Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: AB4C_tP12_124_a_m_c

  • 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)
  • D. Hicks, M. J. Mehl, E. Gossett, C. Toher, O. Levy, R. M. Hanson, G. L. W. Hart, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 2, Comp. Mat. Sci. 161, S1-S1011 (2019). (doi=10.1016/j.commatsci.2018.10.043)
  • D. Hicks, M.J. Mehl, M. Esters, C. Oses, O. Levy, G.L.W. Hart, C. Toher, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 3, Comp. Mat. Sci. 199, 110450 (2021). (doi=10.1016/j.commatsci.2021.110450)

Nb4CoSi Structure: AB4C_tP12_124_a_m_c

Picture of Structure; Click for Big Picture
Prototype : Nb4CoSi
AFLOW prototype label : AB4C_tP12_124_a_m_c
Strukturbericht designation : None
Pearson symbol : tP12
Space group number : 124
Space group symbol : $P4/mcc$
AFLOW prototype command : aflow --proto=AB4C_tP12_124_a_m_c
--params=
$a$,$c/a$,$x_{3}$,$y_{3}$


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} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & = & \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}c \, \mathbf{\hat{z}} & \left(2a\right) & \text{Co} \\ \mathbf{B}_{2} & = & \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{3}{4}c \, \mathbf{\hat{z}} & \left(2a\right) & \text{Co} \\ \mathbf{B}_{3} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(2c\right) & \text{Si} \\ \mathbf{B}_{4} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(2c\right) & \text{Si} \\ \mathbf{B}_{5} & = & x_{3} \, \mathbf{a}_{1} + y_{3} \, \mathbf{a}_{2} & = & x_{3}a \, \mathbf{\hat{x}} + y_{3}a \, \mathbf{\hat{y}} & \left(8m\right) & \text{Nb} \\ \mathbf{B}_{6} & = & -x_{3} \, \mathbf{a}_{1}-y_{3} \, \mathbf{a}_{2} & = & -x_{3}a \, \mathbf{\hat{x}}-y_{3}a \, \mathbf{\hat{y}} & \left(8m\right) & \text{Nb} \\ \mathbf{B}_{7} & = & -y_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} & = & -y_{3}a \, \mathbf{\hat{x}} + x_{3}a \, \mathbf{\hat{y}} & \left(8m\right) & \text{Nb} \\ \mathbf{B}_{8} & = & y_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2} & = & y_{3}a \, \mathbf{\hat{x}}-x_{3}a \, \mathbf{\hat{y}} & \left(8m\right) & \text{Nb} \\ \mathbf{B}_{9} & = & -x_{3} \, \mathbf{a}_{1} + y_{3} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}} + y_{3}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(8m\right) & \text{Nb} \\ \mathbf{B}_{10} & = & x_{3} \, \mathbf{a}_{1}-y_{3} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}}-y_{3}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(8m\right) & \text{Nb} \\ \mathbf{B}_{11} & = & y_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & y_{3}a \, \mathbf{\hat{x}} + x_{3}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(8m\right) & \text{Nb} \\ \mathbf{B}_{12} & = & -y_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & -y_{3}a \, \mathbf{\hat{x}}-x_{3}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(8m\right) & \text{Nb} \\ \end{array} \]

References

  • E. I. Gladyshevskii and Y. B. Kuz'ma, The compounds Nb4FeSi, Nb4CoSi, Nb4NiSi and their crystal structures, J. Struct. Chem. 6, 60–63 (1965), doi:10.1007/BF00743870.

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=AB4C_tP12_124_a_m_c --params=

Species:

Running:

Output: