S-carbon Structure: A_mP8_10_2m2n-001
| Prototype | C |
| AFLOW prototype label | A_mP8_10_2m2n-001 |
| ICSD | None |
| Pearson symbol | mP8 |
| Space group number | 10 |
| Space group symbol | $P2/m$ |
| AFLOW prototype command |
aflow --proto=A_mP8_10_2m2n-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak \beta, \allowbreak x_{1}, \allowbreak z_{1}, \allowbreak x_{2}, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak z_{3}, \allowbreak x_{4}, \allowbreak z_{4}$ |
- This is a predicted
superhard
allotrope of iron. Shortly after this paper was published, two other papers predicted similar structures, differentiated mainly by an origin shift: - F-carbon (Tian 2012): the origin is shifted by $\frac12 \, \mathbf{a_3}$.
- J-carbon (Wang, 2012): the origin is shifted by $\frac12 \left(\mathbf{a_1} + \mathbf{a_3}\right)$.
- This is not the orthorhombic phase found by (He, 2012), which was also called S-carbon.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \cos{\beta} \,\mathbf{\hat{x}}+c \sin{\beta} \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{1}+z_{1} \, \mathbf{a}_{3}$ | = | $\left(a x_{1} + c z_{1} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{1} \sin{\beta} \,\mathbf{\hat{z}}$ | (2m) | C I |
| $\mathbf{B_{2}}$ | = | $- x_{1} \, \mathbf{a}_{1}- z_{1} \, \mathbf{a}_{3}$ | = | $- \left(a x_{1} + c z_{1} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{1} \sin{\beta} \,\mathbf{\hat{z}}$ | (2m) | C I |
| $\mathbf{B_{3}}$ | = | $x_{2} \, \mathbf{a}_{1}+z_{2} \, \mathbf{a}_{3}$ | = | $\left(a x_{2} + c z_{2} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{2} \sin{\beta} \,\mathbf{\hat{z}}$ | (2m) | C II |
| $\mathbf{B_{4}}$ | = | $- x_{2} \, \mathbf{a}_{1}- z_{2} \, \mathbf{a}_{3}$ | = | $- \left(a x_{2} + c z_{2} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{2} \sin{\beta} \,\mathbf{\hat{z}}$ | (2m) | C II |
| $\mathbf{B_{5}}$ | = | $x_{3} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\left(a x_{3} + c z_{3} \cos{\beta}\right) \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}+c z_{3} \sin{\beta} \,\mathbf{\hat{z}}$ | (2n) | C III |
| $\mathbf{B_{6}}$ | = | $- x_{3} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $- \left(a x_{3} + c z_{3} \cos{\beta}\right) \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}- c z_{3} \sin{\beta} \,\mathbf{\hat{z}}$ | (2n) | C III |
| $\mathbf{B_{7}}$ | = | $x_{4} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $\left(a x_{4} + c z_{4} \cos{\beta}\right) \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}+c z_{4} \sin{\beta} \,\mathbf{\hat{z}}$ | (2n) | C IV |
| $\mathbf{B_{8}}$ | = | $- x_{4} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $- \left(a x_{4} + c z_{4} \cos{\beta}\right) \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}- c z_{4} \sin{\beta} \,\mathbf{\hat{z}}$ | (2n) | C IV |
References
- H. Niu, X.-Q. Chen, S. Wang, D. Li, W. L. Mao, and Y. Li, Families of Superhard Crystalline Carbon Allotropes Constructed via Cold Compression of Graphite and Nanotubes, Phys. Rev. Lett. 108, 135501 (2012), doi:10.1103/PhysRevLett.108.135501.
- F. Tian, X. Dong, Z. Zhao, J. He, and H.-T. Wang, Superhard F-carbon predicted by ab initio particle-swarm optimization methodology, J. Phys.: Condens. Matter 24, 165504 (2012), doi:10.1088/0953-8984/24/16/165504.
- J.-T. Wang, C. Chen, and Y. Kawazoe, Phase conversion from graphite toward a simple monoclinic sp$^3$-carbon allotrope, Journal of Chemical Physics 137, 024502 (2012), doi:10.1063/1.4732538.
- C. He, L. Sun, C. Zhang, X. Peng, K. Zhang, and J. Zhong, New superhard carbon phases between graphite and diamond, Solid State Commun. 152, 1560–1563 (2012), doi:10.1016/j.ssc.2012.05.022.
- C. He, L. Z. Sun, and J. Zhong, Prediction of superhard carbon allotropes from the segment combination method, Journal of Superhard Materials 34, 386–399 (2012), doi:10.3103/S1063457612060123.
Prototype Generator
aflow --proto=A_mP8_10_2m2n --params=$a,b/a,c/a,\beta,x_{1},z_{1},x_{2},z_{2},x_{3},z_{3},x_{4},z_{4}$