Ullmanite (NiSSb, $F0_{1}$) Structure: ABC_cP12_198_a_a_a

Picture of Structure; Click for Big Picture
Prototype : NiSSb
AFLOW prototype label : ABC_cP12_198_a_a_a
Strukturbericht designation : $F0_{1}$
Pearson symbol : cP12
Space group number : 198
Space group symbol : $\mbox{P2}_{1}\mbox{3}$
AFLOW prototype command : aflow --proto=ABC_cP12_198_a_a_a
--params=
$a$,$x_{1}$,$x_{2}$,$x_{3}$


Other compounds with this structure

  • CoAsS (Cobaltite), (Co,Ni)SbS, AsBaPt, AsPdS, BiIrS, BiRhSe, CaPtSi, CrPtSb, EuPtSi, IrLaSi, IrSbSe, many others

  • (Ewald, 1928) originally designated CoAsS as Strukturbericht $F1$. This was later changed to $F0_{1}$. We follow (Parthé, 1993) in using NiSbS as the prototype for this structure.

Simple Cubic primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = &x_{1} \, \mathbf{a}_{1}+ x_{1} \, \mathbf{a}_{2}+ x_{1} \, \mathbf{a}_{3}& = &x_{1} \, a \, \mathbf{\hat{x}}+ x_{1} \, a \, \mathbf{\hat{y}}+ x_{1} \, a \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Ni} \\ \mathbf{B}_{2} & = &\left(\frac12 - x_{1}\right) \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}+ \left(\frac12 + x_{1}\right) \, \mathbf{a}_{3}& = &\left(\frac12 - x_{1}\right) \, a \, \mathbf{\hat{x}}- x_{1} \, a \, \mathbf{\hat{y}}+ \left(\frac12 + x_{1}\right) \, a \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Ni} \\ \mathbf{B}_{3} & = &- x_{1} \, \mathbf{a}_{1}+ \left(\frac12 + x_{1}\right) \, \mathbf{a}_{2}+ \left(\frac12 - x_{1}\right) \, \mathbf{a}_{3}& = &- x_{1} \, a \, \mathbf{\hat{x}}+ \left(\frac12 + x_{1}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac12 - x_{1}\right) \, a \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Ni} \\ \mathbf{B}_{4} & = &+ \left(\frac12 + x_{1}\right) \, \mathbf{a}_{1}+ \left(\frac12 - x_{1}\right) \, \mathbf{a}_{2}- x_{1} \, \mathbf{a}_{3}& = &+ \left(\frac12 + x_{1}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 - x_{1}\right) \, a \, \mathbf{\hat{y}}- x_{1} \, a \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Ni} \\ \mathbf{B}_{5} & = &x_{2} \, \mathbf{a}_{1}+ x_{2} \, \mathbf{a}_{2}+ x_{2} \, \mathbf{a}_{3}& = &x_{2} \, a \, \mathbf{\hat{x}}+ x_{2} \, a \, \mathbf{\hat{y}}+ x_{2} \, a \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{S} \\ \mathbf{B}_{6} & = &\left(\frac12 - x_{2}\right) \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+ \left(\frac12 + x_{2}\right) \, \mathbf{a}_{3}& = &\left(\frac12 - x_{2}\right) \, a \, \mathbf{\hat{x}}- x_{2} \, a \, \mathbf{\hat{y}}+ \left(\frac12 + x_{2}\right) \, a \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{S} \\ \mathbf{B}_{7} & = &- x_{2} \, \mathbf{a}_{1}+ \left(\frac12 + x_{2}\right) \, \mathbf{a}_{2}+ \left(\frac12 - x_{2}\right) \, \mathbf{a}_{3}& = &- x_{2} \, a \, \mathbf{\hat{x}}+ \left(\frac12 + x_{2}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac12 - x_{2}\right) \, a \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{S} \\ \mathbf{B}_{8} & = &+ \left(\frac12 + x_{2}\right) \, \mathbf{a}_{1}+ \left(\frac12 - x_{2}\right) \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}& = &+ \left(\frac12 + x_{2}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 - x_{2}\right) \, a \, \mathbf{\hat{y}}- x_{2} \, a \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{S} \\ \mathbf{B}_{9} & = &x_{3} \, \mathbf{a}_{1}+ x_{3} \, \mathbf{a}_{2}+ x_{3} \, \mathbf{a}_{3}& = &x_{3} \, a \, \mathbf{\hat{x}}+ x_{3} \, a \, \mathbf{\hat{y}}+ x_{3} \, a \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Sb} \\ \mathbf{B}_{10} & = &\left(\frac12 - x_{3}\right) \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+ \left(\frac12 + x_{3}\right) \, \mathbf{a}_{3}& = &\left(\frac12 - x_{3}\right) \, a \, \mathbf{\hat{x}}- x_{3} \, a \, \mathbf{\hat{y}}+ \left(\frac12 + x_{3}\right) \, a \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Sb} \\ \mathbf{B}_{11} & = &- x_{3} \, \mathbf{a}_{1}+ \left(\frac12 + x_{3}\right) \, \mathbf{a}_{2}+ \left(\frac12 - x_{3}\right) \, \mathbf{a}_{3}& = &- x_{3} \, a \, \mathbf{\hat{x}}+ \left(\frac12 + x_{3}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac12 - x_{3}\right) \, a \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Sb} \\ \mathbf{B}_{12} & = &+ \left(\frac12 + x_{3}\right) \, \mathbf{a}_{1}+ \left(\frac12 - x_{3}\right) \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}& = &+ \left(\frac12 + x_{3}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 - x_{3}\right) \, a \, \mathbf{\hat{y}}- x_{3} \, a \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Sb} \\ \end{array} \]

References

  • P. P. Ewald and C. Hermann, Strukturbericht 1913-1928 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1931).
  • E. Parthé, L. Gelato, B. Chabot, M. Penso, K. Cenzula, and R. Gladyshevskii, Gmelin Handbook of Inorganic and Organometallic Chemistry: Standardized Data and Crystal Chemical Characterization of Inorganic Structure Types (Springer-Verlag, Berlin, Heidelberg, 1993), 8th edn., doi:10.1007/978-3-662-02909-1_3.

Geometry files


Prototype Generator

aflow --proto=ABC_cP12_198_a_a_a --params=

Species:

Running:

Output: