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The same packing density can also be achieved by alternate stackings of the same close-packed planes of spheres, including structures that are aperiodic in the stacking direction. The Kepler conjecture states that this is the highest density that can be achieved by any arrangement of spheres, either regular or irregular.
Here there is a choice between separating the spheres into regions of close-packed equal spheres, or combining the multiple sizes of spheres into a compound or interstitial packing. When many sizes of spheres (or a distribution ) are available, the problem quickly becomes intractable, but some studies of binary hard spheres (two sizes) are ...
The joint locks (or rather becomes close packed) on one side as weight is transferred from one leg to the other, and through the pelvis the body weight is transmitted from the sacrum to the hip bone. The motions of the sacroiliac joint Anterior innominate tilt of both hip bones on the sacrum (where the left and right move as a unit)
A close packed unit cell, both face-centered cubic and hexagonal close packed, can form two different shaped holes. Looking at the three green spheres in the hexagonal packing illustration at the top of the page, they form a triangle-shaped hole. If an atom is arranged on top of this triangular hole it forms a tetrahedral interstitial hole.
Hexagonal close packed (hcp) unit cell. 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.
In each of the three classes of Laves phase, if the two types of atoms were perfect spheres with a size ratio of /, [2] the structure would be topologically tetrahedrally close-packed. [3] At this size ratio, the structure has an overall packing volume density of 0.710. [ 4 ]
For the hexagonal close-packed structure the derivation is similar. Here the unit cell (equivalent to 3 primitive unit cells) is a hexagonal prism containing six atoms (if the particles in the crystal are atoms).
— — Below is a candidate caption for use in Close-packing article, added 16:33, 26 February 2007 (and revised 20:15, 26 February 2007) — — Shown above is what the science of sphere packing calls a closest-packed arrangement. Specifically, this is the cannonball arrangement or cannonball stack.