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In another example, iron transforms from a body-centered cubic (bcc) structure called ferrite to a face-centered cubic (fcc) structure called austenite when it is heated. [14] The fcc structure is a close-packed structure unlike the bcc structure; thus the volume of the iron decreases when this transformation occurs.
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 diamond crystal structure belongs to the face-centered cubic lattice, with a repeated two-atom pattern.. In crystallography, a crystal system is a set of point groups (a group of geometric symmetries with at least one fixed point).
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.
At 4.2 K it has a rhombohedral crystal system (with a nine-layer repeat spacing); at higher temperatures it transforms to face-centered cubic and then body-centered cubic. At liquid-helium temperatures (4 K) the rhombohedral structure is prevalent. [19] Multiple allotropic forms have been identified for lithium at high pressures. [20]
This concept was first demonstrated with a body-centered cubic symmetry, where the densest-packed planes were exposed on the surface resulting in a rhombic dodecahedron crystal habit. [38] Other habits such as octrahedra, cubes, or hexagonal prisms have been realized using anisotropic nanoparticles or non-cubic unit cells. [39]
It is dual to the tetroctahedrille or half cubic honeycomb, and it is described by two Coxeter diagrams: and . With D 3d symmetry, it can be seen as an elongated trigonal trapezohedron. It can be seen as the Voronoi tessellation of the face-centered cubic lattice. It is the Brillouin zone of body-centered cubic (bcc) crystals.
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 .