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MME 467 Ceramics for Advanced Applications

Lecture 04

Structure of Ceramics 1 Ref: Barsoum, Fundamentals of Ceramics, Ch03, McGraw-Hill, 2000.

Prof. A. K. M. Bazlur Rashid Department of MME, BUET, Dhaka

Topics to discuss....

1. Structure of Ceramics

1. Structure of Crystalline Ionic Ceramics

2. Structure of Some Binary Ionic Ceramics

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q Crystalline microstructures range in complexity

l from single element structures of carbon (such as diamonds, graphite, and fullerenes) - which are not strictly speaking ceramic materials, although they share several properties with them

l through simple compound structures consisting of just two elements (e. g. NaCl)

l to more complex structures such as clays and engineering ceramics designed for particular applications such as superconductors.

STRUCTURE OF CERAMICS

q Amorphous microstructures include the vast silica- based family, and are based on short range rather than long range order.

q For ionic compounds the bonding forces are electrostatic and, therefore, omni-directional.

l the bonding forces should be maximised by packing as many cations around each anion, and as many anions around each cation as possible.

l the coordination numbers are, however, constrained by the stoichiometry of the compound and by the sizes of the atoms.

Example:

For Na+Cl–, there are 6 anions around each cation; because of 1:1 stoichiometry there must also be 6 Na cations around each Cl anoin. For Zr4+O2–

2, there are 8 anions around each cation, but there mush be only 4 cations around each anion.

STRUCTURE OF IONIC CERAMICS

q For compound AmBn we expect ionic bonding to predominate when atom A has low electronegativity and atom B has high electronegativity.

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q Most ionic ceramics structures based on 1. either FCC or HCP close-packing of one type of ion, 2. with the other ions occupying a specific set of interstitial sites.

q Generally the larger ions (usually anions) form the close-packed structure, with smaller ions (cations) occupying the interstices.

Recalling that, although FCC and HCP are the most efficient ways of packing spheres, only 74% of the available space is filled; the 26% free space is in the form of different types of holes or sites, which can be occupied by the smaller cations in the ionic structures.

q Two principle types of cation sites, tetrahedral (TD) and octahedral (OH), exist between layers of close-packed atoms. l the caions need to fit snugly, so they squeeze into holes that are not quite big enough l funny things happen if the hole size is bigger than the size of inclusion atom !!

(as in barium titanate)

q Having determined what types of holes are available, we must now decide: (a) Which sites are occupied by a given cation è This is determined by the radius ratio. (b) How many sites are occupied è This is determined by the stoichiometry.

Octahedral hole Three in each of the two planes Tetrahedral hole

Three anions in one plane, and a single anion in the adjacent plane

q  The nearest neighbour configuration of oxygen atoms around OH and TD cations is independent of whether the basic structure is derived from FCC or HCP.

l FCC and HCP lattices have the same number density of OH and TD sites

Location and Density of Interstitial Sites

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Coordination Number

In TD sites – 4 In OH sites – 6

In compact structures,

No. of Tetrahedral (TD) sites = 2n No. of Octahedral (OH) sites = n

n = No. of atoms per cell Octahedral sites are larger …

T

RED = Octahedral sites = 1/4 x 12 + 1 = 4 per unit cellBLUE = Tetradedral sties = 8 per unit cell

O

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Classification of Ionic Ceramic Structures

1. AX - type Structures Rocksalt, CsCl, and ZnS

2. AX2 - type Structures Fluorite, Rutile

3. AmBnOp - type Structures Spinel, Perovskite

Many structures; But what determines which structure will form ?

Factors Affecting Structures

1. Crystal stoichiometry or Electroneutrality Electrically neutral; charges must be balanced (even when defects are present). Ceramics with AX2 stoichiometry cannot have ROCKSALT structure.

2. Radius ratio To achieve lowest energy state (Etotal), cations and anions tend to pack densely (as determined by the rC/rA ratio), which will maximise attractions and minimise repulsions (and increase the coordination number, CN). An unstable structure cannot be formed.

