1 / 25

Solid state physics

Solid state physics. N. Witkowski. Introduction. 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,

kibo-hicks
Download Presentation

Solid state physics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Solid state physics N. Witkowski

  2. Introduction • 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:witkowski@insp.jussieu.fr • 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» Carl Nordling, Jonny Osterman • Calculator authorized • Second chance in june Given between 23rd feb-6th march Registration : from 9th feb on board F and Q House 4 ground level Info comes later Home work

  3. What is solid state ? Long range order and 3D translational periodicity • Single crystals graphite 1.2 mm 4 nmx4nm • Polycristalline crystals Single crystals assembly diamond • Quasicrystals Long range order no no 3D translational periodicity Al72Ni20Co8 • Amorphous materials Disordered or random atomic structure silicon

  4. Outline Corresponding chapter in Kittel book • [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

  5. Chap.1Crystal structure

  6. Introduction • Aim : • A : defining concepts and definitions • B : describing the lattice types • C : giving a description of crystal structures

  7. A. Concepts, definitions • A1. Definitions • Crystal : 3 dimensional periodic arrangments of atomes in space. Description using a mathematical abstraction : the lattice • Lattice : infinite periodic array of points in space, invariant under translation symmetry. • Basis : atoms or group of atoms attached to every lattice point • Crystal = basis+lattice

  8. A. Concepts, definitions • Translation vector : arrangement of atoms looks the same from r or r’ point • r’=r+u1a1+u2a2+u3a3 : u1, u2 and u3 integers = lattice constant • a1, a2, a3 primitive translation vectors • T=u1a1+u2a2+u3a3 translation vector r = a1+2a2 r’= 2a1- a2 T=r’-r=a1-3a2

  9. A. Concepts, definitions • A2.Primitive cell • Standard model • volume associated with one lattice point • Parallelepiped with lattice points in the corner • Each lattice point shared among 8 cells • Number of lattice point/cell=8x1/8=1 • Vc= |a1.(a2xa3)|

  10. A. Concepts, definitions • Wigner-Seitz cell • planes bisecting the lines drawn from a lattice point to its neighbors

  11. A. Concepts, definitions • A3.Crystallographic unit cell • larger cell used to display the symmetries of the cristal • Not primitive

  12. B. Lattice types • B1. Symmetries : • Translations • Rotation : 1,2,3,4 and 6 (no 5 or 7) • Mirror reflection : reflection about a plane through a lattice point • Inversion operation (r -> -r) three 4-fold axes of a cube four 3-fold axes of a cube six 2-fold axes of a cube planes of symmetry parallel in a cube

  13. B. Lattice types • B2. Bravais lattices in 2D • 5 types • general case : • oblique lattice |a1|≠|a2| , (a1,a2)=φ • special cases : • square lattice: |a1|=|a2| , φ= 90° • hexagonal lattice: |a1|=|a2| , φ= 120° • rectangular lattice: |a1|≠|a2| , φ= 90° • centered rectangular lattice: |a1|≠|a2| , φ= 90°

  14. B. Lattice types • B3. Bravais lattices in 3D: 14

  15. B. Lattice types • B3. Bravais lattices in 3D: 14 Base centered monoclinic

  16. B. Lattice types • B3. Bravais lattices in 3D: 14 Base centered orthorhombic Body centered orthorhombic Face centered orthorhombic

  17. B. Lattice types • B3. Bravais lattices in 3D: 14 Body centered tetragonal

  18. B. Lattice types • B3. Bravais lattices in 3D: 14 Simple cubic sc Body centered cubic bcc Face centered cubic fcc

  19. B. Lattice types • B3. Bravais lattices in 3D: 14

  20. B. Lattice types • B3. Bravais lattices in 3D: 14

  21. B. Lattice types z a3 a2 • B4. Examples : bcc • Bcc cell : a, 90°, 2 atoms/cell • Primitive cell : ai vectors from the origin to lattice point at body centers • Rhombohedron : a1= ½ a(x+y-z), a2= ½ a(-x+y+z), a3= ½ a(x-y+z), edge ½ a • Wigner-Seitz cell y x a1

  22. B. Lattice types z • B5. Examples : fcc • fcc cell : a, 90°, 4 atoms/cell • Primitive cell : ai vectors from the origin to lattice point at face centers • Rhombohedron : a1= ½ a(x+y), a2= ½ a(y+z), a3= ½ a(x+z), edge ½ a • Wigner-Seitz cell x y

  23. B. Lattice types • B6. Examples : fcc - hcp • different way of stacking the close-packed planes • Spheres touching each other about 74% 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

  24. 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/c to obtain the smallest intergers labelled h,k,l • (h,k,l) index of the plan, {h,k,l} serie of planes, [u,v,w] or <u,v,w> direction http://www.doitpoms.ac.uk/tlplib/miller_indices/lattice_index.php

  25. 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)

More Related