Ceramics 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., Al 2 O 3, NaCl, SiC, SiO 2 ) 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), glasses. 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 minerals Glasses -SiO 2 based - attributes: transparent to light, easy to form - applications: windows, containers, lenses, etc. Clays - composed of Al 2 O 3, SiO 2 and chemically bound water - attributes: easy to form with water addition - applications: bricks, tiles, porcelain, pottery, etc. Cements - consisting of CaO, SiO 2 and AL 2 O 3 - attributes: form paste with water and then harden - applications: construction, roads, concrete Engineering Ceramics (advanced, high-performance) - e.g. Al 2 O 3, SiC, Si 3 N 4, ZrO 2 - attributes: excellent physical, chemical or mechanical properties - applications: heat engines, cutting tools, die materials, superconductors
IONIC BONDING and STRUCTURE The crystal structure of an ionically bonded material is determined by the number of atoms of each element required for charge neutrality and the optimum packing based on the relative sizes of the ions. The building criteria for the ceramic 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 leads 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 chemistry and charge balance. (BCC, FCC and HCP structures involved only one type of atom)
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 (Ca 2+ and F - form CaF 2 ). Relative size of the cation and anion. The ratio of the atomic radii (r cation /r anion ) dictates the atomic arrangement. Stable structures have cation/anion contact.
Coordination Number: the number of anions nearest neighbors for a cation. As the ratio gets larger (that is as r cation /r anion ~ 1) the coordination number gets larger and larger. Holes in sphere packing Triangular Tetrahedral Octahedral
Calculating minimum radius ratio for a triangle: B O O B 1 2 AO = 1 AB 2 AO r r r a c a A AB ra + r c = r a r a + r c = cos30 = = 0. 155 C = cosα ( α = 30 ) 3 2 1 2 AO = 1 AB 2 AO r r r a c a AB ra + r c = r a r a A + r c = cos45 = 0. 414 = 2 2 C = cosα ( α = 45 ) o for an octahedral hole
C.N. = 2 r C /r A < 0.155 C.N. = 3 0.155 < r C /r A < 0.225 C.N. = 4 0.225 < r C /r A < 0.414 C.N. = 6 0.414 < r C /r A < 0.732 C.N. = 8 0.732 < r C /r A < 1.0
Ionic (and other) structures may be derived from the occupation of interstitial sites in close-packed arrangements. A 2 X
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) -Zinc 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. A 2 X (ReB 2 ) o/t (all) (Li 3 Bi) (Na 3 As) ½t sphalerite (ZnS) wurtzite (ZnS) (½ o CdCl 2 CdI 2 ) Location and number of tetrahedral holes in a fcc (ccp) unit cell -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)
Crystals having filled Interstitial Sites Octahedral, Oh, Sites Ionic Crystals prefer the NaCl Structure: NaCl structure has Na+ ions at all 4 octahedral sites Large interatomic distance LiH, MgO, MnO, AgBr, PbS, KCl, KBr Na+ ions Cl- ions
Crystals having filled Interstitial Sites Tetrahedral, Th, Sites Both the diamond cubic structure And the Zinc sulfide structures have 4 tetrahedral sites occupied and 4 tetrahedral sited empty. Zn atoms 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 (ZnS, ZnSe, CdS) Cu, Ag Group VII Crystals (AgI, CuCl, CuF) S atoms
AX Type Crystal Structures Rock Salt Structure (NaCl) NaCl structure: r C = r Na = 0.102 nm, r A = r Cl = 0.181 nm r C /r A = 0.56 Coordination = 6 Cl NaCl, MgO, LiF, FeO, CoO Na Cesium Chloride Structure (CsCl) CsCl Structure: r C = r Cs = 0.170 nm, r A = r Cl = 0.181 nm r C /r A = 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
A m X p -Type Crystal Structures If the charges on the cations and anions are not the same, a compound can exist with the chemical formula A m X p, where m and/or p 1. An example would be AX 2, for which a common crystal structure is found in fluorite (CaF 2 ). AmXp -TYPE - cation charges are NOT the same -AX2 (CaF2,UO2, PuO2 and ThO2)
Fluorite CaF 2 Fluorite (CaF 2 ): r C = r Ca = 0.100 nm, r A = r F = 0.133 nm r C /r A = 0.75 From the table for stable geometries we see that C.N. = 8 Other compounds that have this crystal structure include UO 2, PuO 2, and ThO 2.
