CrB ($B33$) Structure: AB_oC8_63_c_c

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Prototype : CrB
AFLOW prototype label : AB_oC8_63_c_c
Strukturbericht designation : $B33$
Pearson symbol : oC8
Space group number : 63
Space group symbol : $\mbox{Cmcm}$
AFLOW prototype command : aflow --proto=AB_oC8_63_c_c
--params=
$a$,$b/a$,$c/a$,$y_{1}$,$y_{2}$


Other compounds with this structure

  • AgCa, AlHf, AlTh, AlY, AlZr, AuGd, BNb, BNi, BTa, BV, BaPb, CaGe, CaSi, CaSn, CeNi, CePt, CeRh, CoTh, DyGa, DyGe, ErNi, GaGd, GaPr, GdGe, GeNi, GePr, HfNi, HfPt, HoNi, ITl, IrTh, LaNi, LaPt, LaRh, LuNi, NdNi, NdRh, NiPr, NiPu, NiSm, NiTb, NiTm, NiZr, PrRh, PtTh, PtZr, RhTh, RuTh, SiSr, and SiY

  • (Gottfried, 1938) originally gave the $B33$ Strukturbericht designation to thallium iodide, TiI. Later, (Smithells, 1955) gave the CrB structure the new designation $B_{f}$. These structures are identical, and we follow (Parthé, 1993) in using $B33$ to designate both structures. Removing either the Cr or B atoms transforms this into the $\alpha$–U (A20) structure.

Base-centered Orthorhombic primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & =& - y_{1} \, \mathbf{a}_{1} + y_{1} \, \mathbf{a}_{2} + \frac14 \, \mathbf{a}_{3}& =& y_{1} \, b \, \mathbf{\hat{y}} + \frac14 \, c \mathbf{\hat{z}}& \left(4c\right) & \mbox{B} \\ \mathbf{B}_{2} & =& y_{1} \, \mathbf{a}_{1} - y_{1} \, \mathbf{a}_{2} + \frac34 \, \mathbf{a}_{3}& =& - y_{1} \, b \, \mathbf{\hat{y}} + \frac34 \, c \mathbf{\hat{z}}& \left(4c\right) & \mbox{B} \\ \mathbf{B}_{3} & =& - y_{2} \, \mathbf{a}_{1} + y_{2} \, \mathbf{a}_{2} + \frac14 \, \mathbf{a}_{3}& =& y_{2} \, b \, \mathbf{\hat{y}} + \frac14 \, c \mathbf{\hat{z}}& \left(4c\right) & \mbox{Cr} \\ \mathbf{B}_{4} & =& y_{2} \, \mathbf{a}_{1} - y_{2} \, \mathbf{a}_{2} + \frac34 \, \mathbf{a}_{3}& =& - y_{2} \, b \, \mathbf{\hat{y}} + \frac34 \, c \mathbf{\hat{z}}& \left(4c\right) & \mbox{Cr} \\ \end{array} \]

References

  • S. Okada, T. Atoda, and I. Higashi, Structural investigation of Cr2B3, Cr3B4, and CrB by single–crystal diffractometry, J. Solid State Chem. 68, 61–67 (1987), doi:10.1016/0022-4596(87)90285-4.
  • C. Gottfried, Strukturbericht Band IV, 1936 (Akademsiche Verlagsgesellschaft M. B. H., Leipzig, 1938).
  • C. J. Smithells, Metals Reference Book (Butterworths Scientific, London, 1955), second edn.
  • E. Parthé, L. Gelato, B. Chabot, M. Penso, 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, Heidelberg, 1993), 8th edn., doi:10.1007/978-3-662-02909-1_3.

Found in

  • P. Villars, Material Phases Data System ((MPDS), CH–6354 Vitznau, Switzerland, 2014). Accessed through the Springer Materials site.

Geometry files


Prototype Generator

aflow --proto=AB_oC8_63_c_c --params=

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