2022 Spring Festival Beijing Crystallography School

2022 Spring Festival Crystallographic School
and
Workshop on Crystal-field Applications

University of Science and Technology Beijing, China
1-14 February 2022

Lecturers:

Massimo Nespolo (MN) (Université de Lorraine, Faculté des Sciences et Technologies, Vandoeuvre-lès-Nancy cedex France)

Mois I. Aroyo (MIA) (Physics Department, University of the Basque Country, UPV/EHU, Bilbao, Spain)

Leopoldo Suescun (LS) (Universidad de la Republica, Montevideo, Uruguay)

Zhen Song (ZS) (University of Science & Technology Beijing, China)

Timetable:

Session1 (2 hours): Lectures and Exercises 15:00 – 17:00 (Beijing time, BJT)[8:00-10:00, CET; 4:00-6:00,UYT]

Tutorial session (optional): 18:00 – 19:00 (Beijing time, BJT)[11:00-12:00, CET; 7:00-8:00, UYT]

Session2  (2 hours): Lectures and Exercises: 19:00 – 21:00 (Beijing time, BJT)[12:00-14:00, CET; 8:00-10:00, UYT]

Check the program for the newest time. Some courses will be hold at different times.

Program: on-line meetings via ZOOM and Tencent Meeting

Day 1 Feb 1, 2022, Tuesday
Session 1: 15:00-17:00 (MN)
Crystal pattern
Crystal lattice vs. crystal pattern and crystal structure. Symmetry directions in a lattice .Unit cells: primitive cells, multiple cells, conventional cells in 2D and 3D. Crystal families. Symmetry groups and types of symmetry in direct space: morphological symmetry; symmetry of physical properties; symmetry of lattices; symmetry of the unit cell content; symmetry of crystallographic patterns.
Tutorial session (optional) (18:00-19:00)
Session 2: 19:00-21:00 (MN)
Crystallographic point groups
Stereographic projection and the morphology of crystals. Hermann-Mauguin symbols for point groups. Basic properties of groups (group axioms, order, multiplication tables, etc.). Subgroups, index, coset decompositions, Lagrange theorem.


Day 2 Feb 2, 2022, Wednesday
Session 1: 15:00-17:00 (MIA)
Crystallographic point groups (Cont.)
Group actions: conjugation and normalizers. Wyckoff positions for point groups. Relations of Wyckoff positions for a group-subgroup pair. Supergroups of point groups. Overview of crystallographic point groups. Coset decomposition of the space group with respect to its translation subgroup.
Tutorial session (optional) (19:00-19:40)
Session 2: 19:40-21:40 (MN)
Space groups – general introduction:
Periodic structure of the crystalline matter: lattices and their basic properties.


Day 3 Feb 3, 2022, Thursday
Session 1: 15:00-17:00 (MN)
Space groups and their descriptions (cont.):
Structure of space groups: Exercises
Tutorial session (optional) (18:00-19:00)
Session 2: 19:00-21:00 (MN)
Space groups and their descriptions (cont.):
Exercises on orthogonal projections of space groups 1.


Day 4 Feb 4, 2022, Friday
Session 1: 15:00-17:00 (MN)
Space groups and their descriptions (cont.):
Exercises on orthogonal projections of space groups 2.
Tutorial session (optional) (18:00-19:00)
Session 2: 19:00-21:00 (MIA)
Space groups and their descriptions (cont.):
Space groups and their description in International Tables for Crystallography, Vol. A: Matrix-column formalism in the description of space-group symmetry. Isometries and crystallographic symmetry operations. Matrix-column presentation of symmetry operations. Symmetry elements: geometric elements and element sets.


Day 5 Feb 7, 2022, Monday
Session 1: 15:15-17:15 (MIA)
Transformations of the coordinate systems:
Change of origin and orientation. Conventional and non-conventional descriptions of space groups; ITA-settings.
Bilbao Crystallographic Server: Computer databases and access tools to crystallographic symmetry data for space groups
Tutorial session (optional) (18:15-19:00)
Session 2: 19:00-21:00 (MIA)
Subgroups of space groups: types of subgroups of space groups. Maximal subgroups in International Tables for Crystallography, Vol. A1. Hermann theorem. Maximal subgroups; series of isomorphic subgroups. Coset decomposition.