3. Propensity for covalency and tetrahedral coordination

l If the bonding has some covalent character, then packing will be less efficient.

l Cations with higher polarising power (Cu2+, Al3+, Zn2+, Hg2+) are bonded with anions that are readily polarisable (I2-, S2-, Se2-), thereby increasing covalent character of bond and forming tetrahedral crystal.

l Atoms that favour sp3 hybridisation (Se, C, Ge) form tetrahedral crystals.

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stable stable unstable

For a specific CN, there is a critical or minimum radius ratio

Anion-Cation Coordination Configuration

rC/rA > Ideal rC/rA = Ideal rC/rA < Ideal

CN Position of cation Range of rC/rA 2 Centre of two linear anions < 0.155 3 Centre of triangle 0.155 – 0.225 4 Centre of tetrahedron 0.225 – 0.414 6 Centre of octahedron 0.414 – 0.732 8 Centre of cube 0.732 – 1.000

Coordination Number Geometries for Various Radius Ratios

predicting structure based on radius ratio

q  Coordination number increases as rC/rA increases

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Effect of Stoichiometry

q  If all of one type of site is full, the remainder have to go into the other types of sites.

Example:

FCC unit cell has 4 OH and 8 TD sites. Now, if for a specific ceramic, each unit cell has 6 cations and the cations prefer OH sites, then 4 will go in OH site, and 2 in TD sites

q  Significant in covalent bonding, or in ionic bonding with a significant covalent character.

Example: SiC Electronegativity: XSi = 1.8, XC = 2.5 Ionic character = 11.5 % only (i.e., 88.5 % covalent bonding) Both Si and C prefer sp3 hybridisation; So, Si get TD sites

Effect of Bond Hybridisation

Predicting Structure Based on rC/rA Ratio

Example Problem 13.2/Callister/P-391 On the basis of ionic radii, which crystal structure would you predict for FeO?

Ionic radius:

Fe2+ = 0.077 Fe3+ = 0.069 O2- = 0.140

rFe+2 0.077 nm rO-2 0.140 nm = = 0.550

The value lies between 0.414 and 0.732. Thus the CN is 6. Since both Fe and O has the same valence, both Fe and O have the same CN of 6. Therefore, the predicted crystal structure of FeO will be ROCKSALT.

Conclusion: It is not only the chemical formula which determine the crystal structure but also the relative sizes of the cations and anions.

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Structure Structure Atomic CN CN Example Type Name Packing Cation Anion of Structure AX Rock salt FCC 6 6 NaCl, MgO, FeO

AX Cesium chloride Simple cubic 8 8 CsCl

AX Zinc blende FCC 4 4 ZnS, SiC

AmXp Fluorite (AX2) Simple cubic 8 4 CaF2, UO2, ThO2

AmXp Corundum HCP Al2O3, Fe2O3

AmBnXp Perovskite (ABX3) FCC 12(A), 6(B) 6 BaTiO3, SrZrO3

AmBnXp Spinel (AB2X4) FCC 4(A), 6(B) 4 MgAl2O4, FeAl2O4

Common Ceramic Crystal Structures

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Cesium Chloride Structures

q  Anions in simple cubic arrangement, with cations in interstices at the cube centres.

q  The radius ratio is 0.94 (>0.732). l The coordination number is 8 for both anions and cations. l Cubic structure.

q  Ceramics having this structure: CsBr, TlCl, TlBr

STRUCTURE OF SOME BINARY IONIC CERAMICS

Rocksalt Structure

q  A close-packed FCC array of larger anions, with an FCC array of smaller cations occupying the octahedral sites.

q  It has 1:1 (AX - type) stoichiometry with the coordination number is 6 for both cations and anions.

Crystal structure of NaCl

q  The radius ratio is (0.102 pm/0.181 pm) = 0.563 (which lies between 0.732 and 0.414).

q  Example of rocksalt ceramic structure:

MgO, CaO, BaO, CdO, MnO, FeO, NiO, all other halides of Na, Li, K and Rb, CsF, AgCl.

