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—directions following the faces of the octahedron where there are fewer bonds and therefore points of structural weakness—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]].
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==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]]
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