ms3001 ceramics 02 crystal(6)
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Advanced Ceramic Materials from CeramaretAdvanced Ceramic Materials from Ceramaret
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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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Crystal Structure in Ceramics
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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Crystal Structure in Ceramics
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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Crystal Structure in Ceramics
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]
Crystal Structure in Ceramics
Crystallographic Planes
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]
Crystal Structure in Ceramics
Crystallographic Planes
Miller Indices:[001]
x y zIntercepts: 1 1 infiniteReciprocals 1 1 0Reciprocals 1 1 0Lowest integers 1 1 0[010]
Plane (110)[100]
Crystal Structure in Ceramics
Crystallographic Planes
Miller Indices:[001]
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]
Crystal Structure in Ceramics
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
Crystal Structure in Ceramics
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
Crystal Structure in Ceramics
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]
Crystal Structure in Ceramics
Crystallographic planes
Miller Indices:[001]
x y zIntercepts: 1/2 infinite 1Reciprocals 2 0 1Reciprocals 2 0 1Lowest integers 2 0 1[010]
Plane: (201)[100]
Crystal Structure in Ceramics
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.
Crystal Structure in Ceramics
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.
Crystal Structure in Ceramics
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
41
21
Body= 53
CornerEdgeFace 842Body
Crystal Structure in Ceramics
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!
64
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.
66
p
Determination of Crystal Structures X-Ray Diffraction - XRD
X-ray source X-ray detector
S l
Bragg angle = θ 2θ = diffraction angle
Sample
67
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
68
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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