The Ideal Square packing Not most space efficient

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 3 D solid

Packing: layers build up 3 D solid

Packing direction ABAB. . Stacked up towards you

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

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

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

A B Packing layers • a more realistic view of how to build up structure C • sometimes not at all related to unit cell A B C A Unit Cells: • a conceptual way to build up structure • sometimes resemble macroscopic crystalline solid • assigned symmetry types, like P 21/c or P 4 mm called space groups • used in X-ray crystallography

Metallic structures of the Elements 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: 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, Small alloy atoms fit into Td sites and Oh sites Other metal atoms, e. g. Cr or W, replace metal atoms

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

Consider red and blue balls the larger anions of A B packed layers; Where do the cations go? larger anions Smaller cations, r+/r- < 0. 41 Larger cations, r+/r- > 0. 41

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

Wurzite = Hexagonal Zn. S hcp S 2 - dianions (A B A packed) with Zn 2+ cations in 1/2 Td holes. Build it! See it! (as Chem 3 D)

Sphalerite or Zinc Blende = Cubic Zn. S ccp S 2 - dianions (A B C packed) with Zn 2+ cations in 1/2 Td holes. Build it! See it! (as Chem 3 D movie)

Fluorite = Cubic Ca. F 2 ccp Ca 2+ cations (A B C packed) with F 2 - anions in all Td holes. Build it! See it! (as Chem 3 D movie)

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

These are the prototype structures: Cs. Cl - simple cubic, cation and anion CN 8, a 1: 1 ionic solid Na. Cl (Halite) - ccp anions & Oh cations; a 1: 1 ionic solid Ca. F 2 (Fluorite) - ccp cations & Td anions; a 1: 2 ionic solid Cubic Zn. S (sphalerite) - ccp anions & 1/2 Td cations; a 1: 1 ionic solid Hexagonal Zn. S (wurzite) - hcp anions & 1/2 Td cations; a 1: 1 ionic solid

Prototype Lattices 1: 1 Ionic Solids Na. Cl (halite) cubic packing type: ccp packing, all Oh sites filled ion sites: both anion and cation six coordinate, Oh Zn. S (sphalerite) packing type: ccp packing, half Td sites filled cubic ion sites: both anion and cation four coordinate, Td Zn. S (wurzite) hexagonal packing type: hcp packing, half Td sites filled ion sites: both anion and cation four coordinate, Td Cs. Cl cubic packing type: bcc packing ion sites: both anion and cation eoght coordinate, Oh 2: 1 Ionic Solids Ca. F 2 (fluorite) cubic packing type: ccp packing, all Td sites filled ion sites: anion four coordinate, Td and cation eight coordinate, Oh

Other Structures are Described Based on Prototypes Example 1. Galena - Pb. S “has the Na. Cl lattice”. Note crystal morphology Example 2. pyrite - Fe(S 2) “has the Na. Cl lattice”, where (S 22 -) occupies Cl- site Note crystal morphology With more deviations: Example 3. tenorite- Cu. O: pseudo cubic where (O 2 -) occupies ABC sites and Cu 2+ occupies 3/4 ‘squashed’ Td sites. Example 4. Cd. I 2: Layered Structure: I- forms hcp (ABA) layers and Cd 2+ occupies all Oh sites between alternate hcp (A B) layers Example 5. Mo. S 2 : Layered Structure: S 22 - forms (AA BB) layers and Mo 4+ occupies all D 3 h sites between AA layers Note similarity to graphite. Used as lubricant.

One Prototype Layered Structure: Cadmium Iodide Layers of hcp w/ Cd 2+ in Oh sites Cd 2+ I- A B A B

Molybdenite, Mo. S 2 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 (Mo. S 2) – also known as moly * Polytetrafluoroethylene (PTFE) – also known as Teflon® * Graphite

Muscovite Na. Al 2(OH)2 Si 3 Al. O 10)

Muscovite: layered silicates

Defects

Types of Defects 1. Schottky defect, a vacancy defect Cl-vacancy Na+ vacancy Most likely

Types of Defects 2. Frenkel defect, an interstitial defect (extra atom or ion) Interstitial Ag+ Most likely

Fluorite, calcium fluoride, Ca. F 2 ummm, not white? ?

Halite, Na. Cl What? ? !! Not white? ? HALITE FROM DELAWARE BASIN, NEW MEXICO http: //csmsgeologypost. blogspot. com/2012/11/blue-purple-halite. html

Types of Defects 3. F- center, (F, farbe, Ger. ) or a color center Trapped electron Na. Cl + hn Na+ + ½ Cl 2 + e. Ca. F 2 + hn Ca 2+ + F 2 + e-

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

Defects: The Beauty of Imperfection

Corundum, Al 2 O 3

Al 2 O 3 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 Be 3 Al 2(Si. O 3)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 Ca 3 Al 2 Si 3 O 12. 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. It has the chemical composition (Mg, Fe)2 Si. O 4, 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 (Si. O 4) Quartz - Si. O 2 -simplest silicate mineral, piezoelectric, chiral! + Ti(3+) sites heat

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 See Chem. Tube animation of Ag 2 Hg. I 4