SiU3 ($D0_{c}$) Structure: AB3_tI16_140_b_ah

Picture of Structure; Click for Big Picture
Prototype : SiU3
AFLOW prototype label : AB3_tI16_140_b_ah
Strukturbericht designation : $D0_{c}$
Pearson symbol : tI16
Space group number : 140
Space group symbol : $\mbox{I4/mcm}$
AFLOW prototype command : aflow --proto=AB3_tI16_140_b_ah
--params=
$a$,$c/a$,$x_{3}$


Other compounds with this structure

  • AlPt_3, GaPt_3, Pt_3Si, GePt_3, Ir_3Si

  • When $c = \sqrt2 a$ and $x_{3} = 1/4$ the atoms are at the positions of the Cu3Au (L12) structure. Many references define both a D0c and a D0'$_{3}$ (Ir3Si) structure. The primary difference seems to be positioning the Si atoms on the (2a) or (2b) sites. Since this is merely an origin shift we will ignore the D0'$_{3}$ structure.

Body-centered Tetragonal primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & =& \frac14 \, \mathbf{a}_{1} + \frac14 \, \mathbf{a}_{2}& =& \frac14 \, c \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{U I} \\ \mathbf{B}_{2} & =& \frac34 \, \mathbf{a}_{1} + \frac34 \, \mathbf{a}_{2}& =& \frac34 \, c \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{U I} \\ \mathbf{B}_{3} & =&\frac34 \, \mathbf{a}_{1} + \frac14 \, \mathbf{a}_{2}+ \frac12 \mathbf{a}_{3}& =&\frac12 \, a \, \mathbf{\hat{y}}+ \frac14 \, c \, \mathbf{\hat{z}}& \left(4b\right) & \mbox{Si} \\ \mathbf{B}_{4} & =&\frac14 \, \mathbf{a}_{1} + \frac34 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& =&\frac12 \, a \, \mathbf{\hat{x}}+ \frac14 \, c \, \mathbf{\hat{z}}& \left(4b\right) & \mbox{Si} \\ \mathbf{B}_{5} & =& \left(\frac12 + x_{3}\right) \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + \left(\frac12 + 2 x_{3}\right) \, \mathbf{a}_{3}& =& x_{3} \, a \, \mathbf{\hat{x}} + \left(\frac12 + x_{3}\right) \, a \, \mathbf{\hat{y}}& \left(8h\right) & \mbox{U II} \\ \mathbf{B}_{6} & =& \left(\frac12 - x_{3}\right) \, \mathbf{a}_{1} - x_{3} \, \mathbf{a}_{2} + \left(\frac12 - 2 x_{3}\right) \, \mathbf{a}_{3}& =& - x_{3} \, a \, \mathbf{\hat{x}} + \left(\frac12 - x_{3}\right) \, a \, \mathbf{\hat{y}}& \left(8h\right) & \mbox{U II} \\ \mathbf{B}_{7} & =& x_{3} \, \mathbf{a}_{1} + \left(\frac12 - x_{3}\right) \, \mathbf{a}_{2} + \frac12 \, \mathbf{a}_{3}& =& \left(\frac12 - x_{3}\right) \, a \, \mathbf{\hat{x}} + x_{3} \, a \, \mathbf{\hat{y}}& \left(8h\right) & \mbox{U II} \\ \mathbf{B}_{8} & =& - x_{3} \, \mathbf{a}_{1} + \left(\frac12 + x_{3}\right) \, \mathbf{a}_{2} + \frac12 \, \mathbf{a}_{3}& =& \left(\frac12 + x_{3}\right) \, a \, \mathbf{\hat{x}} - x_{3} \, a \, \mathbf{\hat{y}}& \left(8h\right) & \mbox{U II} \\ \end{array} \]

References

  • W. H. Zachariasen, Crystal chemical studies of the 5f–series of elements. VIII. Crystal structure studies of uranium silicides and of CeSi2, NpSi2, and PuSi2, Acta Cryst. 2, 94–99 (1949), doi:10.1107/S0365110X49000217.

Geometry files


Prototype Generator

aflow --proto=AB3_tI16_140_b_ah --params=

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