Structure of solids
grain
grain boundary
Atomic arrangement in solids
Chapter 3: The structure of crystalline solids
1
The 14 Bravais lattices
orthorhombic
base
centered
simple
tetragonal
body
centered
face
centered
cubic
Chapter 3: The structure of crystalline solids
2
1
The 14 Bravais lattices
monoclinic
trigonal
base
centered
rhombehedral
Chapter 3: The structure of crystalline solids
hexagonal
3
Unit cells
Chapter 3: The structure of crystalline solids
4
2
Arbitrary labeling of origin
origin for red unit cell
origin for green unit cell
origin for blue unit cell
origin for brown unit cell
They are all the same
Chapter 3: The structure of crystalline solids
5
Common unit cells - simple cubic
z
1/8 of a sphere is
in the unit cell
0,0,0 position
a
y
x
a
R=0.5a
Chapter 3: The structure of crystalline solids
6
3
Body centered cubic (BCC)
z
y
a
x
3a
a
R
2a
a
Chapter 3: The structure of crystalline solids
7
Face centered cubic (FCC)
z
y
a
x
2a
a
Chapter 3: The structure of crystalline solids
8
4
FCC stacking sequence
• ABCABC... Stacking Sequence
• 2D Projection
B
B
C
A
B
B
B
A sites
C
C
B sites
B
B
C sites
A
B
C
• FCC Unit Cell
Chapter 3: The structure of crystalline solids
9
Hexagonal
c
120˚
a
a
Hexagonal close packed (HCP)
2/
3,
1/
3,
1/
2
c
a
Chapter 3: The structure of crystalline solids
a
10
5
HCP stacking sequence
Chapter 3: The structure of crystalline solids
11
Comparison between the two close
packed structures: FCC and HCP
Chapter 3: The structure of crystalline solids
12
6
Diamond structure
Amorphous solids - glasses
Chapter 3: The structure of crystalline solids
13
Single vs Polycrystals
• Single Crystals
E (diagonal) = 273 GPa
-Properties vary with
direction: anisotropic.
• Polycrystals
E (edge) = 125 GPa
200 µm
Chapter 3: The structure of crystalline solids
14
7
Directions in hexagonal unit cells
c
120˚
a
a
Chapter 3: The structure of crystalline solids
15
Family of directions
c
b
a
Chapter 3: The structure of crystalline solids
16
8
Linear Density
[110]
a
Chapter 3: The structure of crystalline solids
17
Crystallographic planes
Chapter 3: The structure of crystalline solids
18
9
Crystallographic planes demo
Indexing crystallographic planes
http://www.doitpoms.ac.uk/tlplib/miller_indices/lattice_index.php
Identifying crystallographic planes demo
http://www.doitpoms.ac.uk/tlplib/miller_indices/questions.php
Family of planes demo
http://www.doitpoms.ac.uk/tlplib/miller_indices/lattice.php
Chapter 3: The structure of crystalline solids
19
Constructive interference
Destructive interference
Chapter 3: The structure of crystalline solids
20
10
Bragg's law
①
②
distance
between (hkl)
planes
Chapter 3: The structure of crystalline solids
21
X-Rays to determine crystal structure
de
“1
”
oi
ng
θ
or
o
g
ut
”
ys
“2
ra
ct
”
”
“2
θ
te
“1
g
in
m
co s
in - r a y
X
extra
distance
travelled
by wave “2”
X-
λ
d
Chapter 3: The structure of crystalline solids
reflections must
be in phase for
a detectable signal
spacing
between
planes
22
11
X-Ray diffraction pattern
z
z
Intensity (relative)
c
a
x
z
c
b
y (110)
a
x
c
b
y
a
x (211)
b
y
(200)
Diffraction angle 2θ
Diffraction pattern for polycrystalline α-iron (BCC)
Chapter 3: The structure of crystalline solids
23
Non-crystalline solids
Crystalline SiO2
Chapter 3: The structure of crystalline solids
Amorphous SiO2
24
12