Physics of Condensed Matter and Materials

Coordinated by: Department of Condensed Matter Physics
Study branch coordinator: doc. RNDr. Stanislav Daniš, Ph.D.

The programme is devoted to experimental and theoretical study of properties of condensed systems, their microphysical interpretation and possible applications, in particular with respect to the current development of materials research. In addition to the common core programme, students select one of the following specializations: Physics of atomic and electronic structures, Physics of macromolecular compounds, Physics of materials, Low temperature physics, Physics of surface modifications. Each of these blocks ensures a general education in condensed matter physics at the contemporary level of knowledge and shapes the graduate in the selected specialization.

Profile of graduates and study aims:
Graduates acquire a broad education in the fundamentals of quantum theory, thermodynamics and statistical physics of condensed systems and the corresponding computing methods. They are able to describe the structure of the systems in different forms, their mechanical, electrical, magnetic and optical properties. They have a general knowledge of experimental methods of characterizing the structure, composition and properties of condensed compounds through for example diffraction, spectroscopic and microscopic techniques, and they are able to apply them in practice. Graduates are able to ssecure suitable positions in institutions of basic physical, chemical and biomedical research, universities, applied research laboratories, testing laboratories, and in hygiene and ecology institutions.

The aim of the study programme is to provide a broad education in quantum theory, thermodynamics and statistical physics in connection with current approaches in the theory of inorganic, organic and macromolecular condensed systems. At the same time, another goal of the study programme is to provide students with an overview of the principles of modern experimental methods and technological procedures. In their chosen specialization, students are provided with a deeper education and practical skills.

6.1 Recommended Course of Study

Prerequisite for this study programme is a bachelor-level knowledge of quantum theory, solid state physics, soft condensed matter physics and condensed system physics.

Compulsory and elective courses (profiling base).

Students choose one of the five specializations: Physics of atomic and electronic structures, Physics of macromolecular substances, Physics of materials, Low temperature Physics and Physics of surface modifications. Students need to obtain at least 25 credits from the elective courses from the profiling base, for the corresponding specialization, as described in the following table.

First year

NFPL145Experimental Methods of Condensed Systems Physics I 93/3 C+Ex
NFPL146Experimental Methods of Condensed Systems Physics II 93/3 C+Ex
NFPL800Thermodynamics of Condensed Matter 52/1 C+Ex
NFPL801Seminar130/2 C
NFPL802Seminar130/2 C
NSZZ023Diploma Thesis I 60/4 C
Specialization Physics of atomic and electronic structures
NFPL143Solid State Physics I 94/2 C+Ex
NFPL144Structure of Matter and Structure Analysis 73/2 C+Ex
NFPL147Solid State Physics II 94/2 C+Ex
Specialization Physics of macromolecular substances
NBCM066Introduction to Macromolecular Chemistry 52/1 C+Ex
NBCM208Fundamentals of Macromolecular Physics 43/0 Ex
NBCM058Relaxation Behaviour of Polymers 32/0 Ex
NBCM038Electrical and Optical Properties of Polymers 32/0 Ex
NBCM231Applied Thermodynamics 32/0 Ex
NBCM204Statistical Thermodynamics of Condensed Systems 52/1 C+Ex
NBCM353Special practical courses of physics of macromolecular solids and nanomaterials 40/3 C
Specialization Physics of materials
NFPL132Condensed Matter Theory 63/1 C+Ex
NFPL133Structure of Materials 43/0 Ex
NFPL135Physics of Materials I 42/1 C+Ex
NFPL139Physics of Materials II 42/1 C+Ex
NFPL137Technology of Materials 32/0 Ex
NFPL136Special practical courses of physics of materials 40/3 C
Specialization Low temperature physics
NFPL143Solid State Physics I 94/2 C+Ex
NFPL168Low Temperature Physics and Techniques 32/0 Ex
NFPL103Positron Annihilation in Solids 32/0 Ex
NFPL169Hyperfine Interactions and Nuclear Magnetism 32/0 Ex
NFPL092Radiofrequency Spectroscopy of Solids 32/0 Ex
NFPL206Selected topics of quantum theory of solids 73/2 C+Ex
Specialization Physics of surface modifications
NBCM066Introduction to Macromolecular Chemistry 52/1 C+Ex
NBCM213Physics of Thin Film Preparation 32/0 Ex
NBCM233Analysis Methods of Surfaces and Thin Layers 52/1 C+Ex
NBCM214Plasma Polymerisation Processes 32/0 Ex
NBCM231Applied Thermodynamics 32/0 Ex
NBCM353Special practical courses of physics of macromolecular solids and nanomaterials 40/3 C

1 As a Field Seminar, students attend one of the following seminars: Structural Analysis seminar (NFPL037), Condensed Matter Theory seminar (NFPL062), Magnetism seminar (NFPL118), Low Temperature Physics seminar (NFPL098), Materials Physics seminar (NFPL113), Polymer Physics seminar (NBCM091), Plasma Polymer study seminar (NBCM200).

