Akademia Górniczo-Hutnicza logotyp
pl en
en
Symmetries in crystal systems
Course description sheet

Basic information

Field of study
Technical Physics
Major
All
Organisational unit
Faculty of Physics and Applied Computer Science
Study level
Second-cycle (engineer) programme
Form of study
Full-time studies
Profile
General academic
Didactic cycle
2025/2026
Course code
JFTCS.IIi1.12381.25
Lecture languages
Polish
Mandatoriness
Obligatory
Block
Major Modules
Course related to scientific research
Yes
Course coordinator
Radosław Strzałka
Lecturer
Radosław Strzałka
Period
Semester 1
Method of verification of the learning outcomes
Completing the classes
Activities and hours
Lectures: 15
Project classes: 30
Number of ECTS credits
4

Goals

C1 Zapoznanie studenta z podstawowymi symetriami w strukturze atomowej ciał stałych, w szczególności w kryształach periodycznych i aperiodycznych.
C2 Pokazanie związku symetrii (periodyczności) z budową atomową i konsekwencje tego związku dla metod analizy strukturalnej kryształów.
C3 Zapoznanie studenta z powszechnie stosowanymi narzędziami informatycznymi do analizy strukturalnej kryształów; wykorzystanie tych narzędzi do konkretnych zastosowań w krystalografii.

Course's learning outcomes

Code Outcomes in terms of Learning outcomes prescribed to a field of study Methods of verification
Knowledge – Student knows and understands:
W1 the concept of symmetry in the atomic structure and its influence on the atomic structure of crystals FTC2A_W01, FTC2A_W03, FTC2A_W04 Activity during classes, Participation in a discussion
W2 features of the diffraction pattern, methods of its formation, and relationship with the atomic structure of crystals FTC2A_W01, FTC2A_W03, FTC2A_W04 Activity during classes, Participation in a discussion
W3 the idea of structure refinement based on diffraction data, related problems, and examples of methods FTC2A_W01, FTC2A_W03, FTC2A_W04 Activity during classes, Participation in a discussion
W4 what are periodic and aperiodic crystals, what are the differences in atomic structure, diffraction pattern, and crystallographic methods for their description FTC2A_W01, FTC2A_W03, FTC2A_W04 Activity during classes, Participation in a discussion
Skills – Student can:
U1 analyze the image of powder diffraction on the crystal using dedicated and self-developed tools FTC2A_U01, FTC2A_U04 Execution of exercises, Project, Involvement in teamwork
U2 carry out the refinement of simple crystal structures using dedicated tools FTC2A_U01, FTC2A_U04 Execution of exercises, Project, Involvement in teamwork
U3 perform a basic analysis of the diffraction pattern and atomic structure in aperiodic systems FTC2A_U01, FTC2A_U04 Execution of exercises, Project, Involvement in teamwork
Social competences – Student is ready to:
K1 take part in a discussion on a given problem and present the results of their own solutions to the problem in the forum of the group. FTC2A_K01 Participation in a discussion, Involvement in teamwork
K2 collaborate in a small team or a larger group on a given issue, using their knowledge and skills to solve a complex problem FTC2A_K02 Participation in a discussion, Involvement in teamwork

Program content ensuring the achievement of the learning outcomes prescribed to the module

Lectures on theoretical issues and discussing the available methods and tools in the structural analysis of crystals, as well as practical (design) classes aimed at familiarizing yourself with the functionality of these tools and independently applying them in given problems of crystal physics.

Student workload

Activity form Average amount of hours* needed to complete each activity form
Lectures 15
Project classes 30
Preparation of project, presentation, essay, report 30
Preparation for classes 15
Realization of independently performed tasks 30
Student workload
Hours
120
Workload involving teacher
Hours
45

* hour means 45 minutes

Program content

No. Program content Course's learning outcomes Activities
1.

Fundamentals of crystallography (reminder): symmetries, crystal structures, unit cell, structural factor, crystal diffraction, basics of structural analysis

 W1 Lectures
2.

Symmetry in crystals: elements of symmetry; crystal lattices; point groups, space groups, Laue classes; crystallographic systems; multidimensional symmetries

 W1 Lectures
3.

X-ray diffraction on crystals: crystal symmetry and diffraction pattern; structure solution, atomic density map; phase problem

 W2 Lectures
4.

Fundamentals of methods for refining periodic structures: phase recovery; atomic structure model; iterative methods; examples of refinements

 W3 Lectures
5.

Modulated structures: modulation vector, proportional and disproportionate modulation; diffraction pattern; the idea of the multidimensional method (superspace); examples

 W2, W3, W4 Lectures
6.

Quasicrystals: atomic structure and diffraction pattern; quasicrystal families; basic properties and applications; modeling methods; refinement; multivariate method.

 W1, W2, W3, W4 Lectures
7.

The statistical method of describing quasicrystals: the concept of the mean unit cell; disorder modeling; relationship with the multivariate method

 W3, W4 Lectures
8.

  1. Modeling and visualization of the atomic structure (VESTA program)

  2. Diffraction on crystals (powder and single crystals): indicating the diffraction pattern, solving the structure (CrysAlis, FullProf)

  3. Refinement of monocrystalline structures (JANA2006 program)

  4. Phase recovery, atomic density maps (structure solution): direct method, LDE method, charge flipping (Superflip program, lodemac)

  5. Diffraction and structural analysis of quasicrystals: statistical and multivariate method (dedicated programs, QUASI package)

 U1, U2, U3, K1, K2 Project classes

Extended information/Additional elements

Teaching methods and techniques :

Discussion, Group work

Activities Methods of verification Credit conditions
Lectures Activity during classes, Participation in a discussion none
Project classes Activity during classes, Participation in a discussion, Execution of exercises, Project, Involvement in teamwork participation in exercises and implementation of tasks, or project execution

Additional info

The lecture is theoretical and introduces the issues of structural analysis of crystals. As part of the project exercises, the student has the opportunity to apply theoretical knowledge and dedicated and own tools to analyze selected examples of crystal structures in two ways: (1) by participating in classes and performing exercises under the supervision of the tutor, or (2) by completing the project (independently or small teams). The path (1) of the student's participation in the exercises requires the student to use their own computer equipment (laptop). In path (2): project topics will be defined by the teacher at the beginning of the class. Projects can be submitted in the form of a study (essay, report + computer programs, if any), or during the presentation at the last class.

