C (T12 Group IV) Structure: A_tP12_138_bi
| Prototype | : | C |
| AFLOW prototype label | : | A_tP12_138_bi |
| Strukturbericht designation | : | None |
| Pearson symbol | : | tP12 |
| Space group number | : | 138 |
| Space group symbol | : | $P4_{2}/ncm$ |
| AFLOW prototype command | : | aflow --proto=A_tP12_138_bi --params=$a,c/a,x_{2},z_{2}$ |
Other elements with this structure
- Si, Ge
- This is a tetragonal allotrope of the diamond structure found computationally in C, Si, and Ge. The authors state
the T12 polymorph naturally accounts for the experimental $d$ spacings and Raman spectra of synthesized metastable Ge and Si–XIII phases with long-puzzling unknown structures, respectively
.
Simple Tetragonal primitive vectors:
\[
\begin{array}{ccc}
\mathbf{a}_1 & = & a \, \mathbf{\hat{x}} \\
\mathbf{a}_2 & = & a \, \mathbf{\hat{y}} \\
\mathbf{a}_3 & = & c \, \mathbf{\hat{z}} \\
\end{array}
\]
Basis vectors:
\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{C I} \\ \mathbf{B}_{2} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{3}{4}a \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{C I} \\ \mathbf{B}_{3} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{3}{4}a \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{C I} \\ \mathbf{B}_{4} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{C I} \\ \mathbf{B}_{5} & = & x_{2} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3} & = & x_{2}a \, \mathbf{\hat{x}} + x_{2}a \, \mathbf{\hat{y}} + z_{2}c \, \mathbf{\hat{z}} & \left(8i\right) & \mbox{C II} \\ \mathbf{B}_{6} & = & \left(\frac{1}{2} - x_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{2}\right) \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - x_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - x_{2}\right)a \, \mathbf{\hat{y}} + z_{2}c \, \mathbf{\hat{z}} & \left(8i\right) & \mbox{C II} \\ \mathbf{B}_{7} & = & \left(\frac{1}{2} - x_{2}\right) \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - x_{2}\right)a \, \mathbf{\hat{x}} + x_{2}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{2}\right)c \, \mathbf{\hat{z}} & \left(8i\right) & \mbox{C II} \\ \mathbf{B}_{8} & = & x_{2} \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{2}\right) \, \mathbf{a}_{3} & = & x_{2}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - x_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{2}\right)c \, \mathbf{\hat{z}} & \left(8i\right) & \mbox{C II} \\ \mathbf{B}_{9} & = & -x_{2} \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{2}\right) \, \mathbf{a}_{3} & = & -x_{2}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{2}\right)c \, \mathbf{\hat{z}} & \left(8i\right) & \mbox{C II} \\ \mathbf{B}_{10} & = & \left(\frac{1}{2} +x_{2}\right) \, \mathbf{a}_{1}-x_{2} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{2}\right)a \, \mathbf{\hat{x}}-x_{2}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{2}\right)c \, \mathbf{\hat{z}} & \left(8i\right) & \mbox{C II} \\ \mathbf{B}_{11} & = & \left(\frac{1}{2} +x_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{2}\right) \, \mathbf{a}_{2}-z_{2} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{2}\right)a \, \mathbf{\hat{y}}-z_{2}c \, \mathbf{\hat{z}} & \left(8i\right) & \mbox{C II} \\ \mathbf{B}_{12} & = & -x_{2} \, \mathbf{a}_{1}-x_{2} \, \mathbf{a}_{2}-z_{2} \, \mathbf{a}_{3} & = & -x_{2}a \, \mathbf{\hat{x}}-x_{2}a \, \mathbf{\hat{y}}-z_{2}c \, \mathbf{\hat{z}} & \left(8i\right) & \mbox{C II} \\ \end{array} \]References
- Z. Zhao, F. Tian, X. Dong, Q. Li, Q. Wang, H. Wang, X. Zhong, B. Xu, D. Yu, J. He, H.–T. Wang, Y. Ma, and Y. Tian, Tetragonal Allotrope of Group 14 Elements, J. Am. Chem. Soc. 134, 12362–12365 (2012), doi:10.1021/ja304380p.