Transcript lecture 6 powerpoint

Types of Primary Chemical Bonds
Isotropic, filled outer shells
• Metallic
– Electropositive: give up electrons
• Ionic
– Electronegative/Electropositive
• Colavent
– Electronegative: want electrons
+
+
e-
e+
+
+
+
+
+
+
+
-
+
-
+
-
+
-
+
e-
– Shared electrons along
bond direction
Close-packed
structures
Metals
Ionic Compounds
anion
cation
Covalent Compounds
sp3
s2p1 s2p2 s2p3 s2p4
s2
Formal Crystallography
• Crystalline
– Periodic arrangement of atoms
– Pattern is repeated by translation
c
• Three translation vectors define:
– Coordinate system
– Crystal system
– Unit cell shape
• Lattice points
b
a
g
b
a
– Points of identical environment
– Related by translational symmetry
– Lattice = array of lattice points
•
•
•
•
•
space filling
defined by 3 vectors
parallelipiped
arbitrary coord system
lattice pts at corners +
hcp
ccp (fcc)
c
b
a
g
a
bcc
Hexagonal unit cell
Specify: a, c
Hexagonal implies:
|a1| = |a2| = a
g = 120°
a = b = 90°
Cubic unit cells
Specify: a
Cubic implies:
|a1| = |a2| = |a3| = a
a = b = g = 90°
But the two types of cubic unit cells are different!
b
Crystal system
Lattices
triclinic
simple
base-centered
monoclinic
Convention:
b = 90°
instead of a
a = 90°
simple
base-centered body-centered face-centered
orthorhombic
a = b = g = 90°
6 or 7
crystal
systems
hexagonal
g = 120°
c
14 lattices
a
a
rhombohedral
(trigonal)
a = b = ga
simple
body-centered
simple
body-centered face-centered
tetragonal
a = b = g = 90°
a=b
cubic
(isometric)
a = b = g = 90°
a=b=c
Centered Lattices
unconventional
choice
conventional
choice
b
a
b
a
b
b
a
unconventional
choice
both are primitive cells
a
conventional
choice
unconventional is primitive
conventional is centered
More on Lattices
X
More on Lattices
X
Lattice types of some structures
Lattice types?
BCC Metal
CsCl Structure
How many lattice points per unit cell?
Lattice types?
Zinc blende (sphaelerite)
Fluorite
Lattice types?
A
M
Diamond
Perovskite: AMO3
O
Crystallographic notation
cubic system
• Position:
a3
– x, y, z
– fractional coordinates
(x2, y2, z2)
x, y, z
• Direction:
– x2-x1, y2-y1, z2-z1
– no magnitude
– specific: [t u v]
– family: t u v
(x1, y1, z1)
a1
a2
Specific vs. family of directions
square lattice
specific: [1, 1]
family <1, 1> includes
a2
a1
[1, 1],
[-1, 1],
[-1, -1],
[1, -1]
Notation peculiarity
_
[-1, 1]  [1, 1]
Specific vs. family
square lattice
specific: [1, 2]
family: <1, 2> includes
a2
[1 2],
[2 1],
[1 2],
[2 1]
 
a1


Correction to lecture:
family <2, 1> is distinct

[2 1],
[1 2],
[2 1],
[1 2]
 

square: do not include those permutations that imply a change in handedness