Square packing: Not most space efficient

Square packing: Not most space efficient Hexagonal packing: Most space efficient

Unit Cells: the simplest repeating motif Can be different shapes and sizes The Rhomb Is the Unit cell Shape Of Hexagonal lattices

Packing: layers build up 3D solid

Packing direction ABABABAB . . . . Packed up towards you

Packing direction A B A B A B A hcp Hexagonal Closest Packing: A B A B … Packing direction

Packing direction A C B A C B A ccp Cubic Closest Packing: A B C A B C … Packing direction

Unit Cells: • a conceptual way to build up structure • sometimes resemble macroscopic crystalline solid • assigned symmetry types, like P21/c or P4mm called space groups • used in X-ray crystallography • ( see quartzpage) • Packing layers • a more realistic view of how to build up structure • sometimes not at all related to unit cell

CCP viewed as packing layers CCP viewed as extended unit cell

ccp hcp bcc

More on Metals Cubic closest packing makes metals malleable: easily bendable Cu and Ag Work- hardening: creation of defects, loss of ccp lattice Work hardening, strain hardening, or cold work is the strengthening of a material by increasing the material's dislocation density. Wikipedia Alloys Sterling Silver = Ag (92.5%) + Cu (7.5%), a substitutional alloy Brass = Cu + Zn, a new structure, an intermetallic alloy Steel = Fe + C (~1%), carbide steel, an interstitial alloy Chrome = steel + Cr = Fe + C(~1%) + Cr(10%) Stainless steel = chrome steel, both interstitial and substitutional alloy “18/10” stainless is 18% Cr and 10% Ni Galvanized Steel = steel with Zn layer Molybdenum steel = Fe + C(<1%) + Cr(14%) + Ni(<2%) + Mo(1 %), “martensitic” steel: very strong and hard

Defects in metal structure

Now consider red and blue balls the larger metal atoms; Where are the interstitial sites? Small alloy atoms, e.g. C, Other metal atoms, e.g. Cr or W, replace metal atoms Small alloy atoms fit into Td sites and Oh sites

Smaller atom like C in iron Larger atom like P in iron Effect of added atoms and grains on metal structure. Defects and grain boundaries “pin” structure. All these inhibit sliding planes and harden the metal. Second crystal phases precipitated

Ionic Solids as “Ideal structures” • Build up Ionic Solids conceptually like this: • assume Anions are larger than Cations, r- > r+ • pack the Anions into a lattice: ccp, hcp or bcc • add Cations to the interstitial spaces r- + r+ 2 x r- 2 x r-

Consider red and blue balls the larger anions of AB packed layers; Where do the cations go? larger anions Larger cations, r+/r- > 0.41 Smaller cations, r+/r- < 0.41

Td cation holes are smaller than Oh holes 2x as many Td holes as Oh holes

Wurzite = Hexagonal ZnS hcp S2- dianions (A B A packed) with Zn2+ cations in 1/2 Td holes. Build it! See it! (as Chem3D)

Sphalerite or Zinc Blende = Cubic ZnS ccp S2- dianions (A B C packed) with Zn2+ cations in 1/2 Td holes. Build it! See it! (as Chem3D movie)

Fluorite = Cubic CaF2 ccp Ca2+cations (A B C packed) with F2- anions in all Td holes. Build it! See it! (as Chem3D movie)

Halite = NaCl ccp Cl anions (A B C packed) with Na cations in all Oh holes. Build it! See it in 3D!

These are the prototype structures: NaCl (Halite) - ccp anions & Oh cations; a 1:1 ionic solid CaF2 (Fluorite) - ccp cations & Td anions; a 1:2 ionic solid Cubic ZnS (sphalerite) - ccp anions & 1/2 Td cations; a 1:1 ionic solid Hexagonal ZnS (wurzite) - hcp anions & 1/2 Td cations; a 1:1 ionic solid

Prototype Lattices 1:1 Ionic Solids NaCl (halite) packing type: ccp packing, all Oh sites filled cubicion sites: both anion and cation six coordinate, Oh ZnS (sphalerite) packing type: ccp packing, half Td sites filled cubicion sites: both anion and cation four coordinate, Td ZnS (wurzite) packing type: hcp packing, half Td sites filled hexagonalion sites: both anion and cation four coordinate, Td CsCl packing type: bcc packing cubicion sites: both anion and cation eoght coordinate, Oh 2:1 Ionic Solids CaF2 (fluorite) packing type: ccp packing, all Td sites filled cubicion sites: anion four coordinate, Td and cation eight coordinate, Oh

Other Structures are Described Based on Prototypes Example 1. Galena - PbS “has the NaCl lattice”. Note crystal morphology Example 2. pyrite - Fe(S2) “has the NaCl lattice”, where (S22-) occupies Cl- site Note crystal morphology With more deviations: Example 3. tenorite- CuO: pseudo cubic where (O2-) occupies ABC sites and Cu2+ occupies 3/4 ‘squashed’ Td sites. Example 4. CdI2: Layered Structure: I- forms hcp (ABA) layers and Cd2+ occupies all Oh sites between alternate hcp (A B) layers Example 5. MoS2 : Layered Structure: S22- forms (AA BB) layers and Mo4+ occupies all D3h sites between AA layers Note similarity to graphite. Used as lubricant.

One Prototype Layered Structure: Cadmium Iodide Layers of hcp w/ Cd in Oh sites Cd2+ A B A B A B A B I-

The funny thing about corundum is, when you have it in a clean single crystal, you get something much different. Sapphire is Gem-quality corundum with Ti(4+) & Fe(2+) replacing Al(3+)

Ruby Gem-quality corundum with ~3% Cr(3+) replacing Al(3+)

Al2O3 Corundum Al(3+): CN=6, Oh O(2-): CN=4, Td Nothing recognizable here..

The same reaction occurs in the commercial drain cleaner Drano. This consists of sodium hydroxide, blue dye, and aluminum turnings. When placed in water, the lye removes the oxide coating from the aluminum pieces,causing them to fizz as they displace hydrogen from water. This makes it sound like the Drano is really working effectively, even though it's the lye that actually cleans out the drain clog.

Square packing: Not most space efficient