- International school on fundamental crystallography
- Scientific Program
- International Program Committee and lecturers
- List of participants
Scientific Program and Time table
Morning session (4 hours):
Lectures 9:00 - 11:00 / 11:30 - 13:30
Coffee break: 11:00 - 11:30
Lunch: 13:30 - 15:00
Afternoon session (4 hours):
Lectures: 15:00 - 17:00 / 17:30 - 19:30
Coffee break: 17:00 - 17:30
Dinner: 20:00 - 21:30
Optional night session: 21:30 - 22:30
Day of arrival: 30 September
Arriving in Sofia and transfer about 1.30h to the northern slopes of Rila Mountain. Accommodation in mountain hotel at 1600m at Guletchitza area.
20:00 Welcome reception.
1st Day (October 1-st): morning session
9:00 - 9:10 Opening of the School (Rosica Nicolova)
9:10 - 11:00 Lectures + Exercises (Mois Aroyo)
1. Matrix calculus applied in crystallography: brief revision
11:30 - 13:30 Lectures + Exercises (Mois Aroyo)
2. Basic properties of groups (group axioms, order, multiplication tables, etc.). Subgroups, index, coset decompositions, Lagrange theorem. Concept of isomorphism and homomorphism. Group actions: conjugation and normalizers.
1st Day: afternoon session
15:00 - 17:00 Lectures + Exercises (Mois Aroyo)
3. Isometries and crystallographic symmetry operations. Crystallographic point and space-group symmetry operations. Matrix-column presentation of symmetry operations. Symmetry elements: geometric elements and element sets. Transformations of the coordinate systems: change of origin and orientation.
17:30 - 19:30 Lectures + Exercises (Massimo Nespolo)
4. Space groups - general introduction: periodic structure of the crystalline matter. 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.
21:30 - 22:30 Optional night session (Mois Aroyo)
Geometric interpretation of the matrix-column presentation of the symmetry operations
2nd Day (October 2-nd):: morning session
9:00 - 11:00 Lectures + Exercises (Massimo Nespolo)
1. 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; Hermann-Mauguin symbols for point groups.
11:30 - 13:30 Lectures + Exercises (Massimo Nespolo)
2. Space groups and their description in International Tables for Crystallography, Vol. A. Classification of space groups: Lattice systems and crystal systems. Hermann-Mauguin symbols for space groups. Space groups with more than one description in International Tables for Crystallography, Vol. A. Synoptic tables of plane and space groups. Generation of space groups.
2nd Day: afternoon session
15:00 - 17:00 Lectures + Exercises (Massimo Nespolo)
3. Orthogonal projections of space groups. Symmetry-elements and generalposition space-group diagrams from Volume A of the International Tables for Crystallography. General and special positions, site-symmetry groups, crystallographic orbits.
17:30 - 19:30 Practical: Symmetry Database of the Online Edition of International Tables for Crystallography (IT) and Bilbao Crystallographic Server (M. I. Aroyo, M. Nespolo, R. Nicolova and B. Shivachev)
4. Computer databases and access tools to crystallographic symmetry data for space groups (International Tables for Crystallography, Volume A: Space-group symmetry): symmetry operations and their matrix-column presentation; geometric interpretation; general and special Wyckoff positions, site symmetry. Conventional and non-conventional descriptions of space groups; ITA-settings
21:30 - 22:30 Optional night session (Massimo Nespolo)
Stereographic projection and morphology of crystals. Types of crystallographic point groups through the stereographic projection
3rd Day (October 3-rd):): morning session:
9:00 - 11:00 Lecture + Exercises (Mois I. Aroyo, Massimo Nespolo)
1. Group-subgroup relations (general considerations): index, coset decomposition and normal subgroups; conjugate elements and conjugate subgroups; factor groups and homomorphism.
11:30 - 13:30 Lecture + Exercises (Mois I. Aroyo, Massimo Nespolo)
2. Group-subgroup relations between space groups: Subgroups of space groups: types of subgroups of space groups; Hermann theorem; maximal subgroups; series of isomorphic subgroups. Coset decomposition. Relations of Wyckoff positions for a group-subgroup pair. Supergroups of space groups.
3rd Day: afternoon session:
15:00 - 17:00 Lecture+Exercises (Massimo Nespolo, Mois I. Aroyo)
3. Normalizers of space groups; Affine and Euclidean normalizers; Wyckoff sets; Euclidean normalizers for specialized metrics. Equivalent crystal structure descriptions.
17:30 - 19:30 Practical: Symmetry Database of the Online Edition of IT and Bilbao Crystallographic Server (M. I. Aroyo, M. Nespolo, R. Nicolova and B. Shivachev)
4. Maximal subgroups data and related computer applications: (i) Introduction and use of the databases of the IT-Online server and the Bilbao Crystallographic server of maximal subgroups, series of isomorphic subgroups and minimal supergroups; (ii) General group-subgroup relations between space groups: computer programs on the IT-Online server and the Bilbao Crystallographic Server.
21:30 Optional night session (Massimo Nespolo)
4th Day (October 4-th):: morning session
9:00 - 11:00 Lectures and exercises (Miroslav Abrashev)
1. Interaction of X-rays with crystalline matter 2. Fourier transforms and convolutions
11:30 - 13:30 Lectures and exercises (Miroslav Abrashev)
3. Crystallographic calculations in reciprocal space
4th Day: afternoon session
15:00 - 17:00 Lectures and exercises (Miroslav Abrashev)
4. Diffraction symmetry: Laue classes, Friedel's law, resonant scattering
5. Integral, zonal and serial reflection conditions and their use to determine the space-group type. Special reflection conditions.
17:30 - 19:30 Lectures and exercises (Miroslav Abrashev)
6. Structure solution and refinement: introductory strategies
21:30 - 22:30 Optional night session (Mois Aroyo, Massimo Nespolo)
Symmetry arguments in the derivation of the general and special reflection conditions listed in International Tables for Crystallography, Vol. A.
5th Day (October 5-th):: morning session:
9:00 - 11:00 Practical: Bilbao Crystallographic Server (M. I. Aroyo, M. Nespolo, R. Nicolova and B. Shivachev)
1. Crystal-structure descriptions I. Basis transformations and crystal-structure descriptions; structure descriptions compatible with symmetry reduction (the program TRANSTRU). 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).
11:30 - 13:30 Practical: Bilbao Crystallographic Server (M. Aroyo, M. Nespolo, R. Nicolova and B. Shivachev)
2. Crystal-structure relations. Group-subgroup relations between space groups and the construction of structure family trees (Baernighausen trees (the program STRUCTURE RELATIONS).
5th Day: afternoon session
15:00-17:00 Practical: Bilbao Crystallographic Server (M. Aroyo, M. Nespolo, R. Nicolova and B. Shivachev)
3. Structural pseudosymmetry. Pseudosymmetry search for new ferroics. Application in structural phase transitions (the program PSEUDO).
17:30 - 19:30 Practical: Bilbao Crystallographic Server (M. Aroyo, M. Nespolo, R. Nicolova and B. Shivachev)
4. Phase transitions with group-subgroup relations between the space groups of the two phases .Inverse Landau problem. Symmetry-mode analysis of displacive phase transitions
20:30 Farewell dinner
Sixth day (October 6-st):
Sixth day (October 6-st):
Travelling back to Sofia
Organised by the Bulgarian Crystallographic Association, the IUCr Commission on Mathematical and Theoretical Crystallography and sponsored by the "International Union of Crystallography" and the European Crystallographic Association