solid state physics intro

8/14/2019 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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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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Wigner-Seitz cell

planes bisecting the lines

drawn from a lattice point to

its neighbors


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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


systemNumber





Tetragonal 2 |a1|=|a2||a3| , ===90

Cubic 3 |a1|=|a2|=|a3| , ===90

Trigonal 1 |a1|=|a2|=|a3| , ==


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B. Lattice types


systemNumber of

latticesCell axes and angles




Tetragonal 2 |a1|=|a2||a3| , ===90

Cubic 3 |a1|=|a2|=|a3| , ===90

Trigonal 1 |a1|=|a2|=|a3| , ==


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B. Lattice types


systemNumber of





Tetragonal 2 |a1|=|a2||a3| , ===90

Cubic 3 |a1|=|a2|=|a3| , ===90

Trigonal 1 |a1|=|a2|=|a3| , ==


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B. Lattice types


systemNumber of





Tetragonal 2 |a1|=|a2||a3| , ===90

Cubic 3 |a1|=|a2|=|a3| , ===90

Trigonal 1 |a1|=|a2|=|a3| , ==


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B. Lattice types


systemNumber





Tetragonal 2 |a1|=|a2||a3| , ===90

Cubic 3 |a1|=|a2|=|a3| , ===90

Trigonal 1 |a1|=|a2|=|a3| , ==


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B. Lattice types


systemNumber of





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
http://www.doitpoms.ac.uk/tlplib/miller_indices/lattice_index.phphttp://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)

solid state physics intro

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