PrRu4P12 Structure: A12BC4_cP34_195_2j_ab_2e

Picture of Structure; Click for Big Picture
Prototype : PrRu4P12
AFLOW prototype label : A12BC4_cP34_195_2j_ab_2e
Strukturbericht designation : None
Pearson symbol : cP34
Space group number : 195
Space group symbol : $P23$
AFLOW prototype command : aflow --proto=A12BC4_cP34_195_2j_ab_2e
--params=
$a$,$x_{3}$,$x_{4}$,$x_{5}$,$y_{5}$,$z_{5}$,$x_{6}$,$y_{6}$,$z_{6}$


  • While FINDSYM identifies space group #195 for this structure (consistent with the reference), AFLOW–SYM and Platon identify #204. Lowering the tolerance value for AFLOW–SYM resolves space group #200, which is also indicated as a possible space group by the reference (Lee, 2004). Lowering AFLOW–SYM's tolerance further yields the expected space group #194. Space groups #195, #200, and #204 are reasonable classifications since they are commensurate with subgroup relations.

Simple Cubic primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & a \, \mathbf{\hat{x}} \\ \mathbf{a}_2 & = & a \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & a \, \mathbf{\hat{z}} \\ \end{array} \]

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{Pr I} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(1b\right) & \mbox{Pr II} \\ \mathbf{B}_{3} & = & x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + x_{3} \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}} + x_{3}a \, \mathbf{\hat{y}} + x_{3}a \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{Ru I} \\ \mathbf{B}_{4} & = & -x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2} + x_{3} \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}}-x_{3}a \, \mathbf{\hat{y}} + x_{3}a \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{Ru I} \\ \mathbf{B}_{5} & = & -x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2}-x_{3} \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}} + x_{3}a \, \mathbf{\hat{y}}-x_{3}a \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{Ru I} \\ \mathbf{B}_{6} & = & x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2}-x_{3} \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}}-x_{3}a \, \mathbf{\hat{y}}-x_{3}a \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{Ru I} \\ \mathbf{B}_{7} & = & x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}} + x_{4}a \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{Ru II} \\ \mathbf{B}_{8} & = & -x_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}} + x_{4}a \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{Ru II} \\ \mathbf{B}_{9} & = & -x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2}-x_{4} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}}-x_{4}a \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{Ru II} \\ \mathbf{B}_{10} & = & x_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2}-x_{4} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}}-x_{4}a \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{Ru