3.012 Fund of Mat Sci: Structure – Lecture 21
NON-CRYSTALLINE MATERIALS
Images of a silicon nanocrystal removed for copyright reasons.
Light amplification for crystalline silicon in a glassy SiO2 matrix
3.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)
Homework for Fri Dec 2
• Study: Chapter 2 of Allen-Thomas
until 2.3.1
3.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)
Last time: 1.
2.
3.
4.
Tensors, and their transformations
Orthogonal matrices
Neumann’s principle
Symmetry constraints on physical
properties
5. Curie’s principle
3.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)
Physical properties and their relation to symmetry
•
•
•
•
•
Density (mass, from a certain volume)
Pyroelectricity (polarization from temperature)
Conductivity (current, from electric field)
Piezoelectricity (polarization, from stress)
Stiffness (strain, from stress)
3.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)
Curie’s Principle
• a crystal under an external influence will
exhibit only those symmetry elements that
are common to both the crystal and the
perturbing influence
3.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)
Loss of periodic order
• Liquids (“fluid”)
• Glasses (“solid”)
– Oxide glasses (continuous random networks)
– Polymeric glasses (self-avoiding random walks
• Oddballs
– Quasicrystals
– Superionics
3.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)
Table of the applications of noncrystalline materials removed for copyright reasons.
3.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)
Principle of operation of a CD-RW
As Deposited (amorphous) After Initialisation/erase
(crystalline)
Written mark (amorphous)
Erase/Write
Readout of data:
Difference in %R between amorphous & crystalline states
E.g. %Ramorphous = 5%; %Rcryst = 25%
Delta R = 20%
Figure by MIT OCW.
3.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)
Principle of operation of a CD-RW
Erasure – Crystalline
Writing - Amorphous
Intermediate laser power is used, so that the active
layer does not melt, but rather remains within the
crystallization temperature region long enough that
the amorphous marks re-crystallize.
The active layer is heated above its melting point
and quenched into the amorphous phase with a
short laser pulse to produce marks.
Liquid
Temperature (oC)
C
600
Crystal
B
99%
1%
200
0
10-2
Amorphous
tmin
0
10
2
10
4
6
10
10
Time (ns)
8
10
Liquid
C
Quench
A
400
800
Melting temperature
Temperature (oC)
800
10
10
Melting temperature
600
Crystallize
A
400
B
99%
1%
200
0
10-2
Amorphous
tmin
10
0
102
104
106
Time (ns)
3.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)
108
1010
Figure by MIT OCW.
Erasure: nucleation and growth of crystalline material
3.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)
Figure by MIT OCW.
Te-Sb-Ge Alloy
3 Element Phase Diagram
Sb
100
Nucleation dominated: 4.7 GB DVD-RAM
(Sb2Te3 to GeTe)
90
80
Growth dominated SbTeGe
om
ic
%
70
Sb2Te3
Sb
At
Growth dominated: CDRW, DVD-RW, Blu-ray
(Sb69Te31 eutectic)
60
50
40
30
20
10
0
0
Ge
10
20
30
40
50
60
GeTe
Ge Atomic %
Figure by MIT OCW.
3.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)
70
80
90
100
Structural Descriptors
• Long-range order
• Short-range order
3.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)
What do ice and silicon have in common ?
Source: Wikipedia
3.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)
What do ice and silicon have in common ?
Photo courtesy of Ansgar Walk.
3.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)
What do ice and silicon have in common ?
Figure by MIT OCW.
Figure by MIT OCW.
3.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)
What do ice and silicon have in common ?
Compression
11 GPa
Si(I) diamond
z=
13 GPa
Si(II) β-tin
z=6
16 GPa
Si(XI) Imma
z=6
36 GPa
Si(V) hexagonal
z=8
42 GPa
Si(VI) orthorhombic
z=10
79 GPa
Si(VII) hcp
z=12
Si(X) fcc
z=12
Slow Pressure Release
Si(II) β-tin
z=6
>480 K
2 GPa
9 GPa
Si(XII) R8
z=
Si(III) BC-8
z=
Si(IV) hex. diamond
z=
Fast Pressure Release
Si(VIII) and Si(IX) tetragonal
3.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)
Figure by MIT OCW.
What do ice and silicon have in common ?
-7.84
Si
400
100
-7.86
sc
4
β-TIN
3
300
0
X
III
V
Hexagonal Ice
VI
VIII
200
II
-100
IX
100
-7.90
2
Diamond
Hexagonal
Diamond
-200
XI
1
0.1
-7.92
0.6
0.7
0.8
0.9
1.0
1.1
1.0
10
Pressure (GPa)
Volume
Figure by MIT OCW.
Figure by MIT OCW.
3.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)
100
0
Temperature (K)
hcp
bcc
-7.88
VII
Liquid
Temperature (oC)
Estructure (Ry/atom)
fcc
Phase transitions in silicon
Energy
B
A
B
A
Volume
3.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)
Order Parameters for Silicon
P
Before compression
1
N
¦ Ti
i
V
§1
¨N
©
During compression
·
¦i T P ¹¸
2
2
1
2
P = 40 GPa
M. J. Demkowicz and A. S. Argon, Phys. Rev. Lett. 93, 25505 (2004)
3.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)
Pair correlation functions
Graphs of the pair-distribution functions for gas, liquid/gas, and monatomic crystal removed for copyright reasons.
See page 41, Figure 2.5 in in Allen, S. M., and E. L. Thomas. The Structure of Materials. New York, NY: J. Wiley & Sons, 1999.
3.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)
Pair correlation function: water
Courtesy of Dr. J. Kolafa. Used with Permission.
See animation at http://www.icpf.cas.cz/jiri/movies/water.htm.
3.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)
Pair correlation function: water
3.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)
Count thy neighbours
Z
r
Thickness dr
Y
X
Figure by MIT OCW.
3.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)
Models of disorder: hard spheres
• Bernal random close packed sphere model
Photos of the Bernal random close-packing model removed for copyright reasons.
See them at the Science & Society Picture Library: Image 1, Image 2.
3.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)
Models of disorder: hard spheres
• Voronoi polyhedra (in a crystal: WignerSeitz cell)
Normal Distance
Facial
Area
Volume
Solid
Angle
Quantitative Definitions of Voronoi Polyhedra
Figure by MIT OCW.
3.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)
Mean Square Displacements
3.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)
Mean Square Displacements
3.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)
Mean Square Displacements
3.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)