Effect of Container Walls on Packing Density of Particles

Abstract

IN recent correspondence¹ in Nature a general theorem on the ordered packing of equal spheres is cited as implying that “the overall voidage of any one of the four possible ordered arrangements of equal spheres packed into a container is independent of the relative size of the container provided its size and shape are such that it will contain an integral number of 'unit' cells of the particular ordered arrangement and in all other cases an ordered packing cannot be obtained”. This is due to a misconception of the 'unit' cell, which in the first three out of the four ordered packings, namely, a sphere having 12, 10, 8 or 6 neighbours, really contains fractions of a sphere totalling to one, and it is only in the fourth case that the unit cell, being a simple cube, contains a whole sphere.