Si$_{24}$ Clathrate Structure: A_oC24_63_3f-001
| Prototype | Si$_{24}$ |
| AFLOW prototype label | A_oC24_63_3f-001 |
| Mineral name | clathrate |
| ICSD | 291479 |
| Pearson symbol | oC24 |
| Space group number | 63 |
| Space group symbol | $Cmcm$ |
| AFLOW prototype command |
aflow --proto=A_oC24_63_3f-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak y_{1}, \allowbreak z_{1}, \allowbreak y_{2}, \allowbreak z_{2}, \allowbreak y_{3}, \allowbreak z_{3}$ |
- Unlike the Si$_{34}$ and Si$_{46}$ clathrates, this is an experimentally determined structure, prepared by removing sodium atoms from an Na$_{4}$Si$_{24}$ predecessor.
- There is no consistency in the naming of these clathrate structures. Si$_{34}$ and Si$_{46}$ were named by their authors based on the size of the primitive unit cell. Here (Kim, 2015) has chosen to name the structure based on the size of the conventional cell. For now, at least, we will follow the authors' naming schemes for these structures.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $- y_{1} \, \mathbf{a}_{1}+y_{1} \, \mathbf{a}_{2}+z_{1} \, \mathbf{a}_{3}$ | = | $b y_{1} \,\mathbf{\hat{y}}+c z_{1} \,\mathbf{\hat{z}}$ | (8f) | Si I |
| $\mathbf{B_{2}}$ | = | $y_{1} \, \mathbf{a}_{1}- y_{1} \, \mathbf{a}_{2}+\left(z_{1} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- b y_{1} \,\mathbf{\hat{y}}+c \left(z_{1} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | Si I |
| $\mathbf{B_{3}}$ | = | $- y_{1} \, \mathbf{a}_{1}+y_{1} \, \mathbf{a}_{2}- \left(z_{1} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $b y_{1} \,\mathbf{\hat{y}}- c \left(z_{1} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | Si I |
| $\mathbf{B_{4}}$ | = | $y_{1} \, \mathbf{a}_{1}- y_{1} \, \mathbf{a}_{2}- z_{1} \, \mathbf{a}_{3}$ | = | $- b y_{1} \,\mathbf{\hat{y}}- c z_{1} \,\mathbf{\hat{z}}$ | (8f) | Si I |
| $\mathbf{B_{5}}$ | = | $- y_{2} \, \mathbf{a}_{1}+y_{2} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $b y_{2} \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (8f) | Si II |
| $\mathbf{B_{6}}$ | = | $y_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}+\left(z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- b y_{2} \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | Si II |
| $\mathbf{B_{7}}$ | = | $- y_{2} \, \mathbf{a}_{1}+y_{2} \, \mathbf{a}_{2}- \left(z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $b y_{2} \,\mathbf{\hat{y}}- c \left(z_{2} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | Si II |
| $\mathbf{B_{8}}$ | = | $y_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}$ | = | $- b y_{2} \,\mathbf{\hat{y}}- c z_{2} \,\mathbf{\hat{z}}$ | (8f) | Si II |
| $\mathbf{B_{9}}$ | = | $- y_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $b y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (8f) | Si III |
| $\mathbf{B_{10}}$ | = | $y_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- b y_{3} \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | Si III |
| $\mathbf{B_{11}}$ | = | $- y_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}- \left(z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $b y_{3} \,\mathbf{\hat{y}}- c \left(z_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | Si III |
| $\mathbf{B_{12}}$ | = | $y_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $- b y_{3} \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (8f) | Si III |
References
- D. Y. Kim, S. Stefanoski, O. O. Kurakevych, and T. A. Strobel, Synthesis of an open-framework allotrope of silicon, Nat. Mater. 14, 169–173 (2015), doi:10.1038/NMAT4140.
Prototype Generator
aflow --proto=A_oC24_63_3f --params=$a,b/a,c/a,y_{1},z_{1},y_{2},z_{2},y_{3},z_{3}$