Second year

NSZZ024Diploma Thesis II 90/6 C
NFPL124Experimental methods of condensed matter physics III 62/2 C+Ex
NSZZ025Diploma Thesis III 150/10 C
Specialization Physics of atomic and electronic structures
Specialization Physics of macromolecular substances
NBCM217Modern Trends in Macromolecular Physics 43/0 Ex
NBCM142Diploma Thesis Seminar 30/2 C
Specialization Physics of materials
Specialization Low temperature physics
Specialization Physics of surface modifications
NBCM219Selected Problems in Physics of Real Surfaces 32/0 Ex
NBCM142Diploma Thesis Seminar 30/2 C

Elective Courses - Set 2

Student need to obtain at least 15 credits for courses from the following set.
Specialization Physics of atomic and electronic structures
NFPL115Electron Microscopy 32/0 Ex
NFPL122Magnetic Properties of Solids 32/0 Ex
NFPL014Dielectric Properties of Solids 32/0 Ex
NFPL040Applied Structure Analysis 31/1 C+Ex
NFPL154Neutron and Synchrotron Radiation in Magnetic Materials 62/2 C+Ex
NFPL030X-ray methods for structure and microstructure investigation of materials 52/1 C+Ex
NFPL082Magnetism and Electronic Structure of Metallic Systems 32/0 Ex
NFPL013X-ray Scattering on Thin Films 32/0 Ex
NFPL155Experimental Study of Real Structure of Solids 42/1 C+Ex
NFPL157Physics in Strong Magnetic Fields 32/0 Ex
NFPL156High Pressure Physics 32/0 Ex
NFPL158Magnetic Structures 42/2 C+Ex
NFPL550Thermal Capacity of Solids 32/0 Ex
NFPL011Computational Physics and Materials Design 32/0 Ex
NFPL004Nonequilibrium Statistical Physics and Thermodynamics 32/0 Ex
NFPL039Methods of Solving and Refining Monocrystal Structures 31/1 C+Ex
NFPL159Modern Materials with Application Potential 32/0 Ex
NFPL551Correlations in Many-Electron Systems 32/0 Ex
Specialization Physics of macromolecular substances
NBCM098X-ray and Electron Structure Analysis of Biomolecules and Macromolecules 32/0 Ex
NBCM211Methods of Measuring Electric Properties of Semiconducting and Insulating Materials 31/1 C+Ex
NFPL018Transport and Surface Properties of Solids 32/0 Ex
NBCM230NMR Spectroscopy of Polymers 32/0 Ex
NBCM209Probabilistic Methods in Macromolecular Physics 32/0 Ex
NBCM076Theory of Polymer Structures 32/0 Ex
NBCM072Fundamentals of Molecular Electronics 32/0 Ex
NBCM062Structural Theories of Polymer Relaxation Behaviour 32/0 Ex
Specialization Physics of materials
NFPL107Fundamentals of Crystallography 31/1 C+Ex
NFPL115Electron Microscopy 32/0 Ex
NFPL055Kinetics of Phase Transformations 32/0 Ex
NFPL305Magnetism of Materials 32/0 Ex
NFPL197Fundamentals of Continuum Mechanics and Dislocation Theory 32/0 Ex
NFPL198Theory of crystal defects 32/0 Ex
NFPL080Acoustic in Physics of Condensed Matter 63/1 MC
NFPL140Physics of Materials III132/0 Ex2/0 Ex
NFPL103Positron Annihilation in Solids 32/0 Ex
Specialization Low Temperature Physics
NFPL171Macroscopic Quantum Phenomena I 32/0 Ex
NFPL172Macroscopic Quantum Phenomena II 32/0 Ex
NFPL093Selected Topics on Magnetic Resonance Theory and Methodology 32/0 Ex
NFPL097Nuclear Spectroscopy Methods in Hyperfine Interaction Studies 31/1 C+Ex
NFPL174Introduction to Fluid Dynamics and Turbulence 32/0 Ex
NFPL210Turbulence 32/0 Ex
NFPL096Moessbauer Spectroscopy 32/0 Ex
NFPL175NMR in Magnetically Ordered Materials 31/1 C+Ex
NFPL129Nuclear Methods in Magnetic Systems Studies 32/0 Ex
NFPL095Fundamentals of Cryogenics 32/0 Ex
NFPL128Selected Topics on Positron Annihilation Spectroscopy 31/1 C+Ex1/1 C+Ex
NFPL184Seminar on Radiofrequency Spectroscopy in Condensed Matter 30/2 C0/2 C
NFPL204Magnetic nanoparticles 32/0 Ex
NFPL179Quantum Description of NMR 52/1 C+Ex
Specialization Physics of surface modifications
NFPL107Fundamentals of Crystallography 31/1 C+Ex
NBCM234Construction of Deposition Apparatuses 52/1 C+Ex
NBCM235Basics of Plasma Physics 32/0 Ex
NFPL149X-ray Study of Real Structure of Thin Films 32/0 Ex
NBCM215Modification of Surfaces and Its Applications 32/0 Ex
NBCM236Nanocomposite and Nanostructured Thin Layers 32/0 Ex
NBCM220Hard and Super-hard Films and Their Applications 32/0 Ex
NBCM232Electrical Properties of Thin Layers 32/0 Ex
NBCM222Optical Properties of Thin Films 32/0 Ex

