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
Packing direction
ABABABAB . . . . Stacked up towards you
Packing direction
Packing direction
A
B
A
B
A
B
A
hcp
Hexagonal
Closest Packing:
ABAB…
Packing direction
Packing direction
A
C
B
A
C
B
A
ccp
Cubic
Closest
Packing:
ABCABC…
A
C
B
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 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
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-
2r- + 2r+
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
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
NaCl (halite)
cubic
packing type: ccp packing, all Oh sites filled
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)
hexagonal
packing type: hcp packing, half Td sites filled
ion sites: both anion and cation four coordinate, Td
CsCl
cubic
packing type: bcc packing
ion sites: both anion and cation eoght coordinate, Oh
2:1 Ionic Solids
CaF2 (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 - PbS “has the NaCl lattice”.
Note crystal morphology
Example 2. pyrite - Fe(S2) “has the NaCl lattice”, where (S22-) occupies Cl- site
Note 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
Cd2+
I-
A
B
A
B
A
B
A
B
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
1. Schottky defect,
a vacancy defect
Cl-vacancy
Na+ 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 + 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. 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)
Quartz - SiO2 -simplest silicate
mineral, piezoelectric, chiral!
sites
heat
+ Ti(3+)
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