PHY.K02UF Molecular and Solid State Physics
The SS25 lectures can be found on TUbe. The pdfs of the lecture slides are at the Teach Center.
Below are some videos from the COVID-19 times.
Reading: Gross & Marx: 3.1.2 Elektronische Struktur der Atome, or Experimental Physik 3, Demtröder - Das Wasserstoffatom, Experimental Physik 3, Demtröder - Atome mit mehreren Elektronen
The solutions to the Schrödinger equation for the hydrogen atom, Atomic orbitals, 1s, 2s, 2pz, Slater's rules, Helium, Many-electron wavefunctions, Slater determinants, Singlet and triplet states, Exchange, Many-electron atoms
Reading: Experimental Physik 3, Demtröder - Moleküle
A quantum mechanical description of molecules, The Born-Oppenheimer approximation, Many-electron wavefunctions, Bond potentials, Rotational states, Vibrational states, Harmonic oscillator,
Solving the molecular orbital Hamiltonian, Linear combination of atomic orbitals (LCAO), Molecular hydrogen ion H2+, Molecular hydrogen H2, Conjugated rings, Benzene, CO, Valence bond theory
Reading: Gross & Marx: 1. Kristallstruktur or Ibach & Lüth: 2. Structure of solid Matter or Kittel: Crystal Structure
Unit cell, Bravais lattices, Miller indices, Drawing Wigner-Seitz cells, Programs to visualize crystal structures
Examples of crystal structures: simple cubic, fcc, bcc, hcp, diamond, silicon, zincblende, wurzite, SiC 4H, NaCl, CsCl, perovskite, graphite, hexagonal boron nitride, CaF2, Fe3C, YBa2Cu3O7, black phosphorus, Spinel MgAl2O4, Magnetite Fe3O4, double perovskite Sr2FeMoO6, ZIF8, ZrO2
Fourier Series in one dimension - Video - (pdf) Fourier series in one dimensionFourier synthesisFourier analysis of real data sets Self assessment questions
Fourier Series in 2D and 3D - VideoTwo dimensional periodic functions Three dimensional periodic functions Self assessment questions
Plane waves and reciprocal space - VideoPlane waves and reciprocal space
Self assessment question
Reading: Gross & Marx: 2. Strukturanalyse mit Beugungsmethoden or Ibach & Lüth: 2. Strukturanalyse or Kittel: Diffraction and the Reiprocal Lattice
Fourier series, Fourier series in 1-D, Reciprocal lattices, Fourier series in 2-D, Fourier series in 3-D, Plane waves and reciprocal space, Fourier transforms, Plotting Fourier transforms
Interference of scattered waves, Brillouin zones of 2D Bravais lattices, Brillouin zones of 3D Bravais lattices, Drawing 3D Brilouin zones
Symmetry points and lines: Simple Cubic, Face Centered Cubic, Body Centered Cubic, Hexagonal, Simple Tetragonal, Body Centered Tetragonal, Simple Orthorhombic, Base Centered Orthorhombic
X-ray atomic form factors, Electron atomic form factors, Structure factor, The reciprocal lattice vector Ghkl is orthogonal to the (hkl) plane., The number of diffraction peaks observed, powder diffraction, Neutron diffraction, Electron diffraction, LEED
Reading: Gross & Marx: 3.3 Die ionische Bindung, or Ibach and Lüth: 1.3 Ionic Bonding, or Kittel: Ionic crystals.
Reading: Photons in vacuum, and Light in a layered material.
Table summarizing the results of the quantization of the wave equation, Empty lattice approximation, Table of photonic crystals.
Reading: Kittel: Phonons I. Crystal Vibrations and Phonons II. Thermal Properties, or Gross & Marx: 5. Dynamik des Kristallgitters und Gross & Marx: 6. Thermische Eigenschaften des Kristallgitters
Normal modes and phonons, Using complex numbers to represent sinusoidal oscillations, Linear chain, Linear chain with two different masses, fcc with linear springs to nearest neighbors, bcc with linear springs to nearest neighbors and next nearest neighbors, simple cubic with linear springs to nearest neighbors and next nearest neighbors, Jupyter python notebook for calculating phonon dispersion equations
Density of states: linear chain, Einstein model, Debye model, linear chain with two masses, simple cubic, bcc, fcc, Ag-fcc, Al-fcc, AlN, Fe-bcc, GaN, Mg-hcp, Mo-bcc, Si-diamond, α-Sn, β-Sn, Ta-bcc, Tb-hcp, Ti-hcp, W-bcc, ZnO (rocksalt), ZnO (zincblende), ZnO (wurtzite), Zr-hcp
Thermodynamic properties: Energy spectral density u(ω,T), Internal energy density u(T), Specific heat cv(T), Helmholtz free energy density f(T), Entropy density s(T), Table summarizing the thermodynamic properties of phonons
Reading: Kittel: Free electron Fermi gas, or Gross & Marx: 7. Das Freie Elektronengas
Free electron model in 1-D, Free electron model in 2-D, Free electron model in 3-D, Fermi function, Table of thermodynamic properties of free electrons, Sommerfeld expansion
Thermodynamic properties: Chemical potential μ(T), Energy spectral density u(E,T), Internal energy density u(T), Specific heat cv(T), Helmholtz free energy density f(T), Grand potential density φ(T)
Reading: Kittel: Energy Bands, or Gross & Marx: 8. Energiebänder
Empty lattice approximation: simple cubic, fcc, bcc, hexagonal, tetragonal, body centered tetragonal, orthorhombic, simple monoclinic
Band structure calculations: Cr, Li bcc, GaAs, GaN, GaP, Ge, InAs, 6H SiC, V
Density of states: Al fcc, Au fcc, Cu fcc, Cr bcc, Li bcc, Na bcc, Pt fcc, W bcc, Si diamond, Fe bcc, Ni fcc, Co fcc, Mn bcc, Cr bcc, Gd hcp, Pd fcc, Pd3Cr, Pd3Mn, PdCr, PdMn, GaN, 6H SiC, GaAs, GaP, Ge, InAs, V bcc
Kinetic theory: Drift and diffusion simulation
Summary: Electron Bands
Reading: An Introduction to Crystal Physics, Ervin Hartmann
The 32 Crystal Classes, Crystal Class Determination Flowchart, SGTE thermodynamic data, Space group → Bravais lattice
Reading: Kittel: Semiconductors (up to Impurity Conductivity), or Gross & Marx: 10. Halbleiter (until 10.1.3.1)
Boltzmann approximation, Thermodynamic properties of intrinsic semiconductors, Table summarizing the thermodynamic properties of semiconductors in the Boltzmann approximation NSM Semiconductor Archive