Welcome to the Experimental Physics 5 – Solid-State Physics lecture, WS2023/24!

Exam

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Lecture notes

last updated 29.01.2024 (lectures 1-12), work in progress, use with caution (and do let me know about any problems and errors)

Problem sheets

Bravais lattice and symmetry (due on 22.10)
Symmetry groups, Crystal structures, Lattice planes (due on 29.10)
Reciprocal lattice and Structure factor (due on 5.11)
Bonding in crystals (due on 12.11)
Mechanical properties, Dielectric properties (due on 19.11)
Phonons (due on 3.12)
Brillouin zone, Heat capacity (due on 10.12)
Thermal expansion and thermal conductivity (due on 17.12)
Drude and Drude-Sommerfeld models (due on 7.01)
Elastic and optical properties of metals (due on 14.01)
Electron dynamics, Fermi surface (due on 28.01)

Moodle link for your solutions

Lecture 26 (31.01.2024). Scattering and its implications

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How resistivity changes with temperature and why metals conduct heat

residual resistivity ratio

dielectric materials

Rudolf Peierls

Lecture 25 (25.01.2024). Landau levels and quantum oscillations

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Cyclotrons, new effective mass, and extremal orbits

Fermi surface determination

2D electron gas

Shubnikov and de Haas

Discovery of quantum oscillations (historical review)
Fourty odd years in the cold (how quantum oscillations turned into a powerful experimental method)

Lecture 24 (24.01.2024). Fermiology

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Where the electrons move, and how solid-state physics meets art

magnetoresistance

copper and its alloys

David Shoenberg

Life on the edge (beginner's guide to the Fermi surface)
Another guide to the Fermi surface (more fundamental)

Lecture 23 (18.01.2024). Description of band structures

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Electronic bands from tight binding

exfoliation

graphene

Andrey Geim

Exploring carbon flatland (review of graphene)
Random walk to graphene ("search, not re-search")

Lecture 22 (17.01.2024). How electrons move?

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Negative (effective) mass and its implications

Hall measurements

strontium titanate

Marvin Cohen

How to use spin Hall effect? (see also an advanced review for experts)
Thermal Hall effect as the probe of quantum materials

Lecture 21 (4.01.2024). All sorts of metals

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How half-metal is different from semi-metal, and are they better than bad metals?

ab initio (density functional) calculations

Li-ion batteries

Lecture 20 (3.01.2024). Optical properties of metals

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Why metals reflect light and what can make them colored

optical spectroscopy

coinage metals

Kramers and Kronig

Optical effects in solids by David Tanner is a good reading on this topic too

Lecture 19 (14.12.2023). Band structure

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Brillouin zone is back, now with the new content

angle-resolved photoemission spectroscopy

alkaline metals

Felix Bloch

Electronic structure of crystals explained in simple language
The story of Bloch and his work, with his personal reminiscences of Leipzig

Lecture 18 (13.12.2023). Metal as quantum gas: Drude-Sommerfeld model

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From mundane heat capacity to white dwarves and neutron stars

specific heat (as a microscopic probe)

white dwarves as Fermi gas

Arnold Sommerfeld

Life and properties of white dwarfs (advanced reading!)
Stellar evolution for dummies: part 1 and part 2

Lecture 17 (7.12.2023). Metal as classical gas: Drude model

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Image by Omegatron (CC-BY-SA)

Cancellation of errors leads to the right answer

resistivity measurements

thermoelectrics

Paul Drude

Drude against Einstein, or pitfalls of the Drude model exposed through the "love letters"
Review of thermoelectric effects and their applications, how to use electricity-heat conversion in a smart way (see also a more advanced version)

Lecture 16 (6.12.2023). Thermal transport

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Image from LibreTexts (CC-BY)

All flavors of heat transfer and thermal conductivity

thermal conductivity measurements

thermal insulators

Joseph Fourier

Lecture 15 (30.11.2023). Thermal expansion

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Phonon anharmonicity breaks in

dilatometry

negative thermal expansion (NTE) materials

Eduard Grüneisen

How to make an ultra-high-resolution dilatometer? (and resolve length changes in the picometer range)
Applications of dilatometry in low-temperature physics, and dual role of the crystal lattice: witness or actor
Demonstration of thermal expansion and Thermal expansion in engineering
See the work of a commercial dilatometer

Lecture 14 (29.11.2023). Phonons and thermodynamics

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Sphere instead of Brillouin zone, or how Debye beats Einstein

calorimetry (specific heat)

ice and glass, residual entropy

Peter Debye

Einstein's work on lattice dynamics, or how to sweep discrepancies under the carpet
Residual entropy in magnetic systems with a far-reaching analogy to water ice
Balloon experiment shows a striking effect of the heat capacity difference

Lecture 13 (23.11.2023). Phonons and reciprocal lattice

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Folding phonons into reciprocal space brings in a new repetition unit, first of its kind

inelastic scattering (light, x-ray, neutron)