1 The course can be taken in either the summer or winter semester.

6.2 Recommended Optional Courses

NFPL038Diffraction of X-rays by Perfect Crystals 32/0 Ex
NFPL130Physical Metallurgy of Wrought Aluminium Alloys 32/0 Ex
NFPL199Physical Methods in Nanostructure Studies 32/0 Ex
NEVF106Microscopy of Surfaces and Thin Films 52/1 C+Ex
NFPL120Modern Problems in Physics of Materials 32/0 Ex
NFPL006High Performance Computing in Physics 31/1 C+Ex
NFPL177Superconductivity 52/1 C+Ex
NFPL072Systems with Correlated f-electrons 32/0 Ex
NFPL141Quantum Theory II 52/1 C+Ex2/1 C+Ex
NFPL051Mechanical Properties of Non-metallic Materials 32/0 Ex
NFPL500Practical application of atomic force microscopy 20/2 C
NFPL192Introductory Seminar on Condensed Systems Physics 30/2 MC
NFPL505Introduction to Soft Condensed Matter Physics 31/1 C+Ex
NFPL502Introduction to Solid State Physics 63/1 C+Ex
NBCM060Fundamentals of Polymer Structure Formation 32/0 Ex
NFPL074Practical Applications of Transmission Electron Microscopy 40/3 C0/3 C
NBCM070Thermodynamics of Nonequilibrium Processes 32/0 Ex
NFPL304Technology and properties of steels and cast irons132/0 Ex2/0 Ex
NBCM352Stochastic thermodynamics and Active matter 32/0 Ex

1 The course can be taken in either the summer or winter semester.

6.3 State Final Exam

Necesary conditions for taking the state final exam

earning at least 120 credits during the course of study
passing all compulsory courses of the chosen specialization
earning at least 25 credits from elective courses of the profiling base of the chosen specialization
earning at least 15 credits from elective courses in Set 2 of the chosen specialization
submission of a completed master’s thesis by the submission deadline

Requirements for the oral part of the state final exam

A Common requirements

1 Electronic states in solids <\TEMA>

Description of solid matter as a many body problem - addition of angular momentum, Hund's rules, consequences of symmetry - symmetry of wave function, Bloch's theorem. Types of bonds in molecules and condensed matter.

Band structure and methods of its calculation: one-electron approximation and methods for solving effective equations (LCAO method, nearly free electrons, LAPW, pseudopotentials). Adiabatic approximation, variational principle and perturbation theory.

Interaction between electrons - second quantization, Hartree-Fock approximation, theory of density functional. Quasiparticles in condensed systems.

Interaction of electromagnetic radiation with matter - photon absorption and emission. Stimulated and spontaneous emissions, selection rules. Lifetime of quantum states, natural spectral line width.

