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The primitive unit cell for the body-centered cubic crystal structure contains several fractions taken from nine atoms (if the particles in the crystal are atoms): one on each corner of the cube and one atom in the center. Because the volume of each of the eight corner atoms is shared between eight adjacent cells, each BCC cell contains the ...
This structure is often confused for a body-centered cubic structure because the arrangement of atoms is the same. However, the caesium chloride structure has a basis composed of two different atomic species. In a body-centered cubic structure, there would be translational symmetry along the [111] direction.
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.
Kepler's conjecture, which postulated that the densest packings of congruent spheres in 3-dimensional space have packing density (fraction of space covered by the spheres) = pi / sqrt 18 = 74.048% was proved by variants of the face-centered cubic (FCC) lattice packing. [6]
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.
BCC is body centered cubic and FCC is face-centered cubic. Iron-carbon eutectic phase diagram, showing various forms of Fe x C y substances. Iron allotropes, showing the differences in structure. The alpha iron (α-Fe) is a body-centered cubic (BCC) and the gamma iron (γ-Fe) is a face-centered cubic (FCC).
A primitive cell is a unit cell that contains exactly one lattice point. For unit cells generally, lattice points that are shared by n cells are counted as 1 / n of the lattice points contained in each of those cells; so for example a primitive unit cell in three dimensions which has lattice points only at its eight vertices is considered to contain 1 / 8 of each of them. [3]
α-Aluminium has a regular cubic close packed structure, fcc, where each aluminium atom has 12 nearest neighbors, 6 in the same plane and 3 above and below and the coordination polyhedron is a cuboctahedron. α-Iron has a body centered cubic structure where each iron atom has 8 nearest neighbors situated at the corners of a cube.