Ceramic Science 4RO3 Lecture 2 September 16, 2013 Tannaz Javadi
Rule 5: In an Ionic structure the chemical environment (cations) that is surrounding an anion should be at least uniform and similar. Although the second rule allowed an anion to have different cations as much as it can neutralize, usually only one of them is accepted and repeated for all the other anions. Example: Ca 3 Al 2 Si 3 O 12 ------------------------Garnet There are three cations in this crystal: EXAMPLE Z= Ca 2+ effective charge= 2/8=1/4 Y= Al 3+ effective charge= 3/6=1/2 X= Si 4+ effective charge=4/4= 1 Based on second rule: the number of cations around one anion is as follows: Si---O---Si x*1=2, x=2 Al OR Al----O---Al Al y*1/2=2, y=4 OR Ca Ca Ca Ca----O---Ca Ca Ca Ca z*1/4=2, z=8 X
So the fifth rule avoid too many different varieties in arrangement and define one arrangement for whole crystal X*1+ Y*1/2+ Z*1/4= 2 X, Y, Z 0, ϵ ᵶ>0 X is not zero and it cannot be 2 as this makes Y and Z be zero, therefore, X=1 Si Y=1 Ca----O---Al Z=2 Ca
Ceramic Crystal Structures Criteria How can we apply Pauling s rules to deduce the unknown structure of an ionic compound? If cation is smaller than anion, FCC or HCP close-packing of the anions will occur. Based on the cation/anion radius ratio, tetrahedral or octahedral interstitial sites will be occupied The stoichiometry of the compound can be examined: MX 1:1 Octahedral coordination is preferred (CN=6): as octahedral/atoms 1:1, all of the octahedral sites will be filled Tetrahedral coordination is preferred (CN=4): as tetrahedral/atoms 2:1, one-half of the tetrahedral sites will be filled The sites will be filled in a manner to maximize the cation separation
Ceramic Crystal Structures FCC or HCP Close packed ions (most of the time anions) Interstitials filled with ions (most of the time cations) FCC-based structures Rocksalt (NaCl, KCl, LiF, MgO, CaO,...)(MX 1:1 compound) FCC anion lattice Cations (Na +, K +, Mg 2+,...) filled all octahedral sites 0.414< r c /r a < 0.732 Octahedra share edges Cl - Na + (110)
Ceramic Crystal Structures FCC-based structures Auntifluorite (M 2 X)(Li 2 O, Na 2 O, K 2 O...) FCC anion lattice Cations (Li +, K +, Na +,...) filled all tetrahedral sites 0.225 < r c /r a < 0.414 Tetrahedra share edges (each tetrahedron shares two of its oxygen ions with a neighboring tetrahedron O 2- Li +
Ceramic Crystal Structures FCC-based structures Fluorite (MX 2 )(CaF 2, ZrO 2, UO 2, CeO 2...) FCC cation lattice (CN=8) Cation is larger than octahedral site. Anions filled all tetrahedral sites Tetrahedra share edges (each tetrahedron shares two of its oxygen ions with a neighboring tetrahedron Ca 2+ F -
FCC-based structures Ceramic Crystal Structures Zincblend (MX)(ZnS, ZnO) FCC anion lattice Cations filled 1/2 tetrahedral sites with divalent cation Maximum cation separation: filling the opposing corners Anion coordination tetrahedra share corners Covalent compounds (β-sic, GaAs,...) Overlap of sp 3 hybridized orbitals with tetragonal directionality. identical atoms: Diamond, Si, Ge Anion Cation
HCP-based structures Ceramic Crystal Structures Wurtzite (MX)(ZnO, ZnS, BeO) & (AlN, α-sic) HCP anion lattice Cations filled 1/2 tetrahedral sites Maximum cation separation: filling tetrahedra of one orientation (either upward or downward) Anion coordination tetrahedra share corners Covalent compounds Overlap of sp 3 hybridized orbitals with tetragonal directionality. Anion Cation
Polymorphs & Polytypes Polymorphs: ZrO 2 same compound different crystal structure (Cubic, Tetragonal, Monoclinic) different symmetry (change in interatomic spacing) same ion coordination Displacive transformation (simple atom displacement) 1240 C 2370 C Monoclinic Tetragonal Cubic Tm= 2680 Cubic Zirconia can be stabilized at room temperature by adding few percent Cao, Mgo, or Y 2 O 3 (metastable phase)= Technologically important material (Oxygen ion conductor, fuel cells) Room temperature metastable tetragonal zirconia phase achieve by slightly using dopant. Tetragonal to monoclinic transformation is the basis for transformation toughening (impeding the propagation of the crack by energy absorption)
Polytypes: special type of polymorphism same structure Zincblend vs. Wurtzite o tetrahedrally filled close-packed anion layers o different stacking sequence o reconstructive transformation (bond breaking and rearrangements)- requires atom diffusion o SiC 1- cubic, zincblende structure (3C- cubic symmetry with 3-layers stacking sequence) 2- hexagonal, wurtzite structure (pure is 2H most common is 6H: requires six close-packed layers to repeat the stacking sequence)
HCP-based structures Ceramic Crystal Structures Corundum (M 2 X 3 )(Al 2 O 3, Fe 2 O 3, Cr 2 O 3, Sapphire,...) HCP anion lattice Cations filled 2/3 of octahedral sites 2/3 of the octahedral sites is filled between two close-packed planes of oxygen Plane shown by above dashed line After 6 layers the arrangement repeats itself In total, the unit cell has a 12.99 angstrom C0
HCP-based structures Ceramic Crystal Structures Ilmenite (ABX 3 )(FeTiO 3,) Same structure as Corundum both A and B prefers octahedral sites alternating cation layers occupied by A and B LiNbO 3 each layer has equal number of Li and Nb. net electric dipole - charge distribution between the Li-Nb pair Ferroelectric crystals
Ceramic Crystal Structures HCP-based structures Polymorphs of TiO 2 1. Rutile 2. Anatase 3. Brookite Rutile (TiO 2 ) HCP anion (Oxygen) lattice Cations filled 1/2 of octahedral sites Strong electrostatic repulsion stretching of basal plane Unit cell is tetragonal; a=b c Columns of unoccupied octahedral sites Anisotropy O 2- c Ti 4+ a a
Ceramic Crystal Structures Perovskite: ternary compounds of ABO 3 formula (BaTiO 3, CaTiO 3, PbZrO 3 ) ra>>>rb No sublattice is closed packed large A cations along with oxygens form FCC structure B cation fills the octahedral sites (has only oxygen ions as nearest neighbours Ba 2+ O 2- Ti 4+ Polymorphisms in Perovskite: Cubic ------------ Tetragonal Tc (BaTiO 3 )= 130 C The oxygen octahedron coordinating Ti is larger than necessary (being expanded by large Ba ions): loose Ti in the octahedral site (Unstable) Ti ion can be easily displaced from the body centered position and change the crystal symmetry
Tetragonal BaTiO 3 Room temperature structure Ti 4+ is displaced by ~ 0.12 A from the center toward one face of the unit cell noncentrosymmetric structure permanent electric dipole (there is a small charge differential between each end of the unit cell ) net polarization that extends over many unit cells electronic applications (piezoelectrics: produces a voltage in response to an applied force, usually a uniaxial compressive force) Differential phase-contrast microscopy at atomic resolution, Shibata, et. al,. Nature physics, 8, 611-615, 2012
Ceramic Crystal Structures Spinel: ternary compounds of AB 2 O 4 formula (MgAl 2 O 4 ) A is divalent and B is trivalent (AO.B 2 O 3 ) Unit cell: 8 FCC oxygen subcells in cubic array I/2 of Octahedrals sites (B 3+ ) & 1/8 of tetrahedral sites (A 2+ ) are filled Normal Spinel Bond strength of A 2+ = 2/4, and B 3+ = 3/6 Each oxygen coordinated by 3 octahedral cations and 1 tetrahedral cation. Inverse spinel B (AB) O 4 1/2 of the B 3+ cations fill the 1/8 tetrahedral sites, remaining half of the B 3+ and A 2+ fill octahedral sites Soft magnetic ferrites (inductors, read/write heads for magnetic storage media)
Ceramic Crystal Structures Covalent Ceramics: hardest, most refractory, and toughest ceramic BN: like Carbon, graphite like hexagonal form (lubricious) like Diamond, cubic zincblend, hard, abrasive
Covalent ceramic crystals SiC: have various polytypes Used in abrasives, refractories, hard wear resistant structural ceramics, and high temperature semiconductors Silicon Nitride Si 3 N 4 Si sp 3 hybridization seeks tetrahedral coordination N sp 2 hybridization seeks ternary coordination Open structure based on SiN 4 tetrahedron Each N is coordinated with 3 Si β-si 3 N 4 => HCP, AB stacking (stable at high T) Blue = nitrogen, grey = silicon α-si 3 N 4 => HCP, ABCD stacking (CD is like AB but glided by a plane) Transformation from α to β is reconstructive dissolution & re-precipitation (slow) interlocking needle-like microstructure- high fracture toughness structural ceramic applications, rotors for automative turbochargers and high-temperature gas turbines
Covalent ceramic crystals TiN & ZrN Rocksalt structure Electrically conductive Extremely hard Cutting tools SIALON: Si-Al-O-N Solid solutions between nitrides and oxides (Al 2 O 3 + β-si 3 N 4 ) First introduced in the early 1970s Low density, High strength Superior thermal shock resistance, Moderate wear resistance Fracture toughness, Mechanical fatigue and creep resistance, Oxidation resistance Applications: Cutting tools, wear components
Ceramic Crystal Structures Crystalline silicates: many ores and minerals Si 4+ /O 2- : tetrahedral coordination Si-O bond ~ 49% ionic and 51% covalent O shared between 2 tetrahedral units (corner sharing) prevents close packing (open structure) Other cations (Al 3+ ) can readily substitute the tetrahedrally coordinated Si 4+ In case of having Al 3+ instead of Si 4+, a charge imbalance can be compensated by the substitution of an OH - ion for O 2- or by adding alkali or alkali earth cations in local interstitial sites The (SiO 4 ) 4- tetrahedron may no longer need to share all corners in order to satisfy Pauling s rule.
How to classify silicates? Crystalline silicates Based on the connectivity between the silica tetrahedra O/Si ratio is a useful parameter for characterizing the degree of connectivity between silica tetrahedra in silicate compounds. O/Si => 2 sharing at corners (SiO 2 ), (quartz, tridymite, cristobalite) (4 corners shared) As O/Si increases, number of shared corners decreases Layered silicates O/Si=2.5 (talc, mica, kaolinite, clays) (3 corners shared) Chain silicates O/Si = 2.75 3 (asbestos)- fibrous like Pyroxenes (MgSiO 3, enstatite)- single chain Cristobalite
Major silicate structures Shared Oxygen O/Si ratio (0) O/Si=4 Mg 2 SiO 4 Forstrite (2) BaTiSi O/Si=3 3 O 9 Benitoit (2) CaMgSi 2 O 6 Diopside O/Si=3 (2.5) Ca 2 Mg 5 (OH) 2 [Si 8 O 22 ] Tremolite O/Si=2.75 (3) O/Si=2.5 Mg 3 (OH) 2 [Si 4 O 10 ] Talc (4) SiO 2 O/Si=2