }2)] 100%% ionic character = [1 – exp(-0.25{Xa – Xb}2)] 100%

Xa and Xb are called electronegativity.

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Gi l l R dil l

Chemical Bonds in CeramicsGive up valence electrons Readily accept electrons

h l i d f Electronegativity: The relative tendency of an atom to accept an electron and become an anion.

Strongly electronegative atoms readily accept electrons Strongly electronegative atoms readily accept electrons.

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Ionic Bonding Occurs between positive

and negative ions. Requires electron transfer. Large difference in

electronegativity required. Example: NaCl

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Covalent Bounding

Requires shared electrons

Example: CH4

C: has 4 valence e needs 4 C: has 4 valence e, needs 4 more

H: has 1 valence e needs 1 H: has 1 valence e, needs 1 more

Electronegativities are Electronegativities are comparable

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Metallic Bonding

Free valence l tPositive Close Free valence

l f iPositive Close packing

f lli ielectrons forming an electron gas

Positive metal ion cores

packing of metallic ions (atoms)

electrons forming an electron gas

metal ion cores

of metallic ions (atoms)

In metallic bonding, the valence electrons from the metal atoms form a “cloud of electrons”, which fills in the space between the

l i d “ l ” h i h h h C l bimetal ions and “glues” the ions together through Coulombic attraction between the electron gas and the positive metal ions.

F P i i l f El i M i l d D i 2 d Editi14

From Principles of Electronic Materials and Devices, 2nd Edition, S.O. Kasap(© McGraw-Hill, 2002), http://Materials.Usask.Ca

Chemical Bonds - Summary

Type Bond energy Comments

Ionic Large Nondirectional (ceramics)

V i bl Di ti lVariable DirectionalCovalent large: Diamond (semiconductors, ceramics

small: Bismuth polymer chains)small: Bismuth polymer chains)

VariableMetallic large: Tungsten Nondirectional (metals)

small: Mercury

DirectionalSecondary Smallest inter-chain (polymer)

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Secondary Smallest inter chain (polymer)inter-molecular

Crystal Structure in Ceramics

Most of the primary chemical bonds found in ceramic materials are

Chemical Bonding in Ceramics

Most of the primary chemical bonds found in ceramic materials are actually a mixture of ionic and covalent types.

It is therefore only a convenient (but quite successful) approximation to treat most ceramics as ionic solids.

Ionic bonds are non-directional in nature, that is the attractive forces occur form all directions.forces occur form all directions.

This non-directional nature allows for hard-sphere packing arrangements of the ions into a variety of crystal structures, with two limitations.

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The first limitation involves the relative size of the anions and the

First Limitation

The first limitation involves the relative size of the anions and the cations.

Anions are usually larger and close-packed, similar to the face-centered cubic or hexagonal close-packed crystal structures found i t lin metals.

Cations on the other hand are usually smaller occupying space Cations, on the other hand, are usually smaller, occupying space (interstices) in the crystal lattice between/among the anions.

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The second limitation on the types of crystal structure that can be

Second Limitation

The second limitation on the types of crystal structure that can be adopted by ionically bonded atoms is based on a law of physics -the crystal must remain electrical neutrality.

This law of electroneutrality results in the formation of very ifi t i hi t i i ifi ti f ti t i th tspecific stoichiometries; i.e, specific ratios of cations to anions that

maintain a net balance between positive and negative charges.

In fact, anions are known to pack around cations, and cations around anions, in order to eliminate local charge imbalance.

This phenomenon is referred to as coordination (number).

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Packing and Energy

Non dense, random packing Energy

typical neighbor

Energytypical neighbor

r

typical neighbor bond length

typical neighbor

yp gbond length

typical neighbor r typical neighbor bond energy

E

typical neighborbond energy

r

Dense, regular packingEnergy

typical neighbor b d le th

Energytypical neighbor bond length

r

bond length

typical neighbor

bond length

typical neighbor r

D d l k d t t t d t h l !

typical neighbor bond energy yp gbond energy

r

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Dense and regular-packed structures tend to have lower energy!