A m B n X p -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 A m B n X p. Barium titanate (BaTiO 3 ), having both Ba 2+ and Ti 4+ cations, falls into this classification. This material has a perovskite crystal structure and rather interesting electromechanical properties. AmBnXp -TYPE - more than one cation charges -BaTiO3, CoTiO3, SrTiO3
CaTiO 3 -dielectric BaTiO 3 - ferroelectric Pb(Mg 1/3 Nb 2/3 )O 3 - relaxor ferroelectric Pb(Zr 1-x Ti x )O 3 - piezoelectric (Ba 1-x La x )TiO 3 semiconductor Perovskite - an Inorganic Chameleon ABX 3 - three compositional variables, A, B and X (Y 1/3 Ba 2/3 )CuO 3 -x - superconductor Na x WO 3 - mixed conductor; electrochromic SrCeO 3 - H - protonic conductor RECoO 3-x - mixed conductor (Li 0.5-3x La 0.5+x )TiO 3 - lithium ion conductor LaMnO 3-x - Giant magnetoresistance
The perovskite structure CaTiO 3 -TiO 6 octahedra -CaO 12 cuboctahedra (Ca 2+ and O 2- form a cubic close packing) preferred basis structure of piezoelectric, ferroelectric and superconducting materials
Density Calculations in Ceramic Structures n ' ( ) ρ = C A V A c + N n : number of formula units in unit cell (all ions that are included in the chemical formula of the compound = formula unit) ΣA C : sum of atomic weights of cations in the formula unit ΣA A : sum of atomic weights of anions in the formula unit V c : volume of the unit cell N A : Avogadro s number, 6.023x10 23 (formula units)/mol A A
Example: NaCl n = 4 in FCC lattice ΣA C = A Na = 22.99 g/mol ΣA A = A Cl = 35.45 g/mol r Na =0.102x10-7 r Cl =0.181x10-7 cm V c = a 3 = (2r Na +2r Cl ) 3 V c = (2 0.102 10-7 + 2 0.181 10-7 ) 3 cm 3 ( 22. 99 + 35. 45) 4 3 = 2. 14g. 3 23 ρ = cm 6. 023 10 [ ] 7 7 2 0. 102 10 + 2 0. 181 10
Silicate Ceramics Composed mainly of silicon and oxygen, two most abundant elements in earth s crust (rocks, soils, clays, sand) Basic building block: SiO 4 4- tetrahedron Si-O bonding is largely covalent, but overall SiO 4 block has charge of 4 Various silicate structures different ways to arrange SiO 4-4 blocks
O O 4- Si O O
Silica = silicon dioxide = SiO 2 Every oxygen atom is shared by adjacent tetrahedra Silica can be crystalline (e.g., quartz) or amorphous, as in glass (fused or vitreous silica) 3D network of SiO 4 tetrahedra in cristobalite High melting temperature of 1710 C
Window glasses Most window glasses produced by adding other oxides (e.g. CaO, Na 2 O) whose cations are incorporated within SiO 4 network. The cations break the tetrahedral network so glasses melt at lower temperature than pure amorphous SiO 2. Lower melting point: easier to mold (e.g., bottles). Other oxides (e.g., TiO 2, Al 2 O 3 ) substitute for silicon and become part of network
Carbon Carbon is not a ceramic Carbon exists in various polymorphic forms: sp 3 diamond, and amorphous carbon, sp 2 graphite and fullerenes/nanotubes. Carbon Diamond Has diamond-cubic structure (like Si, Ge) One of the strongest/hardest material known High thermal conductivity Transparent in the visible and infrared, with high index of refraction. Semiconductor (can be doped to make electronic devices) Metastable (transforms to carbon when heated) Carbon: Graphite Layered structure with strong bonding within the planar layers and weak (van der Waals) between layers Easy interplanar cleavage (lubricant and for writing pencils) Good electrical conductor Chemically stable even at high temperatures Applications include furnaces, rocket nozzles, welding electrodes.
Carbon
Carbon: buckyballs and nanotubes Buckminsterfullerenes (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 nickel-phosphorus alloy 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 sodium 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. r Cs = 0.167nm A Cs = 79.91 g.mol -1 r Br = 0.196nm A Br = 132.91 g.mol -1 (B) For which set of crystallographic planes will a first-order diffraction peak occur at a diffraction angle of 2θ = 44.53 O for FCC nickel (metallic atomic radius R=0.1246nm) when monochromatic radiation having a wavelength of 0.1542nm is used.
(A) r r Cl Br = 0.852 C.N.=8 Lattice Parameter Density Packing Factor a 3a O ρ = ρ = PF O = = 2r Cl = 0. 419nm 1 ( 79. 909 + 132. 905) g. mol 7 3 23 ( 0. 419nm 10 ) ( 6. 023 x10 atoms. mol 4. 8g. cm ( 4π ) 3 + 2r 3 Br = [ 0 196 0 167 ] 3 3 (. ) + (. ) ( 0. 419) 2( 0. 196 3 + 0. 167) = 0. 693 = 0. 726nm 1 )
(B) The first step to solve this nl problem is to compute the d hkl = (1)(0.1542 nm) 2 sin θ interplanar spacing using (2) sin 44.53 2 Bragg equation, Now, employment of equations for cubic systems, and the value of R for nickel leads to = 0.2035 nm h 2 + k 2 + l 2 = a = 2R 2 = d d hkl hkl (2)(0.1246 nm) 2 (0.2035 nm) = 1.732 This means that h 2 + k 2 + l 2 = (1.732) 2 = 3.0 By trial and error, the only three integers 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.
Molybdenum Disulfide (MoS2) Common high tech grease Like graphite, MoS2 has weak van der Waals forces between the basal planes. The bonds between the sulfur 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 molybdenum disulfide, tungsten 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 solid 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 + - Frenkel defect Schottky defect
Equilibrium concentration of defects kt ~ e Q D 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 valence states, (e.g. Fe 2+, Fe 3+ ). 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 nonstoichiometry
Impurities in Ceramics Impurity atoms can exist as either substitutional or interstitial solid solutions Substitutional ions substitute for ions of like type Interstitial ions are small compared to host structure (anion interstitials are unlikely). Solubility high if ion radii and charges match Incorporation of ion with different charge state requires compensation by point defects. Interstitial impurity atom Substitutional impurity ions