PhD courses offered in English (MS-SSP)

Materials Science and Solid State Physics Program


Physical Materials Science I-II.

The course gives an introduction to the physical background of materials science.

  • Necessary background: classical thermodynamics and statistical mechanics, introductory solid state physics.
  • Topics:
    • Microstructure of real materials:
    • Point defects, equilibrium vacancy concentration, experimental methods for the determination of vacancy concentration, quenching and annealing processes. Dislocations and plastic deformation, work hardening. Grain boundaries and interphase boundaries. Ideal and regular solid solutions. Phase diagrams, derivation of phase diagrams from free-energy-concentration functions. Hume-Rothery rules. Diffusion in solids, diffusion coefficient, correlation factor, diffusion in two-component systems, Boltzmann-Matano analysis, Kirkendall effect, Darken equations.
    • Solidification:
    • nucleation, TTT-diagrams, interface stability, dendrite formation, growing of single crystals, solidification of solid solutions, zone-refining, eutectic solidification. Precipitation processes: stability of the initial state, nucleation and growth processes, metastable phases, retrogression, spinodal decomposition, chemical and coherent spinodal, discontinuous precipitation.
    • Strengthening mechanisms:
    • solid solution hardening, elementary interactions of point defects with dislocations, yield stress of solid solutions. Precipitation hardening, dislocation by-passing, Orowan-stress, particle shearing, yield stress of two-phase materials. Diffusion-less phase transformations, structural transformations, ordering, martensitic transformation, shape-memory effect, strength of martensite.
    • Ceramic and glassy materials:
    • crystal structures, different types of ceramics, diffusion in ceramics, physical and mechanical properties of ceramics.
    • Composite materials:
    • production technologies, mechanical properties, material selection diagrams, composite design, functionally graded materials.
  • Literature:
    • R. W. Cahn, P. Haasen: Physical Metallurgy I-II (North Holland 1983)
    • P. Haasen: Physical Metallurgy (Cambridge University Press 1978)
    • Kovács I. és Zsoldos L.: Diszlokációk és képlékeny alakváltozás (Mûszaki Könyvkiadó 1965)
    • P. G. Shewmon: Transformations in Metals (J. Williams, 1983)
    • L. H. van Vleck: Elements of Materials Science and Engineering (Addison-Wesley, 1989)
    • J. W. Christian: The theory of transformations in metals and alloys (Pergamon, 1975)


Solid State Theory I-II.

Atomic motions: molecular dynamics, determination of thermodynamical quantities, correlation function, Nosé thermostat, Anderson pressostat. Monte Carlo simulation, escape rate.

Lattice vibrations: Green function, local quantities, localisation. Anharmonic vibration, anharmonic resonance, phonon-phonon interaction, heat expansion, Grüneisen parameter.

Fock space, Hartree-Fock equation, quasi particles, exchange interaction. Jellium model, homonuclear and ionic bond, bond order.

Quasi crystals, amorphous materials. Covalent bond, electron structure of silicon. Friedel's theory of transition metals. Density functional theory, Car-Parinello method. Intrinsic and extrinsic semiconductors, diode and transistor.


Solid State Research I.

  • Fullerenes: discovery and preparation of C60, structure of Cn molecules.
  • Raleigh scattering, Raman, UV spectroscopy, vibration and rotation of molecules, Doppler broadening
  • Nuclear magnetic resonance, spin-lattice-, spin-spin relaxation, Bloch equations, chemical shift, line broadening, motional narrowing
  • Lattice symmetries, point groups, forbidden symmetries, packing of symmetrical polygons in two dimensions
  • X-ray diffraction, atomic scattering factors, packing density, radial distribution function, interference function
  • Comparison of the crystal structure of diamond, graphite and fullerene, interstitial sites
  • Electron diffraction (SAED, HREM), Ewald sphere, stereographic projections.
  • Comparison of X-ray, neutron and electron diffraction, twinning.
  • Long range order without periodicity: quasycrystals.
  • Interference function of the Fibonacci chain, projection from higher dimension, approximants, decoration, Penrose tiling, electron structure.
  • Thermodynamic, kinetic and structural aspects of glass formation.
  • Glass transition, Fulcher-Vogel law, critical point in vapor condensation and ferromagnetic transition.
  • Typical preparation, trend of glass forming, polymorphism.
  • Relation of crystal structure, chemical bonding, and atomic packing in tetrahedral crystal structures (Si, Ge, SiO2).
  • Structure models of covalent glasses: microcrystalline and continuous random network (CRN) model, ring statistics, Mott (8-n) rule.
  • Preparation of metallic glasses, random packing of hard spheres (DRPHS).
  • Superlattice reflection, prepeaks, Medium range order.
  • Homogeneous nucleation, TTT-diagram.
  • Tunneling in amorphous systems, magnetic analogy, specific heat of crystals and two-level systems, heat conducting of phonons and absorption of ultrasound.
  • Crystallization of transition metal-metalloid glasses, short range order, role of trigonal prism.
  • Mössbauer spectroscopy: f-factor, isomer shift, quadrupole and magnetic hyperfine splitting.


