Weds, 10/29: Crystal Structures

Crystal Structures
Chapter 7
Wednesday, October 29, 2014
Contents of a Unit Cell
Consider
sodium chloride:
rock salt
(not Bravais)
Cl at corners: (8  1/8) = 1
Na at edge centers (12  1/4) = 3
Unit cell contents: 4(Na+Cl-)
Cl at face centres (6  1/2) = 3
Na at body centre = 1
Types of Cubic Cells
Different cubic cells result from different packing of atoms.
r
r
r
Simple Cubic
Body-Centered Cubic
Face-Centered Cubic
Unit Cell
Atoms per
cell
Coordination
Number
Lattice Constant
Packing Fraction
Simple Cubic
1
6
2r
52%
68%
74%
Body-Centered Cubic
2
8
4r
3
Face-Centered Cubic
4
12
2r 2
Close-Packed Structures
The Hexagonal Close-Packed Structure
An HCP crystal is a close-packed structure with the stacking
sequence …ABABAB…
To construct:
1st layer: 2D HCP array (layer A)
2nd layer: HCP layer with each sphere placed in alternate interstices in 1st layer (B)
3rd layer: HCP layer positioned directly above 1st layer (repeat of layer A)
…ABAB…
A
A
B
A
B
A
HCP is two interpenetrating simple hexagonal
lattices displaced by a1/3 + a2/3 + a3/2
The Hexagonal Close-Packed Structure
The Hexagonal Close-Packed Structure
The Cubic Close-Packed Structure
A CCP crystal is a close-packed structure with the stacking
sequence …ABCABC…
To construct:
1st layer: 2D HCP array (layer A)
2nd layer: HCP layer with each sphere placed in alternate interstices in 1st layer (B)
3rd layer: HCP layer placed in the other set of interstitial depressions (squares, C)
4th layer: repeats the 1st layer (A)
…ABCABC…
A
B
C
stacking
of HCP layers
along
body diagonal
It turns out that the CCP structure is
just the FCC Bravais lattice!
Close-Packed Structures
Most common are HCP and CCP, but an infinite number of stacking
sequences are possible.
silicon carbide
Example: silicon carbide has over 250 polytypes
e.g., 6H-SiC stacking sequence …ABCACB…
Metallic Solids
•
Most metals crystallize in ccp, hcp, or bcc structures
•
Metallic bonding is stronger than London dispersion forces, but
weaker than covalent bonding
Solid
M / g mol–1
Melting Point / °C
Kr
83.80
–157
Cu
63.55
1083
C (diamond)
12.01
3500
Interstitial sites in CP Structures
A large number of ionic structures can be regarded as built of CP layers of anions
with the cations placed in interstitial sites
for every anion, there is 1 Octahedral site and 2 Tetrahedral sites
Octahedral Holes in CCP
coordinates:
of O holes
½,0,0
0,½,0
0,0,½
½,½,½
= O site
Tetrahedral Holes in CCP
T+ sites:
¾,¼,¼
¼,¾,¼
¼,¼,¾
¾,¾,¾
T- sites:
¼,¼,¼
¾,¾,¼
¼,¾,¾
¾,¼,¾
Octahedral Holes in CCP and HCP
Tetrahedral Holes in CCP and HCP
Ionic Crystal Structures
Many ionic crystals consist of a Bravais lattice of the larger anions
with the smaller cations occupying interstitial sites.
let’s look
at these
structures
NaCl Structure
CCP with all octahedral holes filled
Coordination = 6, 6
Cation Coord. → Octahedron
Anion Coord. → Octahedron
Connectivity → Edge sharing octahedra
4 NaCl in unit cell
Zinc Blende (ZnS) Structure
CCP with all T+ holes filled
Coordination = 4, 4
Cation Coord. → Tetrahedron
Anion Coord. → Tetrahedron
Connectivity → Corner sharing Tetrahedra
4 ZnS in unit cell
Fluorite (CaF2) and Antifluorite (Li2O)
Fluorite: CCP of Ca2+ with all T+ and T- holes filled with FAntifluorite: CCP of O2- with all T+ and T- holes filled with Li+
Ca2+
Coordination = 8, 4 (fluorite)
Cation Coord. → Cubic
Anion Coord. → Tetrahedral
Connectivity → Edge sharing FCa4
tetrahedra or edge sharing CaF8 cubes
4 CaF2 in unit cell
Alternative Representations of Fluorite
Ca2+
Displacing the unit cell by ¼ of a body diagonal emphasizes the cubic cation coordination:
F-
Fluorite (CaF2) and Antifluorite (Li2O)
Ca2+
• origin of the term “fluorescence”
(George Stokes, 1852)
• fluorite common for fluorides of large,
divalent cations and oxides of large
tetravalent cations (M2+F2 and M4+O2)
• antifluorite common for
oxides/chalcogenides of alkali earths (M2O)
CaF2
with Eu2+ impurities
Wurtzite (ZnS) Structure
HCP with all T+ holes filled
ZnO
50 nm
Coordination = 4, 4
Cation Coord. → Tetrahedron
Anion Coord. → Tetrahedron
Connectivity → Corner sharing Tetra.
2 ZnS per unit cell
Diamond Structure
same as zinc blende, but with only one element
diamond
zinc blende
Coordination = 4
Connectivity → Corner sharing Tetrahedra
8 C atoms per unit cell
CsCl Structure
simple cubic lattice with Cs+ at cube center (not CP, not BCC!)
Coordination = 8, 8
Cation Coord. → Cubic
Anion Coord. → Cubic
Connectivity → face sharing cubes
1 CsCl per unit cell
Adoption by chlorides, bromides and
iodides of larger cations

Download Report