Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: AB11_cP36_221_c_agij

  • M. J. Mehl, D. Hicks, C. Toher, O. Levy, R. M. Hanson, G. L. W. Hart, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 1, Comp. Mat. Sci. 136, S1-S828 (2017). (doi=10.1016/j.commatsci.2017.01.017)
  • D. Hicks, M. J. Mehl, E. Gossett, C. Toher, O. Levy, R. M. Hanson, G. L. W. Hart, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 2, Comp. Mat. Sci. 161, S1-S1011 (2019). (doi=10.1016/j.commatsci.2018.10.043)
  • D. Hicks, M.J. Mehl, M. Esters, C. Oses, O. Levy, G.L.W. Hart, C. Toher, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 3, Comp. Mat. Sci. 199, 110450 (2021). (doi=10.1016/j.commatsci.2021.110450)

BaHg11 ($D2_{e}$) Structure: AB11_cP36_221_c_agij

Picture of Structure; Click for Big Picture
Prototype : BaHg11
AFLOW prototype label : AB11_cP36_221_c_agij
Strukturbericht designation : $D2_{e}$
Pearson symbol : cP36
Space group number : 221
Space group symbol : $\text{Pm}\bar{3}\text{m}$
AFLOW prototype command : aflow --proto=AB11_cP36_221_c_agij
--params=
$a$,$x_{3}$,$y_{4}$,$y_{5}$


Other compounds with this structure

  • A number of Hg and Cd phases with Group I or IIA metals or rare earths. (Pearson, 1972) pp. 751–752.

Simple Cubic primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{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(1a\right) & \text{Hg I} \\ \mathbf{B}_{2} & = &\frac12 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{y}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(3c\right) & \text{Ba} \\ \mathbf{B}_{3} & = &\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(3c\right) & \text{Ba} \\ \mathbf{B}_{4} & = &\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}& \left(3c\right) & \text{Ba} \\ \mathbf{B}_{5} & = &x_{3} \, \mathbf{a}_{1}+ x_{3} \, \mathbf{a}_{2}+ x_{3} \, \mathbf{a}_{3}& = &x_{3} \, a \, \mathbf{\hat{x}}+ x_{3} \, a \, \mathbf{\hat{y}}+ x_{3} \, a \, \mathbf{\hat{z}}& \left(8g\right) & \text{Hg II} \\ \mathbf{B}_{6} & = &- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+ x_{3} \, \mathbf{a}_{3}& = &- x_{3} \, a \, \mathbf{\hat{x}}- x_{3} \, a \, \mathbf{\hat{y}}+ x_{3} \, a \, \mathbf{\hat{z}}& \left(8g\right) & \text{Hg II} \\ \mathbf{B}_{7} & = &- x_{3} \, \mathbf{a}_{1}+ x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}& = &- x_{3} \, a \, \mathbf{\hat{x}}+ x_{3} \, a \, \mathbf{\hat{y}}- x_{3} \, a \, \mathbf{\hat{z}}& \left(8g\right) & \text{Hg II} \\ \mathbf{B}_{8} & = &x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}& = &x_{3} \, a \, \mathbf{\hat{x}}- x_{3} \, a \, \mathbf{\hat{y}}- x_{3} \, a \, \mathbf{\hat{z}}& \left(8g\right) & \text{Hg II} \\ \mathbf{B}_{9} & = &x_{3} \, \mathbf{a}_{1}+ x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}& = &x_{3} \, a \, \mathbf{\hat{x}}+ x_{3} \, a \, \mathbf{\hat{y}}- x_{3} \, a \, \mathbf{\hat{z}}& \left(8g\right) & \text{Hg II} \\ \mathbf{B}_{10} & = &- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}& = &- x_{3} \, a \, \mathbf{\hat{x}}- x_{3} \, a \, \mathbf{\hat{y}}- x_{3} \, a \, \mathbf{\hat{z}}& \left(8g\right) & \text{Hg II} \\ \mathbf{B}_{11} & = &x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+ x_{3} \, \mathbf{a}_{3}& = &x_{3} \, a \, \mathbf{\hat{x}}- x_{3} \, a \, \mathbf{\hat{y}}+ x_{3} \, a \, \mathbf{\hat{z}}& \left(8g\right) & \text{Hg II} \\ \mathbf{B}_{12} & = &- x_{3} \, \mathbf{a}_{1}+ x_{3} \, \mathbf{a}_{2}+ x_{3} \, \mathbf{a}_{3}& = &- x_{3} \, a \, \mathbf{\hat{x}}+ x_{3} \, a \, \mathbf{\hat{y}}+ x_{3} \, a \, \mathbf{\hat{z}}& \left(8g\right) & \text{Hg II} \\ \mathbf{B}_{13} & = &y_{4} \, \mathbf{a}_{2}+ y_{4} \, \mathbf{a}_{3}& = &y_{4} \, a \, \mathbf{\hat{y}}+ y_{4} \, a \, \mathbf{\hat{z}}& \left(12i\right) & \text{Hg III} \\ \mathbf{B}_{14} & = &y_{4} \, \mathbf{a}_{2}- y_{4} \, \mathbf{a}_{3}& = &y_{4} \, a \, \mathbf{\hat{y}}- y_{4} \, a \, \mathbf{\hat{z}}& \left(12i\right) & \text{Hg III} \\ \mathbf{B}_{15} & = &- y_{4} \, \mathbf{a}_{2}+ y_{4} \, \mathbf{a}_{3}& = &- y_{4} \, a \, \mathbf{\hat{y}}+ y_{4} \, a \, \mathbf{\hat{z}}& \left(12i\right) & \text{Hg III} \\ \mathbf{B}_{16} & = &- y_{4} \, \mathbf{a}_{2}- y_{4} \, \mathbf{a}_{3}& = &- y_{4} \, a \, \mathbf{\hat{y}}- y_{4} \, a \, \mathbf{\hat{z}}& \left(12i\right) & \text{Hg III} \\ \mathbf{B}_{17} & = &y_{4} \, \mathbf{a}_{1}+ y_{4} \, \mathbf{a}_{3}& = &y_{4} \, a \, \mathbf{\hat{x}}+ y_{4} \, a \, \mathbf{\hat{z}}& \left(12i\right) & \text{Hg III} \\ \mathbf{B}_{18} & = &y_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{3}& = &y_{4} \, a \, \mathbf{\hat{x}}- y_{4} \, a \, \mathbf{\hat{z}}& \left(12i\right) & \text{Hg III} \\ \mathbf{B}_{19} & = &- y_{4} \, \mathbf{a}_{1}+ y_{4} \, \mathbf{a}_{3}& = &- y_{4} \, a \, \mathbf{\hat{x}}+ y_{4} \, a \, \mathbf{\hat{z}}& \left(12i\right) & \text{Hg III} \\ \mathbf{B}_{20} & = &- y_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{3}& = &- y_{4} \, a \, \mathbf{\hat{x}}- y_{4} \, a \, \mathbf{\hat{z}}& \left(12i\right) & \text{Hg III} \\ \mathbf{B}_{21} & = &y_{4} \, \mathbf{a}_{1}+ y_{4} \, \mathbf{a}_{2}& = &y_{4} \, a \, \mathbf{\hat{x}}+ y_{4} \, a \, \mathbf{\hat{y}}& \left(12i\right) & \text{Hg III} \\ \mathbf{B}_{22} & = &y_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}& = &y_{4} \, a \, \mathbf{\hat{x}}- y_{4} \, a \, \mathbf{\hat{y}}& \left(12i\right) & \text{Hg III} \\ \mathbf{B}_{23} & = &- y_{4} \, \mathbf{a}_{1}+ y_{4} \, \mathbf{a}_{2}& = &- y_{4} \, a \, \mathbf{\hat{x}}+ y_{4} \, a \, \mathbf{\hat{y}}& \left(12i\right) & \text{Hg III} \\ \mathbf{B}_{24} & = &- y_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}& = &- y_{4} \, a \, \mathbf{\hat{x}}- y_{4} \, a \, \mathbf{\hat{y}}& \left(12i\right) & \text{Hg III} \\ \mathbf{B}_{25} & = &\frac12 \, \mathbf{a}_{1}+ y_{5} \, \mathbf{a}_{2}+ y_{5} \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ y_{5} \, a \, \mathbf{\hat{y}}+ y_{5} \, a \, \mathbf{\hat{z}}& \left(12j\right) & \text{Hg IV} \\ \mathbf{B}_{26} & = &\frac12 \, \mathbf{a}_{1}+ y_{5} \, \mathbf{a}_{2}- y_{5} \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ y_{5} \, a \, \mathbf{\hat{y}}- y_{5} \, a \, \mathbf{\hat{z}}& \left(12j\right) & \text{Hg IV} \\ \mathbf{B}_{27} & = &\frac12 \, \mathbf{a}_{1}- y_{5} \, \mathbf{a}_{2}+ y_{5} \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}- y_{5} \, a \, \mathbf{\hat{y}}+ y_{5} \, a \, \mathbf{\hat{z}}& \left(12j\right) & \text{Hg IV} \\ \mathbf{B}_{28} & = &\frac12 \, \mathbf{a}_{1}- y_{5} \, \mathbf{a}_{2}- y_{5} \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}- y_{5} \, a \, \mathbf{\hat{y}}- y_{5} \, a \, \mathbf{\hat{z}}& \left(12j\right) & \text{Hg IV} \\ \mathbf{B}_{29} & = &y_{5} \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ y_{5} \, \mathbf{a}_{3}& = &y_{5} \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}+ y_{5} \, a \, \mathbf{\hat{z}}& \left(12j\right) & \text{Hg IV} \\ \mathbf{B}_{30} & = &y_{5} \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}- y_{5} \, \mathbf{a}_{3}& = &y_{5} \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}- y_{5} \, a \, \mathbf{\hat{z}}& \left(12j\right) & \text{Hg IV} \\ \mathbf{B}_{31} & = &- y_{5} \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ y_{5} \, \mathbf{a}_{3}& = &- y_{5} \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}+ y_{5} \, a \, \mathbf{\hat{z}}& \left(12j\right) & \text{Hg IV} \\ \mathbf{B}_{32} & = &- y_{5} \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}- y_{5} \, \mathbf{a}_{3}& = &- y_{5} \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}- y_{5} \, a \, \mathbf{\hat{z}}& \left(12j\right) & \text{Hg IV} \\ \mathbf{B}_{33} & = &y_{5} \, \mathbf{a}_{1}+ y_{5} \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &y_{5} \, a \, \mathbf{\hat{x}}+ y_{5} \, a \, \mathbf{\hat{y}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(12j\right) & \text{Hg IV} \\ \mathbf{B}_{34} & = &y_{5} \, \mathbf{a}_{1}- y_{5} \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &y_{5} \, a \, \mathbf{\hat{x}}- y_{5} \, a \, \mathbf{\hat{y}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(12j\right) & \text{Hg IV} \\ \mathbf{B}_{35} & = &- y_{5} \, \mathbf{a}_{1}+ y_{5} \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &- y_{5} \, a \, \mathbf{\hat{x}}+ y_{5} \, a \, \mathbf{\hat{y}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(12j\right) & \text{Hg IV} \\ \mathbf{B}_{36} & = &- y_{5} \, \mathbf{a}_{1}- y_{5} \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &- y_{5} \, a \, \mathbf{\hat{x}}- y_{5} \, a \, \mathbf{\hat{y}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(12j\right) & \text{Hg IV} \\ \end{array} \]

References

  • G. Peyronel, Struttura della fase BaHg11, Gazz. Chim. Ital. 82, 679–690 (1952).

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=AB11_cP36_221_c_agij --params=

Species:

Running:

Output: