Nb7Ru6B8 Structure: A8B7C6_hP21_175_ck_aj_k

Picture of Structure; Click for Big Picture
Prototype : Nb7Ru6B8
AFLOW prototype label : A8B7C6_hP21_175_ck_aj_k
Strukturbericht designation : None
Pearson symbol : hP21
Space group number : 175
Space group symbol : $P6/m$
AFLOW prototype command : aflow --proto=A8B7C6_hP21_175_ck_aj_k
--params=
$a$,$c/a$,$x_{3}$,$y_{3}$,$x_{4}$,$y_{4}$,$x_{5}$,$y_{5}$


Hexagonal primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{x}} - \frac{\sqrt3}2 \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac{\sqrt3}2 \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & c \, \mathbf{\hat{z}} \\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & 0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = & 0 \, \mathbf{\hat{x}} + 0 \, \mathbf{\hat{y}} + 0 \, \mathbf{\hat{z}} & \left(1a\right) & \mbox{Nb I} \\ \mathbf{B}_{2} & = & \frac{1}{3} \, \mathbf{a}_{1} + \frac{2}{3} \, \mathbf{a}_{2} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} & \left(2c\right) & \mbox{B I} \\ \mathbf{B}_{3} & = & \frac{2}{3} \, \mathbf{a}_{1} + \frac{1}{3} \, \mathbf{a}_{2} & = & \frac{1}{2}a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} & \left(2c\right) & \mbox{B I} \\ \mathbf{B}_{4} & = & x_{3} \, \mathbf{a}_{1} + y_{3} \, \mathbf{a}_{2} & = & \frac{1}{2}\left(x_{3}+y_{3}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(-x_{3}+y_{3}\right)a \, \mathbf{\hat{y}} & \left(6j\right) & \mbox{Nb II} \\ \mathbf{B}_{5} & = & -y_{3} \, \mathbf{a}_{1} + \left(x_{3}-y_{3}\right) \, \mathbf{a}_{2} & = & \left(\frac{1}{2}x_{3}-y_{3}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{3}a \, \mathbf{\hat{y}} & \left(6j\right) & \mbox{Nb II} \\ \mathbf{B}_{6} & = & \left(-x_{3}+y_{3}\right) \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2} & = & \left(-x_{3}+\frac{1}{2}y_{3}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}y_{3}a \, \mathbf{\hat{y}} & \left(6j\right) & \mbox{Nb II} \\ \mathbf{B}_{7} & = & -x_{3} \, \mathbf{a}_{1}-y_{3} \, \mathbf{a}_{2} & = & -\frac{1}{2}\left(x_{3}+y_{3}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(x_{3}-y_{3}\right)a \, \mathbf{\hat{y}} & \left(6j\right) & \mbox{Nb II} \\ \mathbf{B}_{8} & = & y_{3} \, \mathbf{a}_{1} + \left(-x_{3}+y_{3}\right) \, \mathbf{a}_{2} & = & \left(-\frac{1}{2}x_{3}+y_{3}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{3}a \, \mathbf{\hat{y}} & \left(6j\right) & \mbox{Nb II} \\ \mathbf{B}_{9} & = & \left(x_{3}-y_{3}\right) \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} & = & \left(x_{3}-\frac{1}{2}y_{3}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}y_{3}a \, \mathbf{\hat{y}} & \left(6j\right) & \mbox{Nb II} \\ \mathbf{B}_{10} & = & x_{4} \, \mathbf{a}_{1} + y_{4} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{4}+y_{4}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(-x_{4}+y_{4}\right)a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(6k\right) & \mbox{B II} \\ \mathbf{B}_{11} & = & -y_{4} \, \mathbf{a}_{1} + \left(x_{4}-y_{4}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}x_{4}-y_{4}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{4}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(6k\right) & \mbox{B II} \\ \mathbf{B}_{12} & = & \left(-x_{4}+y_{4}\right) \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \left(-x_{4}+\frac{1}{2}y_{4}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}y_{4}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(6k\right) & \mbox{B II} \\ \mathbf{B}_{13} & = & -x_{4} \, \mathbf{a}_{1}-y_{4} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & -\frac{1}{2}\left(x_{4}+y_{4}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(x_{4}-y_{4}\right)a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(6k\right) & \mbox{B II} \\ \mathbf{B}_{14} & = & y_{4} \, \mathbf{a}_{1} + \left(-x_{4}+y_{4}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \left(-\frac{1}{2}x_{4}+y_{4}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{4}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(6k\right) & \mbox{B II} \\ \mathbf{B}_{15} & = & \left(x_{4}-y_{4}\right) \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \left(x_{4}-\frac{1}{2}y_{4}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}y_{4}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(6k\right) & \mbox{B II} \\ \mathbf{B}_{16} & = & x_{5} \, \mathbf{a}_{1} + y_{5} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{5}+y_{5}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(-x_{5}+y_{5}\right)a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(6k\right) & \mbox{Ru} \\ \mathbf{B}_{17} & = & -y_{5} \, \mathbf{a}_{1} + \left(x_{5}-y_{5}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}x_{5}-y_{5}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{5}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(6k\right) & \mbox{Ru} \\ \mathbf{B}_{18} & = & \left(-x_{5}+y_{5}\right) \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \left(-x_{5}+\frac{1}{2}y_{5}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}y_{5}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(6k\right) & \mbox{Ru} \\ \mathbf{B}_{19} & = & -x_{5} \, \mathbf{a}_{1}-y_{5} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & -\frac{1}{2}\left(x_{5}+y_{5}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(x_{5}-y_{5}\right)a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(6k\right) & \mbox{Ru} \\ \mathbf{B}_{20} & = & y_{5} \, \mathbf{a}_{1} + \left(-x_{5}+y_{5}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \left(-\frac{1}{2}x_{5}+y_{5}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{5}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(6k\right) & \mbox{Ru} \\ \mathbf{B}_{21} & = & \left(x_{5}-y_{5}\right) \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \left(x_{5}-\frac{1}{2}y_{5}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}y_{5}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(6k\right) & \mbox{Ru} \\ \end{array} \]

References

  • Q. Zheng, M. Kohout, R. Gumeniuk, N. Abramchuk, H. Borrmann, Y. Prots, U. Burkhardt, W. Schnelle, L. Akselrud, H. Gu, A. Leithe–Jasper, and Y. Grin, TM7 TM'6B8 (TM = Ta, Nb; TM' = Ru, Rh, Ir): New Compounds with [B6] Ring Polyanions, Inorg. Chem. 51, 7472–7483 (2012), doi:10.1021/ic201978n.

Found in

  • P. Villars and K. Cenzual, Pearson's Crystal Data – Crystal Structure Database for Inorganic Compounds, ASM International (2013).

Geometry files


Prototype Generator

aflow --proto=A8B7C6_hP21_175_ck_aj_k --params=

Species:

Running:

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