- International school on fundamental crystallography
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Scientific Program and Time table
Organised by the Bulgarian Crystallographic Association, the Institute of Mineralogy and Crystallography “Acad. Ivan Kostov" and the IUCr Commission on Mathematical and Theoretical Crystallography
International school on fundamental crystallography:
Introduction to International Tables for
Crystallography,
Vol. A: Space-group symmetry and
Vol. A1Symmetry relations
between space groups,
Gulechitza, Bulgaria, 30 September - 5 October 2013
Timetable
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
Scientific Program
Day of arrival:
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)
Non-characteristic orbits
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
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