Packing and Energy Non dense, random packing

Energy typical neighborbond length

rtypical neighborbond energy

Energy typical neighbor bond length

Dense, ordered packing

r

bond length

typical neighbor

Dense ordered packed structures tend to have lower energies and

typical neighbor bond energy

Dense, ordered packed structures tend to have lower energies and thus are more stable!

Packing and Structure Noncrystalline (amorphous) materials... atoms have no periodic packing occurs for: -complex structures

-rapid coolingp g

noncrystalline SiO2

Crystalline materials...

Si Oxygen Si Oxygen

y atoms pack in periodic, 3D arrays typical of: -metals typical of: metals

-many ceramics-some polymers

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some polymers

crystalline SiO2

N d d ki

Packing and Structure Non dense, random packing Noncrystalline (amorphous)

materialsmaterials Energy is higher, or

metastablemetastable Ceramics are (poly-)

crystalline solids!

Dense, regular packing

crystalline solids!

Crystalline materials

Energy is lower, or more gy ,stable

Crystalline solids have C ysta e so ds aveperiodic structure!

Crystal Structure in Ceramics Periodic Structures

Periodic structures can be represented by periodicity – unit cell. 23

Crystal Structure in Ceramics Unit Cells of Crystals

Lattice parameters

axial lengths: a, b, c

interaxial angles: α, β, γ

cg , β, γ

unit vectors: , , a b

c

b

In general: a ≠ b ≠ c

α ≠ β ≠ γ

a All period unit cells can be described with these vectors and anglesvectors and angles.

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Crystal Structure in Ceramics S (7) C t l S t D / k? Seven (7) Crystal Systems Days/week?

Colors/rainbow?

Simple cubic a = b = cβ 90º

Tetragonala = b ≠ c

Orthorhombica ≠ b ≠ c

Rhombohedrala = b = c

Simple cubic a = b = cβ 90º

Tetragonala = b ≠ c

Orthorhombica ≠ b ≠ c

Rhombohedrala = b = cα = β = γ = 90º α = β = γ = 90º

a ≠ b ≠ cα = β = γ = 90º

a b cα = β = γ ≠ 90ºα = β = γ = 90º α = β = γ = 90º

a ≠ b ≠ cα = β = γ = 90º

a b cα = β = γ ≠ 90º

Monoclinic T i li i H lMonoclinic T i li i H l

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Monoclinica ≠ b ≠ c

γ ≠ α = β = 90º

Triclinica ≠ b ≠ c

α ≠ β ≠ γ ≠ 90º

Hexagonala = b ≠ c

α = β = 90º, γ = 120º

Monoclinica ≠ b ≠ c

γ ≠ α = β = 90º

Triclinica ≠ b ≠ c

α ≠ β ≠ γ ≠ 90º

Hexagonala = b ≠ c

α = β = 90º, γ = 120º

Crystal Structure in Ceramics Th (3) T f P ki f C bi C t l S t Three (3) Types of Packing of Cubic Crystal System

Primitive Face-centered Body-centered

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cubic cubicycubic

S (7) C t l S t + F t (14) C t l L tti

Crystal Structure in Ceramics Seven (7) Crystal Systems + Fourteen (14) Crystal Lattices

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Crystal Structure in Ceramics C t l Pl Crystal Planes

Planes in a crystal can be specified b i i ll d Millby using a notation called Miller indices.

Miller indices were introduced in 1839 by the British mineralogist William Hallowes Miller (6 AprWilliam Hallowes Miller (6 Apr 1801 – 20 May 1880, British mineralogist and crystallographer).g y g p )

The Miller index is indicated by the notation [hkl] where h, k, and l are [ ] , ,reciprocals of the plane with the x, y, and z axes.

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Crystal Structure in Ceramics C t l Pl Crystal Planes

To obtain the Miller indices of a given plane requires the following ffour steps:

Step 1. The plane in question is placed on a unit cell. p p q p

Step 2. Its intercepts with each of the crystal axes are then foundfound.

Step 3. The reciprocal of the intercepts are taken.

Step 4. These are multiplied by a scalar to insure that is in the simple ratio of whole numbers.

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Crystallographic Planes

Miller Indices:[001]

x y zIntercepts: 1 infinite infiniteReciprocals 1 0 0Reciprocals 1 0 0Lowest integers 1 0 0[010]

Plane: (100)[100]



Miller Indices:[001] x y z

Intercepts: -1 infinite infiniteReciprocals 1 0 0

[001]

? Reciprocals -1 0 0Lowest integers -1 0 0

?

Plane: (100)[010]

[100]




x y zIntercepts: 1 1 infiniteReciprocals 1 1 0Reciprocals 1 1 0Lowest integers 1 1 0[010]

Plane (110)[100]




x y zIntercepts: 1 1 1Reciprocals 1 1 1Reciprocals 1 1 1Lowest integers 1 1 1

[010]Plane: (111)

[100]

Mill I di C t ll hi l

Crystal Structure in CeramicsMiller Indices:

x y zIntercepts: -1/2 infinite 1

Crystallographic planes [001]

Intercepts: 1/2 infinite 1Reciprocals -2 0 1Lowest integers -2 0 1

Plane: (201)[010]

[100]

[010][001]

[010]

[100]


Example: to determine plane (112)

Miller Indices:

x y z

z

x y z

Intercepts: 1 1 1/2

R i l 1 1 21/2 Reciprocals 1 1 2

Lowest integers 1 1 211/2

Plane: (112)y1x


Example: to determine plane (234)

Miller Indices:

x y z

z

x y z

Intercepts: 1/2 1/3 1/4

R i l 2 3 4Reciprocals 2 3 4

Lowest integers 2 3 41/31/4

Plane: (234)y1/21/3

x


Why anions are larger than cations?

How many crystal systems are there? 7How many crystal systems are there?

How many lattice types are there?

7

14

How many steps used to determine Miller indices of crystal planes?

4

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Mill I di C t ll hi l

Crystal Structure in CeramicsMiller Indices:

x y zIntercepts: -1/2 infinite 1

Crystallographic planes [001]

Intercepts: 1/2 infinite 1Reciprocals -2 0 1Lowest integers -2 0 1

Plane: (201)[010]

[100]

[010][001]

[010]

[100]


Crystallographic planes


x y zIntercepts: 1/2 infinite 1Reciprocals 2 0 1Reciprocals 2 0 1Lowest integers 2 0 1[010]

Plane: (201)[100]


Families of Planes

A family of planes is represented by{hkl} A family of planes is represented by{hkl}

Thus, indices {hkl} represent all the planes equivalent to thel (hkl) i l

)001(),100(),010(),001(),010(),100(}100{

plane (hkl) in a crystal.

)111(),111(),111(),111(),111(),111(),111(),111(}111{)001(),100(),010(),001(),010(),100(}100{

There are many other families of planes in a crystal.


Crystallographic Directions

[001][001]

[101][011][111]

<100> cube edges[ ]

<011> face diagonals[010]

<111> cube diagonals[100]

[110]

Th ll hi di i di l h i The crystallographic directions are perpendicular to their corresponding planes.

Crystal Structure in Ceramics Summary

Because a crystal is periodic, there exist families of equivalent directions and planes.

Notations allow for distinction between a specific direction or l d f ili f h i di i

Miller conventions - { } vs ( ) and [ ] vs < >

plane and families of such periodicity.

Use the ( ) notation to identify a specific plane, e.g. (113).Use the { } notation to identify a family of equivalent planes, e.g. {311}.

Use the [ ] notation to identify a specific direction, e.g. [101].U th t ti t id tif f il f i l tUse the < > notation to identify a family of equivalent directions, e.g. <110>.

A bar above a index is equivalent to a minus sign42

A bar above a index is equivalent to a minus sign.


Terminology

Summary

gy Planes ( ) Families of equivalent planes { }q p { } Directions [ ] Families of directions < >Families of directions

(100)=“bar one zero zero” and NOT “one bar zero zero”( )

Crystal Structure in Ceramics Spacing between Planes in a Cubic Crystal

(100) (110) (111)

a=d

(100) (110) (111)

1 l+k+h=222

l + k + h = d

222hkl22 a =

dhkl

where dhkl = inter-planar spacing between planes with Miller indices h, k and l.l tti t t ( d f th b )a = lattice constant (edge of the cube)

h, k, l = Miller indices of cubic planes being considered.

Crystal Structure in Ceramics Spacing between planes in a cubic crystal

Calculate plane spacing of (100), (110), (111), (112) and (234) p p g ( ), ( ), ( ), ( ) ( )planes, of a crystal of cubic structure, with a = 4.05 Å.

04

05.4001

05.4100 222 + +

= dl + k + h

a = d222hkl

571.3205.4

011

05.4110 222 + +

= d

643.1605.4

211

05.4112 222 ++

= d011

338.2305.405.4

111 222 = d

432.02905.405.4

234 222 = d

3111 222 + + 29432 222 ++

The larger the values of the Miller indices, the smaller the spacing

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of the planes will be.

Ionic Radii and Coordination NumberC.N.=2 Linear RC/RA: <0.155

C.N.=3 Triangular RC/RA: 0.225-0.155

C.N.=4 Tetrahedral RC/RA: 0.414-0.225

C.N.=6 Octahedral RC/RA: 0.732-0.414

C N =8 Cubic R /R : 1 0 0 73246

C.N.=8 Cubic RC/RA: 1.0-0.732

Ionic Radii and Coordination Number Stable ceramic crystal structures require that anions surrounding a

cation are all in contact with that cation.

For a specific coordination number, there is a critical or minimum cation-anion radius ratio, rC/rA, for which this contact can be

i t i dmaintained.

Unstable StableStable

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U stab e

Ionic Radii and Coordination NumberExample

D t t th t th i i ti t i di ti f Demonstrate that the minimum cation-to-anion radius ratio for the coordination number 8 is 0.732 for stable ceramic crystal structures.structures.

In stable ceramic crystal structures, anions surrounding a cation are all in contact with that cation.

For a specific coordination number, there is a critical or minimum cation-anion radius ratio rC/rA, for which this contact can be maintained.

This problem asks us to show that the minimum cation-to-anion

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radius ratio for a coordination number of 8 is 0.732.

Ionic Radii and Coordination Number From the cubic unit cell shown below (Ions are reduced in size for

the sake of clarity.)Anion QAnion

M

Q

M

N P

Cation2rA

Q

Cation y M

x 2rA

492rAN P

Ionic Radii and Coordination Number The unit cell edge length is 2rA, and from the base of the unit cell,

there is2r

Q

r8 = r2 + r2 = x 2A

2A

2A

22rA

y M

x2r

yM

so

2r2=x A

x 2rA

PA

No from the triangle that in ol es and the nit cell edge can

2rAN P

Now from the triangle that involves x and y, the unit cell edge canbe calculated.

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Ionic Radii and Coordination NumberQ

2CA22

A2 2r+r2 = y = r2 + x 2rA

Q

2CA2A

2

A r2+r2=r4 + 2r2y M CAAA

x 2rA

22 r2+r2=r212rA

CAA r2+r2 =r21N P

0 73213CrCAA r2+r2 = r32

Cr=1 3rA 0.732=13=

A

C

r51

CA A

Perovskite Structure Number of Atoms/Ions of a Given Unit

Corner Edge Face Shared by eight

units

g Shared by four

units

Shared by two units

1/8 1/4 1/2

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Perovskite StructureCorner atom: 1/8

Edge atom: 1/4

Corner atom: 1/8

g

Edge atom: 1/4

Face atom: 1/2Face atom: 1/2

Body atom: 1Body atom: 1Body atom: 1y

CornerEdgeFace NNNNN 81

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21

Body= 53

CornerEdgeFace 842Body


Terminologies regarding Miller indices:

Review

g g g

Planes ( ) Families of equivalent planes { }

Directions [ ] Directions [ ] Families of directions < >

Perovskite StructureCorner atom: 1/8

Edge atom: 1/4

Corner atom: 1/8 Review

g

Edge atom: 1/4

Face atom: 1/2Face atom: 1/2

Body atom: 1Body atom: 1Body atom: 1y

CornerEdgeFace NNNNN 81

41

21

Body= 55

CornerEdgeFace 842Body

Perovskite Structure

Ca (A) Calcium Titanate

Ca (A)

Ti (B)Ti (B)( )

O2- (O)

( )

O2- (O)( )

Ca (A) = 8 × 1/8 = 1

( )

( ) Ti (B) = 1 × 1 = 1 O2- (O) = 6 × 1/2 = 3

Chemical formula: CaTiO3 (ABO3) Lattice parameter: a = 3.8967 Å

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p Mineral name: Perovskite

Perovskite Structure Barium Titanate

Ba (A)Ba (A)

Ti (B)Ti (B)

O2- (O)

Ba (A) = 8 × 1/8 = 1

( )

Ba (A) 8 1/8 1 Ti (B) = 1 × 1 = 1 O2- (O) = 6 × 1/2 = 3

BaTiO3 (Perovskite type) (ABO3) a = 4.0185Å

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a 4.0185Å

Perovskite Structure Brief Summary

General formula: ABO33

General valency: A2+B4+O3 – CaTiO3, SrTiO3, BaTiO3, PbTiO3

Alternative (i): A3+B3+O3 – LaFeO3, LaNiO3

Al i (ii) A1+B5+O LiNbO N NbO KNbO Alternative (ii): A1+B5+O3 – LiNbO3, NaNbO3, KNbO3

Alternative (iii): A(B′1-xB′′x)O3 – Pb(Zr1-xTix)O3( ) ( 1 x x) 3 ( 1 x x) 3

Alternative (iv): (A′1-xA′′x) BO3 – (Ba1-xSrx)TiO3

Alternative (v): (A′1-xA′′x) (B′1-yB′′y)O3 – (Pb1-xBax)(Zr1-yTiy)O3

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Spinel Structure

A site: tetragonal, General Formula

A site

B site

64×(1/8) = 8 B site: octahedral,

32×(1/2) = 16

A site

B site

O2-32×(1/2) = 16

O2- site: 32 Formula: AB2O4×(8)

O2-

2 4 ( ) A2+, B3+, O2-

Charge neutrality

W. H. Bragg, The structure of the spinel group of crystals, Philos.

2×1+3×2=|-2×4|

W. H. Bragg, The structure of the spinel group of crystals, Philos. Mag., 30, 305-315 (1915).

S. Nishikawa, Structure of some crystals of the spinel group, Proc.

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Math. Phys. Soc. Tokyo, 8, 199-209 (1915).

Spinel Structure

Spinel structure is named after the mineral spinel (MgAl2O4).

Brief Summary

p p ( g 2 4)

Their general formula is AB2O4.

It i ti ll bi ith O2 i f i f (f t It is essentially cubic, with O2- ions forming a fcc (face center cubic) lattice.

Th ti ( ll t l ) 1/8 f th t t h d l it d The cations (usually metals) occupy 1/8 of the tetrahedral sites and 1/2 of the octahedral sites and there are 32 O2- ions in the unit cell.

Thi d li d b i i b d i ld b l k This sounds complicated, but it is not as bad as it could be; look at the drawing.

We “simply” have two types of cubic building units inside a big fccO-ion lattice, filling all 8 octants.

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Spinel Structure

All spinels

Normal, Inverse and Mixed Spinel

p

AB2O4 (×8)

Unit cell: 32 fcc O Inverse spinelsUnit cell: 32 fcc O

64 tetrahedral sites: 8 filled (ratio = 1/8)

Normal spinels

8 A on tetrahedral sites

p

8 B on tetrahedral sites,

32 octahedral sites: 16 filled (ratio = 1/2)

16 B on octahedral sites

(A2+)T[B3+B3+]OO2-4

8 B on octahedral sites, and

(1 cation)T[2 cations]OO2-4

(x8)

(x8) 8 A on octahedral sites

A and B randomly d iarranged on oct sites

(B3+)T[A2+B3+]OO2-4

(x8) The general formula for mixed spinel is

(A B ) [A B ] O (×8)

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(x8)(A1-xBx)T[AxB2-x]OO4 (×8)

Determination of Crystal Structures X-Ray Diffraction - XRD

XRD can be used to text powder, bulk, thin film samples.

