- 2 Year
- Mathematics for new materials design Pathway
- Gdansk University of Technology Place
- 60 ECTS Credits
- Read here Qualification
Base knowledge on physics, mathematics and chemistry.
Application of quantum methods in cases of solving of electronic-structure change for systems of molecules and crystals, axioms of quantum mechanics and their applications, commonly utilized quantum methods based on wave functions and electron densities: HF, CI, MCSCF, MPn, CC, DFT, basis sets.
1. Frank Jensen, Introduction to Computational Chemistry, Wydawnictwo Wiley, 2007,
2. Yung-Kuo Lim, Problems and Solutions on Quantum Mechanics, Wydawnictwo World Scientific, 2005,
3. C. J. Ballhausen, H. B. Gray, Molecular Orbital Theory, Wydawnictwo W. A. Benjamin Inc. 1964,
Gaining knowledge on fundamentals of nanotechnology and low-dimensional systems and experimental methods
1. Fundamentals of Nanotechnology (M. Gazda)
a. Synthesis of nanomaterials: examples of processes top-down and bottom-up;
b. Imaging nanomaterials: e.g. scanning probe microscopy, electron microscopy;
c. Examples of nanomaterials: e.g. graphene, Ag and Au nanoparticles, quantum dots;
d. Surface and its importance
e. Structure, structural phase transition and morphology of nanomaterials;
f. Selected mechanical and thermal properties of nanomaterials and nanostructured materials;
g. Selected electronic, optical and magnetic properties of nanomaterials;
h. Examples of applications of nanomaterials .
Institute of Physical Chemistry, University of Stuttgart,
Stuttgart, Germany The Royal Society of Chemistry 2006
Basic concepts of classical physics -- force, acceleration, potential. Basic knowledge of calculus (Riemann's
integral, minimisation of a function, partial and total derivatives).
We introduce the basics of physics of materials, with particular attention to the relationships between atomic
structure and macroscopic physical properties. Classical computational particle methods are covered, mainly
the molecular dynamics (MD) approach -- its basic theory (integration of e.o.m.) and practicalities (potentials,
boundary conditions, initialisation, neighbourhood, cut-off radius) followed by a brief tour of more advanced
concepts of MD (rigid molecules, shell model, constrained dynamics, thermostats, barostats, Ewald method).
Section devoted to physics of materials:
Crystalline and glassy materials (short-range, medium-range and long-range order, radial and angular
distribution functions); thermodynamics of phase transitions; glass transition; gels (classification and
applications); quasicrystals; liquid crystals; auxetics.
Basic concepts of crystallography (Bravais lattice, primitive and elementary cell, simple and complex
lattice, Miller indices, etc.); symmetry operations; crystallographic point groups and space groups; models of
amorphous systems (CRN, RCP, random-coil); reciprocal lattice and its properties; conditions
for Bragg’s diffraction and Laue diffraction.
Bonding in crystals (ionic, covalent, metallic, molecular and hydrogen); binding energies (lattice sums,
Madelung energy, the Evjen method and Ewald method); fluctuation-dissipation effects.
Structural defects: point defects (Schottky, Frenkel, substitutions, vacancies, intercalations); line defects
(screw and edge dislocations, Frank network, mechanisms of dislocation generation, relationship with the
strength of materials), planar defects (low-angle boundaries, stacking faults, twinning).
Defects in the electronic structure (plasmons, excitons, polarons, magnons, F-centers).
Lattice vibrations (mono- and diatomic chain, optical and acoustic branches, dispersion relations); normal
vibrations; models of lattice heat capacity (classical, Einstein, Debye); the most significant
Principles of the Drude model, electrical conductivity of metals, magnetoresistive effect and the Hall
The Fermi gas of free electrons, the Fermi-Dirac distribution, Fermi level and chemical potential, degenerate
and non-degenerate gas, density of states, Wiedemann-Franz law.
Thermoemission and cold emission from metal to vacuum; contact voltage.
The model principles of the band theory; Bloch’s theorem; classification of solids on the basis of the band
theory; effective mass and quasi-momentum.
Dependence of electrical conductivity on temperature in semiconductors and metals (due to changes
in the carrier densities and in the relaxation time). Deviations from Ohm’s law (collisional ionisation, Zener
effect, Poole-Frenkel effect, field dependence of relaxation time).
Section devoted to the molecular dynamics method:
Motivation behind computational approaches to nanotechnology, continuum and particle methods, classical
and quantum-based methods, scaling of computational effort.
The molecular dynamics method, its advantages and limitations. Conservation of energy in Newtonian
mechanics. Phase space and trajectories.
Periodic, open and mixed boundary conditions, minimum image convention, quasiinifinity, limitations of
PBCs. Cut-off radius and its consequences. Hockney’s linked cells and Verlet neighbour list.
Initializing an MD simulation (positions, velocities), skew start, equilibration.
Integration of the equations of motion. Verlet, leapfrog and predictor-corrector methods. Sources of error in
integrating the equations of motion.
Visualization in MD, calculating macroscopic quantities (energy, temperature, virial, pressure, specific heat,
RDF, ADF, S(k), MSD, D(T)).
