Blooming Trees: Space-Efficient Structures for Data Representation
Square packing: Not most space efficient Hexagonal packing: Most space efficient.
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Transcript of Square packing: Not most space efficient Hexagonal packing: Most space efficient.
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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 . . . . Packed up towards you
Packing direction
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Packing direction
A B A B A B A
hcp Hexagonal Closest Packing:A B A B …
Packing direction
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Packing direction
A C B A C B A
ccp CubicClosestPacking:A B C A B C …
Packing direction
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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
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CCP viewed as extended unit cell
CCP viewed as packing layers
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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 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
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Defectsin metal structure
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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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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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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+
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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:
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
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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/ Cd in Oh sites
AB
AB
AB
AB
I-
Cd2+
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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+)
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Ruby
Gem-quality corundum
with ~3% Cr(3+) replacing Al(3+)
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Al2O3
Corundum
Al(3+): CN=6, OhO(2-): CN=4, Td
Nothing recognizable here..
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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.