Structure of solids - University of California, San...
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1 1 Chapter 3: The structure of crystalline solids Structure of solids grain grain boundary Atomic arrangement in solids 2 Chapter 3: The structure of crystalline solids The 14 Bravais lattices cubic tetragonal orthorhombic base centered body centered face centered simple
Transcript of Structure of solids - University of California, San...
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1Chapter 3: The structure of crystalline solids
Structure of solidsgrain grain boundary
Atomic arrangement in solids
2Chapter 3: The structure of crystalline solids
The 14 Bravais lattices
cubic
tetragonal
orthorhombic
basecentered
bodycentered
facecentered
simple
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3Chapter 3: The structure of crystalline solids
The 14 Bravais lattices
rhombehedral
trigonal
hexagonal
monoclinic
basecentered
4Chapter 3: The structure of crystalline solids
Unit cells
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5Chapter 3: The structure of crystalline solids
origin for red unit cell
Arbitrary labeling of origin
origin for blue unit cell
They are all the same
origin for brown unit cell
origin for green unit cell
6Chapter 3: The structure of crystalline solids
Common unit cells - simple cubic
y
xa
z 1/8 of a sphere isin the unit cell
0,0,0 position
a
R=0.5a
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7Chapter 3: The structure of crystalline solids
Body centered cubic (BCC)
y
xa
z
a
a 2
a 3
R a
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Face centered cubic (FCC)
y
xa
z
a
2 a
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9Chapter 3: The structure of crystalline solids
A sites
B B
B
BB
B B
C sites
C C
CAB
B sites
• ABCABC... Stacking Sequence• 2D Projection
• FCC Unit Cell
FCC stacking sequence
B B
B
BB
B B
B sitesC C
CAC C
CA
AB
C
10Chapter 3: The structure of crystalline solids
Hexagonal
c120˚
a
a
c aa
2/3,1/3,1/2
Hexagonal close packed (HCP)
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11Chapter 3: The structure of crystalline solids
HCP stacking sequence
12Chapter 3: The structure of crystalline solids
Comparison between the two closepacked structures: FCC and HCP
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13Chapter 3: The structure of crystalline solids
Diamond structure
Amorphous solids - glasses
14Chapter 3: The structure of crystalline solids
• Single Crystals-Properties vary with direction: anisotropic.
• Polycrystals200 µm
Single vs Polycrystals
E (diagonal) = 273 GPa
E (edge) = 125 GPa
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15Chapter 3: The structure of crystalline solids
Directions in hexagonal unit cells
c120˚
a
a
16Chapter 3: The structure of crystalline solids
Family of directions
a
c
b
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17Chapter 3: The structure of crystalline solids
Linear Density
a
[110]
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Crystallographic planes
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19Chapter 3: The structure of crystalline solids
Crystallographic planes demo
http://www.doitpoms.ac.uk/tlplib/miller_indices/lattice_index.php
Indexing crystallographic planes
Identifying crystallographic planes demohttp://www.doitpoms.ac.uk/tlplib/miller_indices/questions.php
Family of planes demohttp://www.doitpoms.ac.uk/tlplib/miller_indices/lattice.php
20Chapter 3: The structure of crystalline solids
Destructive interference
Constructive interference
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21Chapter 3: The structure of crystalline solids
Bragg's law①
②
distancebetween (hkl)planes
22Chapter 3: The structure of crystalline solids
X-Rays to determine crystal structure
reflections must be in phase for a detectable signal
spacing between planes
d
incoming
X-rays
outgo
ing X
-rays
detector
θλ
θextra distance travelled by wave “2”
“1”
“2”
“1”
“2”
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23Chapter 3: The structure of crystalline solids
X-Ray diffraction pattern
(110)
(200)
(211)
z
x
ya b
c
Diffraction angle 2θ
Diffraction pattern for polycrystalline α-iron (BCC)
Inte
nsity
(rel
ativ
e)z
x
ya b
cz
x
ya b
c
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Non-crystalline solids
Crystalline SiO2 Amorphous SiO2
