Solid State Physics Intro
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Transcript of Solid State Physics Intro
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Solid state physics
N. Witkowski
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Based on Introduction to Solid State Physics 8th edition Charles Kittel
Lecture notes from Gunnar Niklasson
http://www.teknik.uu.se/ftf/education/ftf1/FTFI_forsta_sidan.html
40h Lessons with N. Witkowski house 4, level 0, office 60111,
e-mail:[email protected]
6 laboratory courses (6x3h): 1 extended report + 4 limited reports Semiconductor physics
Specific heat
Superconductivity
Magnetic susceptibility
X-ray diffraction
Band structure calculation Evaluation : written examination 13 march (to be confirmed)
5 hours, 6 problems
document authorized Physics handbook for science and engineering CarlNordling, Jonny Osterman
Calculator authorized
Second chance in june
Introduction
Given between 23rd feb-6th march
Registration : from 9th feb on board F and Q
House 4 ground level
Info comes later
Home work
http://www.teknik.uu.se/ftf/education/ftf1/FTFI_forsta_sidan.htmlhttp://www.teknik.uu.se/ftf/education/ftf1/FTFI_forsta_sidan.html -
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What is solid state ?
Single crystals
Polycristallinecrystals
Amorphous
materials
Quasicrystals Long range order no no 3Dtranslational periodicity
Long range order and 3D
translational periodicity
Single crystals assembly
Disordered or random atomic
structure
4 nmx4nm1.2 mmgraphite
diamond
Al72Ni20Co8
silicon
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Outline
[1] Crystal structure 1
[2] Reciprocal lattice 2
[3] Diffraction 2
[4] Crystal binding no lecture 3 [5] Lattice vibrations 4
[6] Thermal properties 5
[7] Free electron model 6
[8] Energy band 7,9
[9] Electron movement in crystals 8
Metals and Fermi surfaces 9 [10] Semiconductors 8
[11] Superconductivity 10
[12] Magnetism 11
Correspondingchapter in Kittel book
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Chap.1
Crystal structure
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Introduction
Aim :
A : defining concepts and definitions
B : describing the lattice types
C : giving a description of crystal structures
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A. Concepts, definitions A1. Definitions
Crystal : 3 dimensional periodicarrangments of atomes inspace. Description using amathematical abstraction : thelattice
Lattice: infinite periodic arrayof points in space, invariantunder translation symmetry.
Basis: atoms or group ofatoms attached to every latticepoint
Crystal = basis+lattice
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A. Concepts, definitions
Translation vector :arrangement of atoms looksthe same from ror r point
r=r+u1a1+u2a2+u3a3: u1, u2and u3integers = latticeconstant
a1, a2, a3primitivetranslation vectors
T=u1a1+u2a2+u3a3translation vector
r = a1+2a2r= 2a1- a2
T=r-r=a1-3a2
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A. Concepts, definitions
A2.Primitive cell Standard model
volume associated with onelattice point
Parallelepiped with latticepoints in the corner
Each lattice point sharedamong 8 cells
Number of latticepoint/cell=8x1/8=1
Vc= |a1.(a2xa3)|
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A. Concepts, definitions
Wigner-Seitz cell
planes bisecting the lines
drawn from a lattice point to
its neighbors
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A. Concepts, definitions
A3.Crystallographic unit
cell
larger cell used to display
the symmetries of the cristal
Not primitive
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B. Lattice types
B1. Symmetries :
Translations
Rotation : 1,2,3,4 and 6
(no 5 or 7)
Mirror reflection : reflection
about a plane through alattice point
Inversion operation (r-> -r)
three 4-fold axes
of a cubefour 3-fold
axes of a cube
six 2-fold
axes of a cube
planes of symmetry parallel in a cube
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B. Lattice types
B2. Bravais lattices in 2D
5 types
general case :
oblique lattice |a1||a2| , (a1,a2)=
special cases :
