Mg3P2 ($D5_{5}$) Structure : A3B2_cP10_224_d_b

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Prototype : Mg3P2
AFLOW prototype label : A3B2_cP10_224_d_b
Strukturbericht designation : $D5_{5}$
Pearson symbol : cP10
Space group number : 224
Space group symbol : $Pn\bar{3}m$
AFLOW prototype command : aflow --proto=A3B2_cP10_224_d_b
--params=
$a$


Other compounds with this structure

  • Al3P2, Cd3P2, Zn3P2, Mg3As2, Zn3As2, and Ag2O3

  • (Parthé, 1993) lists As2O3 as the prototype for $D5_{5}$.
  • (Passerini, 1928) gives the atomic positions in setting 1 of space group $Pn\overline{3}m$ #224. We have shifted this to the standard, setting 2.

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} & = & 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(4b\right) & \mbox{P} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} & \left(4b\right) & \mbox{P} \\ \mathbf{B}_{3} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{P} \\ \mathbf{B}_{4} & = & \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{P} \\ \mathbf{B}_{5} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{3}{4}a \, \mathbf{\hat{y}} + \frac{3}{4}a \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{Mg} \\ \mathbf{B}_{6} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{3}{4}a \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{Mg} \\ \mathbf{B}_{7} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \frac{3}{4}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{Mg} \\ \mathbf{B}_{8} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{3}{4}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{Mg} \\ \mathbf{B}_{9} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{Mg} \\ \mathbf{B}_{10} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{3}{4}a \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{Mg} \\ \end{array} \]

References

  • L. Passerini, Struttura cristallina di alcuni fosfuri di metalli bivalenti e trivalenti, Gazz. Chim. Ital. 58, 655–664 (1928).
  • 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.

Found in

  • 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_cP10_224_d_b --params=

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