Senarmontite (Sb2O3, $D6_{1}$) Structure : A3B2_cF80_227_f_e

Picture of Structure; Click for Big Picture
Prototype : O3Sb2
AFLOW prototype label : A3B2_cF80_227_f_e
Strukturbericht designation : $D6_{1}$
Pearson symbol : cF80
Space group number : 227
Space group symbol : $Fd\bar{3}m$
AFLOW prototype command : aflow --proto=A3B2_cF80_227_f_e
--params=
$a$,$x_{1}$,$x_{2}$


Other compounds with this structure

  • As2O3 (arsenolite)

  • (Ewald, 1931) designated this as Strukturbericht $D6_{1}$, however (Parthé, 1993) and (Villars, 1991) label this as Strukturbericht $D5_{4}$, and Parthé uses As2O3 as the prototype. While this structure obviously fits better with the $D5$ series ($A2B3) than $D6$ ($A2B4), the $D5_{4}$ structure was (inadvertently?) omitted from (Hermann, 1937), which jumps from $D5_{3}$ to $D5_{5}$. We will follow this historical record (Ewald, 1931) here.
  • This is the cubic form of Sb2O3. For the orthorhombic form see the valentinite ($D5_{11}$) structure.
  • (Svensson, 1975) gave the atomic coordinates in setting 1 of space group $Fd\overline{3}m$ #227. We used FINDSYM to shift the coordinates to the standard setting 2.

Face-centered Cubic primitive vectors:

