Sem 3 GUT Material Sci.

Sem 3 GUT Material Sci.

Applications  @  GUT  30 ECTS credits

Advanced computational methods in material science

The Gdansk (GUT) partner's curriculum will focus on "Advanced Computational Methods in Material Science". As is well-known, modelling of materials at the atomic scale becomes more and more important in all fields of material science and engineering. At present, due to the increased power of computers, systems containing hundreds of million atoms can be simulated with particle methods involving empirical force-fields and thousands of atoms with advanced ab initio methods. Thus, investigations of molecular mechanisms of a great variety of technically important phenomena and their atomic-scale (and even sub-atomic) modelling are now possible. Since computer methods are generally much less costly and more convenient to perform than real experiments, the development of computer-aided material engineering has the potential for large economical impact. The graduates will be trained in advanced methods of computer modelling and design of inorganic and organic materials mainly at the molecular level, although macro-scale calculations will be also taught. The stress will be posed on methods (physical background, algorithms) and tools (programming, practical knowledge of commercial modelling/design programme packages, modern computer systems), thus the graduates will be well prepared to perform simulations of a very wide variety of materials and phenomena: properties of surface layers, bulk properties, friction and lubrication mechanisms, cracks, indentation, nanoelasticity and nanoplasticity in mechanical engineering, electro-optical and chemical properties of materials in materials science, just to invoke several representative examples. The general formation towards modelling methods at molecular scale, although focused on materials, will also enable our graduates students to switch easily to high-level simulations of biomolecular systems or other complex organic compounds (drug design, for example). Graduates will be able to find employment in any research institute, or industrial development/research units, where advanced molecular modelling finds application.

 

Below you can find information about the subjects for this semester.

Classical simulations with particles [6 credits]

  • ECTS credits 6
  • Semester 3
  • University Gdansk University of Technology
  • Objectives

     

    During this course the basic principles of classical equilibrium and non-equilibrium molecular dynamics simulations will be presented, with stress posed on applications to materials' properties modelling. The students will learn how to use the molecular dynamics method, will be familiar with the method's limitations, will be able to evaluate critically the numerical results and carefully compare them with experimental data.

  • Topics

     

    1. Things to be simulated
    a. Structure of crystals and glasses. Quasiperiodic structures. Crystallization and glass formation.
    b. Elements of crystallography. Bravais lattices, crystal symmetry, reciprocal lattice, diffraction.
    c. Bonding in solids. Binding energies.
    d. Lattice vibrations. Dispersion relations, normal modes, phonons. Specific heat of crystals, classical, Einstein and Debye models.
    e. Lattice defects: point defects, dislocations, plane defects.
    f. Free electron gas. Drude model. Electric and thermal conductivities of solids.
    g. Optical properties of metals and dielectrics.
    h. Magnetism of solids. Superconductivity.

    2. Simulations with classical particles – molecular dynamics methods
    a. Simulation box and periodic boundary conditions
    b. Basic Molecular Dynamics algorithm
    c. Numerical integration methods for equations of motion: basic Verlet algorithm and
    velocity Verlet algorithm
    d. Methods for describing interactions: interatomic potentials
    e. Identification of nearest neighbors: Verlet list and linked-list cell algorithm
    f. Starting simulation: choosing initial positions and initial velocities, system equilibration and velocity
    rescaling
    g. Calculating thermodynamic parameters: temperature and pressure
    h. Simulations in various thermodynamic ensembles: thermostatic and barostating

Quantum simulations with particles [6 credits]

  • ECTS credits 6
  • Semester 3
  • University Gdansk University of Technology
  • Objectives

     

    During this course the students will study basic principles of quantum chemistry and electronic structure of molecules and solids. A wide spectrum of methods, from semi-empirical to self-consistent ones, and methods of calculation of band structures and density of states will be presented. Particular stress will be posed on practical practical aspects i.e. the capacity to choose the most proper computational method for given problem.

  • Topics

     

    1. Axioms of quantum mechanics

    2. Exact solutions of Schrodinger equation:
    a. free particle (in one dimension)
    b. particle in box (one- and two-dimensional)
    c. harmonic oscillator (one-dimension)
    d. rigid rotor (two- and three-dimensional)
    e. hydrogen atom (separation of motion of the center of mass, solutions - orbitals (s, p(x,y,z), d(5
    orbitals), energies, quantum numbers, radial density of probability, average distance of
    electron from nuclei, average kinetic energy)
    f. variational method: optimization of parameter c in trial function f(r,c) = exp(-cr) (expected
    values of hamiltonian and variational calculation).

    3. Periodic quantum systems (Bloch states, SF, HF, band theory, APW, KKR, DFT, etc.)
    a. The molecule and crystal Hamiltonians
    b. The Born-Oppenheimer approximation
    c. The variational principle
    d. Spin. The Slater determinant
    e. The Hartree-Fock equations
    f. The Roothan equations
    g. The Hartree-Fock equations
    h. The density functional theory
    i. The Bloch theorem. Common principles of solving the problems of zones. Dispersion equation
    j. The Kronig-Penney model of a crystal. Conductors, insulators, semiconductors.
    k. Electrons in empty lattice. The Fermi energy.
    l. Computer practice in computer solving of equations of quantum mechanics
    m. The model of weakly bond electrons
    n. Computer practice in solving of equations of quantum mechanics
    o. The model of tightly bond electrons

Computer modelling and design of materials [6 credits]

  • ECTS credits 6
  • Semester 3
  • University Gdansk University of Technology
  • Objectives

     

    During this course the metodology of Computer Aided Material Design (CAMD) will be presented. It will be shown how to use the computer to virtually "produce" new materials and investigate their properties. Despite of providing practical skills in materials simulations, the laboratory classes will provide a good opportunity to focus also on the computer science aspects (computer architectures, data operating systems, parallelization, time-sharing, optimisation, etc).

