GdSI Structure: ABC_hP12_174_cj_fk_aj

Picture of Structure; Click for Big Picture
Prototype : GdSI
AFLOW prototype label : ABC_hP12_174_cj_fk_aj
Strukturbericht designation : None
Pearson symbol : hP12
Space group number : 174
Space group symbol : $P\bar{6}$
AFLOW prototype command : aflow --proto=ABC_hP12_174_cj_fk_aj
--params=
$a$,$c/a$,$x_{4}$,$y_{4}$,$x_{5}$,$y_{5}$,$x_{6}$,$y_{6}$


Hexagonal primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{x}} - \frac{\sqrt3}2 \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac{\sqrt3}2 \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & c \, \mathbf{\hat{z}} \\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & 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{S I} \\ \mathbf{B}_{2} & = & \frac{1}{3} \, \mathbf{a}_{1} + \frac{2}{3} \, \mathbf{a}_{2} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} & \left(1c\right) & \mbox{Gd I} \\ \mathbf{B}_{3} & = & \frac{2}{3} \, \mathbf{a}_{1} + \frac{1}{3} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(1f\right) & \mbox{I I} \\ \mathbf{B}_{4} & = & x_{4} \, \mathbf{a}_{1} + y_{4} \, \mathbf{a}_{2} & = & \frac{1}{2}\left(x_{4}+y_{4}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(-x_{4}+y_{4}\right)a \, \mathbf{\hat{y}} & \left(3j\right) & \mbox{Gd II} \\ \mathbf{B}_{5} & = & -y_{4} \, \mathbf{a}_{1} + \left(x_{4}-y_{4}\right) \, \mathbf{a}_{2} & = & \left(\frac{1}{2}x_{4}-y_{4}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{4}a \, \mathbf{\hat{y}} & \left(3j\right) & \mbox{Gd II} \\ \mathbf{B}_{6} & = & \left(-x_{4}+y_{4}\right) \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2} & = & \left(-x_{4}+\frac{1}{2}y_{4}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}y_{4}a \, \mathbf{\hat{y}} & \left(3j\right) & \mbox{Gd II} \\ \mathbf{B}_{7} & = & x_{5} \, \mathbf{a}_{1} + y_{5} \, \mathbf{a}_{2} & = & \frac{1}{2}\left(x_{5}+y_{5}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(-x_{5}+y_{5}\right)a \, \mathbf{\hat{y}} & \left(3j\right) & \mbox{S II} \\ \mathbf{B}_{8} & = & -y_{5} \, \mathbf{a}_{1} + \left(x_{5}-y_{5}\right) \, \mathbf{a}_{2} & = & \left(\frac{1}{2}x_{5}-y_{5}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{5}a \, \mathbf{\hat{y}} & \left(3j\right) & \mbox{S II} \\ \mathbf{B}_{9} & = & \left(-x_{5}+y_{5}\right) \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2} & = & \left(-x_{5}+\frac{1}{2}y_{5}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}y_{5}a \, \mathbf{\hat{y}} & \left(3j\right) & \mbox{S II} \\ \mathbf{B}_{10} & = & x_{6} \, \mathbf{a}_{1} + y_{6} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{6}+y_{6}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(-x_{6}+y_{6}\right)a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(3k\right) & \mbox{I II} \\ \mathbf{B}_{11} & = & -y_{6} \, \mathbf{a}_{1} + \left(x_{6}-y_{6}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}x_{6}-y_{6}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{6}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(3k\right) & \mbox{I II} \\ \mathbf{B}_{12} & = & \left(-x_{6}+y_{6}\right) \, \mathbf{a}_{1}-x_{6} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \left(-x_{6}+\frac{1}{2}y_{6}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}y_{6}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(3k\right) & \mbox{I II} \\ \end{array} \]

References

  • C. Dagron and F. Thevet, Répartition des types cristallins dans la série des iodosulfures et fluorosulfures des éléments des terres rares et d'yttrium, C. R. Hebd. Séances Acad. Sci. C 268, 1867–1869 (1969).

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=ABC_hP12_174_cj_fk_aj --params=

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