square packing: not most space efficient hexagonal packing: 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

TheRhomb Is the Unit cellShapeOfHexagonallattices

Packing: layers build up 3D solid

Packing: layers build up 3D solid

ABABABAB . . . . Packed up towards you

Packing direction

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 CubicClosestPacking: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 extended unit cell

CCP viewed as packing layers

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

AlloysSterling 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 layerMolybdenum steel = Fe + C(<1%) + Cr(14%) +

Ni(<2%) + Mo(1 %),“martensitic” steel: very

strong and hard

Defectsin 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 atomsSmall alloy atoms fit into

Td sites and Oh sites

Effect of addedatoms andgrainson metal structure.

Smaller atom like C in iron

Larger atom like P in iron

Second crystal phasesprecipitated

Defects and grain boundaries “pin” structure. All these inhibit sliding planes and harden the metal.

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

2 x r-

2 x r-

r- + r+

Consider red and blue balls the larger anions of A B packed layers;Where do the cations go?

largeranions

Smaller cations, r+/r- < 0.41

Larger cations, r+/r- > 0.41

Td cation holes are smaller than Oh holes2x as many Td holes as Oh holes

Wurzite = Hexagonal ZnShcp 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 ZnSccp 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 solidCubic ZnS (sphalerite) - ccp anions & 1/2 Td cations; a 1:1 ionic solidHexagonal 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 filledcubic ion sites: both anion and cation six coordinate, Oh

ZnS (sphalerite) packing type: ccp packing, half Td sites filledcubic ion sites: both anion and cation four coordinate, Td

ZnS (wurzite) packing type: hcp packing, half Td sites filledhexagonal ion sites: both anion and cation four coordinate, Td

CsCl packing type: bcc packingcubic ion sites: both anion and cation eoght coordinate, Oh

2:1 Ionic Solids CaF2 (fluorite) packing type: ccp packing, all Td sites filledcubic ion 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- siteNote 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

AB

AB

AB

AB

I-

Cd2+

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, OhO(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.