Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: A3B_hR12_166_ach_bc-001

If you are using this page, please cite:
H. Eckert, S. Divilov, M. J. Mehl, D. Hicks, A. C. Zettel, M. Esters. X. Campilongo and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 4. Submitted to Computational Materials Science.

Links to this page

https://aflow.org/p/3QUZ
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NbBe$_{3}$ Structure: A3B_hR12_166_ach_bc-001

Picture of Structure; Click for Big Picture
Prototype Be$_{3}$Nb
AFLOW prototype label A3B_hR12_166_ach_bc-001
ICSD 58723
Pearson symbol hR12
Space group number 166
Space group symbol $R\overline{3}m$
AFLOW prototype command aflow --proto=A3B_hR12_166_ach_bc-001
--params=$a, \allowbreak c/a, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak x_{5}, \allowbreak z_{5}$

Other compounds with this structure

DyNi$_{3}$,  ErNi$_{3}$,  GdNi$_{3}$,  HoNi$_{3}$,  LaNi$_{3}$,  PrNi$_{3}$,  PuCo$_{3}$,  PuNi$_{3}$,  SmNi$_{3}$,  TaBe$_{3}$,  TbNi$_{3}$,  ThFe$_{3}$,  TiBe$_{3}$,  TmNi$_{3}$,  YNi$_{3}$,  YbNi$_{3}$


  • Hexagonal settings of this structure can be obtained with the option --hex.

\[ \begin{array}{ccc} \mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{\sqrt{3}}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}} \end{array}\]

Basis vectors

Lattice coordinates Cartesian coordinates Wyckoff position Atom type
$\mathbf{B_{1}}$ = $0$ = $0$ (1a) Be I
$\mathbf{B_{2}}$ = $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ = $\frac{1}{2}c \,\mathbf{\hat{z}}$ (1b) Nb I
$\mathbf{B_{3}}$ = $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ = $c x_{3} \,\mathbf{\hat{z}}$ (2c) Be II
$\mathbf{B_{4}}$ = $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ = $- c x_{3} \,\mathbf{\hat{z}}$ (2c) Be II
$\mathbf{B_{5}}$ = $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ = $c x_{4} \,\mathbf{\hat{z}}$ (2c) Nb II
$\mathbf{B_{6}}$ = $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ = $- c x_{4} \,\mathbf{\hat{z}}$ (2c) Nb II
$\mathbf{B_{7}}$ = $x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \left(x_{5} - z_{5}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{5} - z_{5}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{5} + z_{5}\right) \,\mathbf{\hat{z}}$ (6h) Be III
$\mathbf{B_{8}}$ = $z_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ = $- \frac{1}{2}a \left(x_{5} - z_{5}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{5} - z_{5}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{5} + z_{5}\right) \,\mathbf{\hat{z}}$ (6h) Be III
$\mathbf{B_{9}}$ = $x_{5} \, \mathbf{a}_{1}+z_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ = $- \frac{1}{\sqrt{3}}a \left(x_{5} - z_{5}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{5} + z_{5}\right) \,\mathbf{\hat{z}}$ (6h) Be III
$\mathbf{B_{10}}$ = $- z_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \left(x_{5} - z_{5}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{5} - z_{5}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{5} + z_{5}\right) \,\mathbf{\hat{z}}$ (6h) Be III
$\mathbf{B_{11}}$ = $- x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ = $- \frac{1}{2}a \left(x_{5} - z_{5}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{5} - z_{5}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{5} + z_{5}\right) \,\mathbf{\hat{z}}$ (6h) Be III
$\mathbf{B_{12}}$ = $- x_{5} \, \mathbf{a}_{1}- z_{5} \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ = $\frac{1}{\sqrt{3}}a \left(x_{5} - z_{5}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{5} + z_{5}\right) \,\mathbf{\hat{z}}$ (6h) Be III

References

  • D. E. Sands, A. Zalkin, and O. H. Krikorian, The crystal structure of NbBe$_{2}$ and NbBe$_{3}$, Acta Cryst. 12, 461–464 (1959), doi:10.1107/S0365110X59001384.

Found in

  • W. B. Pearson, A Handbook of Lattice Spacings and Structures of Metals and Alloys, Volume 2, International Series of Monographs on Metal Physics and Physical Metallurgy, vol. 8 (Pergamon Press, Oxford, London, Edinburgh, New York, Toronto, Sydney, Paris, Braunschweig, 1967).

Prototype Generator

aflow --proto=A3B_hR12_166_ach_bc --params=$a,c/a,x_{3},x_{4},x_{5},z_{5}$

Species:

Running:

Output: