the ideal. square packing: not most space efficient hexagonal packing: most space efficient
TRANSCRIPT
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The Ideal
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Square packing:Not most space efficient
Hexagonal packing:Most space efficient
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Unit Cells: the simplest repeating motif
Can be different shapes and sizes
TheRhomb Is the Unit cellShapeOfHexagonallattices
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Packing: layers build up 3D solid
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Packing: layers build up 3D solid
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ABABABAB . . . . Stacked up towards you
Packing direction
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Pack
ing
dir
ect
ion A
B A B A B A
hcp Hexagonal Closest Packing:A B A B …
Packing direction
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Pac
king
dir
ecti
on
A C B A C B A
ccp CubicClosestPacking:A B C A B C …
Packing direction
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CCP viewed as extended fcc unit cell
CCP viewed as packing layers
A C B A C B A
View ccp/fcc copper
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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
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ccp hcp bcc
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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
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Defects:creates useful materials
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Defectsin
metal structure
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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.
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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
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The Ideal
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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+
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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
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Td cation holes are smaller than Oh holes2x as many Td holes as Oh holes
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Wurzite = Hexagonal ZnShcp S2- dianions (A B A packed) with Zn2+ cations in 1/2 Td holes. Build it! See it! (as Chem3D)
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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)
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Fluorite = Cubic CaF2
ccp Ca2+ cations (A B C packed) with F2- anions in all Td holes. Build it! See it! (as Chem3D movie)
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Halite = NaCl ccp Cl anions (A B C packed) with Na cations in all Oh holes. Build it! See it in 3D!
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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
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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
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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.
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One Prototype Layered Structure:Cadmium Iodide
Layers of hcp w/ Cd2+ in Oh sites
ABABABAB
I-
Cd2+
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Molybdenite, MoS2
Mo
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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
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MuscoviteNaAl2(OH)2Si3AlO10)
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Muscovite: layered silicates
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Defects
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Types of Defects
1.Schottky defect,
a vacancy defect
Na+ vacancy
Cl-vacancy
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Types of Defects
2. Frenkel defect,
an interstitial defect(extra atom or ion)
Interstitial Ag+
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Types of Defects
3. F- center, (F, farbe, Ger.)or a color center
Trapped electron
NaCl + h Na+ + Cl + e-
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Fluorite,calcium fluoride,CaF2
ummm, not white????
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Types of Defects
4. Atom interchange5. Substitutional
Cu and Au swap positions in an alloy
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Defects:The Beauty of Imperfection
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Corundum, Al2O3
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Al2O3
Corundum
Al(3+): CN=6, OhO(2-): CN=4, Td
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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
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Ruby
Gem-quality corundum
with ~3% Cr(3+) replacing Al(3+)
in octahedral sites
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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.
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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.
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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.
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heat
Fe (2+)
in Td (SiO4)
sitesQuartz - SiO2 -simplest
silicate mineral, piezoelectric, chiral!
+ Ti(3+)
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Defects:creates useful materials
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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
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heat heat
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