Condensed Matter Physics 1

Crystal structure and structural analysis:

periodic lattices – basic terms, definitions and basic forms
specific crystal structures
defects and real crystals
reciprocal lattice and diffraction 

Crystal binding: 

van-der-Waals, ionic binding
covalent and metallic binding
hydrogen bond

Elastic properties:

continuum approximation
strain components
elastic waves

Lattice dynamics:

classical theory of lattice dynamics
quantisation of lattice vibrations
density of states in the phonon spectrum
 

Thermal properties:

specific heat capacity
anharmonic effects and thermal expansion
heat conductivity

Electrons in solids:

free-electron gas
Bloch states and band structure
classification scheme for metals, semi-metals, semiconductors, insulators
Fermi surfaces

Dynamics of electrons in solids:

semiclassical modell
scattering
Boltzmann equation and coefficients

The lecture and exercise group allow the students to:

- apply basic concepts from Condensed Matter Physics, to explain physical properties related to the condensed state of matter by considering the crystalline nature. In particular, mechanical properties, lattice dynamics, specific heat, heat conduction, basics of electron transport can be addressed;

- know the impact of pioneers in the field of condensed matter physics for the most relevant inventions and discoveries;

- sketch important experimental techniques;

- explain physical properties by considering classical theories, quantum theory and thermodynamics;

- apply expert knowledge to daily life situations concerned with condensed matter physics, lab excercises, internships and future experiments.

Knowledge of experimental physics, electromagnetism, electrodynamics, thermodynamics, quantum mechanics.

In the thematically structured lecture the learning content is presented. With cross references between different topics the universal concepts in physics are shown. In scientific discussions the students are involved to stimulate their analytic-physics intellectual power.

In the exercise the learning content is deepened and exercised using problem examples and calculations. Thus the students are able to explain and apply the learned physics knowledge independently.

Hand written notes on the tablet PC, sketches of experimental setups, presentation of relevant data using powerpoint, handouts of relevant slides. A pdf version of the lecture content will be provided via the internet for download. At the same time, there will be exercises for download and discussion in exercise groups.

R. Gross, A. Marx, (in German) "Festkörperphysik", 3. Auflage, De Gruyter (2018).

N.W. Ahcroft, N.D Mermin, "Solid State Physics", Holt-Saunders International Editions.

C. Kittel, "Introduction to Solid State Physics", Wiley. 

Ch. Weißmantel, C. Hamann, (in German) "Grundlagen der Festkörperphysik", Wiley-VCH.

H. Ibach, H. Lüth, (in German) "Festkörperphysik: Einführung in die Grundlagen", Springer.

There will be a written exam of 90 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using calculation problems and comprehension questions.

For example an assignment in the exam might be:

• Provide the primitive lattice vectors, the conventional cubic cell, the number of atoms within the conventional cell and the coordination number for the diamond lattice
• Provide the Bravais lattice, the primitice lattice vectors and the rotational symmetry of an example lattice structure
• Calculate the c/a ratio for the hexagonal close-packed (hcp) lattice structure
• Calculated the package density of the sc, bcc, fcc and hcp structure
• Calculate the structure factor of e.g. diamnond, CsCl or the CsI
• Calculate the number of phonons generated by a short monochromatic ultrasound pulse and the resulting temperature increase after thermalization
• Calculate the equilibrium disstance and the vibrational frequency of a biatomic molecule at given potential curve
• Calculate the dispersion relation of the lattice vibrations for a monoatomic chainn of equal atoms and a biatomic chain of different atoms
• Discuss the difference between the Laue-, the Debye-Scherrer and the rotating crystal methode in x-ray diffraction
• Calculate the Miller indices for given lattice planes of e.g. the cubic lattice
• Calculate the volume of the 1. Brillouin zone and the reciprocal lattice vectors of a given real space lattice
• Calculate the lattice specific heat in the limit of high and low temperature
• Calculate the density of states of a 1D, 2D and 3D free electron gas

In the exam the following learning aids are permitted: hand-written sheet with formulas, double-sided

Participation in the exercise classes is strongly recommended since the exercises prepare for the problems of the exam and rehearse the specific competencies.

There will be a bonus (one intermediate stepping of "0,3" to the better grade) on passed module exams (4,3 is not upgraded to 4,0). The bonus is applicable to the exam period directly following the lecture period (not to the exam repetition) and subject to the condition that the student passes the mid-term of passing the voluntary test exam during the semester