Structure of solids

One of the general objectives of the CMI theme is to show how the properties of a material depend on its composition or structure. The Solid State Structure course forms an essential basis for this program, by answering two essential questions about the structure of crystallized materials: how to describe it, and how to determine it.

The teaching objectives of this course, which is closely linked to the Practical Work in Inorganic Chemistry, are as follows:
- Describe a crystalline structure and reconstruct a structure from its description
- Recognize and identify simple structures and the more complex ones derived from them
- Analyze a scientific text dealing with the use of X-ray diffraction in materials science.

- Use crystallographic databases (international crystallography tables, crystal structure resources).

Elements of the crystallography program for the PC preparatory classes: notions of mesh and pattern, compact stacks, simple structural types.

Basic notions of diffraction.

The first part of the course is devoted to describing crystals in terms of symmetry. After a historical introduction to crystallography, the notions of lattice, mesh, mode and pattern are defined, starting with the translational group. The various symmetry operations are detailed, and the principles of point group construction are developed, in relation to crystal systems and Bavais lattices. Finally, space groups are described. Simple crystallographic structures are used as examples, providing an introduction to crystallochemistry. Three descriptions are covered: (i) asymmetric unit and space group, (ii) stacking and occupied sites, (iii) coordination polyhedra. The reciprocal lattice is introduced and applied to simple crystallographic calculations. The crystal is modeled in terms of the convolution of an electron density and a sum of Dirac distributions.
X-ray diffraction is the subject of the second part of the course. After a brief review of diffraction, Laue's equations are obtained from the calculation of the intensity diffracted by a crystal, interpreted in the reciprocal grating and from which Bragg's equation is deduced. Structural factors are calculated to explain systematic extinctions. The diffraction pattern is interpreted in terms of the Fourier transform of the crystal's electron density. Finally, we show how the diffracted intensity can be used to determine atomic positions. The practical use of X-ray diffraction as an analytical tool is then discussed, after a presentation of X-ray production and powder diffractometers.

Inorganic Chemistry and Materials

Bibliography, available from the ENSCBP library:

Chemie inorganique, A. Casalot and J. Durupthy, Hachette: undergraduate level.
Introduction à la cristallographie et à la chimie structurale, M. van Meerssche and J. Feneau-Dupont, Peeters, 1984: more comprehensive.
Fundamentals of crystallography, C. Giacovazzo et al, Oxford University Press, 1992: very complete, rather complex.
To see crystals: musee.ensmp.fr/gm//photos.html (page consulted on 04/07/2011)