Radial Distribution Functions from Small Packings of Spheres

Abstract

SCOTT¹ has derived a radial distribution function from a packing of about 1,000 spheres by measuring the Cartesian co-ordinates of each sphere and calculating the individual distribution functions of each of a group of 25 spheres known to be in the centre of the packing. These 25 separate distribution functions were averaged to give the final result. Clearly the edge of the packing interferes and limits both the maximum radial distance to which the distribution function can be determined and the number of centres that can be found sufficiently far from this edge. An improvement would be to use all the spheres in the packing as centres and to correct the distribution function obtained for the effect of the edge. A maximum separation equal to the diameter of the packing would be obtainable together with better statistics in the histogram. Alternatively, results similar to those of Scott¹ could be obtained from packings of half the linear size containing only about 125 spheres.