FeB ($B27$) Structure: AB_oP8_62_c_c-003
| Prototype | BFe |
| AFLOW prototype label | AB_oP8_62_c_c-003 |
| Strukturbericht designation | $B27$ |
| ICSD | 33577 |
| Pearson symbol | oP8 |
| Space group number | 62 |
| Space group symbol | $Pnma$ |
| AFLOW prototype command |
aflow --proto=AB_oP8_62_c_c-003
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak x_{1}, \allowbreak z_{1}, \allowbreak x_{2}, \allowbreak z_{2}$ |
Other compounds with this structure
CoB, CuCe, HfGe, MnB, NiDy, NiGd, NiHo, NiLu, NiTm, NiY, PdTh, PtDy, PtEr, PtGd, PtHo, PtLu, PtNd, PtPr, PtSm, PtTb, PtTm, PtY, PuSi, ThSi, TiSi, USi, ZrSi
- (Hermann, 1937), assigns the Strukturbericht designation $B15$ to this structure. This was superseded by the current $B27$ structure in (Gottfried, 1937). Here we follow (Parthé, 1993), who prefers the $B27$ designation.
- FeAs ($B14$), GeS ($B16$), FeB ($B27$), SnS ($B29$), MnP ($B31$), and $\eta$–NiSi ($B_{d}$) all share the same AFLOW label, AB_oP8_62_c_c. The structures are generated by the same symmetry operations with different sets of parameters (
--params) specified in their corresponding CIF files.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{1} \, \mathbf{a}_{3}$ | = | $a x_{1} \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+c z_{1} \,\mathbf{\hat{z}}$ | (4c) | B I |
| $\mathbf{B_{2}}$ | = | $- \left(x_{1} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\left(z_{1} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{1} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{3}{4}b \,\mathbf{\hat{y}}+c \left(z_{1} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4c) | B I |
| $\mathbf{B_{3}}$ | = | $- x_{1} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{1} \, \mathbf{a}_{3}$ | = | $- a x_{1} \,\mathbf{\hat{x}}+\frac{3}{4}b \,\mathbf{\hat{y}}- c z_{1} \,\mathbf{\hat{z}}$ | (4c) | B I |
| $\mathbf{B_{4}}$ | = | $\left(x_{1} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}- \left(z_{1} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{1} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}- c \left(z_{1} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4c) | B I |
| $\mathbf{B_{5}}$ | = | $x_{2} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (4c) | Fe I |
| $\mathbf{B_{6}}$ | = | $- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\left(z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{3}{4}b \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4c) | Fe I |
| $\mathbf{B_{7}}$ | = | $- x_{2} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+\frac{3}{4}b \,\mathbf{\hat{y}}- c z_{2} \,\mathbf{\hat{z}}$ | (4c) | Fe I |
| $\mathbf{B_{8}}$ | = | $\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}- \left(z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}- c \left(z_{2} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4c) | Fe I |
References
- S. B. Hendricks and P. R. Kosting, The Crystal Structure of Fe$_2$P, Fe$_2$N, Fe$_3$N and FeB, Z. Kristallogr. 74, 511–533 (1930), doi:10.1524/zkri.1930.74.1.511.
- C. Hermann, O. Lohrmann, and H. Philipp, eds., Strukturbericht Band II 1928-1932 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1937).
- C. Gottfried and F. Schossberger, eds., Strukturbericht Band III 1933-1935 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1937).
- E. 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. See Table 4.3, pp. 363–371, for a comprehensive compilation of {\em Strukturbericht symbols.
Found in
- R. T. Downs and M. Hall-Wallace, The American Mineralogist Crystal Structure Database, Am. Mineral. 88, 247–250 (2003).
Prototype Generator
aflow --proto=AB_oP8_62_c_c --params=$a,b/a,c/a,x_{1},z_{1},x_{2},z_{2}$