Upload
buithuy
View
230
Download
0
Embed Size (px)
Citation preview
Advanced solid state physics SS2014Kapitel 1.1: Crystal structure
1
System Lengths &
Angles
Number ofLattices
Cubic a = b = c
α = β = γ = 90°3
Tetragonal a =b ≠ c
α = β = γ = 90°2
Orthorhombic a ≠ b ≠c
α = β = γ = 90°4
Rhombohedral a = b = c
α = β = γ ≠ 90°1
Monoclinic a ≠ b ≠c
α = γ = 90° ≠ β2
Triclinic a ≠ b ≠ c
α ≠ β ≠ γ1
Hexagonal a = b ≠ c
α = β = 90°γ = 120°
1
α
b
c
a
β
γ
Bravais Lattice
There are 14 different basic crystal lattices
Definition according to unit cell edge lengths and angles
Advanced solid state physics SS2014Kapitel 1.1: Crystal structure
2
Bravais Lattices
cubic
tetragonal
orthorhombic
rhombohedral
monoclinic
hexagonaltriclinic
Advanced solid state physics SS2014Kapitel 1.1: Crystal structure
3
Closed Packed Lattices: fcc and hcp
Layer Sequence
ABA:hcp
ABC:fcc
fccface centeredcubic
hcphexagonalclose packed
Advanced solid state physics SS2014Kapitel 1.1: Crystal structure
4
Diamond Lattice
fcc Lattice with Basis(000) a, (1/4,1/4,1/4) a
View with bonds
Examples:Diamond, Silicon, Germanium
xy
z
a
4/
4/
4/
a
a
a
Advanced solid state physics SS2014Kapitel 1.1: Crystal structure
5
Crystal Structures of the Elements
Ch. Kittel, Einführung in die Festkörperphysik
Advanced solid state physics SS2014Kapitel 1.1: Crystal structure
6
Diffraction with Waves (Light and Particles)
Diffraction of electrons and X-rays from Silver
a) 36 keV - electrons
b) Copper-Kα-Radiation
λ = 0,154 nm.
==p
hλde Broglie: 0,006 nm
Advanced solid state physics SS2014Kapitel 1.1: Crystal structure
7
X-ray diffraction: radiation source
X-ray tube
Voltage U =10 kV -100 kV
Spectrum of the radiation
Bremsstrahlungcharakteristic radiation
Copper-Anode, 38 kVeU
hchv ==
λ
minimalwavelength
Alternative:Synchrotron-radiation
Advanced solid state physics SS2014Kapitel 1.1: Crystal structure
8
Debye-Scherrer Method
• monochromatic source of light
• crystal powder (averaging overall orientations)
Crystals Film
Diffraction pattern of a fcc-crystal(MgO)
Structurfactor fcc: all indices are even or all odd !
Advanced solid state physics SS2014Kapitel 1.1: Crystal structure
9
Debye-Scherrer Method
(semi) sc-Crystal (KCl)
Visible Rings (inside out) :(100), (110), (111), (200), (210), (211), (220), (221)..
fcc-Crystal (Al)
Visible Rings (inside out) :(111), (200), (220), (311), (222)..
Advanced solid state physics SS2014Kapitel 1.1: Crystal structure
10
Debye-Scherrer Method
Salt Crystal
same size atoms (KCl):„sc“
different size atoms (KBr): fcc
Advanced solid state physics SS2014Kapitel 1.1: Crystal structure
11
Debye-Scherrer Method
FeCo – Crystalordered: sc (with Basis)unordered: bcc
sc
bcc
Structure factor bcc:Sum of all indices must be even!
Advanced solid state physics SS2014Kapitel 1.1: Crystal structure
12
Laue Method
• „white“ x-ray light
• oriented single crystal
Diffraction on NaCl (KCl?)in direction <100>
Gerthsen Physik
Advanced solid state physics SS2014Kapitel 1.1: Crystal structure
13
Laue Method
Diffraction on Si (fcc with basis)
forward direction <111>3-fold symmetry!
Backward scattering in direction <111>
direction <100>4-fold symmetry!
Advanced solid state physics SS2014Kapitel 1.1: Crystal structure
14
Protein crystal diffraction
Advanced solid state physics SS2014Kapitel 1.1: Crystal structure
15
structure reconstruction
Advanced solid state physics SS2014Kapitel 1.1: Crystal structure
16
record: 5 million atom image
virus capsid
Protein structure databank:www.rcsb.org
Advanced solid state physics SS2014Kapitel 1.1: Crystal structure
17
quasi-crystals
Ho-Mg-Zn quasi-crystal
(Al-Pd-Mn) quasicrystal