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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.
The Wigner–Seitz cell of the face-centered cubic lattice is a rhombic dodecahedron. [9] In mathematics, it is known as the rhombic dodecahedral honeycomb . The Wigner–Seitz cell of the body-centered tetragonal lattice that has lattice constants with c / a > 2 {\displaystyle c/a>{\sqrt {2}}} is the elongated dodecahedron .
(This is the unique body-centered cubic packing of edge-length spheres of the tesseractic honeycomb.) Just outside this shell of kissing 3-spheres of diameter 1 is another less dense shell of 24 non-kissing 3-spheres of diameter 1; they are centered in the adjacent 24-cells with which the central 24-cell shares an octahedral facet.
For face-centered cubic (fcc) and body-centered cubic (bcc) lattices, the primitive lattice vectors are not orthogonal. However, in these cases the Miller indices are conventionally defined relative to the lattice vectors of the cubic supercell and hence are again simply the Cartesian directions.
This model for disorder in a crystal starts with the structure factor of a perfect crystal. In one-dimension for simplicity and with N planes, we then start with the expression above for a perfect finite lattice, and then this disorder only changes S ( q ) {\displaystyle S(q)} by a multiplicative factor, to give [ 1 ]
I body centered (from the German Innenzentriert) F face centered (from the German Flächenzentriert) A centered on A faces only; B centered on B faces only; C centered on C faces only; R rhombohedral; A reflection plane m within the point groups can be replaced by a glide plane, labeled as a, b, or c depending on which axis the glide is along.
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 ...
The reciprocal lattice to an FCC lattice is the body-centered cubic (BCC) lattice, with a cube side of . Consider an FCC compound unit cell. Locate a primitive unit cell of the FCC; i.e., a unit cell with one lattice point. Now take one of the vertices of the primitive unit cell as the origin.