PtSn4 ($D1_{c}$) Structure: AB4_oC20_41_a_2b

Picture of Structure; Click for Big Picture
Prototype : PtSn4
AFLOW prototype label : AB4_oC20_41_a_2b
Strukturbericht designation : $D1_{c}$
Pearson symbol : oC20
Space group number : 41
Space group symbol : $\mbox{Aba2}$
AFLOW prototype command : aflow --proto=AB4_oC20_41_a_2b
--params=
$a$,$b/a$,$c/a$,$z_{1}$,$x_{2}$,$y_{2}$,$z_{2}$,$x_{3}$,$y_{3}$,$z_{3}$


Other compounds with this structure

  • AuSn4, IrSn4, PdSn4

  • The published atomic positions have $x_{2} = y_{3}$, $x_{3} = y_{2}$ and $z_{2} = - z_{3}$. This puts the system into space group Ccca. To get space group Aba2 we shifted the $z_{3}$ position slightly.

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

References

  • K. Schubert and U. Rösler, Die Kristallstruktur von PtSn4, Z. Metallkd. 41, 298–300 (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. 5001.

Geometry files


Prototype Generator

aflow --proto=AB4_oC20_41_a_2b --params=

Species:

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