[IUCr Home Page] [Commission Home Page]
next up previous
Next: Thermodynamics and kinetics Up: (IUCr) Crystal Packing Previous: (IUCr) Crystal Packing

Introduction

We all know by everyday experience that matter has many different states of aggregation. Chemists also know that matter is made of atoms, ions and molecules, and that the macroscopic properties of any object depend on the size, shape and energies of these microscopic constituents.

One mole of gaseous substance occupies about 24 litres at room temperature, while the volume of the same amount of substance in the liquid or solid state is a few tens to a few hundred millilitres. It follows that the molecules1 are much, much closer to each other in a liquid and a solid than in a gas. An easy calculation shows that in condensed phases the average volume per molecule is about one and a half times the volume of the molecule itself. Molecules are tightly packed in space, and therefore the compressibility of condensed media is very small. You can sit on a rock simply because its atoms and molecules are so close to each other that they cannot give way under external pressure.

A gas will diffuse very quickly out of an open bottle, while a solid can usually be left in the open air almost indefinitely without apparent change in size and shape (there are exceptions, like mothballs). Besides repelling each other at short distances, molecules in a solid are reluctant to leave their neighbours; this means that some sort of attraction is holding them together. Temperature has a much more dramatic effect on all this than pressure: ordinary liquids boil when heated mildly, and even solid rock melts and vaporizes in volcanic depths.

Through simple reasoning on elementary evidence, we are led to the following conclusions: upon cooling or with increasing pressure, molecules stick together and form liquid and solid bodies, in which the distance between them is of the same order of magnitude as the molecular dimensions; and an increasing repulsion arises if they are forced into closer contact. The reverse occurs upon heating or lowering the external pressure.

While a layman may be more than satisfied at this point, a scientist must ask him- or herself at least two further questions: (1) What is the nature and magnitude of the forces holding molecules together? (2) What is the geometrical arrangement of molecules at close contact? Restricting the scope, as we do in this pamphlet, to crystalline solids, these questions define the subject of crystal packing. Since crystals are endowed with the beautiful gift of order and symmetry, the spatial part (2) is not trivial. Packing forces and crystal symmetry determine the chemical and physical properties of crystalline materials.


next up previous
Next: Thermodynamics and kinetics Up: (IUCr) Crystal Packing Previous: (IUCr) Crystal Packing

Copyright © 2005 International Union of Crystallography

IUCr Webmaster