Diffraction patterns are obtained after a scanning over a certain range of angles.

The patterns are used to identify the crystal structure of the samples tested.

Transmission Electron Microscope (TEM)

p

TEM samples for powders are made by dispersing the powders in a certain liquid and then deposit on sample holder.

Preparation of bulk samples is a challenging work.

TEM can be used to observe sample morphology and determine

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TEM can be used to observe sample morphology and determine crystal structure.

Determination of Crystal Structures X-Ray Diffraction - XRD Wilhelm Röntgen

Diffraction occurs when gratings have spacingsNobel

Diffraction occurs when gratings have spacings comparable to the wavelength of diffracted radiation.

For crystals, spacing is the distance between parallel

Prize in Physics in 1901 y , p g p

planes of atoms.

Determination of Crystal Structures iff i ( ) X-Ray Diffraction (XRD) Sir William Henry Bragg

Diffraction!

Nobel Prize in Physics inDiffraction! Physics in 1915

Cancelled out!

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Lawrence

Determination of Crystal Structures iff i ( ) X-Ray Diffraction (XRD)

λ is the wavelengthλ is the wavelength of the X-ray.

id

QTSQn sinsin hklhkl ddn

id65

sin2 hkldn Bragg’s law! sin2 hkld

Determination of Crystal Structures

sin2 hkld λ = 1.54 Å for copper target.hkl

hkld Plane spacing can be calculated by

the experimental diffraction anglesin2hkl the experimental diffraction angle

from XRD pattern.

sin From plane spacing of a given

material diffraction angle can be

hkld2sin material, diffraction angle can be

calculated or predicted, thus giving out XRD pattern.

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p

Determination of Crystal Structures X-Ray Diffraction - XRD

X-ray source X-ray detector

S l

Bragg angle = θ 2θ = diffraction angle

Sample

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Determination of Crystal Structures iff i ( ) X-ray diffraction (XRD)

(100)2θ=21.67º,

12000

15000

(110

)

PS)

2θ 21.67 , θ=10.84º,

9000

1)nsity

(CP

)8410sin(254.1

100

d

3000

6000 (21

210)(2

00)

(111

)

Inte

n

(100

) )84.10sin(2

541

20 30 40 50 60(2

2 (o)

188.0254.1

2 (o)

XRD patter of a perovskite type

096.4

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polycrystal material.

Determination of Crystal Structures iff i ( )

(100): 2θ=21.67º, θ=10.84º, d100=4.096 Å

X-Ray Diffraction (XRD)

( ) , , 100

(110): 2θ=30.86º, θ=15.43º, d110=2.894 Å

(111): 2θ=38.13º, θ=19.07º, d111=2.357 Å

(200) 2θ 44 35º θ 22 18º d 2 040 Å(200): 2θ=44.35º, θ=22.18º, d200=2.040 Å

(210): 2θ=49.86º, θ=24.93º, d210=1.827 Å( ) 210

(211): 2θ=55.04º, θ=27.52º, d211=1.666 Å

The higher the diffraction angles, the smaller the plane spacings will be

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will be.

i i i ( )

Determination of Crystal Structures Transmission Electron Microscope (TEM)

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SummaryMost of the primary chemical bonds found in ceramic materials are

actually a mixture of ionic and covalent types.

Crystal structures of ceramics with predominantly ionic bonding are based on:

The relative sizes of the cations and anions - cation tends to have maximum possible number of anion nearest neighbors and vice-versa.

Magnitude of the electrical charge on each ion, whose balance g gdictates chemical formula.

X-ray diffraction (XRD) and transmission electron microscopy X-ray diffraction (XRD) and transmission electron microscopy (TEM) are powerful tools to examine crystal structures of ceramics.

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MS3001 Ceramics 02 Crystal(6)

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