Si$_{34}$ Clathrate Structure: A_cF136_227_aeg-001
| Prototype | Si |
| AFLOW prototype label | A_cF136_227_aeg-001 |
| ICSD | none |
| Pearson symbol | cF136 |
| Space group number | 227 |
| Space group symbol | $Fd\overline{3}m$ |
| AFLOW prototype command |
aflow --proto=A_cF136_227_aeg-001
--params=$a, \allowbreak x_{2}, \allowbreak x_{3}, \allowbreak z_{3}$ |
Other compounds with this structure
Ge (high pressure)
- Silicon clathrates are open structures of pentagonal dodecahedra connected so that all of the silicon atoms have sp3 bonding. In nature these structures are stabilized by alkali impurity atoms.
- This structure and the Si$_{46}$ structure are proposed
pure
silicon clathrate structures. - For more information about these structures and their possible stability, see (Adams, 1994).
- See (Gryko, 2000) for a possible experimental realization of this structure (Si$_{34}$Na$_{x}$, were x is very small).
- We have used the fact that all vectors of the form $(0,\pm a/2,\pm a/2)$, $(\pm a/2,0,\pm a/2)$, and $(\pm a/2,\pm a/2,0)$ are primitive vectors of the face-centered cubic lattice to simplify the positions of some atoms in both lattice and Cartesian coordinates.
- (Dong, 1999) study a similar, but not identical structure (ICSD 56271), and (Schwarz, 2008) find a similar high-pressure phase of germanium (ICSD 245948).
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{8} \, \mathbf{a}_{1}+\frac{1}{8} \, \mathbf{a}_{2}+\frac{1}{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (8a) | Si I |
| $\mathbf{B_{2}}$ | = | $\frac{7}{8} \, \mathbf{a}_{1}+\frac{7}{8} \, \mathbf{a}_{2}+\frac{7}{8} \, \mathbf{a}_{3}$ | = | $\frac{7}{8}a \,\mathbf{\hat{x}}+\frac{7}{8}a \,\mathbf{\hat{y}}+\frac{7}{8}a \,\mathbf{\hat{z}}$ | (8a) | Si I |
| $\mathbf{B_{3}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (32e) | Si II |
| $\mathbf{B_{4}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}- \left(3 x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (32e) | Si II |
| $\mathbf{B_{5}}$ | = | $x_{2} \, \mathbf{a}_{1}- \left(3 x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32e) | Si II |
| $\mathbf{B_{6}}$ | = | $- \left(3 x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32e) | Si II |
| $\mathbf{B_{7}}$ | = | $- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+\left(3 x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (32e) | Si II |
| $\mathbf{B_{8}}$ | = | $- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (32e) | Si II |
| $\mathbf{B_{9}}$ | = | $- x_{2} \, \mathbf{a}_{1}+\left(3 x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}+a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32e) | Si II |
| $\mathbf{B_{10}}$ | = | $\left(3 x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32e) | Si II |
| $\mathbf{B_{11}}$ | = | $z_{3} \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{2}+\left(2 x_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+a z_{3} \,\mathbf{\hat{z}}$ | (96g) | Si III |
| $\mathbf{B_{12}}$ | = | $z_{3} \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{2}- \left(2 x_{3} + z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a z_{3} \,\mathbf{\hat{z}}$ | (96g) | Si III |
| $\mathbf{B_{13}}$ | = | $\left(2 x_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(2 x_{3} + z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}- a \left(z_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | Si III |
| $\mathbf{B_{14}}$ | = | $- \left(2 x_{3} + z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(2 x_{3} - z_{3}\right) \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | Si III |
| $\mathbf{B_{15}}$ | = | $\left(2 x_{3} - z_{3}\right) \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $a z_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (96g) | Si III |
| $\mathbf{B_{16}}$ | = | $- \left(2 x_{3} + z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $a z_{3} \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | Si III |
| $\mathbf{B_{17}}$ | = | $z_{3} \, \mathbf{a}_{1}+\left(2 x_{3} - z_{3}\right) \, \mathbf{a}_{2}- \left(2 x_{3} + z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (96g) | Si III |
| $\mathbf{B_{18}}$ | = | $z_{3} \, \mathbf{a}_{1}- \left(2 x_{3} + z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(2 x_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | Si III |
