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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.
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.
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]
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.
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.
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).
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 .
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.