PARTICLE PACKING AND PARTICLE SHAPE*

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Abstract
Spherical particles of equal size theoretically may be packed in five different ways, e.g. (1) cubical with a theoretical void space of 47.64%, (2) single‐staggered or cubical‐tetrahedral with a theoretical void space of 39.55%, (3) double‐staggered with a theoretical void space of 30.20%, (4) pyramidal, and (5) tetrahedral; the void spaces in the latter two are identical, 25.95%.Secondary, ternary, quaternary, and quinary spheres each set smaller than its predecessor, may be fitted into the voids in this last type of packing and the voids reduced theoretically to 14.9%.The use of very fine filler in the remaining voids will then reduce the voids theoretically to 3.9%.The use of particles of elliptical shape does not appear to reduce the porosity, but cylindrical‐shaped particles, if properly arranged, would reduce the porosity below that possible with spheres.The practical application of these theoretical methods of packing was studied, and the possibility of crushing ceramic materials to spherical shapes is discussed with particular emphasis on the higher‐priced materials such as fused alumina, mullite (fused, synthetic, and natural), chromite, magnesite, forsterite, silicon carbide, and also silica, owing to the particular rounded character of natural sand grains.Study of experimental work shows the possibility of approaching the theoretical densest packing arrangement by the use of spherical‐shaped grains. Allowance must be made in some instances for the porosity of the grains themselves.Surface areas can be calculated and the bonding mediums proportioned accordingly. Some commercial refractories investigated, which have relatively low porosity, seem to have taken advantage of a careful study of the laws of particle packing, both in the manner of packing of the grog grains and in the shape of the grains themselves.

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