Solid State Research II.

  • Localization - delocalization
  • Free-volume model of glass transition
  • Metal-nonmetal transition: Mott transition, Anderson localization, mobility edge
  • Scaling, weak localization in two dimensions, logarithmic correction, magnetoresistance
  • Quantum interference effects, Aharonov-Bohm effect
  • Percolation: site-bond percolation, percolation threshold, critical exponents, fractal dimension, scaling laws, Bethe lattice, continuous percolation, critical volume fraction, applications of localization-delocalization
  • Magnetism
  • Spin, orbital magnetic moments, spin-orbital coupling, Lande g factor, effects of crystal field (3d, 4d)
  • Generation of magnetic fields
  • Magnetic measurements (induction-, force method, SQUID)
  • Neutron diffraction, magnetic structures (ferromagnetic, antiferromagnetic, ferrimagnetic, helimagnetic, sinusoidally modulated)
  • Exchange interaction (direct, super, RKKY), distance-dependence
  • Magnetic anisotropy
  • Domain wall, single-domain particle
  • Permanent magnets
  • Magnetic thin layers, surface anisotropy, oscillating coupling, giant magnetoresistance


Experimental Methods in Solid State Physics I.

  • Elements of kinematic diffraction theory

    Amplitude and intensity of the diffracted beam; reciprocal lattice, Bragg's law and the Ewald sphere; atomic scattering factor and the structure factor; systematic extinction, Debye-Waller temperature factor.

  • X-ray methods

    X-ray sources; detectors; absorption spectroscopy; radiography; single crystal diffraction; powder diffraction; phase identification; quantitative phase analysis; indexing and lattice parameter determination; X-ray topography.

  • Electron methods

    The particularities of electron diffraction; deviation parameter; transmission electron microscopy; image formation in TEM and diffraction; Kikuchi lines; the basic equations of the two-beam kinematic and dynamic theory; rocking curve; images of dislocations and other crystal defects; high-resolution electron microscopy. Scanning electron microscopy: priciples of SEM and imaging modes; analytical electron microscopy; electron energy loss spectroscopy.

  • Neutron methods

    Neutron sources and detectors; absorption; nuclear scattering; magnetic scattering; basic properties of neutron diffraction; time-of-flight method; applications: structure analysis; Rietveld refinement; hydrogen atom location; residual stresses; neutron inelastic scattering and its application.

  • Positron annihilation spectroscopy

    Positron sources; positron annihilation; positronium; positron in solid matter; measuring methods: angular correlation, time-life, Doppler broadening; meauring apparatuses; applications: fermiology; positron trapping at crystal defects; positron emission tomography.

  • Calorimetry

    Low temperature calorimetry: low temperature measurement of specific heat; elemental excitations; critical parameters; phase transformations; low temperature measuring methods; instrumentation. High temperature calorimetry: classical DTA; Boersma DTA; differential scanning calorimeter (DSC); phase transformations; kinematical investigations.


Experimental Methods in Solid State Physics II.

  • Scanning probe microscopy and spectroscopy

    Scanning tunneling microscopy (STM): theoretical background; one-dimensional elastic tunneling; imaging and spectroscopy; STM design and instrumentation; basics of the work; applications: metals and semiconductors, layered materials. Scanning force microscopy (SFM): design and instrumentation; imaging in contact mode; non-contact force microscopy; applications.

  • Mössbauer spectroscopy

    Physical background of the resonance-absorption; recoil energy loss; Doppler-broadening; recoil-free emission; Mössbauer-Lamb factor; experimental techniques; sources and detectors; Doppler velocity drive; measuring possibilities; hyperfine interactions: isomer shift; quadrupole splitting; magnetic hyperfine structure; relativistic effects; application in solid state physics.

  • High-energy ion beam spectroscopy

    The common characteristics of the high energy ion beam methods; Rutherford backscattering (RBS): kinematic factor and mass resolution; elastic scattering cross sections; energy loss in solids; applications: composition and stoichiometry of the sample; thickness measurement; depth profiling; heavy ion backscattering; non-Rutherford backscattering. Channeling: channeling equipment; crystal alignment; defect analysis methods; surface relaxation. Elastic recoil detection (ERD): principles of ERD; experimental setup; applications. Proton induced X-ray emission (PIXE). Charged particle activation analysis.

  • Nuclear magnetic resonance spectroscopy

    Classical and quantum properties of the angular momentum; transformation in rotating coordinate system; Bloch equation; spin-spin and spin lattice relaxation; experimental methods: continuous-wave method; Fourier method; instrumentation; different method in pulsed NMR for measuring relaxation times; applications in solid state physics and chemistry: Knight shift; Korringa relation; chemical shift; NMR tomography.

  • Electronic and vibrational spectroscopy

    Infrared spectra; Raman spectra; atomic spectroscopy; laser spectroscopy.


Structure determination, and the physics of diffraction I.

  • The fundamentals of diffraction:
  • Fundamentals of crystallography, lattice plane, translational symmetry, Miller indices, fundamental crystal structures, reciprocal lattice. X-rays, X-ray spectra, X-ray sources in the laboratory and at synchrotrons. Electrons, neutrons, comparison of the three different beams. Absorption, absorbtion edges and spectra. Scattering mechanisms.

  • Scattering by crystals, Laue equations, Bragg equation, Ewald construction.
  • The fundamentals of kinematic scattering, electron scattering factor, atomic scattering factor, structure factor, systematic extinction.
  • The fundamentals of single crystal diffraction, the Laue method, other simplel methods, the fundamentals of structure determination.
  • Powder diffraction.
  • Extraction of single crystal data from powder diffractograms, a synchrotron method.
  • Special applications:
  • Powder diffraction methods, diffractometers, indexing powder diffractograms, phase analysis, data banks. Scattering of non-crystalline materials, determination of pair correlation. X-ray small angle scattering, neutron small angle scattering. Qualitative and quantitative phase analysis by powder diffraction. X-ray line profile analysis. The method of extended X-ray absorbtion fine structure (EXAFS).


Structure determination, and the physics of diffraction II.

  • Dynamic scattering:
  • The effect of anomalous transmission and the Bormann effect. Descrition on the basis of Maxwell's equations, with indications to the analogy with Schroedinger's equation. Periodic refraction index and the importance of the extinction length. Fundamentals of the derivation of the dispersion surface in the two ray approximation. Properties of the dispersion surface. Different absorption properties of the two rays corresponding to the two different branches of the dispersion surface. Examples in TEM micrographs. Energy propagation, Authier's principle. Total reflection, the theory and operation of monochromators. Standing waves, and examples. The complementarity between monochromacy and parallelism.

  • Neutron diffraction:
  • Fundamental properties of neutrons, thermal neutrons, neutron sources, cold source. Fundamentals of n scattering, coherent and incoherent scattering, different cross sections. Scattering mechanisms, nuclear scattering, magnetic scattering, magnetic structures.Neutron small angle scattering, relevance to protein crystallography.



Electronic properties

autumn semester

3+1 hours per week

This intermediate course on solid-state physics treats the electronic properties of solids.

Prerequisite: introductory course on solid-state physics, quantum mechanics, statistical physics

  • Band structure of electron states
  • Methods of band-structure calculation
  • Semiclassical dynamics of electrons
  • Electrons in strong magnetic fields, Landau levels
  • de Haas-van Alphen effect
  • Methods of Fermi surface determination
  • Intrinsic semiconductors
  • Extrinsic semiconductors
  • The physics of semiconductor devices
  • Electron-phonon interaction, polaron
  • Transport properties
  • Hall effect, quantum Hall effect
  • Optical properties of solids
  • Direct and indirect exchange
  • Ferro- and antiferromagnetism
  • Ginzburg-Landau theory of superconductivity
  • Vortices in type II superconductors
  • Tunneling, Josephson effect



Interactions and correlations

spring semester

2 hours per week

This advanced course on solid-state physics treats the role of electronic interactions and correlations in solids.

Prerequisite: intermediate course on solid-state physics, course on many-body problem

  • Electron-electron interaction, Hartree-Fock approximation, correlations
  • Dielectric formalism, screening, plasmons
  • Landau theory of Fermi liquids
  • Luttinger liquids
  • Symmetry breaking in the system of electrons, itinerant magnetism
  • Charge and spin density waves
  • BCS theory of superconductivity
  • Infrared singularities in solids, Kondo effect
  • Strongly correlated electron systems
  • Heavy fermion systems and high Tc superconductivity


Introduction to Micro- and Nanotechnology

  • Basics of nanotechnology
  • Size ranges and technologies; specific properties of nanosize particles; ancient nanotechnology; instinctive nanotechnology; natural nanotechnology; beginning of conscious nanotechnology; nanoscience and nanotechnologies; ways to the nanoworld.
  • Methods of measuring nanoproperties
  • Microscopy: transmission electron microscopy; high resolution TEM; scanning electron microscopy; scanning probe microscopy (AFM, STM).

    Diffraction: X-ray diffraction; electron diffraction;

    Spectroscopy: photoelectron spectroscopy; optical spectroscopy; infrared spectroscopy; Raman spectroscopy; nuclear magnetic spectroscopy; positron annihilation spectroscopy.

  • Properties of individual nanoparticles
  • Characterization of nanoparticles; synthesis of nanoparticles; structure; fluctuations; reactivity; conduction electrons and dimensionality; partial and total confinement.
  • Bulk nanostructured materials
  • Disordered nanostructured materials: glasses containing metallic nanoclasters, porous silicon. Ordered nanomaterials: multilayers; giant magnetic resistance; nanostructured crystals; crystals of metal nanoparticles; arrays of nanoparticles in zeolites; photonic crystals.
  • Carbon nanostructures
  • Nature of carbon bond; graphite, diamond; carbon nanoparticles; fullerenes; fullerene crystals; carbon nanotubes; geometrical structure; dispersion relation; vibrational properties; mechanical properties; fabrication of nanotubes; applications.
  • Self-assembly
  • Intermolecular interactions; molecular recognition; colloid systems, properties of amphypatic molecules; self-assemby in 3D: micelles; membranes; nanoporous systems; self-assembled polymers; dendrimers, applications.
  • Organic nanolayers
  • Self-assembled monolayers (SAMs), chemical composition, preparation and structure; application in surface chemistry, biosensors, nanolitography. Formation and properties of the Lagmuir-film; Langmuir-Blodgett technics; surface patterning, applications.
  • Electron transport through nanoobjects
  • Quantum wells, wires and dots; conduction electrons and dimensionality; electron transport in nanosytems; ballistic and quasi-ballistic transport; quantum coherency; weak localization; conductivity fluctuation; Aharonov-Bohm effect; quantum Hall effect; Landauer formula; quantum resistance; single electron tunneling; Coulomb blockade; single electron transistor;
  • Micro- and nanolithography
  • Short history of microtechnology, tendencies and limitations of the development; photolithography; nanolithography: X-ray lithography; electron lithography; ion beam lithography; the state of the art of nanolithography.
  • Integrative systems
  • Micro-elecromechanical systems (MEMS); fabrication technologies, integration of micromachining with microelectronics; micromechanical sensors; applications; tendencies in development; nano-electromechanical systems (NEMS).
  • Applications, risks and ethics issues
  • Application of new materials and devices today and in the near future; survey of the main fields: informatics; computer techniques; medicine; energy and environment; military use; space research; short-time and long-time risks of the new technology; ethics issues.


Physics of semiconductors

In this course fundamentals of semiconductor materials and device physics are introduced - differences between general solid state physics and specific semiconductor properties are emphasized. Most recent applications are treated in some more details.

Background: Elements of solid state physics and basic knowledge of quantum mechanics.

  • Crystal physics - structure, structure of thin layers, interfaces, epitaxy, organic and amorphous semiconductors.
  • Electron states - band structure, role of bonding, k.p perturbation, hole states.
  • Motion of electrons - effective Hamiltonian, effective mass tensor, valence band, impurity states, shallow and deep impurities, scattering of electrons and holes.
  • Statistics of semiconductors - intrinsic, extrinsic semiconductors, degeneracy, compensation, semi-insulators.
  • Basic transport - phenomenology, Onsager relation, microscopic kinetic model, Boltzmann equation, conductivity,
  • Hall effect, magnetoresistivity.
  • Advanced electron transport - high field, instability, Gunn effect.
  • A.C. transport - microwave, propagation of light below band-gap, cyclotron resonance.
  • Thermal transport - thermal conductivity of electrons, bipolar (heat) conductivity, Peltier effect, thermoelectric heating and cooling.
  • Quantum transport - reduced dimensionality, space-charge layers, quantum hall effect (integer, fractional).
  • Inhomogeneous semiconductors - diffusion, lifetime, injection, p-n junction, MOS structure.
  • Fundamental experimental techniques for characterization of semiconductor materials and device structures.
  • Basic devices - p-n junction diode, transistor, tunnel diode, MOS device, Zener diode.
  • Light and semiconductors; optoelectronics - LED, laser diode, light detectors, MOS imaging, CCD physics.
  • Light and semiconductors; solar cells - basics, theoretical limits, practical limits, future.
  • Highlights of Hungarian pure and applied semiconductor research.