II} \\ \mathbf{B}_{11} & = & x_{5} \, \mathbf{a}_{1} + y_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}} + y_{5}a \, \mathbf{\hat{y}} + z_{5}a \, \mathbf{\hat{z}} & \left(12j\right) & \mbox{P I} \\ \mathbf{B}_{12} & = & -x_{5} \, \mathbf{a}_{1}-y_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}}-y_{5}a \, \mathbf{\hat{y}} + z_{5}a \, \mathbf{\hat{z}} & \left(12j\right) & \mbox{P I} \\ \mathbf{B}_{13} & = & -x_{5} \, \mathbf{a}_{1} + y_{5} \, \mathbf{a}_{2}-z_{5} \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}} + y_{5}a \, \mathbf{\hat{y}}-z_{5}a \, \mathbf{\hat{z}} & \left(12j\right) & \mbox{P I} \\ \mathbf{B}_{14} & = & x_{5} \, \mathbf{a}_{1}-y_{5} \, \mathbf{a}_{2}-z_{5} \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}}-y_{5}a \, \mathbf{\hat{y}}-z_{5}a \, \mathbf{\hat{z}} & \left(12j\right) & \mbox{P I} \\ \mathbf{B}_{15} & = & z_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} + y_{5} \, \mathbf{a}_{3} & = & z_{5}a \, \mathbf{\hat{x}} + x_{5}a \, \mathbf{\hat{y}} + y_{5}a \, \mathbf{\hat{z}} & \left(12j\right) & \mbox{P I} \\ \mathbf{B}_{16} & = & z_{5} \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2}-y_{5} \, \mathbf{a}_{3} & = & z_{5}a \, \mathbf{\hat{x}}-x_{5}a \, \mathbf{\hat{y}}-y_{5}a \, \mathbf{\hat{z}} & \left(12j\right) & \mbox{P I} \\ \mathbf{B}_{17} & = & -z_{5} \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2} + y_{5} \, \mathbf{a}_{3} & = & -z_{5}a \, \mathbf{\hat{x}}-x_{5}a \, \mathbf{\hat{y}} + y_{5}a \, \mathbf{\hat{z}} & \left(12j\right) & \mbox{P I} \\ \mathbf{B}_{18} & = & -z_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2}-y_{5} \, \mathbf{a}_{3} & = & -z_{5}a \, \mathbf{\hat{x}} + x_{5}a \, \mathbf{\hat{y}}-y_{5}a \, \mathbf{\hat{z}} & \left(12j\right) & \mbox{P I} \\ \mathbf{B}_{19} & = & y_{5} \, \mathbf{a}_{1} + z_{5} \, \mathbf{a}_{2} + x_{5} \, \mathbf{a}_{3} & = & y_{5}a \, \mathbf{\hat{x}} + z_{5}a \, \mathbf{\hat{y}} + x_{5}a \, \mathbf{\hat{z}} & \left(12j\right) & \mbox{P I} \\ \mathbf{B}_{20} & = & -y_{5} \, \mathbf{a}_{1} + z_{5} \, \mathbf{a}_{2}-x_{5} \, \mathbf{a}_{3} & = & -y_{5}a \, \mathbf{\hat{x}} + z_{5}a \, \mathbf{\hat{y}}-x_{5}a \, \mathbf{\hat{z}} & \left(12j\right) & \mbox{P I} \\ \mathbf{B}_{21} & = & y_{5} \, \mathbf{a}_{1}-z_{5} \, \mathbf{a}_{2}-x_{5} \, \mathbf{a}_{3} & = & y_{5}a \, \mathbf{\hat{x}}-z_{5}a \, \mathbf{\hat{y}}-x_{5}a \, \mathbf{\hat{z}} & \left(12j\right) & \mbox{P I} \\ \mathbf{B}_{22} & = & -y_{5} \, \mathbf{a}_{1}-z_{5} \, \mathbf{a}_{2} + x_{5} \, \mathbf{a}_{3} & = & -y_{5}a \, \mathbf{\hat{x}}-z_{5}a \, \mathbf{\hat{y}} + x_{5}a \, \mathbf{\hat{z}} & \left(12j\right) & \mbox{P I} \\ \mathbf{B}_{23} & = & x_{6} \, \mathbf{a}_{1} + y_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & x_{6}a \, \mathbf{\hat{x}} + y_{6}a \, \mathbf{\hat{y}} + z_{6}a \, \mathbf{\hat{z}} & \left(12j\right) & \mbox{P II} \\ \mathbf{B}_{24} & = & -x_{6} \, \mathbf{a}_{1}-y_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & -x_{6}a \, \mathbf{\hat{x}}-y_{6}a \, \mathbf{\hat{y}} + z_{6}a \, \mathbf{\hat{z}} & \left(12j\right) & \mbox{P II} \\ \mathbf{B}_{25} & = & -x_{6} \, \mathbf{a}_{1} + y_{6} \, \mathbf{a}_{2}-z_{6} \, \mathbf{a}_{3} & = & -x_{6}a \, \mathbf{\hat{x}} + y_{6}a \, \mathbf{\hat{y}}-z_{6}a \, \mathbf{\hat{z}} & \left(12j\right) & \mbox{P II} \\ \mathbf{B}_{26} & = & x_{6} \, \mathbf{a}_{1}-y_{6} \, \mathbf{a}_{2}-z_{6} \, \mathbf{a}_{3} & = & x_{6}a \, \mathbf{\hat{x}}-y_{6}a \, \mathbf{\hat{y}}-z_{6}a \, \mathbf{\hat{z}} & \left(12j\right) & \mbox{P II} \\ \mathbf{B}_{27} & = & z_{6} \, \mathbf{a}_{1} + x_{6} \, \mathbf{a}_{2} + y_{6} \, \mathbf{a}_{3} & = & z_{6}a \, \mathbf{\hat{x}} + x_{6}a \, \mathbf{\hat{y}} + y_{6}a \, \mathbf{\hat{z}} & \left(12j\right) & \mbox{P II} \\ \mathbf{B}_{28} & = & z_{6} \, \mathbf{a}_{1}-x_{6} \, \mathbf{a}_{2}-y_{6} \, \mathbf{a}_{3} & = & z_{6}a \, \mathbf{\hat{x}}-x_{6}a \, \mathbf{\hat{y}}-y_{6}a \, \mathbf{\hat{z}} & \left(12j\right) & \mbox{P II} \\ \mathbf{B}_{29} & = & -z_{6} \, \mathbf{a}_{1}-x_{6} \, \mathbf{a}_{2} + y_{6} \, \mathbf{a}_{3} & = & -z_{6}a \, \mathbf{\hat{x}}-x_{6}a \, \mathbf{\hat{y}} + y_{6}a \, \mathbf{\hat{z}} & \left(12j\right) & \mbox{P II} \\ \mathbf{B}_{30} & = & -z_{6} \, \mathbf{a}_{1} + x_{6} \, \mathbf{a}_{2}-y_{6} \, \mathbf{a}_{3} & = & -z_{6}a \, \mathbf{\hat{x}} + x_{6}a \, \mathbf{\hat{y}}-y_{6}a \, \mathbf{\hat{z}} & \left(12j\right) & \mbox{P II} \\ \mathbf{B}_{31} & = & y_{6} \, \mathbf{a}_{1} + z_{6} \, \mathbf{a}_{2} + x_{6} \, \mathbf{a}_{3} & = & y_{6}a \, \mathbf{\hat{x}} + z_{6}a \, \mathbf{\hat{y}} + x_{6}a \, \mathbf{\hat{z}} & \left(12j\right) & \mbox{P II} \\ \mathbf{B}_{32} & = & -y_{6} \, \mathbf{a}_{1} + z_{6} \, \mathbf{a}_{2}-x_{6} \, \mathbf{a}_{3} & = & -y_{6}a \, \mathbf{\hat{x}} + z_{6}a \, \mathbf{\hat{y}}-x_{6}a \, \mathbf{\hat{z}} & \left(12j\right) & \mbox{P II} \\ \mathbf{B}_{33} & = & y_{6} \, \mathbf{a}_{1}-z_{6} \, \mathbf{a}_{2}-x_{6} \, \mathbf{a}_{3} & = & y_{6}a \, \mathbf{\hat{x}}-z_{6}a \, \mathbf{\hat{y}}-x_{6}a \, \mathbf{\hat{z}} & \left(12j\right) & \mbox{P II} \\ \mathbf{B}_{34} & = & -y_{6} \, \mathbf{a}_{1}-z_{6} \, \mathbf{a}_{2} + x_{6} \, \mathbf{a}_{3} & = & -y_{6}a \, \mathbf{\hat{x}}-z_{6}a \, \mathbf{\hat{y}} + x_{6}a \, \mathbf{\hat{z}} & \left(12j\right) & \mbox{P II} \\ \end{array} \]

References

  • C. H. Lee, H. Matsuhata, H. Yamaguchi, C. Sekine, K. Kihou, and I. Shirotani, A study of the crystal structure at low temperature in the metal–insulator transition compound PrRu4P12, J. Magn. Magn. Mater. 272–276, 426–427 (2004), doi:10.1016/j.jmmm.2003.12.433.
  • 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).

Geometry files


Prototype Generator

aflow --proto=A12BC4_cP34_195_2j_ab_2e --params=

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