Day 6 Feb 8, 2022, Tuesday
Session 1: 15:00-17:00 (MN)
Group-subgroup relations between space groups (cont.)
Domain-structure analysis in structural phase transitions. Relations of Wyckoff positions for a group-subgroup pair.
Tutorial session (optional) (18:00-19:00)
Session 2: 19:00-21:00 (LS)
Reciprocal space
Crystallographic calculations in reciprocal space. Introduction to diffraction.


Day 7 Feb 9, 2022, Wednesday
Session 1: 15:00-17:00 (LS)
Diffraction symmetry
Laue classes, Friedel’s law, resonant scattering. Integral, zonal and serial reflection conditions and their use to determine the space-group type. Special reflection conditions.
Tutorial session (optional) (18:00-19:00)
Session 2: 19:00-21:00 (MIA)
Group-subgroup relations between space groups (cont.)
Computer databases and access tools to crystallographic symmetry data for space groups. Maximal subgroups data and related computer application in the Bilbao Crystallographic Server.


Day 8 Feb 10, 2022, Thursday
Session 1: 15:15-17:15 (MIA)
Crystal-structure tools of the Bilbao Crystallographic Server
Crystal-structure descriptions. Descriptions of crystal structures with respect to different ITA settings of the space groups (the program SETSTRU). Equivalent crystal structure descriptions (the programs EQUIVSTRU and COMPSTRU). Crystal-structure descriptions compatible with symmetry reduction (the program TRANSTRU).
Hands-on practicals with the computer tools for crystal-structure descriptions
Tutorial session (optional) (18:15-19:00)
Session 2: 19:00-21:00 (LS)
Crystal-structure tools of the Bilbao Crystallographic Server (cont.)
Crystal-structure relationships. Family trees (Baernighausen trees) of crystal structures: aristotype (basic) and hettotypes (derivative) structures).
Hands-on practicals with the program STRUCTURE RELATIONS.


Day 9 Feb 11, 2022, Friday
Session 1: 15:15-17:00 (MIA)
Crystal-structure tools of the Bilbao Crystallographic Server (cont.)
Structural pseudosymmetry. Pseudosymmetry search for new ferroics. Application in structural phase transitions.
Hands-on practicals with the program PSEUDO.
Tutorial session (optional) (18:15-19:00)
Session 2: 19:00-21:00 (MIA)
General remarks on representations
Representations of discrete groups: definition and basic properties. Reducible and irreducible representations. Equivalence of representations. Theorem of orthogonality. Characters of representations and character tables. Subduced and direct-product representations


Day 10 Feb 14, 2022, Monday
Session 1: 15:15-17:15 (MIA)
Representations of point groups
Representations of Abelian groups: cyclic groups and direct products of cyclic groups. Character tables of representations of point groups. Database of Bilbao Crystallographic Server on point-group representations.
Tutorial session (optional) (18:15-19:00)
Session 2: 19:00-21:00 (ZS)
Crystal-field theory
Group theory-based selection rules, energy level splitting on symmetry degradation, crystal-field potentials of point groups.


Registration

ZOOM user
Register via the following link to get the ZOOM link. You will also have the opportunity to ask questions and get help directly from the teachers.
Tencent Meeting user
The course will be broadcasted simultaneously via Tencent Meeting: 447-4154-9220

Tutorial session

The tutorial session will be optional. One or more teachers will answer questions on-line. However, it will be only hold via ZOOM.

Course PDFs and Exercises

Local organizer

Quanlin Liu University of Science and Technology Beijing (USTB)

Zhen Song University of Science and Technology Beijing (USTB)

For any inquires, please refer to zsong%ustb.edu.cn (change % to @).

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