Specific literature is given at the end of each Section.


Introduction to Materials Science and Technology

Materials science and engineering is concerned with the generation and application of knowledge relating the composition, structure, and processing of materials to their properties and use. The present course is intended for Ph.D. students of physics. At their B.Sc. and M.Sc. studies, the students learn a lot on the atomic structure, the electronic, magnetic, optical and other properties of solids. Their knowledge on the structure - property relationship is, in general, adequate. Less is known on the processing and its importance in the formation of structure and properties. Therefore processing and its influence on the structure and performance has been chosen as a guiding principle in the selection of topics in this course.

The following topics are covered:
  • Basic techniques of materials processing (heat generation, temperature measurements and control, environment control)
  • Solidification of melts (fundamentals on the nucleation and growth, techniques for growth of single crystals from melt, techniques for rapid solidification of melts)
  • Powder processing (preparation of powders, forming, sintering, mechanical alloying, applications)
  • Thin film technologies (structure of thin films, PVD, CVD, epitaxy, MBE, LPE)
  • Surface modification processes (ionimplantation, thermal spraying)
  • Special metallic microstructures (metallic glasses, microcrystalline alloys, nanocrystalline materials)
  • Advanced ceramics (structure, mechanical properties, applications)
  • Composites (fibre, particulate reinforced and laminate composites). Nanocomposites.


  • [1] G. Konczos, I. Bársony and P. Deák: Introduction to materials science and technology, 1998, pp. 200,
  • [2] Konczos G.: Advanced materials technologies (Korszerû anyagtechnológiák, in Hungarian). Manuscript, 2004


Current Topics in Materials Science I.

  • Fundamentals of plastic deformation: geometrical considerations, single crystals, Schmid factor, Taylor factor single slip, multiple slip.
  • The effect of temperature and strain rate. Simple fcc, bcc and hcp metals.
  • Work hardening: discussion of the different mechanisms of work hardening. Taylor's equation, the effect of different boundaries, the Hall-Petch relation, its correlation with Taylor's equation, the inverse Hall-Petch relation and its criticism. Work hardening stages, Mecking's plot. Twinning versus dislocation glide. The effect of stacking fault energy. Plastic deformation in nanocrystalline or submicron grain-size materials.
  • Pattern formation in dislocation systems: Wavy glide versus planar glide, the effect of alloying elements. Vein structure and the formation of persistent slip bands (PSB) in fatigue. Cyclic stress strain curves, plateau behaviour in single crystals. The formation of intrusions and extrusions during fatigue and the Essmann-Mughrabi-Goesele model. Woehler's diagram, fatigue limit and its microstructural relevance. The impact of PSB formation on fatigue limits.
  • Internal stresses: The classification of internal stresses. Macroscopic-, mesoscopic-, and microscopic internal stresses and their relation to the microstructure of materials. The effect of elastic anisotropy on the formation of internal stresses. The effect of heterogeneous microstructures on the formation of internal stresses. The measurement of mesoscopic internal stresses by time-of-flight neutron diffraction, with special emphasis on the SMART diffractometer in the LANSE laboratory in Los Alamos, New Mexico.
  • X-ray Line Profile Analysis (XLPA): The measurement of macroscopic-, mesoscopic-, and microscopic internal stresses by the method of X-ray line profile analysis. Long range internal stresses and characteristic X-ray line asymmetry. Microstructural parameters obtained by XLPA and their correlation with transmission electronmicroscopy (TEM) data. High temperature deformation: Fundamentals of creep, sections of creep. Empirical relation between the temperature and stress dependence of the rate of deformation. The mechanisms of creep: dislocation mechanism, activation volume, diffusional mechanisms, Nabarro-Herring and Cobble creep, and their temperature and stress dependence. Power-Law-Creep, the PLC effect, solute-dragg and temperature and stress dependence. Concomitant dislocation and diffusional mechanisms, parallel and serial switching, independent and sequential creep mechanisms. Dislocation-climb and glide mechanisms. The Hazzledine-Weertman model of dislocation-climb and glide. Deformation maps.
  • Temperature anomaly in the Ni3Al ordered intermetallic alloy system: Stacking faults in the LI2 structure. The definition of γ surfaces. Different sections through the γ surface of the ordered Ni3Al intermetallic alloy system. The description and operation of the Kaer-Wilsdorf lock.
  • Ni base γ/γ' superalloys: The structure and morphology of Ni base γ/γ' superalloys. Creep properties, rafting, deterioration. Deformation mechanisms, internal stresses. XLPA measurement of structural changes. Microdiffraction measurements at a syncrotron source for following the spatial heterogeneities developing in flying turbine blades.


