Mn$_{3}$As (D0$_{d}$) Structure: AB3_oC16_63_c_3c-001
| Prototype | AsMn$_{3}$ |
| AFLOW prototype label | AB3_oC16_63_c_3c-001 |
| ICSD | 40437 |
| Pearson symbol | oC16 |
| Space group number | 63 |
| Space group symbol | $Cmcm$ |
| AFLOW prototype command |
aflow --proto=AB3_oC16_63_c_3c-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak y_{1}, \allowbreak y_{2}, \allowbreak y_{3}, \allowbreak y_{4}$ |
Other compounds with this structure
Te$_{3}$Nd, DyGe$_{3}$
- (Nowotny, 1951) set the structure of Mn$_{3}$As 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 that latter two works and assign the $D0_e$ 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.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $- y_{1} \, \mathbf{a}_{1}+y_{1} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $b y_{1} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4c) | As I |
| $\mathbf{B_{2}}$ | = | $y_{1} \, \mathbf{a}_{1}- y_{1} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- b y_{1} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (4c) | As I |
| $\mathbf{B_{3}}$ | = | $- y_{2} \, \mathbf{a}_{1}+y_{2} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $b y_{2} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4c) | Mn I |
| $\mathbf{B_{4}}$ | = | $y_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- b y_{2} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (4c) | Mn I |
| $\mathbf{B_{5}}$ | = | $- y_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $b y_{3} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4c) | Mn II |
| $\mathbf{B_{6}}$ | = | $y_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- b y_{3} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (4c) | Mn II |
| $\mathbf{B_{7}}$ | = | $- y_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $b y_{4} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4c) | Mn III |
| $\mathbf{B_{8}}$ | = | $y_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- b y_{4} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (4c) | Mn III |
References
- H. Nowotny, R. Funk, and J. Pesi, Kristallchemische Untersuchungen in den Systemen Mn-As, V-Sb, Ti-Sb}, Monat. Chem. 82, 513–525 (1951), doi:10.1007/BF00900849. \bibitem{parthe93:TYPIXE. Parthé, L. Gelato, B. Chabot, M. Penso, K. Cenzula, and R. Gladyshevskii, Standardized Data and Crystal Chemical Characterization of Inorganic Structure Types, Gmelin Handbook of Inorganic and Organometallic Chemistry}, vol. 2 (Springer-Verlag, Berlin, Heidelberg, 1993), 8 edn., doi:10.1007/978-3-662-02909-1_3.\bibAnnoteFile{parthe93:TYPIX}\bibitem{brandes92:SmithellsE. A. Brandes and G. B. Brook, eds., Smithells Metals Reference Book} (Butterworth Heinemann, Oxford, Auckland, Boston, Johannesburg, Melbourne, New Delhi, 1992), seventh edn.\bibAnnoteFile{brandes92:Smithells}\bibitem{villars91:pearsonP. Villars and L. D. Calvert, eds., Pearson's Handbook of Crystallographic Data for Intermetallic Phases} (ASM International, Materials Park, Ohio, 1991), 2$^{nd}$ edn.\bibAnnoteFile{villars91:pearson
Prototype Generator
aflow --proto=AB3_oC16_63_c_3c --params=$a,b/a,c/a,y_{1},y_{2},y_{3},y_{4}$