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The structure as you can also see has a large void in the center of unit cell made by cations
These empty spaces make such oxides good ionic conductors which is useful in applicationssuch as energy storage eg batteries
For having some fun with the structure we can also draw as projection of this material on(110) plane Here you can see the row of empty octahedral sites along [110]-direction
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Module 1 Structure of Ceramics Compounds based on FCC Packing of Ions
173 Zinc Blende (MX) Structure
MX type compounds also called as sphalerite structured compounds based on a mineralname of sphalerite
Mostly oxides and sulphides follow this structure Examples are ZnO ZnS BeO etc
Some covalently bonded materials and compounds have similar structure such as GaAs SiCBN You can also visualize diamond also having similar structure with both anion and cationbeing of same type
Typically compounds with tetrahedral co-ordination assume this structure
In this structure anions form FCC lattice and cations occupy the tetrahedral interstices
Due to stoichiometry half of the tetrahedral sites are filled
Compounds with radius ratio 0225-0414 follow this structure with a few exceptions
where bonding favours a tetrahedral coordination despite unfavourable radius ratio especiallycovalently bonded compounds
ExamplesZn2+ - 006 nmBe2+ - 0027 nmO2- - 014 nm S2-- 0184 nm
Figure 129 Zinc Blende or Sphaleritestructure
Coordination numbers M - 4 X - 4
Lattice type FCC
Motif M ndash 0 0 0 X ndash frac14 frac14 frac14
4 formula units per unit cell
Tetrahedra are shared at corners
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Module 1 Structure of Ceramics Compounds based on FCC Packing of Ions
174 Spinel Structure
Formulae ndash (A2+)(B3+)2O4 or AB2O4 or AOB2O3
FCC Packing of anions
Partial occupancy of both tetrahedral and octahedral sites ie18th of tetrahedral and frac12 of theoctahedral sites are occupied
A spinel unit-cell is made up of eight FCC cells made by oxygen ions in the configuration2times2times2 so it is a big structure consisting of 32 oxygen atoms 8 A atoms and 16 B atoms
Depending on how cations occupy different interstices spinel structure can be Normal orInverse
1741 Normal Spinel
Chemical formula (A2+)(B3+)O4
Examples are many aluminates such as MgAl2O4 FeAl2O4 CoAl2O4 and a few ferrites such
as ZnFe2O4 and CdFe2O4
In this structure all the A2+ ions occupy the tetrahedral sites and all the B3+ ions occupy theoctahedral sites
Apply bond strength rule to verify the stoichiometry
Cations - A2+ - 24 B3+ - 36
Oxygen valence = (24x1)+ (36x3) = 2
Figure 130 Schematic of spinel structure
1742 Inverse Spinel B(AB)O4
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Chemical formula (A2+)(B3+)2O4 but can be more conveniently written as B(AB)O4
Most ferrite follow this structure such as Fe3O4 (or FeOFe2O3) NiFe2O4 CoFe2O4 etc
In this structure frac12 of the B3+ ions occupy the tetrahedral sites and remaining frac12 B3+ and all
A2+ ions occupy the octahedral sites (now you can hopefully make sense of the formula in theprevious line)
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Module 1 Structure of Ceramics Other Cubic Structures
18 Other Cubic Structures
There are a few structures which appear as if they are based on cubic closed packing ofanions However the actual structure is rather different and many of these structures are merelybased on the cubic packing of anions Here we discuss the perovskite structure based onABO3 structure CsCl structure and ReO3 structure
181 Perovskite (ABO3) Structure
ABO3 type compounds
Examples are many titanates like BaTiO3 SrTiO3 PbTiO3 etc which happen to be
technologically very useful compounds as we will see in later modules
In ABO3 structured compounds A ion is twelve fold coordinated by oxygen (like a
dodecahedra) and B ion is octahedrally coordinated by oxygen ions
Oxygen atoms form an FCC-like (not FCC) cell with atoms missing from the corners whichare occupied by A atoms
Bond strength check
Cation Ba 212 = 16 and Ti 46 = 23
Oxygen valence = 16 x Coordination number by Ba + 23 x coordination number by Ti
Figure 131 Perovskite structure
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Figure 132 Polyhedra model of perovskitestructure
Lattice type Primitive Cubic (NOT FCC)
Motif A ion - 0 0 0 B ion ndash frac12 frac12 frac12 O ion - frac12 frac12 0 0 frac12 frac12 frac12 0 frac12
One Formula unit per unit cell
Coordination
B cation is surrounded by oxygen octahedra which share corners
A cation is surrounded by oxygen dodecahedra which touch faces of octahedra
An important parameters about perovskites is the their ldquoTolerance Factor (t)rdquo which is definedas
This is derived from the geometry of a cube in which the atoms are of such sizes that theytouch each other and hence the face diagonal of the unit cell would be times the unit-celllength as result t = 1 for a perfect cubic perovskite
However due to variations in ionic radii of various ions many perovskites show deviationsfrom t = 1 and may not even have a cubic structure Deviations from t = 1 signify the level oflattice distortion
For example BaTiO3 has cubic structure only above ~120degC while it is tetragonal at room
temperature and further adopts orthorhombic and rhombohedral structure if cooled below RT
Perovskites can also have various combinations of ionic valence such as
eg A2+B4+O4 BaTiO3 PbTiO3 CaTiO3 SrTiO3 etc
eg A3+B3+O4 LaAlO3 LaGaO3 BiFeO3 etc
Mixed Perovskites
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A2+(B2+13B5+
23)O3 eg Pb(Mg13Nb23)O3
A2+(B3+12B5+
12)O3 eg Pb(Sc12Ta12)O3
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Module 1 Structure of Ceramics Other Cubic Structures
182 ReO3 Structure
Stoichiometry MX3
Lattice type Primitive cubic
Atomic Positions M- 0 0 0 X - frac12 0 0 0 frac12 0 0 0 frac12
Coordination Numbers M CN = 6 Octahedral coordination X CN = 2 Linear coordination
Can be visualized as perovskite ABO3 structure with empty B-sites
Representative Oxides
ReO3 UO3 WO3
Used for gas sensing and electrochromic applications
Figure 133 ReO3 structure and polyhedramodel
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Module 1 Structure of Ceramics Other Cubic Structures
183 CsCl Structure
MX type compounds parent compound being CsCl
Examples Halides such as CSCl AgI AgBr etc
Radius ratio governs cubic co-ordination of both cations and anions
Lattice type Primitive cubic lattice
Motif Anions (X) 0 0 0 Cations (M) frac12 frac12 frac12
One formula unit per unit cell
Figure 134 (a) CsCl structure (b) Ball-stickmodel
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Module 1 Structure of Ceramics Orthogonal Structures
19 Orthogonal Structures
Many superconductors follow the structures which are perovskite based ie the structurecontains the perovskite structured units stacked along c-axis or [001]-direction in most casesThe examples are superconductors such as YBa2Cu3O7 ferroelectrics such as Bi4Ti3O12
etc In some other compounds such as La-Sr-Cu-O the structure is composed of alternatingperovskite and rocksalt structure units Such a representation makes it easy to understandthem
Here we will take examples of Y-Ba-Cu-O and La-Sr-Cu-O and discuss them very briefly
191 Yttrium Barium Copper Oxide or YBCO (YBa2Cu3O7)
Parent compound is Y3Cu3+3O9 (see Fig 135) which also contains perovskite units
Doping of Y by Ba leads to structure modification (step 1) as well as reduction of Cu3+ to
Cu2+ state (step 2) and thus resulting in the reduction in the number of required oxygen ionsand hence creates oxygen vacancies in the structure This gives a transition temperature of~92 K below which the compound has zero electrical resistance ie is a superconductor
Y3Cu3+3O9rarrYBa2Cu3+
3O8rarr YBa2Cu2+2Cu3+O7-x
Figure 135 Origin of the structure of YBa2Cu3O7-x as a triple-perovskite unit (DM Smyth PP1-10 in ceramic superconductors IIResearch Update 1988 MFYan Ed The American Ceramic Society1988)
Here Cu coordination is of interest
Cu2+ atoms have four-fold coordination along Cu-O chains
Cu3+ atoms have five-fold coordination in the Cu-O planes
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Figure 136 Atomic coordination inYBCO
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Module 1 Structure of Ceramics Orthogonal Structures
192 Lanthanum Strontium Copper Oxide La2-xSrxCuO4
Parent compound La2CuO4 is actually a mixture of one Rocksalt structured compound LaO
and one perovskite structured compound LaCuO3 and can also be written as LaOLaCuO3
The structure shows a layered structure with layers stacked as A4O-AO4-A4O as shown
below where A is La
Substitution of La by Sr results in the compound La2-x Srx CuO4 turning into a
superconductor with a Tc ~ 35K
Figure 137 (a) Origin of La2-xSrxCuO4 structure shown in(b) as two perovskite and cells
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Module 1 Structure of Ceramics
Structures based on HCP Packing of Ions
110 Structures based on HCP packing of ions
Similar to FCC packing of anions many ceramic structures are also based on another type of closed packing of anions ie hexagonal closed packed (HCP) In this category we will look at the following structures
Wurzite structured compounds
Corundum structured compounds
Ilmenite structure compounds
Lithium niobate structured compounds and
Rutile structure
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Module 1 Structure of Ceramics Structures based on HCP Packing of Ions
1101 Wurtzite (MX) structured compounds
Compounds with M2+X2- stoichiometry
Examples are the polymorphs of Sphalerite structured compounds such as ZnS ZnO SiC
Co-ordination of both anions and cations is 4 as in Sphalerite structured compounds
Anions form an HCP lattice with frac12 of the tetrahedral sites occupied by cations
