Ionic Compounds anion cation Ceramics

Radius Ratio Rules CN (cation) Geometry min rc/RA (f) 2 linear none 3 trigonal planar 0.155 4 tetrahedral 0.225 6 octahedral 0.414 8 cubic 0.732 12 cubo-octahedral 1 sites occur within close-packed arrays common in ionic compounds if rc is smaller than fRA, then the space is too big and the structure is unstable

Summary: Sites in HCP & CCP 2 tetrahedral sites / close-packed atom 1 octahedral site / close-packed atom sites are located between layers: number of sites/atom same for ABAB & ABCABC

Discussed Already CN f 4 0.225 6 0.414 8 0.732 ZnS: Zinc Blende CaF2: Fluorite S2- Ca2+ Zn2+ F- rCa/RF = 0.77 CN(Ca2+) = 8 rZn/RS = 0.33 – 0.41 CN(Zn2+) = 4 Cations in close-packed array

NaCl (rock salt) Cl- ~ 1.81 Å; Na+ ~ 0.98 Å; rc/RA = 0.54 Na+ is big enough for CN = 6 also big enough for CN = 4, but adopts highest CN possible Cl- in cubic close-packed array Na+ in octahedral sites Na:Cl = 1:1  all sites filled CN f 4 0.225 6 0.414 8 0.732 CNA also = 6; RA/rc = 1.85, Cl- is definitely large enough for CNA = 6

Rock Salt Structure Cl Na ccp array with sites shown CN(Cl-) also = 6 CNA also = 6; RA/rc = 1.85, Cl- is definitely large enough for CNA = 6 ccp array with sites shown CN(Cl-) also = 6 RA/rc > 1  Cl- certainly large enough for 6-fold coordination

Lattice Constant Evaluation rock salt ccp metal a R a R 4R = 2 a a = 2(RA + rc) > ( 4/2)RA

CsCl Cl- ~ 1.8 Å; Cs+ ~ 1.7 Å; Cs+ is big enough for CN = 8 rc/RA = 0.94 Cs+ is big enough for CN = 8 But there are no 8-fold sites in close-packed arrays CsCl unrelated to close-packed structures Simple cubic array of anions Cs- in cuboctahedral sites RA / rc> 1  clorine ideally also has large CN Ca:Cl = 1:1  all sites filled

Cesium Chloride Cl- 1 Cs+/unit cell 1 Cl-/unit cell CN(Cs) = 8 Cs+

Unit Cells & Lattice Points BCC Metal CsCl Structure How many lattice points per unit cell?

Covalent Compounds sp3 s2p1 s2p2 s2p3 s2p4 s2 semi-conductors

Covalent Structures Recall: zinc blende  both species tetrahedral ZnS: +2 -2 GaAs: +3 -3 or sp3 single element: C or Si or Sn 4 4 diamond How many lattice points per unit cell?

Brief Review Metals Ionic structures Covalent structures Close-packed structures (CN = 12) Cubic close-packed, hexagonal close-packed Subtle reasons for selecting one over the other Slightly less close-packed Body centered cubic (CN = 8) Influence of covalency Ionic structures Close-packed with constraints Covalent structures Not close-packed, bonding is directional Any can be strongly or weakly bonded (Tm)

Diamond vs. CCP 8 atoms/cell, CN = 4 4 atoms/cell, CN = 12 ½ tetrahedral sites filled

Computing density Establish unit cell contents Compute unit cell mass Compute unit cell volume Unit cell constant, a, given (or a and c, etc.) Or estimate based on atomic/ionic radii Compute mass/volume, g/cc Example: NaCl Contents = 4 Na + 4 Cl Mass = 4(atom mass Na + atomic mass Cl)/No Vol = a3 Units = Cl Na Avogardo’s #

Single Crystal vs. Polycrystalline Rb3H(SO4)2 Diamond Quartz (SiO2) Ba(Zr,Y)O3-d Regions of uninterrupted periodicity amalgamated into a larger compact Periodicity extends uninterrupted throughout entirety of the sample External habit often reflects internal symmetry = grains delineated by grain boundaries

Polycrystallinity