Current Topics in Materials Science II.

This is a paper reading course. The topics below are valid until 2005. and are updated whenever the course starts newly:

  • Bulk amorphous materials
  • Deformation of amorphous materials
  • Atom Probe Microanalysis
  • Indentation tests
  • Hidrogen storage
  • Nanocrystalline materials
  • Nanotechnology
  • Microstructure charcterization


Modern theory of nucleation and growth

In this course recent advances made in describing crystal nucleation and polycrystalline solidification are reviewed.

Required background: statistical physics.

  • I. Interfacial properties
    • experiment;
    • atomistic simulations;
    • continuum theory.
  • II. Nucleation theory
    • Droplet model & kinetic theory.
    • Classical nucleation theory.
    • Advanced droplet models:
      • self-consistent theory;
      • phenomenological diffuse interface theory;
      • field theoretic models (Cahn-Hilliard, density functional, and phase field approaches).
    • Comparison with experiment and computer simulation.
  • III. Continuum models of crystal growth.
  • IV. Modeling of polycrystalline solidification:
      multi-phase-field theory;
      phase field theory with orientation field(s) in 2D and 3D    homogeneous and heterogeneous nucleation;    primary and secondary nucleation.
  • V. Future trends.


  • K. F. Kelton: Crystal Nucleation in Liquids and Glasses. Solid State Phys.     45, 75 (1991).
  • L. Granasy, F. Igloi:  Comparison of Experiment and Modern Theories of    Crystal Nucleation. J. Chem. Phys. 107, 3634 (1997).
  • L. Granasy, P.F. James: Non-Classical Theory of Crystal Nucleation:     Application to Oxide Glasses: Review. J. Non-Cryst. Solids 253, 210     (1999).
  • L. Granasy, T. Borzsonyi, T. Pusztai: Nucleation and Bulk Crystallization     in Binary Phase Field Theory. Phys. Rev. Lett. 88, 206105 (2002).
  • L. Granasy, T. Pusztai, T. Borzsonyi, J. A. Warren, J. F. Douglas: A General     Mechanism of Polycrystalline Growth. Nature Mater. 3, 645 (2004).
  • D. T. Wu, L. Granasy, F. Spaepen: Nucleation and the Solid-Liquid Interfacial     Free Energy. MRS Bulletin 29, 945 (2004).
  • L. Granasy, T. Pusztai, J. A. Warren: Modelling Polycrystalline Solidification     Using Phase Field Theory (Topical Review). J. Phys.: Condens. Matter 16,     R1 (2004).


Nonequilibrium Materials

Basic thermodynamic theory in the frame of the quasichemical model for predicting phase diagrams with special emphasis on the eutectic type phase diagrams and their significance in the non-equilibrium solidification. Theconcept of the T0 temperature as the decisive factor between the supersaturated solid solution and metallic glass formation. Elements of nucleation concepts and the the reduced glass transition temperature as the decisive factor for the critical cooling rate. Glass transition phenomenon. Free-volume and entropic models. Glass transition as a phase transition from the ergodic liquid to non-ergodic glassy state.

The structural description of multi-component non-crystalline materials. Partial structure factors and radial distribution functions and the basic procedure for their experimental determination. Theoretical concepts from dense random packing to stoichiometrically defined models.

Simple models of magnetism and electric transport in amorphous metallic materials. The limitations of nearly free electron or rigid-band type models.

Some highlights of magnetism of amorphous metallic systems from sophisticated electronic stucture modelling.


Electron microscopy and electron diffraction

  • Basic concepts of crystallography, Miller indices, reciprocal space.
  • Order and disorder in materials: crystals and defects, textures, amorphous structures, ordering is amorphous state, quasicrystals.
  • The electron microscope as a vacuum system.
  • The electron microscope as an optical system, electromagnetic lenses.
  • Basic modes of operation:
    • microscopy: bright field, dark field, high resolution imaging
    • diffraction: selected area diffraction, small angle diffraction
  • Resolution of the electron microscope, lens aberrations, optical analogy
  • Image recording: photographic, digital
  • Calibration procedures: magnification, diffraction, rotation
  • Geometrical theory of electron diffraction, Bragg low, Ewald construction, determination of crystallographic directions, lattice parameters, size and type of the unit cell, phase analysis
  • Convergent beam diffraction, applications
  • Kikuchi patterns, applications
  • Kinematical theory of electron diffraction
    • Amorphous materials
    • Crystals, selection rules, size and stress effects
  • Kinematical theory of image formation: basic assumptions, intensity, effect of the thickness and bending of the crystal, dark field and bright field imaging, lattice resolution. Imaging of crystal defects.
  • Limits of application.
  • Dynamical theory of image formation, basic assumptions, effect of absorption, intensity, effect of the thickness and bending of the crystal, dark field and bright field imaging, imaging of crystal defects.
  • High resolution microscopy. Phase contrast, contrast transfer function. Scherzer focus. Interpretable resolution, information limit. Phase and amplitude objects. Resolution (acceptance) test of an electron microscope. Image simulation, interpretation of high resolution images
  • Electron holography