Léon Brillouin

Review of methods for elasticity measurements, from Young to Brillouin

Lecture 12 (16.11.2023). Phonons and light

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Unforeseen link between lattice vibrations and permittivity

infrared spectroscopy

greenhouse gases

Max Born and Edward Teller

Optical effects in solids by David Tanner is the best ever reading about light, crystals, and research applications of IR spectroscopy
Demonstration of an infrared spectrometer
Simple demonstration of the greenhouse gas effect, appreciate the atmospheric hurdles

Lecture 11 (15.11.2023). Phonons and sound

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Lattice vibrations make noise and help in detecting earthquakes

ultrasound spectroscopy

Earth

Thomas Young

Vibrations of a diatomic chain visualized
Introduction into resonant ultrasound spectroscopy (free copy available here)
Seismic waves visualized, and basics of seismology

Lecture 10 (9.11.2023). Dielectric properties

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Image by Ümit Kaya, LibreTexts (CC-BY-NC)

Polarization from orientation, and how to use your microwave oven

dielectric spectroscopy

water and ice

Lorentz and Lorenz

How much water is there in the Ocean? (on the importance of clustering in water)
Generation of microwaves, and why there are cold spots in a microwave oven

Lecture 9 (8.11.2023). Mechanical properties

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Stress, strain, and how to tear things apart

high-pressure XRD, mechanical tests

iron alloys

Robert Hooke

Mechanical testing made simple, and a closer view of the tensile test
Design principle for auxetic materials (negative Poisson's ratio)

Lecture 8 (2.11.2023). Bonding in crystals: Covalent and van der Waals

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When strong bonds become weaker, weak bonds become stronger

identifying bond lengths and polyhedra

tin

Johannes Diderik van der Waals

Lecture 7 (1.11.2023). Bonding in crystals: Ionic

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Close packings, holes, radii, and why size matters

calorimetry and Born-Haber cycle

salt

Linus Pauling

Lecture 6 (26.10.2023). Structure factor: all shades of diffraction

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When extinctions are important, and how to catch light elements

neutron diffraction

solid hydrogen

DNA team

Dubious story of metallic hydrogen
Historical account of structural studies for macromolecules, including DNA
(resolving structures without finding atoms)

Lecture 5 (25.10.2023). Spaces of crystallography: Reciprocal lattice

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Image by Ümil Kaya, LibreTexts (CC-BY-NC)

From real space to the reciprocal space; x-rays as the tool for space travel

synchrotron x-ray diffraction

aperiodic crystals

Max von Laue and Paul Ewald

On-line textbook by the Spanish Center for Crystallography offers one of the most intuitive (and animated!) descriptions of x-ray diffraction experiments (check chapters 5 and 6)
Crystal Structure Determination by Werner Massa is the best ever textbook on x-ray diffraction and crystal structure solution
Aperiodic crystals: Crystallographic excursion in superspace and Manifestations in biology

Lecture 4 (19.10.2023). Unpacking the crystal structure

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Solid-state physics for dummies: a simple guide to crystal structures and their experimental probes

x-ray powder diffraction

diamond

William Bragg

VESTA and Open Crystallography Database, the two main tools for crystal structure visualization
Bilbao Crystallographic Server can answer most of your questions about space groups, Wyckoff positions, and symmetry operations
How to draw lattice planes in VESTA?
Video introduction into x-ray powder diffraction + a more technical one, should you want to see the real instrument

Lecture 3 (18.10.2023). Systematics of crystals: symmetry groups

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Solid-state physics for nerds: Universal classification of crystals and their properties

circular dichroism

chiral crystals and molecules

Evgraf Fedorov

mindat.org, the largest collection of minerals and their shapes (try to guess crystal symmetries)
...or check the gallery of minerals, or simply visit Terra Mineralia in Freiberg
Behold and comprehend 230 space groups: real structure types and symmetry diagrams
Some examples of color-changing minerals: tanzanite, tourmaline, iolite
Demonstration of optical rotation and optical activity of sugars

Lecture 2 (12.10.2023). Symmetry as the guiding principle

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What it means to be symmetric, and when wrong symmetry makes you aperiodic

polarimetry and birefringence

quasicrystals

Dan Shechtman

Faszination Kristalle und Symmetrie by Frank Hoffmann is a very fun reading about symmetry and crystallography; English version available too
The discovery of quasicrystals, or Shechtman against Pauling: part 1, part 2, part 3
Symmetry properties of tensors, or a simple reading that clarifies applications of Neumann's principle

Lecture 1 (11.10.2023). Bravais lattice, or how to pack a crystal?

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We will learn how to build a lattice, and how large the kissing number can be

electron microscopy

photonic crystals

Paintings by M.C. Escher – an artistic exploration of periodic structures
Catalogue of lattices and kissing numbers – more than 160 000 entries in dimensions up to 40!
Animated view of the close packing + another, more practical one
Electron microscopy: a brief introduction
Photonic crystals: physics and manifestations in nature (advanced reading for a later time)

N.B. Lecture slides contain images from publications that may be licensed differently from the rest of this webpage.