| $\mathbf{B_{19}}$ | = | $z_{3} \, \mathbf{a}_{1}+\left(2 x_{3} - z_{3}\right) \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a z_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (96g) | Si III |
| $\mathbf{B_{20}}$ | = | $z_{3} \, \mathbf{a}_{1}- \left(2 x_{3} + z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a z_{3} \,\mathbf{\hat{y}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | Si III |
| $\mathbf{B_{21}}$ | = | $- \left(2 x_{3} + z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{2}+\left(2 x_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}- a \left(z_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | Si III |
| $\mathbf{B_{22}}$ | = | $\left(2 x_{3} - z_{3}\right) \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{2}- \left(2 x_{3} + z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (96g) | Si III |
| $\mathbf{B_{23}}$ | = | $- z_{3} \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{2}+\left(2 x_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a z_{3} \,\mathbf{\hat{z}}$ | (96g) | Si III |
| $\mathbf{B_{24}}$ | = | $- z_{3} \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{2}- \left(2 x_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}- a z_{3} \,\mathbf{\hat{z}}$ | (96g) | Si III |
| $\mathbf{B_{25}}$ | = | $- \left(2 x_{3} - z_{3}\right) \, \mathbf{a}_{1}+\left(2 x_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+a \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | Si III |
| $\mathbf{B_{26}}$ | = | $\left(2 x_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(2 x_{3} - z_{3}\right) \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | Si III |
| $\mathbf{B_{27}}$ | = | $- \left(2 x_{3} - z_{3}\right) \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{2}+\left(2 x_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (96g) | Si III |
| $\mathbf{B_{28}}$ | = | $\left(2 x_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{2}- \left(2 x_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+a \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | Si III |
| $\mathbf{B_{29}}$ | = | $- z_{3} \, \mathbf{a}_{1}- \left(2 x_{3} - z_{3}\right) \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a z_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (96g) | Si III |
| $\mathbf{B_{30}}$ | = | $- z_{3} \, \mathbf{a}_{1}+\left(2 x_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a z_{3} \,\mathbf{\hat{y}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | Si III |
| $\mathbf{B_{31}}$ | = | $- z_{3} \, \mathbf{a}_{1}- \left(2 x_{3} - z_{3}\right) \, \mathbf{a}_{2}+\left(2 x_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (96g) | Si III |
| $\mathbf{B_{32}}$ | = | $- z_{3} \, \mathbf{a}_{1}+\left(2 x_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(2 x_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | Si III |
| $\mathbf{B_{33}}$ | = | $\left(2 x_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $- a z_{3} \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | Si III |
| $\mathbf{B_{34}}$ | = | $- \left(2 x_{3} - z_{3}\right) \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $- a z_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (96g) | Si III |
References
- G. B. Adams, M. O'Keeffe, A. A. Demkov, O. F. Sankey, and Y.-M. Huang, Wide-band-gap Si in open fourfold-coordinated clathrate structures, Phys. Rev. B 49, 8048–8053 (1994), doi:10.1103/PhysRevB.49.8048.
- J. Gryko, P. F. McMillan, R. F. Marzke, G. K. Ramachandran, D. Patton, S. K. Deb, and O. F. Sankey, Low-density framework form of crystalline silicon with a wide optical band gap, Phys. Rev. B 62, R7707–7710 (2000), doi:10.1103/PhysRevB.62.R7707.
- J. Dong, O. F. Sankey, and G. Kern, Theoretical study of the vibrational modes and their pressure dependence in the pure clathrate-II silicon framework, Phys. Rev. B 60, 950–958 (1999), doi:10.1103/PhysRevB.60.950.
- U. Schwarz, A. Wosylus, B. Böhme, M. Baitinger, M. Hanfland, and Y. Grin, A 3D Network of Four-Bonded Germanium: A Link between Open and Dense, Angew. Chem. Int. Ed. 47, 6790–6793 (2008), doi:10.1002/anie.200800914.
Prototype Generator
aflow --proto=A_cF136_227_aeg --params=$a,x_{2},x_{3},z_{3}$