Analytical electron microscopy

  • Place of analytical electron microscopy within microscopies and analytical techniques
  • Theory of elastic scattering of high energy electrons in thin samples
  • Convergent beam electron diffraction techniques (CBED, LACBED, …), as compared to selected area electron diffraction (SAED)
  • Inelastic electron scattering
  • Electron energy loss spectroscopy (EELS) and energy-filtered images
  • Energy dispersive X-ray spectrometry (EDXRS)
  • Atomic resolution Z-contrast imaging in scanning transmission electron microscopy (STEM)
  • Current trends in electron microscopy

Lecture topics are accompanied with practical laboratorydemonstrations of equipment and students are also exposed to practical problems to solve.


Computational Material Science

  • Cellular Automatons
  • Modelling fluid dynamics by cellular automatons
  • Modelling spinodal decomposition by Boltzmann cellular automaton
  • Principles of molecular dynamics
  • How to add thermostat
  • Empirical 2 particle potentials
  • Derivation of the Finnis Sinclair potential
  • Other multi- particle potentials
  • First principle methods
  • Phase field theories to modell precipitations
  • Discrete dislocation dynamics
  • Continuum theory of dislocations
  • Finite element methods


The finite element method and applications in material science

The aim of this course is to provide the student with the basics of the Finite Element Method (FEM) and to show how the method can be applied to some selected problems of materials science. It is intended for the students to work with the commercial FE software MSC.MARC. The development of a model for specific problem is a prerequisite to participate at the examination. The one semester course covers the following main topics:

  • Historical aspects and the origin of the FEM.
  • Residual methods for approximate solutions of differential equations (the Rayleigh-Ritz, Gallerkin and weighted residual methods)
  • Variational principles and the FEM, connection between FEM and finite differences.
  • Application to elasticity. The principle of virtual work. The stiffness matrix and stiffness equation.
  • Application of Laplace equation to describe the mechanical equilibrium of a bar, to the one dimensional fluid flow, and to radial heat-flow between two cylindrical surfaces.
  • Two and three-dimensional elasticity problems. Taking into account the work done by surface and body forces.
  • The principle of complementary energy and the stress driven FE.
  • Principal aspects of the heory of Interpolation. Direct evaluation of the shape matrix. Higher order and refined FE, isoparametric FE.
  • How to evaluate the error of the FE approximation? Superconvergency and recovery of the derivatives.
  • The Zienkiewicz-Zhu error criterion.
  • Solution of linear systems of equations. Direct and iterative methods. Solution of nonlinear systems of equations.
  • Application to materials science:
    • Understanding the origin of misfit dislocations in quantum-dot systems.
    • Estimation of effective properties of real heterogeneous structures (mechanical and thermal properties of particle reinforced metal-matrix composites)
    • Crystal plasticity of polycrystalline materials.
    • Raftening of super-alloys.


Surfaces, thin layers, nanocrystals

In the last decades, the surfaces, interfaces and low dimensional nanostructures have become increasingly interesting subjects of condensed matter physics and in interdisciplinary sciences. Their importance is not only in the basic science but also in technological developments, especially, in microelectronics, data storage, catalysis and corrosion. They are also important in biological and medical applications. Important progress in the surface science has been developed because of the application of new techniques for the preparation of the materials and new methods for the determination their structure and the atomic interaction processes.

The lectures listed below cover the important aspects of low dimensional systems for doctorands.

  • Introduction. The general interrelation of the three objects given in the title . The surfaces. Formation of layers. The surface - volume specific ratio. General interests.
  • The concept of surface energy and surface tension. The shape and structure of the surfaces. Surface atoms.
  • Microstructures. Reconstructions.
  • The deposition of layers on clean surfaces. The cleanness, UHV.
  • On the UHV techniques.
  • The MBE method.
  • STM, AFM and the new methods applied for surface studies.
  • The deposition of layers II. The statistical description of interfaces. States in equilibrium and in nonequilibrium.
  • The growth of films. The surfactant effect.
  • Epitaxy and its conditions.
  • The ion implantation in layers.
  • The physical interactions in the layers. Interaction between layers.
  • The formation of nanostructures.
  • The general characteristics of nanostructures.