The only difference to Sphalerite structure is that here anions pack in the form ofABCABChellip stacking
Figure 138 Wurtzite structure and polyhedralmodel
As you can notice all the tetrahedrons point in one direction ie along the c-axis of the unit-cell and they share the corners
Lattice type Primitive HCP
Motif M 0 0 0 and X and
The filling of structure can be seen below
>
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Figure 139 Layer by layer filling in Wurtzite
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Module 1 Structure of Ceramics Structures based on HCP Packing of Ions
1102 Corundum (Al2O3) Structured Compounds
M2X3 type of compounds
- Alumina or Sapphire (Al2O3) is the parent compound
Other examples are compounds like Cr2O3 Fe2O3
Anions form an HCP lattice
Two-third of octahedral voids are occupied by the cations to maintain the stoichiometry
Coordination numbers M 6 X 4
This arrangement preserves the charge neutrality as you can also verify using bond strengthformula
This can be best viewed when we look at the basal plane of (0001)-plane of the unit-cell andstart filling the interstices
Figure 140 Layered filling of Corundum
One unit-cell consists of six layers of oxygen ions
A side view of the structure on plane can be seen below where you can see columns of
cations along the c-axis with 23 rd filling of octahedral sites
>
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Figure 141 View of 1010 plane ofCorundum
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Module 1 Structure of Ceramics Structures based on HCP Packing of Ions 1103 Ilmenite Structure
The stoichiomteric formula is ABO3 (different to perovskite ABO3)
The parent compound is FeTiO3
Other compounds which follow this structure are CdTiO3 CoTiO3 CrRhO3 FeRhO3 FeVO3 LiNbO3
MgGeO3 MgTiO3
This structure is very similar to Corundum or a - Al2O3
Imagine the Corundum structure and replace Al atoms in the octahedral sites in one (0001)-layer ie half ofthe total aluminum atoms by Fe and the remaining half in the next layer by Ti atoms in the octahedral sitesand continue this order of substitution along the c-axis of the unit-cell
Hence the atomic arrangement is similar to Al2O3 except with alternate layers of Fe and Ti in place of Al
Coordination numbers both Fe and Ti remain octahedrally coordinated while O is coordinated by 4 cations ie 2 Fe and 2 Ti
Bond strength rule gives correct oxygen valence
+ =2=Oxygen
valence
Figure 142 Layered filling of Ilmenite
>
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One unit-cell consists of six layers of oxygen ions
A side view of the structure on 10-10 plane as shown below shows the columns of cations along the c-
axis with 23rd filling of octahedral sites which are alternately filled by Fe and Ti ions and then followed by a
vacant site
Figure 143 Ilmenite structure on 10-10plane
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Module 1 Structure of Ceramics Structures based on HCP Packing of Ions
1104 Lithium Niobate Structure
Structure is similar to Al2O3 except that Al sub-lattice is substituted in an ordered manner by
Li and Nb ions in the same layer unlike in alternating layer in Fe2O3
The parent compound LiNbO3 is ferroelectric in nature and hence is technologically
important
LiNbO3 also has highly anisotropic refractive index and it shows birefringence which is
changeable by electric field
Such materials are used in electro-optic devices
Figure 144 Atomic arrangement of a layer inLiNbO3 structure
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Figure 145 Structure on 10-10 plane in LiNbO3
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Module 1 Structure of Ceramics Structures based on HCP Packing of Ions
1105 Rutile Structure
Polymorph of titanium di-oxide or TiO2
Other forms are Anatase and Brookite
It is formed by quasi-HCP packing of anions
Half of the octahedral sites are filled by cations
The resulting structure has a tetragonal crystal structure due to a slight distortion in the lattice
Anisotropic diffusion properties of cations are found in TiO2
Materials shows large and anisotropic refractive index and high birefringence
TiO2 is often used as pigments and is non-toxic
Figure 146 Structure of a layer of oxygen and Titanium inRutile
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Figure 147 Unit-cell of Rutile
Figure 148 Polyhedral model of Rutile
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Module 1 Structure of Ceramics Summary
Summary
In ionic solids anions typically form the base lattice
Interstices can be completely or partially filled depending on the size of cations andstoichiometry
Paulingrsquos rules play an important role in structure determination and deviations lead tostructural distortions
Most ceramic compounds follow three types of common structures based on packing ofanions ie
Structures based on FCC packing of anions
Structures based on HCP packing of anions
Primitive cubic or other structures