Ceramics 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 elements

Always 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 insulators Can be optically opaque, semi-transparent, or transparent Traditional ceramics – based on clay (china, bricks, tiles, porcelain), . “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 • Glasses

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

- composed of Al2O3, SiO2 and chemically bound - 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 IONIC BONDING and

The structure of an ionically bonded material is determined by the number of of each element required for charge neutrality and the optimum packing based on the relative sizes of the . The building criteria for the 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 atoms This to atomic contact (hard sphere model), configurations where anions (-) have the highest number of cation (+) neighbors and vice versa. Structure types: AX, AmXp, AmBnXp... based on and charge balance. (BCC, FCC and HCP involved only one type of ) Charge Neutrality: --Net charge in the structure should be zero.

The structure maximizes the number of nearest oppositely charged neighbors. Since cations are usually smaller than anions, the crystal structure is usually determined by the maximum number of anions that it is possible 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 by The 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. : 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 ratio O for a triangle: B

B O

A C C A 1 1 = rAB = rAB a a 2 2 for an octahedral += rrAO += rrAO ca ca 1 AB 1 AB 2 = cos αα °)30=( 2 = cos αα °)45=( AO AO r 3 r 2 a cos30 == a cos45o == + rr ca 2 + rr ca 2 r r c = .1550 c = .4140 ra ra 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 CRYSTAL STRUCTURE TYPES AX-TYPE anion - cation charges are the same (equal + and -) -Rock Salt Structure -NaCl, MgO, MnS, LiF, FeO -Cesium Chloride Structure (CsCl) - 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) Comparison between structures with filled octahedral and tetrahedral holes o/t fcc(ccp) hcp all oct. NaCl NiAs

all tetr. A2X(ReB2)

o/t (all) (Li3Bi) (Na3As) ½t (ZnS) (ZnS)

(½ o CdCl2 CdI2) Location and number of tetrahedral holes in a fcc (ccp)

-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) having filled Interstitial Sites

Octahedral, Oh, Sites

Ionic Crystals prefer the NaCl Structure:

• Large interatomic distance NaCl structure has Na+ ions • LiH, MgO, MnO, AgBr, PbS, at all 4 octahedral sites KCl, KBr

Na+ ions

Cl- ions Crystals having filled Interstitial Sites Tetrahedral, Th, Sites

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 Both the cubic structure And the structures (ZnS, ZnSe, CdS) have 4 tetrahedral sites occupied • Cu, Ag – Group VII Crystals and 4 tetrahedral sited empty. (AgI, CuCl, CuF) Zn atoms

S atoms AX Type Crystal Structures Rock Salt Structure (NaCl)

NaCl structure: rC = rNa = 0.102 nm,

rA = rCl = 0.181 nm rC/rA = 0.56 Coordination = 6 Cl Na NaCl, MgO, LiF, FeO, CoO

Cesium Chloride Structure (CsCl)

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

Coordination = 8 Cl Cs Is this a body centered cubic structure? Zinc Blende Structure (ZnS) radius ratio = 0.402 Coordination = 4 S Zn

ZnS, ZnTe, SiC have this crystal structure AmXp-Type Crystal Structures If 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 (CaF2). AmXp -TYPE - cation charges are NOT the same -AX2 (CaF2,UO2, PuO2 and ThO2) Fluorite CaF2

Fluorite (CaF2): rC = rCa = 0.100 nm, rA = rF = 0.133 nm ⇒ rC/rA = 0.75 From the table for stable geometries we see that C.N. = 8 Other compounds that have this crystal structure include UO2 , PuO2 , and ThO2. AmBnXp-Type Crystal Structures It 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 . titanate 2+ 4+ (BaTiO3), having both Ba and Ti cations, falls into this classification. This material has a 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

•(Y1/3Ba2/3)CuO3-x - superconductor

•NaxWO3 - mixed conductor; electrochromic

•SrCeO3 - H - protonic conductor •CaTiO3 - •RECoO3-x - mixed conductor •BaTiO3 - ferroelectric •(Li0.5-3xLa0.5+x)TiO3 - •Pb(Mg1/3Nb2/3)O3 - relaxor ferroelectric conductor •Pb(Zr Ti )O - piezoelectric •LaMnO3-x - Giant magneto- 1-x x 3 resistance •(Ba1-xLax)TiO3 – 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 (' +× AAn ) ρ = ∑ C ∑ A ×NV Ac 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 unit ΣAA: sum of atomic weights of anions in the formula unit Vc: volume of the unit cell 23 NA: Avogadro’s number, 6.023x10 (formula units)/mol Example: NaCl n’ = 4 in FCC