Nuclear Solid-State Physics I.

  • Electromagnetic properties and electromagnetic transition of nuclei.
  • Gamma radiation detectors.
  • Hyperfine interactions.
  • Mössbauer spectroscopy and its applications in solid-state physics, chemistry and materials sciences.


Nuclear Solid-State Physics II.

  • Perturbed gamma-gamma angular correlation.
  • Nuclear magnetic resonance (NMR).
  • Nuclear orientation, NMR on oriented nuclei.
  • Muon Spin Rotation.
  • Positron annihilation.


Nuclear Solid-State Physics III.

  • Principles on neutron scattering.
  • Neutron sources, neutron detectors, monochromators.
  • Neutron diffraction.
  • Small-angle neutron scattering.
  • Inelastic and quasielastic neutron scattering.
  • Neutron spin echo.
  • Backscattering of high-energy ions from matter.
  • Ion-beam analysis with backscattering and elastic recoil detection.
  • Channelining, lattice location studies.
  • Nuclear reaction analysis.


Lattice defects I-II.

  • Point defects: vacancies, formation energy and number of vacancies, cohesive energy, kinetics of vacancy, diffusion, colour centres, interstitionals, substitutional and interstitional impurities, anti site defect, effect of the point defects to the resistance and thermoelectric power, impurities in fcc and bcc. Martensitic transformation, ordered alloys.
  • Line defects: dislocations and disclinations, Burgers vector, screw and edge dislocations, Orowan relation, force acting to the dislocations, Conservative and nonconservative motion, Schmidt's law,. Multiplication of dislocations, cross slip.
  • Elasticity: compatibility, Green function, elastic field of point defects, field of dislocation, energy, line tension, pile up, dislocations models, dislocations in fcc, bcc and hcp crystals, anomal flow
  • Dislocation in anisotropic medium, Stroh's formalism.
  • Grain boundaries: Physical properties of grain boundaries, classification of grain boundaries, dislocation model of grain boundary, Frank-Bilby formula, coince site lattice, displacement shift complete, sigma, structure unit model
  • Surfaces: Methods of investigation of surfaces, surface relaxation, surface reconstruction, anisotropic surface energy, Wulff construction.
  • Plastic deformation: Ideal plastic material, flow stress, Peierls stress, effect of impurities and precipitates. Hook and Newton body, Tresca and Mises flow stress, twist in elastic-plastic material. Rigid-plastic approximation. Slip lines.
  • Work hardening, I., II. and III stage of work hardening in fcc.
  • Fracture: brittle and ductile fracture, Griffith theory.


Nuclear Techniques in Material Science

  • Physical background of Mössbauer spectroscopy (MS):
  • Experimental techniques of the transmission, reflection and conversion electron MS. Mössbauer measurements with synchrotron radiation.
  • Theoretical aspects of positron annihilation spectroscopy (PAS):
  • The methods of angular correlation (ACS), Doppler broadening (DBS) and positron- and postironium-lifetime spectroscopies (PLS)

  • Description of the phenomena of muon spin-relaxation, -rotation, and - resonance (μSR) and their applications for structural studies.
  • The formation of heavy exotic atoms and their interactions with matter as a probe for material science.
  • Several applications of the discussed techniques in structural chemistry and material science.


  • A. Vértes, I. Kiss: Nuclear Chemistry, Akadémiai Kiadó, Elsevier, 1987
  • A. Vértes, L. Korecz, K. Burger: Mössbauer Spectroscopy, Akadémiai Kiadó, Elsevier, 1979
  • A. Vértes, S. Nagy, Z. Klencsár (editors) Handbook of Nuclear Chemistry, Kluwer Academic Publishers, 2003


Nanophase metals

The course (10-12 lectures, 90 minutes each) is based on courses given yearly under the same title at the Eötvös University, Budapest since 1996, at the Tokyo Metropolitan University in 2000 and, in a shortened form, at the University of Bristol in 1999.

It is intended for final year undergraduates and for Ph.D. students in solid state physics as well as materials science.


  • Introduction to, classification of and interest in (metallic) nanophases
  • Preparation, structure and thermal stability of metallic nanophases
  • Magnetic properties of nanoscale particles, bulk nanocrystalline metals and nanophase composites
  • Magnetic properties of nanoscale films and multilayers (magnetic anisotropy, exchange coupling)
  • Electrical transport in nanoscale films, multilayers and nanocrystalline metals
  • Electrical transport in nanophase metals in external magnetic field (AMR, GMR, TMR, spin electronics)
  • Possible applications of nanophase metals (permanent magnets; soft magnetic materials; information storage; magnetic refrigeration; hydrogen storage)