C17 (Fe$_{2}$B) Structure (Obsolete): AB2_tI12_121_ab_i-001
| Prototype | BFe$_{2}$ |
| AFLOW prototype label | AB2_tI12_121_ab_i-001 |
| Strukturbericht designation | $C17$ |
| ICSD | 16809 |
| Pearson symbol | tI12 |
| Space group number | 121 |
| Space group symbol | $I\overline{4}2m$ |
| AFLOW prototype command |
aflow --proto=AB2_tI12_121_ab_i-001
--params=$a, \allowbreak c/a, \allowbreak x_{3}, \allowbreak z_{3}$ |
- (Wever, 1930) placed this structure in space group $I42m$ #121, and this was used to designate the structure as $C17$ in (Ewald, 1931). However, even then it was recognized that changing $z_{3}$ from the value of 0.2 assigned by Wever to 1/4 would add an inversion symmetry to the crystal, change the space group to $I4/mcm$ #140, and make the structure look very much like Al$_{2}$Cu, Strukturbericht $C16$. This has become the accepted structure, as in (Kapfenberger, 2006), so the label $C17$ is depreciated. We retain it here for historical interest.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | B I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2b) | B II |
| $\mathbf{B_{3}}$ | = | $\left(x_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} + z_{3}\right) \, \mathbf{a}_{2}+2 x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (8i) | Fe I |
| $\mathbf{B_{4}}$ | = | $- \left(x_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} - z_{3}\right) \, \mathbf{a}_{2}- 2 x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (8i) | Fe I |
| $\mathbf{B_{5}}$ | = | $- \left(x_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} - z_{3}\right) \, \mathbf{a}_{2}$ | = | $a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (8i) | Fe I |
| $\mathbf{B_{6}}$ | = | $\left(x_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} + z_{3}\right) \, \mathbf{a}_{2}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (8i) | Fe I |
References
- F. Wever and A. Müller, Über das Zweistoffsystem Eisen-Bor und über die Struktur des Eisenborides Fe$_{4}$B$_{2}$, Z. Anorganische und Allgemeine Chemie 192, 317–336 (1930), doi:10.1002/zaac.19301920125.
- P. P. Ewald and C. Hermann, eds., Strukturbericht 1913-1928 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1931).
- C. Kapfenberger, B. Albert, R. Pöttgen, and H. Huppertz, Structure refinements of iron borides Fe$_{2}$B and FeB, Z. Kristallgr. 221, 477–481 (2006), doi:10.1524/zkri.2006.221.5-7.477.
Prototype Generator
aflow --proto=AB2_tI12_121_ab_i --params=$a,c/a,x_{3},z_{3}$