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

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(32e\right) & \mbox{Sb} \\ \mathbf{B}_{2} & = & x_{1} \, \mathbf{a}_{1} + x_{1} \, \mathbf{a}_{2} + \left(\frac{1}{2} - 3x_{1}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{1}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{1}\right)a \, \mathbf{\hat{y}} + x_{1}a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{Sb} \\ \mathbf{B}_{3} & = & x_{1} \, \mathbf{a}_{1} + \left(\frac{1}{2} - 3x_{1}\right) \, \mathbf{a}_{2} + x_{1} \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{1}\right)a \, \mathbf{\hat{x}} + x_{1}a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{1}\right)a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{Sb} \\ \mathbf{B}_{4} & = & \left(\frac{1}{2} - 3x_{1}\right) \, \mathbf{a}_{1} + x_{1} \, \mathbf{a}_{2} + x_{1} \, \mathbf{a}_{3} & = & x_{1}a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{1}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{1}\right)a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{Sb} \\ \mathbf{B}_{5} & = & -x_{1} \, \mathbf{a}_{1}-x_{1} \, \mathbf{a}_{2} + \left(\frac{1}{2} +3x_{1}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{1}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{1}\right)a \, \mathbf{\hat{y}}-x_{1}a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{Sb} \\ \mathbf{B}_{6} & = & -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(32e\right) & \mbox{Sb} \\ \mathbf{B}_{7} & = & -x_{1} \, \mathbf{a}_{1} + \left(\frac{1}{2} +3x_{1}\right) \, \mathbf{a}_{2}-x_{1} \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{1}\right)a \, \mathbf{\hat{x}}-x_{1}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{1}\right)a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{Sb} \\ \mathbf{B}_{8} & = & \left(\frac{1}{2} +3x_{1}\right) \, \mathbf{a}_{1}-x_{1} \, \mathbf{a}_{2}-x_{1} \, \mathbf{a}_{3} & = & -x_{1}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{1}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{1}\right)a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{Sb} \\ \mathbf{B}_{9} & = & \left(\frac{1}{4} - x_{2}\right) \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} + x_{2} \, \mathbf{a}_{3} & = & x_{2}a \, \mathbf{\hat{x}} + \frac{1}{8}a \, \mathbf{\hat{y}} + \frac{1}{8}a \, \mathbf{\hat{z}} & \left(48f\right) & \mbox{O} \\ \mathbf{B}_{10} & = & x_{2} \, \mathbf{a}_{1} + \left(\frac{1}{4} - x_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} - x_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{2}\right)a \, \mathbf{\hat{x}} + \frac{1}{8}a \, \mathbf{\hat{y}} + \frac{1}{8}a \, \mathbf{\hat{z}} & \left(48f\right) & \mbox{O} \\ \mathbf{B}_{11} & = & x_{2} \, \mathbf{a}_{1} + \left(\frac{1}{4} - x_{2}\right) \, \mathbf{a}_{2} + x_{2} \, \mathbf{a}_{3} & = & \frac{1}{8}a \, \mathbf{\hat{x}} + x_{2}a \, \mathbf{\hat{y}} + \frac{1}{8}a \, \mathbf{\hat{z}} & \left(48f\right) & \mbox{O} \\ \mathbf{B}_{12} & = & \left(\frac{1}{4} - x_{2}\right) \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} + \left(\frac{1}{4} - x_{2}\right) \, \mathbf{a}_{3} & = & \frac{1}{8}a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{2}\right)a \, \mathbf{\hat{y}} + \frac{1}{8}a \, \mathbf{\hat{z}} & \left(48f\right) & \mbox{O} \\ \mathbf{B}_{13} & = & x_{2} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} + \left(\frac{1}{4} - x_{2}\right) \, \mathbf{a}_{3} & = & \frac{1}{8}a \, \mathbf{\hat{x}} + \frac{1}{8}a \, \mathbf{\hat{y}} + x_{2}a \, \mathbf{\hat{z}} & \left(48f\right) & \mbox{O} \\ \mathbf{B}_{14} & = & \left(\frac{1}{4} - x_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} - x_{2}\right) \, \mathbf{a}_{2} + x_{2} \, \mathbf{a}_{3} & = & \frac{1}{8}a \, \mathbf{\hat{x}} + \frac{1}{8}a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{2}\right)a \, \mathbf{\hat{z}} & \left(48f\right) & \mbox{O} \\ \mathbf{B}_{15} & = & \left(\frac{3}{4} +x_{2}\right) \, \mathbf{a}_{1}-x_{2} \, \mathbf{a}_{2} + \left(\frac{3}{4} +x_{2}\right) \, \mathbf{a}_{3} & = & \frac{3}{8}a \, \mathbf{\hat{x}} + \left(\frac{3}{4} +x_{2}\right)a \, \mathbf{\hat{y}} + \frac{3}{8}a \, \mathbf{\hat{z}} & \left(48f\right) & \mbox{O} \\ \mathbf{B}_{16} & = & -x_{2} \, \mathbf{a}_{1} + \left(\frac{3}{4} +x_{2}\right) \, \mathbf{a}_{2}-x_{2} \, \mathbf{a}_{3} & = & \frac{3}{8}a \, \mathbf{\hat{x}}-x_{2}a \, \mathbf{\hat{y}} + \frac{3}{8}a \, \mathbf{\hat{z}} & \left(48f\right) & \mbox{O} \\ \mathbf{B}_{17} & = & -x_{2} \, \mathbf{a}_{1} + \left(\frac{3}{4} +x_{2}\right) \, \mathbf{a}_{2} + \left(\frac{3}{4} +x_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{3}{4} +x_{2}\right)a \, \mathbf{\hat{x}} + \frac{3}{8}a \, \mathbf{\hat{y}} + \frac{3}{8}a \, \mathbf{\hat{z}} & \left(48f\right) & \mbox{O} \\ \mathbf{B}_{18} & = & \left(\frac{3}{4} +x_{2}\right) \, \mathbf{a}_{1}-x_{2} \, \mathbf{a}_{2}-x_{2} \, \mathbf{a}_{3} & = & -x_{2}a \, \mathbf{\hat{x}} + \frac{3}{8}a \, \mathbf{\hat{y}} + \frac{3}{8}a \, \mathbf{\hat{z}} & \left(48f\right) & \mbox{O} \\ \mathbf{B}_{19} & = & -x_{2} \, \mathbf{a}_{1}-x_{2} \, \mathbf{a}_{2} + \left(\frac{3}{4} +x_{2}\right) \, \mathbf{a}_{3} & = & \frac{3}{8}a \, \mathbf{\hat{x}} + \frac{3}{8}a \, \mathbf{\hat{y}}-x_{2}a \, \mathbf{\hat{z}} & \left(48f\right) & \mbox{O} \\ \mathbf{B}_{20} & = & \left(\frac{3}{4} +x_{2}\right) \, \mathbf{a}_{1} + \left(\frac{3}{4} +x_{2}\right) \, \mathbf{a}_{2}-x_{2} \, \mathbf{a}_{3} & = & \frac{3}{8}a \, \mathbf{\hat{x}} + \frac{3}{8}a \, \mathbf{\hat{y}} + \left(\frac{3}{4} +x_{2}\right)a \, \mathbf{\hat{z}} & \left(48f\right) & \mbox{O} \\ \end{array} \]

References

  • C. Svensson, Refinement of the crystal structure of cubic antimony trioxide, Sb2O3, Acta Crystallogr. Sect. B Struct. Sci. 31, 2016–2018 (1975), doi:10.1107/S0567740875006759.
  • P. P. Ewald and C. Hermann, eds., Strukturbericht 1913–1928 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1931).
  • E. Parthé, L. Gelato, B. Chabot, M. Penso, K. Cenzual, and R. Gladyshevskii, in Standardized Data and Crystal Chemical Characterization of Inorganic Structure Types (Springer–Verlag, Berlin, Heidelberg, 1993), Gmelin Handbook of Inorganic and Organometallic Chemistry, vol. 2, chap. Crystal Chemical Characterization of Inorganic Structure Types, 8 edn., doi:10.1007/978-3-662-02909-1_3.
  • P. Villars and L. Calvert, Pearson's Handbook of Crystallographic Data for Intermetallic Phases (ASM International, Materials Park, OH, 1991), 2nd edn.
  • C. Hermann, O. Lohrmann, and H. Philipp, eds., Strukturbericht Band II 1928–1932 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1937).

Geometry files


Prototype Generator

aflow --proto=A3B2_cF80_227_f_e --params=

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