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The optimal packing density or packing constant associated with a supply collection is the supremum of upper densities obtained by packings that are subcollections of the supply collection. If the supply collection consists of convex bodies of bounded diameter, there exists a packing whose packing density is equal to the packing constant, and ...
The atomic packing factor of a unit cell is relevant to the study of materials science, where it explains many properties of materials. For example, metals with a high atomic packing factor will have a higher "workability" (malleability or ductility ), similar to how a road is smoother when the stones are closer together, allowing metal atoms ...
The strictly jammed (mechanically stable even as a finite system) regular sphere packing with the lowest known density is a diluted ("tunneled") fcc crystal with a density of only π √ 2 /9 ≈ 0.49365. [6] The loosest known regular jammed packing has a density of approximately 0.0555. [7]
The packing constant of a geometric body is the largest average density achieved by packing arrangements of congruent copies of the body. For most bodies the value of the packing constant is unknown. [1] The following is a list of bodies in Euclidean spaces whose packing constant is known. [1]
A compact binary circle packing with the most similarly sized circles possible. [7] It is also the densest possible packing of discs with this size ratio (ratio of 0.6375559772 with packing fraction (area density) of 0.910683). [8] There are also a range of problems which permit the sizes of the circles to be non-uniform.
Hexagonal close packed (hcp) is one of the two simple types of atomic packing with the highest density, the other being the face-centered cubic (fcc). However, unlike the fcc, it is not a Bravais lattice, as there are two nonequivalent sets of lattice points.
At this size ratio, the structure has an overall packing volume density of 0.710. [4] Compounds found in Laves phases typically have an atomic size ratio between 1.05 and 1.67. [3] Analogues of Laves phases can be formed by the self-assembly of a colloidal dispersion of two sizes of sphere. [2]
The density of quartz is around 2.65 g/cm 3 but the (dry) bulk density of a mineral soil is normally about half that density, between 1.0 and 1.6 g/cm 3. In contrast, soils rich in soil organic carbon and some friable clays tend to have lower bulk densities ( <1.0 g/cm 3 ) due to a combination of the low-density of the organic materials ...