Conditions and the manner of completing each form of classes, including the rules of making retakes, as well as the conditions for admission to the exam

During the classes, the following are assessed:

  • student activity during lectures and exercises (participation in discussions, involvement in work)
  • implementation of tasks during exercises, including independence, the degree of mastery of tools, obtaining results (path (1))
  • project, including the degree of advancement of the topic and correct implementation of the topic, method of presenting the result (path (2))

Method of determining the final grade

Assessment of the implementation of tasks during exercises (path (1)) or assessment for the project (path (2)) will be increased by activity during the lecture or exercises.

Manner and mode of making up for the backlog caused by a student justified absence from classes

Independent work on the issue raised during classes, consultation with the teacher in order to clarify doubts.

Rules of participation in given classes, indicating whether student presence at the lecture is obligatory

  1. Participation in the lecture is optional (in accordance with the AGH Study Regulations)
  2. Participation in the design exercises is:
    • compulsory, if the student chooses the path (1) of carrying out the classes (performing exercises recommended by the teacher on an ongoing basis)
    • optional, if the student chooses the path (2) of the course (project)

Literature

Obligatory
  1. "Fundamentals of Crystallography", C. Giacovazzo, H.L. Monaco, G. Artioli, D. Viterbo, G.Ferraris, G. Gilli, G. Zanotti, M. Catti, z serii IUCr Texts on Crystallography, Oxford University Press 2002 (lub starsze/nowsze)
  2. "Rentgenografia strukturalna monokryształów", P. Luger, PWN Warszawa 1989.
  3. "Crystallography of Quasicrystals. Concepts, Methods and Structures", W. Steurer, S. Deloudi, Springer-Verlag Berlin Heidelberg 2009.
  4. "Quasicrystals. A Primer", C. Janot, z serii Ofxord Science Publications, Oxford Univeristy Press, New York 1992.
Optional
  1. Statistical approach to diffraction of periodic and non-periodic crystals – review / Radosław STRZAŁKA, Ireneusz BUGAŃSKI, Janusz WOLNY // Crystals [Dokument elektroniczny]. — Czasopismo elektroniczne ; ISSN 2073-4352. — 2016 vol. 6 iss. 9, [art. no.] 104, s. [1-19]. — Wymagania systemowe: Adobe Reader. — Tryb dostępu: http://www.mdpi.com/2073-4352/6/9/104/pdf [2016-09-27]. — Bibliogr. s. 17–19, Abstr.. — Publikacja dostępna online od: 2016-08-26
  2. Model refinement of quasicrystals / Janusz WOLNY, Ireneusz BUGAŃSKI, Radosław STRZAŁKA // Crystallography Reviews ; ISSN 0889-311X. — 2018 vol. 24 no. 1, s. 22–64. — Bibliogr. s. 58–64, Abstr.. — tekst: https://www-1tandfonline-1com-15qtywsv0030c.wbg2.bg.agh.edu.pl/doi/pdf/10.1080/0889311X.2017.1340276

Scientific research and publications

Research
  1. "Badania strukturalne kwazikryształów dekagonalnych i ikozaedrycznych - nieporządek atomowy, budowa klastrowa i własności fizyczne." - projekt NCN OPUS 2020-2022, kierownik prof. Janusz Wolny
  2. "Badanie struktury kwazikryształów ikozaedrycznych - analiza dyfrakcyjna i modelowanie" - projekt NCN PRELUDIUM 2015-2017, kierownik dr Radosław Strzałka
  3. "Własności strukturalne i mechaniczne metali - od prostych struktur do złożonych stopów metali na przykładzie kwazikryształów i innych układów międzymetalicznych" - projekt NCN OPUS 2014-2016, kierownik prof. Janusz Wolny
Publications
  1. Model refinement of quasicrystals / Janusz WOLNY, Ireneusz BUGAŃSKI, Radosław STRZAŁKA // Crystallography Reviews ; ISSN 0889-311X. — 2018 vol. 24 no. 1, s. 22–64. — Bibliogr. s. 58–64, Abstr.. — tekst: https://www-1tandfonline-1com-15qtywsv0030c.wbg2.bg.agh.edu.pl/doi/pdf/10.1080/0889311X.2017.1340276
  2. Statistical approach to diffraction of periodic and non-periodic crystals – review / Radosław STRZAŁKA, Ireneusz BUGAŃSKI, Janusz WOLNY // Crystals [Dokument elektroniczny]. — Czasopismo elektroniczne ; ISSN 2073-4352. — 2016 vol. 6 iss. 9, [art. no.] 104, s. [1-19]. — Wymagania systemowe: Adobe Reader. — Tryb dostępu: http://www.mdpi.com/2073-4352/6/9/104/pdf [2016-09-27]. — Bibliogr. s. 17–19, Abstr.. — Publikacja dostępna online od: 2016-08-26
  3. https://bpp.agh.edu.pl/autor/?idA=06874&fodR=0&fdoR=2021&fagTP=4&fagIF=0&fagPM=0&afi=1&vt=c#vtype