Potential and its relationship with force. General and particular forms of potentials. Selected potentials: LJ,
Born-Mayer, harmonic, Morse, Stillinger-Weber, Sutton-Chen, GAFF, AMOEBA).
Polarizability and shell models (Cochran, Fincham).
Constrained dynamics, formal approach, SHAKE, RATTLE, QSHAKE.
(Optionally): Rigid molecules in MD simulations, Euler angles, rotation matrix, vector transformations,
Coulombic interactions in MD, Ewald method.
NVT and NpT ensembles, primitive thermostats, ESM and CSM thermo- and barostats: Andersen,
Berendsen, Hoover-Evans, Nose-Hoover, Nose-Andersen, Parrinello-Rahman.
(Optionally): Hybrid (QM/MM) methods.
The aim of the course is the answer on the question of ethics influence on the accuracy of the science
investigation procedure and presentation in the public results of the research and measurement results.
The content of the course is the analysis and verification of existing codes of the ethics in the subjects of the
research and development in science. Understanding and analyzing the ethic code in the field of
nanotechnology. The analysis is also the history and evolution of content included within the applicable
codex. In addition, the lecture will be analyzed as current controversial statements and publications in the
field of science and especially nanotechnology.
The Ethics of Nanotechnology, Andrew Chen
The course aims at presentation of modern methods of thinking applied in science and technology
1. INTRODUCTION. Ontological, psychological, semiotic, theory-cognitive terminology. Formal logic.
Philosophy of logic. Methodology vs. science. Science vs. logic.
2. PHENOMENOLOGICAL METHOD. Objectivity of phenomenologists. Return to "issue in itself", intuitive
3. SEMIOTIC METHODS. Sign and its three dimensions. Formalism. Essence of formalism - calculation.
Application of calculation to non-mathematical subjects. Validation of formalism. Eidetic and operational
sense. Models. Artificial language. Syntactic rules of sense. Construction of language. Atomic and molecular
expressions. Notion of syntactic category. Functors and arguments. Examples of syntactic nonsense.
Semantic functions and levels Two semantic functions of sign. Designation and significance. Semantic
levels. Language and meta-language. Semantic meaning and verifiability. Rule of verifiability. Verification
levels: technical possibility, physical possibility, logical possibility, transempirical possibility. Principle of
intersubjectivity. Verifiability of general clauses.
4. AXIOMATIC METHOD. Structure of indirect cognition. Law and rule. Two basic forms of inference:
deduction and reduction. Reliable and unreliable rules of inference. Concept of axiomatic system. Structure
of axiomatic clause system. Requirements for axiomatic system. Constitutional system. Progressive and
regressive deduction. Mathematical logic. Methodological significance. Implication and derivability. Definition
and creation of concepts. Basic types of definition. Real and nominal definitions. Syntactic and semantic
definitions. Analytical and synthetic definitions. Types of syntactic definitions: clear definitions, contextual
definitions, recursive definitions, definitions by axiomatic system. Semantic deictic definitions. Real
definitions. Application of axiomatic method. Axiomatization of logic of Hilbert-Ackermann clauses.
5. REDUCTION METHODS. Historical introductory remarks. Concept and division of reduction. Concept of
verification and explanation. Regressive reduction. Reduction sciences. Structure of natural sciences.
Observation clauses. Progress in natural sciences. Verification of hypotheses. Experience and thinking.
Types of explanatory sentences. Causal explanation and teleological explanation. Co-occurrence laws and
functional laws. Deterministic laws and statistical laws. Authentic and non-authentic induction. Division of
induction. Primary and secondary induction. Qualitative and quantitative induction. Deterministic and
statistical induction. Enumerative and eliminatory induction. Postulates of determinism, closed system,
relationship between laws, simplicity.
J. M. Bocheński, Współczesne metody myślenia, wydawnictwo "Wdrodze", Poznań (1992)
K. Popper, Logika odkrycia naukowego, PWN (1983)
M. Grzegorczyk, Logika matematyczna, PWN (1979)
The topic of the thesis can be proposed to the student by the local InterMaths coordinator or by the student him/herself. In any case, the InterMaths executive committee is the responsible to approve the thesis project before its formal start. The taste and expectations of the students are respected whenever possible. The local InterMaths coordinator in the hosting institution is the responsible to provide an academic advisor to the student, although proposals from the students will always be heard in this respect. In some cases, after the agreement with the local InterMaths coordinator, the thesis topic can be related to a problem proposed by a private company. In this case, a tutor will be designated by the company as responsible person of the work of the student, especially if he/she is eventually working in the facilities of the company; however, the academic advisor is, in any case, the responsible to ensure the progress, adequacy and scientific quality of the thesis. The necessary agreements between the university and the company will be signed in due time, according to the local rules, in order that academic credits could be legally obtained during an internship, and the students be covered by the insurance against accidents outside the university. NOTE: Although the thesis is scheduled for the 4th semester, some preliminary work may be anticipated due to the local rules - such as preliminary local courses in the 3rd semester, ensuring that the student can follow the main courses of the 3rd semester without problems. In this point, the personalised attention to the students has to be intensified, and decisions taken case by case.