ΣAC = ANa = 22.99 g/mol ΣAA = ACl = 35.45 g/mol

-7 -7 rNa=0.102x10 rCl=0.181x10 cm 3 3 Vc = a = (2rNa+2rCl) -7 -7 3 3 Vc = (2×0.102×10 + 2×0.181×10 ) cm

×( + .. 453599224 ) −3 ρ = 3 = 142 .. cmg []. −7 . −7 . ××××+×× 10023610181021010202 23 Ceramics ¾ Composed mainly of and , two most abundant elements in earth’s crust (rocks, soils, clays, sand) 4- ¾ Basic building block: SiO4 ¾ Si-O bonding is largely covalent, but overall SiO4 block has charge of –4 -4 ¾ Various silicate structures – different ways to arrange SiO4 blocks 4- O

O Si O O

Silica = = SiO2

¾ Every oxygen atom is shared by adjacent tetrahedra ¾ Silica can be crystalline (e.g., ) or amorphous, as in (fused or vitreous silica)

3D network of SiO4 tetrahedra in High melting temperature of 1710 °C Window glasses Most window glasses produced by adding other (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 : easier to mold (e.g., bottles). Other oxides (e.g., TiO2, Al2O3) substitute for silicon and become part of network Carbon is not a ceramic Carbon exists in various polymorphic forms: sp3 diamond, and , sp2 and fullerenes/nanotubes. Carbon Diamond Carbon: Graphite Has diamond-cubic structure (like Layered structure with strong Si, Ge) bonding within the planar layers One of the strongest/hardest and weak (van der Waals) between material known layers High Easy interplanar (lubricant Transparent in the visible and and for writing pencils) infrared, with high index of Good electrical conductor refraction. Semiconductor (can be Chemically stable even at high doped to make electronic devices) temperatures Metastable (transforms to carbon Applications include furnaces, when heated) rocket nozzles, electrodes. Carbon Carbon: buckyballs and nanotubes (buckyballs) and carbon nanotubes are expected to play an important role in future nanotechnology applications (nanoscale materials, sensors, machines, and computers). Nanotube holepunching /etching

Carbon nanotube T-junction

Nano-gear Nanotubes as reinforcing fibers in nano-composites

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 gaps between the "blades.“ The substance has a total reflective index of 0.045 percent - which is more than three times darker than the - 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 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. -1 rCs = 0.167nm ACs = 79.91 g.mol -1 rBr = 0.196nm ABr = 132.91 g.mol (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 0.1542nm is used. (A) r Cl = .8520 C.N.=8 rBr

Lattice rra BrClO =+=+= .)..( 7260167019602223 nm Parameter aO = .4190 nm + 90513290979 .)..( molg −1 Density ρ = .( nm − 37 .() ××× 100236104190 23 molatomsx −1). ρ = 84 .. cmg −3 4π 3 3 Packing []+ 16701960 ).().()( PF = 3 = .6930 Factor 4190 ).( 3 (B) The first step to solve this nl (1)(0.1542 nm) problem is to compute the d = = 0 .2035 nm hkl 2 sin θ ⎛ 44.53 ° ⎞ interplanar spacing using (2)⎜ sin ⎝ 2 ⎠ Bragg equation, Now, employment of equations for cubic systems, and the value of R for nickel leads to

2 2 2 a 2R 2 (2)(0.1246 nm) 2 h +k +l = = = =1.732 d d hkl hkl (0.2035 nm)

2 2 2 2 This means that h +k +l = (1.732) =3.0

By trial and error, the only three which are all odd or even, 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. Disulfide (MoS2)

Common high tech grease Like graphite, MoS2 has weak van der Waals forces between the basal planes. The bonds between the 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 , 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 veins within granite. Imperfections in Ceramics 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 + -

Schottky defect Frenkel defect Equilibrium concentration of defects Q − D ~ e kT These defects create the electrical conductivity in ceramics. An increasing number of defects increases the conductivity.

Impurities must also satisfy charge balance Imperfections in Ceramics • 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 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 Impurities in Ceramics ¾ Impurity atoms can exist as either substitutional or interstitial solid solutions ¾ Substitutional ions substitute for ions of like type ¾ Interstitial ions are small compared to host structure (anion interstitials are unlikely). ¾Solubility high if ion radii and charges match ¾Incorporation of ion with different Interstitial impurity atom charge state requires compensation by point defects. Substitutional impurity ions