VN (Low–temperature) Structure: AB_tP8_111_n_n
| Prototype | : | VN |
| AFLOW prototype label | : | AB_tP8_111_n_n |
| Strukturbericht designation | : | None |
| Pearson symbol | : | tP8 |
| Space group number | : | 111 |
| Space group symbol | : | $P\bar{4}2m$ |
| AFLOW prototype command | : | aflow --proto=AB_tP8_111_n_n --params=$a,c/a,x_{1},z_{1},x_{2},z_{2}$ |
- FINDSYM identifies space group #111 for this structure (consistent with the reference); however, since $c/a \approx 1$, AFLOW–SYM and Platon identify #215. Lowering the tolerance value for AFLOW–SYM resolves the expected space group #111. Space groups #111 and #215 are both reasonable classifications since they are commensurate with subgroup relations.
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:
\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & x_{1} \, \mathbf{a}_{1} + x_{1} \, \mathbf{a}_{2} + z_{1} \, \mathbf{a}_{3} & = & x_{1}a \, \mathbf{\hat{x}} + x_{1}a \, \mathbf{\hat{y}} + z_{1}c \, \mathbf{\hat{z}} & \left(4n\right) & \mbox{N} \\ \mathbf{B}_{2} & = & -x_{1} \, \mathbf{a}_{1}-x_{1} \, \mathbf{a}_{2} + z_{1} \, \mathbf{a}_{3} & = & -x_{1}a \, \mathbf{\hat{x}}-x_{1}a \, \mathbf{\hat{y}} + z_{1}c \, \mathbf{\hat{z}} & \left(4n\right) & \mbox{N} \\ \mathbf{B}_{3} & = & x_{1} \, \mathbf{a}_{1}-x_{1} \, \mathbf{a}_{2}-z_{1} \, \mathbf{a}_{3} & = & x_{1}a \, \mathbf{\hat{x}}-x_{1}a \, \mathbf{\hat{y}}-z_{1}c \, \mathbf{\hat{z}} & \left(4n\right) & \mbox{N} \\ \mathbf{B}_{4} & = & -x_{1} \, \mathbf{a}_{1} + x_{1} \, \mathbf{a}_{2}-z_{1} \, \mathbf{a}_{3} & = & -x_{1}a \, \mathbf{\hat{x}} + x_{1}a \, \mathbf{\hat{y}}-z_{1}c \, \mathbf{\hat{z}} & \left(4n\right) & \mbox{N} \\ \mathbf{B}_{5} & = & x_{2} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3} & = & x_{2}a \, \mathbf{\hat{x}} + x_{2}a \, \mathbf{\hat{y}} + z_{2}c \, \mathbf{\hat{z}} & \left(4n\right) & \mbox{V} \\ \mathbf{B}_{6} & = & -x_{2} \, \mathbf{a}_{1}-x_{2} \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3} & = & -x_{2}a \, \mathbf{\hat{x}}-x_{2}a \, \mathbf{\hat{y}} + z_{2}c \, \mathbf{\hat{z}} & \left(4n\right) & \mbox{V} \\ \mathbf{B}_{7} & = & x_{2} \, \mathbf{a}_{1}-x_{2} \, \mathbf{a}_{2}-z_{2} \, \mathbf{a}_{3} & = & x_{2}a \, \mathbf{\hat{x}}-x_{2}a \, \mathbf{\hat{y}}-z_{2}c \, \mathbf{\hat{z}} & \left(4n\right) & \mbox{V} \\ \mathbf{B}_{8} & = & -x_{2} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2}-z_{2} \, \mathbf{a}_{3} & = & -x_{2}a \, \mathbf{\hat{x}} + x_{2}a \, \mathbf{\hat{y}}-z_{2}c \, \mathbf{\hat{z}} & \left(4n\right) & \mbox{V} \\ \end{array} \]References
- F. Kubel, W. Lengauer, K. Yvon, K. Knorr, and A. Junod, Structural phase transition at 205 K in stoichiometric vanadium nitride, Phys. Rev. B 38, 12908 (1988), doi:10.1103/PhysRevB.38.12908.
- H. T. Stokes and D. M. Hatch, FINDSYM: Program for identifying the space group symmetry of a crystal, J. Appl. Crystallogr. 38, 237–238 (2005), doi:10.1107/S0021889804031528.
- D. Hicks, C. Oses, E. Gossett, G. Gomez, R. H. Taylor, C. Toher, M. J. Mehl, O. Levy, and S. Curtarolo, it AFLOW–SYM: platform for the complete, automatic and self–consistent symmetry analysis of crystals, Acta Crystallogr. Sect. A 74, 184–203 (2018), doi:10.1107/S2053273318003066.
- A. L. Spek, Single–crystal structure validation with the program PLATON, J. Appl. Crystallogr. 36, 7–13 (2003), doi:10.1107/S0021889802022112.
Found in
- P. Villars and K. Cenzual, Pearson's Crystal Data – Crystal Structure Database for Inorganic Compounds, ASM International (2013).