Diamond cubic 1893981 218607898 2008-06-11T11:48:17Z Mgblaber 6940449 Added '-' to space group. Fd-3m to represent bar. [[Image:Diamonds glitter.png|thumb|250px|right|One unit cell of the diamond cubic [[crystal structure]]. [[Bond length]] shown is for [[carbon]].]] [[Image:DiamondPoleFigure111.png|thumb|250px|[[Pole figure]] in [[stereographic projection]] of the diamond lattice showing the 3-fold symmetry along the [[Miller index|[111] direction]].]] The '''diamond cubic''' [[crystal structure]] is a repeating pattern that atoms may adopt as certain [[material]]s solidify. While the first known example was [[diamond]], other elements in group IV also adopt this structure, including [[tin]], the [[semiconductor]]s [[silicon]] and [[germanium]], and silicon/germanium [[alloy]]s in any proportion. Diamond cubic is in the Fd-3m [[space group]], which follows the face-centered [[cubic (crystal system)|cubic]] [[bravais lattice]]. The lattice describes the repeat pattern; for diamond cubic crystals this lattice is "decorated" with a ''motif'' of two [[tetrahedron|tetrahedrally]] bonded atoms in each primitive cell, separated by 1/4 of the width of the unit cell in each dimension. Many [[compound semiconductor]]s such as [[gallium arsenide]], β-[[silicon carbide]] and [[indium antimonide]] adopt the analogous [[zinc blende]] structure, where each atom has nearest neighbors of an unlike element. This structure's space group is F4<span style="text-decoration: overline">3</span>m, but many of its structural properties are quite similar. The [[atomic packing factor]] of the diamond cubic structure is <math>\frac{\sqrt{3} \pi}{16}</math> with eight atoms per unit cell. Mathematically, the points of the diamond cubic structure can be given coordinates as a subset of a three-dimensional [[integer lattice]] by using a cubical unit cell four units across. Atomic placement in unit cell of side length a is given by the following placement vectors. <math>\mathbf{r}_0 = \vec{0}</math> <math>\mathbf{r}_1 = (a/4)(\hat{x} + \hat{y} + \hat{z})</math> <math>\mathbf{r}_2 = (a/4)(2\hat{x} + 2\hat{y})</math> <math>\mathbf{r}_3 = (a/4)(3\hat{x} + 3\hat{y} + \hat{z})</math> <math>\mathbf{r}_4 = (a/4)(2\hat{x} + 2\hat{z})</math> <math>\mathbf{r}_5 = (a/4)(2\hat{y} + 2\hat{z})</math> <math>\mathbf{r}_6 = (a/4)(3\hat{x} + \hat{y} + 3\hat{z})</math> <math>\mathbf{r}_7 = (a/4)(\hat{x} + 3\hat{y} + 3\hat{z})</math> See also [[crystallography]]. ==Manufacturing considerations== [[Image:Diamond structure.png|framed|left|A diamond cubic crystal viewed from a [[Crystallography#Notation|<110>]] direction.]] Since this class of material is important for [[electronics]], it is important to know that they present open, hexagonal ion channels when [[ion implantation]] is carried out from any of the <110> directions (that is, 45 degrees from one of the cube edges). Their open structure also results in a volume reduction upon melting or [[amorphous solid|amorphization]], as is also seen in [[ice]]. They display [[octahedron|octahedral]] [[cleavage (crystal)|cleavage]], which means that they have four planes&mdash;directions following the faces of the octahedron where there are fewer bonds and therefore points of structural weakness&mdash;along which single crystals can easily split, leaving smooth surfaces. Similarly, this lack of bonds can guide chemical [[industrial etching|etching]] of the right chemistry (i.e., [[potassium hydroxide]] solutions for Si) to produce pyramidal structures such as mesas, points, or etch pits, a useful technique for [[MEMS]]. <br clear="all"> ==Video== Animations of this structure are available at [[Wikimedia Commons]]: ;'''GIF:''' [[Media:Diamond animation.gif|Rotating crystal]] [[Media:Diamond stereo animation.gif|Stereo view]] ;'''ogg Theora:''' [[Media:Diamond animation.ogg|Rotating crystal]] [[Media:Diamond stereo animation.ogg|Stereo view]] [[Category:Condensed matter physics]] [[Category:Crystallography]] [[Category:Lattice points]] [[de:Diamantstruktur]] [[fr:Diamant (cristal)]]