  • Topics

     

    1. Applications of classical simulations with particles
    a. Implementation of basic Molecular Dynamics algorithm
    b. Visualization of molecular systems
    c. Introduction to the LAMMPS program
    d. Dispersion curve of argon dimmer
    e. Specific heat of argon single crystal
    f. Bulk modulus of argon single crystal
    g. Melting temperature of argon single crystal
    h. Analysis of structure of molten metals (Cu, Mn, Al, ...)

    2. Applications of quantum simulations with particles
    a. Choice of molecular structures for quantum calculations, proposition/prediction of possible reactions mechanisms, electronic-structure change during the processes.
    b. Internal and cartesian coordinate systems, constrains.
    c. SCF-based algorithms in quantum calculations, choice of the best methods for open-shell and closed-shell electronic configurations,
    d. Introduction to GAMESS package of programs, operating with GAMESS, its documentation,
    e. Optimization of C2H5OH molecular structure,
    f. Optimization of stationary point's structures of substituted p-xylylene-based diradical dimmers by means of Hartree-Fock methods,
    g. Calculation of energy profiles for reactions of substituted acethylene molecule with diradical p-xylylene dimmers.
    h. Looking for saddle points of all reactions studied, calculations of hessians, vibrational normal modes analysis.
    i. Calculations of relative energies.
    j. Comparison of all results: for each substituent in acethylene structure and for each possible kinetic barriers with appropriate reactions of vinyls with diradical p-xylylenes.
    k. Comparison with possible initiation of polymerization reactions of two acethylene molecules and two p-xylylene molecules.
    l. Graphical represenation of the results: diagrams (gnuplot), electron orbitals (molden), vibrational modes (molden).

Introduction to low dimensional systems and nanotechnology [6 credits]

  • ECTS credits 6
  • Semester 3
  • University Gdansk University of Technology
  • Objectives

     

    During this course basic physics of nanosystems and nanodevices will be presented, together with related technological and applicative aspects; the role and importance of molecular modelling in nanotechnology will be underlined. Particlual stress will be posed on size effects and quantum physics od 0-, 1-, and 2-dimensional systems.

  • Topics

     

    1. Fundamentals of Nanotechnology
    a. Synthesis of nanomaterials: examples of processes top-down and bottom-up;
    b. Imaging nanomaterials;
    c. Examples of nanomaterials;
    d. Selected mechanical and thermal properties of nanomaterials and nanostructured materials;
    e. Selected electronic, optical and magnetic properties of nanomaterials;
    f. Examples of applications of nanomaterials .

    2. Computer modeling of structure and mechanical and thermodynamic properties of nanostructures
    a. Molecular Dynamics simulation of graphehe: setting up a model
    b. Molecular Dynamics calculations of Young's modulus of graphene
    c. Molecular Dynamics calculations of Poisson's ratio of graphene
    d. Molecular Dynamics studies of influence of defects on mechanical properties of graphene

  • Books

     

    Emil Roduner , Nanoscopic Materials. Size-dependent Phenomena, Stuttgart, Germany The Royal Society of Chemistry 2006

Continuum and discrete-contimuum models [6 credits]

  • ECTS credits 6
  • Semester 3
  • University Gdansk University of Technology
  • Objectives

     

    Solid continuum mechanics from many years have a very well developed theory and numerical algorithms and programme packages. These wide fields of modelling will be reviewed in a very concise manner. The course will teach how to simulate elestic and unelastic properties of solids within classial continuum theorz and recent discrete-continuum models. Aspects important for cross-scale simulations (hand-shaking between continuum and molecular approaches) will be underlined. Applications to multi-phase solids (laminates, systems containind nanoparticles, etc), granular solids, multiphase flows with complex geometry will be discussed.

  • Topics

     

    1. Basic continuum theory
    a. Tensors and tensor fields
    b. Analysis of Stress-Strain
    c. Deformation and Strain
    d. Shear Strain
    e. General Elasticity
    f. Waves
    g. Introduction to thermoelasticity
    h. Multi-dimensional theories of thermoelasticity

    2. Plasticity, discrete-continuous models, granular matter, composites, non-newtonian liquids, etc.
    a. Classical continual models of plasticity
    b. Discrete models as generalized solutions of continuum equations
    c. Review of modern discrete-continuous models: three kinds of models
    d. Hybrid discrete-continuous models
    e. Some mathematical results for the theory of elasticity equations
    f. Numerical methods of solving of equations of continual models
    g. Numerical methods of solving of equations of continual models
    h. Newtonian and non-Newtonian fluids
    i. Computer practice in computer solving of equations of discrete-continuum models
    j. Newtonian and non-Newtonian fluids
    k. Granular and multiphase materials, composite materials
    l. Granular and multiphase materials. The case of high-concentrated materials.

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Our partners' addresses

University of L'Aquila, Italy (UAQ)

Department of Information Engineering, Computer Science and Mathematics, via Vetoio (Coppito), 1 – 67100 L’Aquila (Italy)

Autonomous University of Barcelona, Catalonia - Spain (UAB)

Departament de Matemàtiques, Edifici Cc - Campus UAB 08193 Bellaterra – Catalonia

Gdansk University of Technology, Poland (GUT)

Department of Solid State Physics, G. Narutowicza 11/12, 80-952 Gdansk, Poland

University of Hamburg, Germany (UHH)

Department of Mathematics
Bundesstr. 55 20146 Hamburg - Germany

University of Nice - Sophia Antipolis, France (UNS)

Laboratoire J.A.Dieudonné
Parc Valrose, France-06108 NICE Cedex 2

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