File:Self organization 01.jpg

Snow Crystal. In the beginning of quantum mechanics and statistical physics it was believed that a crystalline structure can be calculated by determining the minimum of the free energy. This may be true, e.g. for ionic crystals, such as sodium chloride, or metals. In this case, the Schrödinger equation for the ground state or possibly low lying states must be solved. In general, this requires the solution of a many particle problem. As the example of snow crystals shows, this picture is too narrow. It is not only necessary to calculate binding forces, but rather the whole kinetics, e.g. of dendritic growth. Besides kinetics, also symmetry, may play a decisive role, e.g. the hexagonal symmetry of the snowflake is caused by the symmetry of H2O which acts as a nucleation center. This example shows that in the formation of crystals, such as the snowflake, kinetic processes and the problem of binding forces are strongly interwoven with each other.