Introduction to matrix algebra: operations with matrices, determinants, inversion and eigenvalues of a matrix; linear transformations, rotations; scalar and vector product. Fundamental group theory: group axioms, generators, subgroups; group decomposition, direct product of groups; irreducible representations, character tables; examples of symmetry groups. Crystallographic groups: point groups, plane groups, space groups; examples of the common groups and symmetry operations. Matrix representation of crystallographic transformations: coordinate transformations; keeping the right-handed coordinate system in transformations; conventions for standard and non-standard settings for space groups. Symmetry and physical properties of crystals: tensors of the second rank; elastic properties of crystals, piezoelectricity; group theory in connection with physical properties of crystals; Brillouin's zones, wave vectors, thermal properties of crystals. Thermal vibrations of crystals: vibrations of crystal lattice; molecular vibrations, normal modes of vibration; atomic thermal parameters; representation of anisotropic vibrations as thermal ellipsoids (ORTEP plots); symmetry constrains on thermal parameters. T,L,S matrices; correction of bond lengths due to thermal motion; Hirshfeld's model.
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- OBVEZNA LITERATURA:
C. Giacovazzo ed., Fundamentals of Crystallography, Oxford University Press, 1992.
Edward Prince, Mathematical Techniques in Crystallography and Material Science, Springer-Verlag, 1982.
Ivan Bernal, Walter C. Hamilton, John S. Ricci, Symmetry-A Stereoscopic Guide for Chemists, W.H. Freeman & Company, San Francisco, 1972.
B.T.M. Willis, A.W. Pryor, Thermal Virations in Crystallography, Cambridge University Press, 1975.
Theo Hahn, Hans Wondratschek, Symmetry of Crystals - Introduction to International Tables for Crystallography Vol. A, Heron Press Ltd. Sofia, Bulgaria, 1994.
W.A. Wooster, Tensors snd group theory for the physical properties of crystals, Clarendon Press, Oxford, 1973.
International Tables for Crystallography, Volume A, Edited by Theo Hahn, D. Reidel Publishing Company, Dordrecht, Holland, 1983.
Hirshfeld, F.L. Can X-ray data distinguish bonding effects from vibrational smearing? Acta Crystallographica, A32, 1976, 239-244.
F. H. Herbstein and R. E. Marsh, More Space-Group Corrections: From Triclinic to Centred Monoclinic and to Rhombohedral; Also From P1 to P-1 and From Cc to C2/c, Acta Cryst. (1998). B54, 677-686.
- DOPUNSKA LITERATURA:
revijalni članci i znanstvene monografije
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