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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.
A network model of a primitive cubic system The primitive and cubic close-packed (also known as face-centered cubic) unit cells. In crystallography, the cubic (or isometric) crystal system is a crystal system where the unit cell is in the shape of a cube. This is one of the most common and simplest shapes found in crystals and minerals.
This type of structural arrangement is known as cubic close packing (ccp). The unit cell of a ccp arrangement of atoms is the face-centered cubic (fcc) unit cell. This is not immediately obvious as the closely packed layers are parallel to the {111} planes of the fcc unit cell. There are four different orientations of the close-packed layers.
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 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 ...
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.
The spinels are any of a class of minerals of general formulation AB 2 X 4 which crystallise in the cubic (isometric) crystal system, with the X anions (typically chalcogens, like oxygen and sulfur) arranged in a cubic close-packed lattice and the cations A and B occupying some or all of the octahedral and tetrahedral sites in the lattice.
If the close packed structures are considered as being built of layers of spheres, then the difference between hexagonal close packing and face-centred cubic is how each layer is positioned relative to others. The following types can be viewed as a regular buildup of close-packed layers: