Mn3As ($D0_{d}$) Structure : AB3_oC16_63_c_3c

Picture of Structure; Click for Big Picture
Prototype : AsMn3
AFLOW prototype label : AB3_oC16_63_c_3c
Strukturbericht designation : $D0_{d}$
Pearson symbol : oC16
Space group number : 63
Space group symbol : $Cmcm$
AFLOW prototype command : aflow --proto=AB3_oC16_63_c_3c
--params=
$a$,$b/a$,$c/a$,$y_{1}$,$y_{2}$,$y_{3}$,$y_{4}$


Other compounds with this structure

  • Te3Nd, DyGe3

  • (Nowotny, 1951) set the structure of Mn3As in space group $Pmmn$ #59. This was repeated by (Villars, 1991) and (Brandes, 1992). However, (Carrillo–Cabrera, 1983) showed that the structure actually reduces to space group $Cmcm$ #63, and this was recognized by (Parthé, 1993). We follow the latter two works and assign the $D0_{d}$ structure to space group $Cmcm$.
  • (Carrillo–Cabrera, 1983) placed the structure in setting $Bmmb$ of space group #63, but we have shifted it to the standard $Cmcm$ setting.

Base-centered Orthorhombic primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & -y_{1} \, \mathbf{a}_{1} + y_{1} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & y_{1}b \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{As} \\ \mathbf{B}_{2} & = & y_{1} \, \mathbf{a}_{1}-y_{1} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & -y_{1}b \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{As} \\ \mathbf{B}_{3} & = & -y_{2} \, \mathbf{a}_{1} + y_{2} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & y_{2}b \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{Mn I} \\ \mathbf{B}_{4} & = & y_{2} \, \mathbf{a}_{1}-y_{2} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & -y_{2}b \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{Mn I} \\ \mathbf{B}_{5} & = & -y_{3} \, \mathbf{a}_{1} + y_{3} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & y_{3}b \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{Mn II} \\ \mathbf{B}_{6} & = & y_{3} \, \mathbf{a}_{1}-y_{3} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & -y_{3}b \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{Mn II} \\ \mathbf{B}_{7} & = & -y_{4} \, \mathbf{a}_{1} + y_{4} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & y_{4}b \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{Mn III} \\ \mathbf{B}_{8} & = & y_{4} \, \mathbf{a}_{1}-y_{4} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & -y_{4}b \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{Mn III} \\ \end{array} \]

References

  • W. Carrillo–Cabrera, The Crystal Structure of TiCu2P and Its Relationship to the Structure of Mn3As, Acta Chem. Scand. 37a, 93–98 (1983), doi:10.3891/acta.chem.scand.37a-0093.
  • H. Nowotny, R. Funk, and J. Pesl, Kristallchemische Untersuchungen in den Systemen Mn–As, V–Sb, Ti–Sb, Monatsh. Chem. Verw. Teile\ Anderer\ Wiss. 82, 513–525 (1951), doi:10.1007/BF00900849.
  • 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.
  • E. A. Brandes and G. B. Brook, eds., Smithells Metals Reference Book (Butterworth Heinemann, Oxford, Auckland, Boston, Johannesburg, Melbourne, New Delhi, 1992), seventh edn. Strukturbericht designations start on page 6–36 (163 in PDF), see table 6.3 on page 6–63 (190).
  • P. Villars and L. D. Calvert, eds., Pearson's Handbook of Crystallographic Data for Intermetallic Phases (ASM International, Materials Park, Ohio, 1991), 2nd edn.

Geometry files


Prototype Generator

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