Hypothetical Tetrahedrally Bonded Carbon with 3-Member Rings Model Structure: A_hP6_194_h-001
| Prototype | C |
| AFLOW prototype label | A_hP6_194_h-001 |
| Pearson symbol | hP6 |
| Space group number | 194 |
| Space group symbol | $P6_3/mmc$ |
| AFLOW prototype command |
aflow --proto=A_hP6_194_h-001
--params=$a, \allowbreak c/a, \allowbreak x_{1}$ |
- This structure was proposed in (Schultz, 1999) to show that it was energetically possible to form three-member rings in amorphous sp$^{3}$ carbon structures.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{1}+2 x_{1} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{1} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{1} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6h) | C I |
| $\mathbf{B_{2}}$ | = | $- 2 x_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{1} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{1} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6h) | C I |
| $\mathbf{B_{3}}$ | = | $x_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- \sqrt{3}a x_{1} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6h) | C I |
| $\mathbf{B_{4}}$ | = | $- x_{1} \, \mathbf{a}_{1}- 2 x_{1} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{1} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{1} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6h) | C I |
| $\mathbf{B_{5}}$ | = | $2 x_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{1} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{1} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6h) | C I |
| $\mathbf{B_{6}}$ | = | $- x_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\sqrt{3}a x_{1} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6h) | C I |
References
- P. A. Schultz, K. Leung, and E. B. Stechel, Small rings and amorphous tetrahedral carbon, Phys. Rev. B 59, 733–741 (1999), doi:10.1103/PhysRevB.59.733.
First cited in
- M. J. Mehl, D. Hicks, C. Toher, O. Levy, R. M. Hanson, G. L. W. Hart, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 1, Comp. Mat. Sci. 136, S1-S828 (2017). (doi=10.1016/j.commatsci.2017.01.017)
Geometry files
Prototype Generator
aflow --proto=A_hP6_194_h --params=$a,c/a,x_{1}$