Goal of this project was to design an algorithm to produce a dense random packing of hard spheres with different diameters. This project was made in cooperation with the "Institut für Werkstoffe" at the Technical University of Braunschweig.

A short abstract of our paper:

"The Packing Density of Randomly Packed Spheres and the Structural Stability of Metallic Glasses"
Carsten Möhrmann, Andreas Jung and Erik Woldt
Institut für Werkstoffe, Technische Universität Braunschweig, D-38106 Braunschweig, Germany

In order to check whether the stability of certain amorphous alloy compositions is based on a particular dense arrangement due to an advantageous choice of the size of the atoms involved the packing density of steel balls and spheres in a computer simulation was investigated. While the mixing and heaping of steel balls was straight forward it proved impossible to avoid unmixing effects. Overall the computer simulations gave the same results as the heaping experiments but presented much less scatter and no unmixing due to the chosen strategy. For the ternary mixture investigated the composition was varied in steps of 10% and the maximum packing density was found in the binar mixture of the smallest and largest balls or spheres, respectively. The results of the ternary system were compared to the stability of the alloy system La-Al-Ni with very similar ratios of the diameters of the atoms. No agreement of packing density and stability of the alloy system either in form of crystallization temperature or width of the supercooled region could be found. This is taken as an indication that the chemical character of the elements plays a much more important role for the stability of amorphous alloys than a particular dense packing.

Key words: packing density, randomly packed spheres, bulk amorphous metals


The computer program is called "Atompack" and it is designed to work not only on a single computer, but to use for example a Cray or any other cluster, having a message passing interface (MPI) installed, as a workfarm. The program is able to handle an unlimited number of different hard spheres, which should be packed in 2D or 3D. An extension to more dimensions is no problem.

The program is written in C, so it should be able to be compiled on nearly every platform. If you would like to download it and use it for your computations, please do so. The program is licensed under the GNU General Public License. My E-mail is