FeB ($B27$) Structure: AB_oP8_62_c_c

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Prototype : FeB
AFLOW prototype label : AB_oP8_62_c_c
Strukturbericht designation : $B27$
Pearson symbol : oP8
Space group number : 62
Space group symbol : $\mbox{Pnma}$
AFLOW prototype command : aflow --proto=AB_oP8_62_c_c
--params=
$a$,$b/a$,$c/a$,$x_{1}$,$z_{1}$,$x_{2}$,$z_{2}$


Other compounds with this structure

  • GeSe, GeS, GeTe, PbS, PbSe, PbTe, SnS, SnSe, SnTe

  • (Hermann, 1937), 7, assigns the Strukturbericht designation B15 to this structure. This was superseded by the current B27 structure in in (Gottfried, 1937) 12. Here we follow (Parthé, 1993), who prefers the B27 designation. Note that GeS (AB_oP8_62_c_c, GeS), MnP (AB_oP8_62_c_c, MnP), FeB (AB_oP8_62_c_c, FeB), and SnS (AB_oP8_62_c_c, SnS) have the same AFLOW prototype label. They are generated by the same symmetry operations with different sets of parameters (––params) specified in their corresponding CIF files.

Simple Orthorhombic primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & =&x_{1} \, \mathbf{a}_{1}+ \frac14 \, \mathbf{a}_{2}+ z_{1} \, \mathbf{a}_{3}& =&x_{1} \, a \, \mathbf{\hat{x}}+ \frac14 \, b \, \mathbf{\hat{y}}+ z_{1} \, c \, \mathbf{\hat{z}}& \left(4c\right) & \mbox{B} \\ \mathbf{B}_{2} & =&\left(\frac12 - x_{1}\right) \, \mathbf{a}_{1}+ \frac34 \, \mathbf{a}_{2}+ \left(\frac12 + z_{1}\right) \, \mathbf{a}_{3}& =&\left(\frac12 - x_{1}\right) \, a \, \mathbf{\hat{x}}+ \frac34 \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{1}\right) \, c \, \mathbf{\hat{z}}& \left(4c\right) & \mbox{B} \\ \mathbf{B}_{3} & =&- x_{1} \, \mathbf{a}_{1}+ \frac34 \, \mathbf{a}_{2}- z_{1} \, \mathbf{a}_{3}& =&- x_{1} \, a \, \mathbf{\hat{x}}+ \frac34 \, b \, \mathbf{\hat{y}}- z_{1} \, c \, \mathbf{\hat{z}}& \left(4c\right) & \mbox{B} \\ \mathbf{B}_{4} & =&\left(\frac12 + x_{1}\right) \, \mathbf{a}_{1}+ \frac14 \, \mathbf{a}_{2}+ \left(\frac12 - z_{1}\right) \, \mathbf{a}_{3}& =&\left(\frac12 + x_{1}\right) \, a \, \mathbf{\hat{x}}+ \frac14 \, b \, \mathbf{\hat{y}}+ \left(\frac12 - z_{1}\right) \, c \, \mathbf{\hat{z}}& \left(4c\right) & \mbox{B} \\ \mathbf{B}_{5} & =&x_{2} \, \mathbf{a}_{1}+ \frac14 \, \mathbf{a}_{2}+ z_{2} \, \mathbf{a}_{3}& =&x_{2} \, a \, \mathbf{\hat{x}}+ \frac14 \, b \, \mathbf{\hat{y}}+ z_{2} \, c \, \mathbf{\hat{z}}& \left(4c\right) & \mbox{Fe} \\ \mathbf{B}_{6} & =&\left(\frac12 - x_{2}\right) \, \mathbf{a}_{1}+ \frac34 \, \mathbf{a}_{2}+ \left(\frac12 + z_{2}\right) \, \mathbf{a}_{3}& =&\left(\frac12 - x_{2}\right) \, a \, \mathbf{\hat{x}}+ \frac34 \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{2}\right) \, c \, \mathbf{\hat{z}}& \left(4c\right) & \mbox{Fe} \\ \mathbf{B}_{7} & =&- x_{2} \, \mathbf{a}_{1}+ \frac34 \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}& =&- x_{2} \, a \, \mathbf{\hat{x}}+ \frac34 \, b \, \mathbf{\hat{y}}- z_{2} \, c \, \mathbf{\hat{z}}& \left(4c\right) & \mbox{Fe} \\ \mathbf{B}_{8} & =&\left(\frac12 + x_{2}\right) \, \mathbf{a}_{1}+ \frac14 \, \mathbf{a}_{2}+ \left(\frac12 - z_{2}\right) \, \mathbf{a}_{3}& =&\left(\frac12 + x_{2}\right) \, a \, \mathbf{\hat{x}}+ \frac14 \, b \, \mathbf{\hat{y}}+ \left(\frac12 - z_{2}\right) \, c \, \mathbf{\hat{z}}& \left(4c\right) & \mbox{Fe} \\ \end{array} \]

References

  • S. B. Hendricks and P. R. Kosting, The Crystal Structure of Fe2P, Fe2N, Fe3N and FeB, Zeitschrift für Kristallographie – Crystalline Materials 74, 511–533 (1930), doi:10.1524/zkri.1930.74.1.511.
  • C. Hermann, O. Lohrmann, and H. Philipp, Strukturbericht Band II, 1928–1932 (Akademsiche Verlagsgesellschaft M. B. H., Leipzig, 1937).
  • C. Gottfried and F. Schossberger, Strukturbericht Band III, 1933–1935 (Akademsiche Verlagsgesellschaft M. B. H., Leipzig, 1937).
  • E. Parthé, L. M. Gelato, B. Chabot, M. Penzo, K. Cenzula, and R. Gladyshevskii, Gmelin Handbook of Inorganic and Organometallic Chemistry: Standardized Data and Crystal Chemical Characterization of Inorganic Structure Types (Springer–Verlag, Berlin and Heidelberg, 1993), 8th edn., doi:10.1007/978-3-662-02909-1_3. Online edition available at DOI. See Table 4.3, pp. 363–371, for a comprehensive compilation of Strukturbericht symbols.

Found in

  • R. T. Downs and M. Hall–Wallace, The American Mineralogist Crystal Structure Database, Am. Mineral. 88, 247–250 (2003).

Geometry files


Prototype Generator

aflow --proto=AB_oP8_62_c_c --params=

Species:

Running:

Output: