$C17$ (Fe2B) (obsolete) Structure : AB2_tI12_121_ab_i

Picture of Structure; Click for Big Picture
Prototype : BFe2
AFLOW prototype label : AB2_tI12_121_ab_i
Strukturbericht designation : $C17$
Pearson symbol : tI12
Space group number : 121
Space group symbol : $I\bar{4}2m$
AFLOW prototype command : aflow --proto=AB2_tI12_121_ab_i
--params=
$a$,$c/a$,$x_{3}$,$z_{3}$


  • (Wever, 1930) placed this structure in space group #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 0.25 would add an inversion symmetry to the crystal, change the space group to $I4/mcm$ #140, and make the structure look very much like Al2Cu, Strukturbericht $C16$. This has become the accepted structure, as in (Kapfenberger, 2006), and so $C17$ is an obsolete designation. We retain it here for historical interest.

Body-centered Tetragonal primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & 0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = & 0 \, \mathbf{\hat{x}} + 0 \, \mathbf{\hat{y}} + 0 \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{B I} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} & = & \frac{1}{2}c \, \mathbf{\hat{z}} & \left(2b\right) & \mbox{B II} \\ \mathbf{B}_{3} & = & \left(x_{3}+z_{3}\right) \, \mathbf{a}_{1} + \left(x_{3}+z_{3}\right) \, \mathbf{a}_{2} + 2x_{3} \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}} + x_{3}a \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(8i\right) & \mbox{Fe} \\ \mathbf{B}_{4} & = & \left(-x_{3}+z_{3}\right) \, \mathbf{a}_{1} + \left(-x_{3}+z_{3}\right) \, \mathbf{a}_{2}-2x_{3} \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}}-x_{3}a \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(8i\right) & \mbox{Fe} \\ \mathbf{B}_{5} & = & \left(-x_{3}-z_{3}\right) \, \mathbf{a}_{1} + \left(x_{3}-z_{3}\right) \, \mathbf{a}_{2} & = & x_{3}a \, \mathbf{\hat{x}}-x_{3}a \, \mathbf{\hat{y}}-z_{3}c \, \mathbf{\hat{z}} & \left(8i\right) & \mbox{Fe} \\ \mathbf{B}_{6} & = & \left(x_{3}-z_{3}\right) \, \mathbf{a}_{1} + \left(-x_{3}-z_{3}\right) \, \mathbf{a}_{2} & = & -x_{3}a \, \mathbf{\hat{x}} + x_{3}a \, \mathbf{\hat{y}}-z_{3}c \, \mathbf{\hat{z}} & \left(8i\right) & \mbox{Fe} \\ \end{array} \]

References

  • F. Wever and A. Müller, Über das Zweistoffsystem Eisen–Bor und über die Struktur des Eisenborides Fe4B2, Z. Anorg. Allg. Chem. 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 Fe2B and FeB, Zeitschrift für Kristallographie – Crystalline Materials 221, 477–481 (2006), doi:10.1524/zkri.2006.221.5-7.477.

Geometry files


Prototype Generator

aflow --proto=AB2_tI12_121_ab_i --params=

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