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 The Rhomb Is the Unit cell Shape Of Hexagonal lattices

Packing: layers build up 3D solid

Packing: layers build up 3D solid

ABABABAB . . . . Stacked up towards you Packing direction ABABABAB . . . . Stacked up towards you

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

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

A C B CCP viewed as packing layers CCP viewed as extended fcc unit cell View ccp/fcc copper

a more realistic view of how to build up structure Packing layers a more realistic view of how to build up structure sometimes not at all related to unit cell 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 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

creates useful materials Defects: creates useful materials

Defects in metal structure

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

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

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 r- + r+ Diagonal= 2r- + 2r+ 2 x r- 2 x r-

Consider red and blue balls the larger anions of A B 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: CsCl - simple cubic, cation and anion CN 8, a 1:1 ionic solid 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 2:1 Ionic Solids NaCl (halite) packing type: ccp packing, all Oh sites filled cubic ion sites: both anion and cation six coordinate, Oh ZnS (sphalerite) packing type: ccp packing, half Td sites filled cubic ion sites: both anion and cation four coordinate, Td ZnS (wurzite) packing type: hcp packing, half Td sites filled hexagonal ion sites: both anion and cation four coordinate, Td CsCl packing type: bcc packing cubic ion sites: both anion and cation eoght coordinate, Oh 2:1 Ionic Solids CaF2 (fluorite) packing type: ccp packing, all Td sites filled cubic 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- site 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 A B Cd2+ I- Layers of hcp w/ Cd2+ in Oh sites A B Cd2+ I-

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

Muscovite NaAl2(OH)2Si3AlO10)

Muscovite: layered silicates

Defects

Types of Defects Schottky defect, a vacancy defect Cl-vacancy Na+ vacancy

an interstitial defect (extra atom or ion) 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 + hn  Na+ + Cl + e-

Fluorite, calcium fluoride, CaF2 ummm, not white????

Types of Defects 4. Atom interchange 5. Substitutional Cu and Au swap positions in an alloy

Defects: The Beauty of Imperfection

Corundum, Al2O3

Al2O3 Corundum Al(3+): CN=6, Oh O(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.

Peridot is the gem-quality form of the mineral Olivine 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. Polarized micrograph

Fe (2+) in Td (SiO4) sites heat + Ti(3+) Quartz - SiO2 -simplest silicate mineral, piezoelectric, chiral! heat + Ti(3+)

creates useful materials Defects: creates useful materials

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

heat heat