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Zinc Blende Structure

q  Zinc sulfide (ZnS) is a unique compound that forms two types of crystalline structures.

Wurtzite – hexagonal structure Zinc blende (a.k.a. sphalerite) – cubic

q  The radius ratio is (0.074/0.140) = 0.529. The size argument predict Zn2+ in OH sites, but found in TD sites. So why Zn2+ in TD sites?

q  Oxides and sulfides with smaller cations that prefer tetrahedral coordination tend to form this structure, e.g., ZnS, ZnO and BeO, as well as covalent compound such SiC, BN and GaAs.

Bonding hybridisation of zinc favours TD sites. So Zn2+ has 4 neighbouring O2-, instead of 6.

q  In order to satisfy the MX stoichiometry, only one half of the tetrahedral sites are needed to fill with divalent cations.

diamond structure

q  Zinc blende structure can be viewed as a derivative of the fully covalently bonded diamond cubic structure. If all atoms in zinc blende structure are identical, we obtain diamond structure.

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Wurtzite Structure

q  The wurtzite structure is based on the HCP close-packing of anions, with one-half of TD sites occupied by the cations.

q  Filling of cation is only in tetrahedral of one orientation (apex upward).

q  The coordination number of each ion is 4. This is the same as zinc blende structure.

q  Examples: AgI, ZnO, CdS, AlN, GaN, BN andα-SiC.

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Unit cell of the Wurtzite structure

Wurtzite Unit cell Wurtzite structure

The grey balls represent metal atoms, and yellow balls represent sulfur atoms.

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Antifluorite and Fluorite Structures

q  In antifluorite strucutre, the rC/ra ratio is close to 1, which renders it’s cubic arrangement. The anions are in FCC arrangement and all tetrahedral sites are filled by cation. The coordination numbers of cation and anion are 4 and 8, respectively.

q  The chemical stoichiometry is M2X. The connectivity of the tetrahedra is completely edge sharing; each tetrahedron shares two of its oxygen ions with a neigboring tetahedron.

q  Examples: Oxides of alkaline metals such as Li2O, Na2O and K2O, and chalcogenides such as Li2S, Li2Se.

q  Fluorite structure is the reverse of antifluorite and the crystal will show stoichiometry as MX2. The structure is based on FCC close-packing of the cations with all tetrahedral interstices filled by anions.

q  Examples: CaF2 (the mineral fluorite), BaF2, ZrO2 , UO2 and CeO2,

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(a) Antifluorite structure, typified by compounds Li2O (b) (110) plane of the fluorite structure compounds ZrO2.

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Rutile Structures

q  Rutile is one polymorph of the mineral TiO2 (anatase and brookite are being the other structures)

q  The structure is based on quasi-HCP packing of oxygen atoms with cation fill one-half of the available OH site.

q  The radius ratio is 0.745/1.26 = 0.591. With this ratio, the cubic holes are too large (rhole/r = 0.732) to be suitable.

q  The titanium(IV) ions will prefer to occupy OH holes in a FCC structure. Nature chooses to pack the oxide ions in rutile in a HCP structure.

q  The rutile structure has (6,3)-coordination. Observe that none of the TD holes are occupied. The titanium(IV) ions lie in OH holes.

The unit cell of rutile. Ti atoms are gray; O atoms are red.

q  The occupation of Ti in OH site is repeated in the third layer of oxygen HCP stacking, resulting in arrangement as TD unit cell. However, the atoms do relax from their positions since partial occupancy of highly charged Ti4+ .

  q  Arrangement of Ti4+ causes anisotropic diffusion of cation; along

the c-axis is much faster than in the a-axis direction. This makes TiO2 having highly anisotropic refractive index, and application for opacifying pigment for paints, paper and fabric.

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Unit cell of rutile structure One-half filling of octahedral sites in a close-packed plane (rutile structure)

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Next Class

Lecture 05

Structure of Ceramics 2 Ref: Barsoum, Fundamentals of Ceramics, Ch03, McGraw-Hill, 2000.