square lattice: |a1|=|a2| , = 90 hexagonal lattice: |a1|=|a2| , = 120
rectangular lattice: |a1||a2| , = 90
centered rectangular lattice: |a1||a2|, = 90
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B. Lattice types
B3. Bravais lattices in 3D: 14
systemNumber
of latticesCell axes and angles
Triclinic 1 |a1||a2||a3| ,
Monoclinic 2 |a1||a2||a3| , ==90
Orthorhombic 4 |a1||a2||a3| , ===90
Tetragonal 2 |a1|=|a2||a3| , ===90
Cubic 3 |a1|=|a2|=|a3| , ===90
Trigonal 1 |a1|=|a2|=|a3| , ==
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B. Lattice types
B3. Bravais lattices in 3D: 14
systemNumber
of latticesCell axes and angles
Triclinic 1 |a1||a2||a3| ,
Monoclinic 2 |a1||a2||a3| , ==90
Orthorhombic 4 |a1||a2||a3| , ===90
Tetragonal 2 |a1|=|a2||a3| , ===90
Cubic 3 |a1|=|a2|=|a3| , ===90
Trigonal 1 |a1|=|a2|=|a3| , ==
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B. Lattice types
B3. Bravais lattices in 3D: 14
systemNumber of
latticesCell axes and angles
Triclinic 1 |a1||a2||a3| ,
Monoclinic 2 |a1||a2||a3| , ==90
Orthorhombic 4 |a1||a2||a3| , ===90
Tetragonal 2 |a1|=|a2||a3| , ===90
Cubic 3 |a1|=|a2|=|a3| , ===90
Trigonal 1 |a1|=|a2|=|a3| , ==
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B. Lattice types
B3. Bravais lattices in 3D: 14
systemNumber of
latticesCell axes and angles
Triclinic 1 |a1||a2||a3| ,
Monoclinic 2 |a1||a2||a3| , ==90
Orthorhombic 4 |a1||a2||a3| , ===90
Tetragonal 2 |a1|=|a2||a3| , ===90
Cubic 3 |a1|=|a2|=|a3| , ===90
Trigonal 1 |a1|=|a2|=|a3| , ==
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B. Lattice types
B3. Bravais lattices in 3D: 14
systemNumber of
latticesCell axes and angles
Triclinic 1 |a1||a2||a3| ,
Monoclinic 2 |a1||a2||a3| , ==90
Orthorhombic 4 |a1||a2||a3| , ===90
Tetragonal 2 |a1|=|a2||a3| , ===90
Cubic 3 |a1|=|a2|=|a3| , ===90
Trigonal 1 |a1|=|a2|=|a3| , ==
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B. Lattice types
B3. Bravais lattices in 3D: 14
systemNumber
of latticesCell axes and angles
Triclinic 1 |a1||a2||a3| ,
Monoclinic 2 |a1||a2||a3| , ==90
Orthorhombic 4 |a1||a2||a3| , ===90
Tetragonal 2 |a1|=|a2||a3| , ===90
Cubic 3 |a1|=|a2|=|a3| , ===90
Trigonal 1 |a1|=|a2|=|a3| , ==
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B. Lattice types
B3. Bravais lattices in 3D: 14
systemNumber of
latticesCell axes and angles
Triclinic 1 |a1||a2||a3| ,
Monoclinic 2 |a1||a2||a3| , ==90
Orthorhombic 4 |a1||a2||a3| , ===90
Tetragonal 2 |a1|=|a2||a3| , ===90
Cubic 3 |a1|=|a2|=|a3| , ===90
Trigonal 1 |a1|=|a2|=|a3| , ==
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B. Lattice types B4. Examples : bcc
Bcc cell : a, 90, 2 atoms/cell
Primitive cell : ai vectors from theorigin to lattice point at bodycenters
Rhombohedron : a1= a(x+y-z),a2= a(-x+y+z), a3= a(x-y+z),
edge a
Wigner-Seitz cell
xy
z
a1
a2a3
3
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B. Lattice types B5. Examples : fcc
fcc cell : a, 90, 4 atoms/cell
Primitive cell : aivectors from theorigin to lattice point at face centers
Rhombohedron : a1= a(x+y), a2= a(y+z), a3= a(x+z), edge a
Wigner-Seitz cell
x
y
z
2
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B. Lattice types B6. Examples : fcc - hcp
different way of stacking the close-packed planes
Spheres touching each other about74% of the space occupied
B7. Example : diamond structure fcc structure
4 atoms in tetraedric position
Diamond, silicon
fcc : 3 planes A B C hcp : 2 planes A B
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C. Crystal structures C1. Miller index
lattice described by set of parallel planes
usefull for cristallographic interpretation
In 2D, 3 sets of planes
Miller index
Interception between plane and lattice axis a,
b, c Reducing 1/a,1/b,1/cto obtain the smallest
intergers labelled h,k,l
(h,k,l) index of the plan, {h,k,l}serie ofplanes, [u,v,w]or direction
http://www.doitpoms.ac.uk/tlplib/miller_indices/lattice_index.php
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C. Crystal structures C2. Miller index : example
plane intercepts axis : 3a1, 2a2, 2a3
inverses : 1/3 , 1/2 , 1/2
integers : 2, 3, 3
h=2 , k=3 , l=3
Index of planes : (2,3,3)