2 Thermodynamics and statistical physics of condensed systems

Thermodynamic equilibrium, state variables and equations of state. The laws of thermodynamics and their consequences, entropy and absolute temperature. Thermodynamic potentials, conditions of balance and stability. Critical phenomena, phase transitions, Landau's phase transitions theory. Description of nonequilibrium processes, linear nonequilibrium thermodynamics. Statistical description of state, distribution function and density matrix. Liouville's equation. Gibbs stationary files, file centering, derivation of state equations. Classic and quantum systems of non-interacting particles. Brownian motion, diffusion in the external field.

3 Fundamentals of condensed matter physics
Structure of condensed systems - crystal structure, point and translational symmetry, basics of crystallography. Reciprocal space, Brillouin zone.

Real structure of substances - defects of crystal structure, long and short -term ordering. Amorphous substances and their description, pair distribution functions. Description of topology, spatial and electronic structure of macromolecules.

Movement of atoms and molecules in condensed matter - diffusion, lattice oscillations, phonons, heat capacity.

Electrical properties - polarization mechanisms, dielectric susceptibility. Interaction of ionic crystal lattice with electromagnetic wave. Electric current transport - Sommerfeld model, electrons in the periodic potential, band structure of metals and semiconductors. Basic knowledge of superconductivity.

Magnetic properties - diamagnetism and paramagnetism, magnetization, magnetic susceptibility. Spontaneous alignment of magnetic moments. Magnetization processes in ferromagnets.

Mechanical force field - elastic and plastic deformation, viscosity. Viscoelasticity and rubber elasticity of polymer systems, glass transition, principle of time-temperature superposition.

4 Experimental methods
Structure determination methods - basic diffraction methods: scattering and diffraction of x-rays, electrons, neutrons, atoms and ions. Microscopic methods - optical, scanning and transmission electron microscopy.

Macroscopic and microscopic methods of studying mechanical, thermal, dielectric, optical, transport and magnetic properties of matter.

Basic spectroscopic methods (radio frequency, microwave, optical, X – ray, gamma, photoemission) and their applications.

B Specializations

The student chooses a set of questions corresponding to his specialization.

1 Physics of atomic and electronic structures

Atomic structure of matter
Point and space groups. Symmetry of physical properties. Structure of crystals, quasicrystals, modulated structures and amorphous substances. Using of structural databases. Kinematic theory of diffraction - scattering of x-rays on electrons, atoms and molecules; dispersion on periodic and low-dimensional structures. Fundamentals of dynamic theory of diffraction. Use of neutrons and synchrotron radiation to study the structure of matter. Computer simulations, ab-initio calculations.

Electron structure and physical properties of substances
Conductivity electrons in materials (classical and quantum description), electrons in periodic potential. Electronic structure of metals, semiconductors and insulators, optical properties. Chemical bonding, cohesion, hybridization of electronic states. Electron-phonon interaction, electrical and thermal transport. Coulomb and exchange interaction, correlations of electrons, the formation of magnetic moment. Magnetic ordering, symmetry. Microscopic models of magnetism. Low dimensional systems. Specific heat, temperature dilatation. Magnetotransport and magnetoelastic phenomena. Dielectrics, electrical permittivity, ferroelectrics and antiferroelectrics. Electro-optical and magneto-optical phenomena. Utilization of microscopic and macroscopic methods. Influence of external pressure, physics in high magnetic fields. Ab initio calculations of electronic structure and physical properties. Applications of electronic properties of materials. Nanomaterials.

Collective phenomena
Spontaneous symmetry breaking and the ordering parameter. Microscopic description of phase transitions, mean field theory, fluctuations. Structural and magnetic phase transitions. Spontaneous ordering of nuclear moments. Kondo lattice and heavy fermion systems. Bose-Einstein condensation of an atom. Superconductivity and superfluidity. Cooperative phenomena out of equilibrium, lasers.

2 Physics of macromolecular substances

Structure of macromolecules
Configuration, conformation, tacticity and stereoregularity of polymer chains. Architecture of macromolecular systems. Methods of preparation of macromolecular systems, chemical structure of polymers, methods of construction of polymer networks, gelation point. Distribution and molar mass averages.

