Systematic packing from the standpoint of the primitive cell
By: by Richard McGaw
Contributors: Cold Regions Research and Engineering Laboratory (U.S.)
Series: Research report - Cold Regions Research and Engineering Laboratory -- 201,
Publisher: U.S. Army Materiel Command, Cold Regions Research & Engineering Laboratory
Published: 1967
Place of publication: Hanover, N.H
Language: eng
Number of pages: 23
Subjects: Porosity; Sphere
Description: The systematic packing of uniform spheres is generalized by describing the primitive rhombohedral cell which characterizes the arrangement between layers. Volume and porosity are found to depend on only two angular parameters, alpha and beta: V = 8 R cubed sin alpha sin beta n = 1 - (pi/6 sin alpha sin beta). Beta is the angle between rows in a layer, and alpha is the altitude angle between members of adjacent layers. An azimuth angle gamma determines the position of the plane in which alpha is measured but does not enter into the porosity calculation. Four critical stacking arrangements are described, the porosities of which may be written as functions of the single parameter beta. The stable packings studied by Graton and Fraser (1935) are special cases of the critical positions. Typically unstable packings lie between these positions. Tables and graphs are presented which give the porosity of the primitive cell, as a function of alpha and beta, over the entire range from open to close packing for every possible layer configuration. (Author).
Notes: "DA task 1V014501B52A02."

Includes bibliographical references (p. 22-23).