T-Carbon Structure: A_cF32_227_e-001
| Prototype | C |
| AFLOW prototype label | A_cF32_227_e-001 |
| ICSD | 689215 |
| Pearson symbol | cF32 |
| Space group number | 227 |
| Space group symbol | $Fd\overline{3}m$ |
| AFLOW prototype command |
aflow --proto=A_cF32_227_e-001
--params=$a, \allowbreak x_{1}$ |
- This was predicted by (Sheng, 2011) and found experimentally by (Xu, 2020) and others.
- The ICSD entry is from (Kang, 2020), who gave the atomic positions in terms of setting 1 of space group $Fd\overline{3}m$ #227. We used FINDSYM to change this to the standard setting 2.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}+x_{1} \, \mathbf{a}_{3}$ | = | $a x_{1} \,\mathbf{\hat{x}}+a x_{1} \,\mathbf{\hat{y}}+a x_{1} \,\mathbf{\hat{z}}$ | (32e) | C I |
| $\mathbf{B_{2}}$ | = | $x_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}- \left(3 x_{1} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{1} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{1} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a x_{1} \,\mathbf{\hat{z}}$ | (32e) | C I |
| $\mathbf{B_{3}}$ | = | $x_{1} \, \mathbf{a}_{1}- \left(3 x_{1} - \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{1} \, \mathbf{a}_{3}$ | = | $- a \left(x_{1} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a x_{1} \,\mathbf{\hat{y}}- a \left(x_{1} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32e) | C I |
| $\mathbf{B_{4}}$ | = | $- \left(3 x_{1} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}+x_{1} \, \mathbf{a}_{3}$ | = | $a x_{1} \,\mathbf{\hat{x}}- a \left(x_{1} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{1} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32e) | C I |
| $\mathbf{B_{5}}$ | = | $- x_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}+\left(3 x_{1} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{1} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{1} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a x_{1} \,\mathbf{\hat{z}}$ | (32e) | C I |
| $\mathbf{B_{6}}$ | = | $- x_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}- x_{1} \, \mathbf{a}_{3}$ | = | $- a x_{1} \,\mathbf{\hat{x}}- a x_{1} \,\mathbf{\hat{y}}- a x_{1} \,\mathbf{\hat{z}}$ | (32e) | C I |
| $\mathbf{B_{7}}$ | = | $- x_{1} \, \mathbf{a}_{1}+\left(3 x_{1} + \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{1} \, \mathbf{a}_{3}$ | = | $a \left(x_{1} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a x_{1} \,\mathbf{\hat{y}}+a \left(x_{1} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32e) | C I |
| $\mathbf{B_{8}}$ | = | $\left(3 x_{1} + \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}- x_{1} \, \mathbf{a}_{3}$ | = | $- a x_{1} \,\mathbf{\hat{x}}+a \left(x_{1} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{1} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32e) | C I |
References
- X.-L. Sheng, Q.-B. Yan, F. Ye, Q.-R. Zheng, and G. Su, T-Carbon: A Novel Carbon Allotrope, Phys. Rev. Lett. 106, 155703 (2011), doi:10.1103/PhysRevLett.106.155703.
- S. Kang, Z. Xiang, H. Mu, and Y. Cai, Mechanical properties, lattice thermal conductivity, infrared and Raman spectrum of the fullerite C$_{24}$, Phys. Lett. A 384, 126035 (2020), doi:10.1016/j.physleta.2019.126035.
- K. Xu, H. Liu, Y.-C. Shi, J.-Y. You, X.-Y. Ma, H.-J. Cui, Q.-B. Yan, G.-C. Chen, and G. Su, Preparation of T-carbon by plasma enhanced chemical vapor deposition, Carbon 157, 270–276 (2020), doi:10.1016/j.carbon.2019.10.032.
Prototype Generator
aflow --proto=A_cF32_227_e --params=$a,x_{1}$