Physical properties of macromolecular systems
Relaxation properties, glass transition and free volume theory, time-temperature superposition. Concept of linear viscoelasticity, viscoelastic functions, Boltzmann's principle of superposition. Thermodynamics of polymer solutions, mixtures and block copolymers, phase diagrams. Flory-Huggins theory, swelling equilibrium. Colligative properties of polymers, solutions. Coil-globule transition. Crystallization of polymers. Electrical and optical properties of polymers, generation and charge transport in organic structures.

Experimental methods
Methods of studying the glass transition, measuring of rheological and viscoelastic properties, dynamic mechanical analysis. Measurement of dielectric and electrical properties, thermal depolarization. Detection of thermal transitions, differential scanning calorimetry. Methods for determining the molecular weights and structure of polymers. Diffraction / scattering and spectroscopic methods for studying the structure of macromolecular systems.

3 Physics of materials

Defects of crystal lattice
Crystal lattice, vacancies, interstitials, stacking faults, sub boundaries, grain boundaries, twins, inclusions, dispersoids, precipitates. Interaction of crystal lattice defects. Experimental methods of studying crystal defects: mechanical tests, diffraction and imaging methods, thermal analysis, acoustic emission.

Mechanical properties
Plastic deformation, theory of strengthening, creep and fracture. Static and dynamic softening, recovery of lattice defects, superplasticity, instability of plastic deformation, shape memory.

Thermodynamics of multicomponent systems
Binary and ternary phase diagrams, nearest neighbors model, lever rule, intermedial phase. Phase transformations, solidification of alloys, segregation processes. Diffusion and diffusionless transformations in solids, TTT-diagrams, Avrami equations. Diffusion in solids.

Modern materials and technologies
Intermetallic compounds, ceramic and composite materials, submicrocrystalline and nanocrystalline materials, quasicrystals, shape memory materials, technologies of preparation of modern materials.

4 Low Temperature Physics

Electronic structure of solids
Methods of electronic structure calculation. Electronic structure and magnetic properties of solids. Magnetic moments of free atom / ion, interaction with crystal field, correlation phenomena, exchange interactions, localized and itinerant magnetic moments.

Physics and technology of low temperatures
Methods of obtaining low and very low temperatures, basic properties of cryofluids. Low temperature thermometry.

Macroscopic quantum phenomena
Superconductivity, Cooper pairs, Meissner effect, weak superconductivity. Superconductors of type I. and II., high temperature superconductivity. Superfluidity of 4He, 3He, macroscopic wave function, Bose-Einstein condensation.

Hyperfine interactions and nuclear magnetism
Electric and magnetic moments of atomic nuclei, electric and magnetic hyperfine interaction. Spin Hamiltonian, hyperfine splitting of energy levels, the role of symmetry of the nucleus vicinity.

Experimental methods of studying hyperfine interactions (nuclear magnetic resonance, electron paramagnetic resonance, muon spin rotation, Mössbauer's effect, nuclear orientation, method of perturbed angular correlations) and their use for study of atomic, electronic and magnetic structures.

5 Physics of real surfaces

Surface physics
Molecule binding on the surface, absorption, ideal and real surface, electronic structure of surfaces, surface states, work function, emission of charged particles, electron emission, principle of electron spectroscopy, interaction of particles and radiation with the surface, photoemission, principle of photoelectron spectroscopy, secondary electron emissions, diffraction. Energy of surfaces and interfaces.

Experimental methods of surface study
Electron spectroscopy methods (AES, REED), ion spectroscopy methods (SIMS, SNMS), methods of photoelectron spectroscopy (UPS, XPS) and their practical use. Methods of electron microscopy. Surface energy measurement: static and dynamic methods of measuring the contact angle. Infrared spectroscopy ATR FTIR, methods of X-ray diffraction — small - angle scattering.

Preparation of thin films
Thin film definition, concept of thin film thickness, initial stage and mechanisms of thin film growth. Basic methods of thin film deposition: evaporation in vacuum, DC and radio-frequency (RF) sputtering, CVD, PE CVD of inorganic and organic coatings (plasma polymerization). Methods of diagnostics of thin film growth, measurement of deposition rate and thin film thickness, determination of structure, morphology, mechanical, electrical and optical properties of thin films. Surface modifications, changes in surface energy and chemical activity. Application of thin films — hard, abrasion resistant coatings, protective and passivation layers, optical thin films, coatings for microelectronics.


Charles University, Faculty of Mathematics and Physics
Ke Karlovu 3, 121 16 Praha 2, Czech Republic
VAT ID: CZ00216208

HR Award at Charles University

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