Teaching Crystal Structures with 3-D Surfaces

TCE

The Chemical Educator

ISSN: 1430-4171 (electronic version)

Table of Contents

Abstract Volume 5 Issue 6 (2000) pp 296-305

Teaching Crystal Structures with 3-D Surfaces

A. Mosset,* and M. Jacob

Laboratoire de Cristallographie, CNRS, BP 166, 38042 Grenoble Cedex, France* and Institutionen för Skydd och Material, FOA, 14725 Tumba, Sweden

Published online: 17 November 2000

Abstract. Using mathematics from the method of the exponential scale, crystals inner and outer structures are given. A number of fundamental crystal structures are described as mathematical functions. Plotting the equations gives the classical ball representation of the structures. In the case of intricate structures, the pedagogical interest lies in the possibility of describing the whole structure as the sum of very simple partial structures, each corresponding to a part of the equation. Structures given are primitive cubic packing, primitive hexagonal packing, face-centered-cubic close-packing, hexagonal close-packing, body-centered packing, CsCl, diamond, zinc blende, CaF₂, ReO₃, perovskite, NaCl, Mg₃NF₃, SiO₂, Cu₃Au, NiAs, wurtzite, and graphite.

A crystal-structure dynamics is described. Varying a constant in the equation, it is possible to modify the representation of the structure from small ball-shaped atoms to packing of interconnected polyhedrons and finally to minima-like surfaces. This last description gives a much deeper understanding of the actual structure in term of forces and open spaces. The final, and maybe the main, interest of this concept of surfaces is the possibility of shedding light on the difficult problems of structure–property relationships.

Key Words: In the Classroom; physical chemistry; crystalography

(*) Corresponding author. (E-mail: mosset@labs.polycnrs-gre.fr)

Article in PDF format (693 KB) HTML format