Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: AB2_oC24_41_2a_2b

  • 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)

PdSn2 ($C_{e}$) Structure: AB2_oC24_41_2a_2b

Picture of Structure; Click for Big Picture
Prototype : PdSn2
AFLOW prototype label : AB2_oC24_41_2a_2b
Strukturbericht designation : $C_{e}$
Pearson symbol : oC24
Space group number : 41
Space group symbol : $\text{Aba2}$
AFLOW prototype command : aflow --proto=AB2_oC24_41_2a_2b
--params=
$a$,$b/a$,$c/a$,$z_{1}$,$z_{2}$,$x_{3}$,$y_{3}$,$z_{3}$,$x_{4}$,$y_{4}$,$z_{4}$


Other compounds with this structure

  • CoGe2, GaGe3Ni2, RhSn2

Base-centered Orthorhombic primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & =& - z_{1} \, \mathbf{a}_{2} + z_{1} \, \mathbf{a}_{3}& =& z_{1} \, c \, \mathbf{\hat{z}}& \left(4a\right) & \text{Pd I} \\ \mathbf{B}_{2} & =& \frac12 \, \mathbf{a}_{1} + \left(\frac12 - z_{1}\right) \, \mathbf{a}_{2} +\left(\frac12 + z_{1}\right) \, \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, b \, \mathbf{\hat{y}} + z_{1} \, c \, \mathbf{\hat{z}}& \left(4a\right) & \text{Pd I} \\ \mathbf{B}_{3} & =& - z_{2} \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3}& =& z_{2} \, c \, \mathbf{\hat{z}}& \left(4a\right) & \text{Pd II} \\ \mathbf{B}_{4} & =& \frac12 \, \mathbf{a}_{1} + \left(\frac12 - z_{2}\right) \, \mathbf{a}_{2} +\left(\frac12 + z_{2}\right) \, \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, b \, \mathbf{\hat{y}} + z_{2} \, c \, \mathbf{\hat{z}}& \left(4a\right) & \text{Pd II} \\ \mathbf{B}_{5} & =& x_{3} \, \mathbf{a}_{1} + \left(y_{3} - z_{3}\right) \, \mathbf{a}_{2} + \left(y_{3} + z_{3}\right) \, \mathbf{a}_{3}& =& x_{3} \, a \, \mathbf{\hat{x}} + y_{3} \, b \, \mathbf{\hat{y}} + z_{3} \, c \, \mathbf{\hat{z}}& \left(8b\right) & \text{Sn I} \\ \mathbf{B}_{6} & =& - x_{3} \, \mathbf{a}_{1} - \left(y_{3} + z_{3}\right) \, \mathbf{a}_{2} + \left(z_{3} - y_{3}\right) \, \mathbf{a}_{3}& =& - x_{3} \, a \, \mathbf{\hat{x}} - y_{3} \, b \, \mathbf{\hat{y}} + z_{3} \, c \, \mathbf{\hat{z}}& \left(8b\right) & \text{Sn I} \\ \mathbf{B}_{7} & =& \left(\frac12 + x_{3}\right) \, \mathbf{a}_{1} +\left(\frac12 - y_{3} - z_{3}\right) \,\mathbf{a}_{2} + \left(\frac12 - y_{3} + z_{3}\right) \, \mathbf{a}_{3}& =& \left(\frac12 + x_{3}\right) \, a \, \mathbf{\hat{x}} + \left(\frac12 - y_{3}\right) \, b \, \mathbf{\hat{y}} + z_{3} \, c \, \mathbf{\hat{z}}& \left(8b\right) & \text{Sn I} \\ \mathbf{B}_{8} & =& \left(\frac12 - x_{3}\right) \, \mathbf{a}_{1} +\left(\frac12 + y_{3} - z_{3}\right) \,\mathbf{a}_{2} + \left(\frac12 + y_{3} + z_{3}\right) \, \mathbf{a}_{3}& =& \left(\frac12 - x_{3}\right) \, a \, \mathbf{\hat{x}} + \left(\frac12 + y_{3}\right) \, b \, \mathbf{\hat{y}} + z_{3} \, c \, \mathbf{\hat{z}}& \left(8b\right) & \text{Sn I} \\ \mathbf{B}_{9} & =& x_{4} \, \mathbf{a}_{1} + \left(y_{4} - z_{4}\right) \, \mathbf{a}_{2} + \left(y_{4} + z_{4}\right) \, \mathbf{a}_{3}& =& x_{4} \, a \, \mathbf{\hat{x}} + y_{4} \, b \, \mathbf{\hat{y}} + z_{4} \, c \, \mathbf{\hat{z}}& \left(8b\right) & \text{Sn II} \\ \mathbf{B}_{10} & =& - x_{4} \, \mathbf{a}_{1} - \left(y_{4} + z_{4}\right) \, \mathbf{a}_{2} + \left(z_{4} - y_{4}\right) \, \mathbf{a}_{3}& =& - x_{4} \, a \, \mathbf{\hat{x}} - y_{4} \, b \, \mathbf{\hat{y}} + z_{4} \, c \, \mathbf{\hat{z}}& \left(8b\right) & \text{Sn II} \\ \mathbf{B}_{11} & =& \left(\frac12 + x_{4}\right) \, \mathbf{a}_{1} +\left(\frac12 - y_{4} - z_{4}\right) \,\mathbf{a}_{2} + \left(\frac12 - y_{4} + z_{4}\right) \, \mathbf{a}_{3}& =& \left(\frac12 + x_{4}\right) \, a \, \mathbf{\hat{x}} + \left(\frac12 - y_{4}\right) \, b \, \mathbf{\hat{y}} + z_{4} \, c \, \mathbf{\hat{z}}& \left(8b\right) & \text{Sn II} \\ \mathbf{B}_{12} & =& \left(\frac12 - x_{4}\right) \, \mathbf{a}_{1} +\left(\frac12 + y_{4} - z_{4}\right) \,\mathbf{a}_{2} + \left(\frac12 + y_{4} + z_{4}\right) \, \mathbf{a}_{3}& =& \left(\frac12 - x_{4}\right) \, a \, \mathbf{\hat{x}} + \left(\frac12 + y_{4}\right) \, b \, \mathbf{\hat{y}} + z_{4} \, c \, \mathbf{\hat{z}}& \left(8b\right) & \text{Sn II} \\ \end{array} \]

References

  • K. Schubert and H. Pfisterer, Zur Kristallchemie der B–Metall–reichsten Phasen in Legierungen von Übergangsmetallen der Eisen– und Platintriaden mit Elementen der vierten Nebengruppe, Z. Metallkd. 41, 433–441 (1950).

Found in

  • P. Villars and L. Calvert, Pearson's Handbook of Crystallographic Data for Intermetallic Phases (ASM International, Materials Park, OH, 1991), 2nd edn., pp. 4929-4930.

Geometry files


Prototype Generator

aflow --proto=AB2_oC24_41_2a_2b --params=

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