The Ideal

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 . . . . Stacked up towards you

Packing direction

Pack

ing

dir

ect

ion A

B A B A B A

hcp Hexagonal Closest Packing:A B A B …

Packing direction

Pac

king

dir

ecti

on

A C B A C B A

ccp CubicClosestPacking:A B C A B C …

Packing direction

CCP viewed as extended fcc unit cell

CCP viewed as packing layers

A C B A C B A

View ccp/fcc copper

Packing layers • a more realistic view

of how to build up structure

• sometimes not at all related to unit cell

A

B

C

A

B C A

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

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 latticeWork 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 alloyChrome = steel + Cr = Fe + C(~1%) + Cr(10%) Stainless steel = chrome steel, both interstitial and substitutional alloy

“18/10” stainless is 18% Cr and 10% NiGalvanized Steel = steel with Zn layerMolybdenum steel = Fe + C(<1%) + Cr(14%) + Ni(<2%) + Mo(1 %),

“martensitic” steel: very strong and hard

Defects:creates useful materials

Defectsin

metal structure

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.

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

The Ideal

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+

Diagonal=

2r- + 2r+

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:

CsCl - simple cubic, cation and anion CN 8, a 1:1 ionic solidNaCl (Halite) - ccp anions & Oh cations; a 1:1 ionic solidCaF2 (Fluorite) - ccp cations & Td anions; a 1:2 ionic solid

Cubic 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/ Cd2+ in Oh sites

ABABABAB

I-

Cd2+

Molybdenite, MoS2

Mo

Solid Film Lubricants: A Practical Guide Extreme conditions could include high and low shaft speeds, high and low temperatures, high pressures, concentrated atmospheric and process contaminants, and inaccessibility.

Mineral oil-based fluid lubricants (oil and grease materials) function properly where the designed surface areas and shaft speeds allow for the effective formation of an oil film, as long as the machine operating temperature envelope falls between -20°C and 100°C (-4°F to 212°F). The only absolute limits that apply for fluid lubricants, regardless of the base oil type, are conditions that cause a change in the state of the fluid that prohibits fluid film formation. Fortunately, that is not the end of the story.

Various materials that protect interacting surfaces after the fluid film is lost have been either discovered or created. These materials may be applied to a surface in the form of an additive to a fluid lubricant, or in a pure form, and may also be added or alloyed into the surface when the component is being manufactured. The more common types of materials include the following:

* Molybdenum disulfide (MoS2) – also known as moly * Polytetrafluoroethylene (PTFE) – also known as Teflon®

* Graphite

MuscoviteNaAl2(OH)2Si3AlO10)

Muscovite: layered silicates

Defects

Types of Defects

1.Schottky defect,

a vacancy defect

Na+ vacancy

Cl-vacancy

Types of Defects

2. Frenkel defect,

an interstitial defect(extra atom or ion)

Interstitial Ag+

Types of Defects

3. F- center, (F, farbe, Ger.)or a color center

Trapped electron

NaCl + h Na+ + Cl + e-

Fluorite,calcium fluoride,CaF2

ummm, not white????

Types of Defects

4. Atom interchange5. Substitutional

Cu and Au swap positions in an alloy

Defects:The Beauty of Imperfection

Corundum, Al2O3

Al2O3

Corundum

Al(3+): CN=6, OhO(2-): CN=4, Td

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+) in octahedral sites

Ruby

Gem-quality corundum

with ~3% Cr(3+) replacing Al(3+)

in octahedral sites

Emerald is the mineral beryl with substitution defects of Cr(3+) or V(3+) replacing Al(3+).

Beryl has the chemical composition Be3Al2(SiO3)6 and is classified as a cyclosilicate. It is the principal ore for the element beryllium.

Tsavorite is a variety of the mineral garnet a calcium-aluminosilicate with the formula Ca3Al2Si3O12. Crystal form is cubic. Trace amounts of vanadium or chromium provide the green color.

It is often called the Rolls-Royce of greens at Cadillac prices. From a collectors perspective, tsavorite is 200 times more rare than emerald, it is cleaner, more brilliant and not oiled or treated in any way.

Polarized micrograph

Peridot is the gem-quality form of the mineral Olivine. It has the chemical composition (Mg,Fe)2SiO4, with Mg in greater quantities than Fe. The depth of green depends on how much iron is contained in the crystal structure, and varies from yellow-green to olive to brownish green. Peridot is also often referred to as "poor man's emerald". Olivine is a very abundant mineral, but gem-quality peridot is rather rare.

heat

Fe (2+)

in Td (SiO4)

sitesQuartz - SiO2 -simplest

silicate mineral, piezoelectric, chiral!

+ Ti(3+)

Defects:creates useful materials

Replace:-S with I-Zn with Hg(at vertices)-Zn with Cu(in middle)

Replace:-S with I-Zn with Hg(at vertices)-Zn with Ag(in middle)

Sphalerite lattice

heat heat