Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: A4B_oP20_62_2cd_c

  • 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)

MgB4 Structure: A4B_oP20_62_2cd_c

Picture of Structure; Click for Big Picture
Prototype : MgB4
AFLOW prototype label : A4B_oP20_62_2cd_c
Strukturbericht designation : None
Pearson symbol : oP20
Space group number : 62
Space group symbol : $\text{Pnma}$
AFLOW prototype command : aflow --proto=A4B_oP20_62_2cd_c
--params=
$a$,$b/a$,$c/a$,$x_{1}$,$z_{1}$,$x_{2}$,$z_{2}$,$x_{3}$,$z_{3}$,$x_{4}$,$y_{4}$,$z_{4}$


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} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{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) & \text{B I} \\ \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) & \text{B I} \\ \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) & \text{B I} \\ \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) & \text{B I} \\ \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) & \text{B II} \\ \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) & \text{B II} \\ \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) & \text{B II} \\ \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) & \text{B II} \\ \mathbf{B}_{9} & =&x_{3} \, \mathbf{a}_{1}+ \frac14 \, \mathbf{a}_{2}+ z_{3} \, \mathbf{a}_{3}& =&x_{3} \, a \, \mathbf{\hat{x}}+ \frac14 \, b \, \mathbf{\hat{y}}+ z_{3} \, c \, \mathbf{\hat{z}}& \left(4c\right) & \text{Mg} \\ \mathbf{B}_{10} & =&\left(\frac12 - x_{3}\right) \, \mathbf{a}_{1}+ \frac34 \, \mathbf{a}_{2}+ \left(\frac12 + z_{3}\right) \, \mathbf{a}_{3}& =&\left(\frac12 - x_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac34 \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{3}\right) \, c \, \mathbf{\hat{z}}& \left(4c\right) & \text{Mg} \\ \mathbf{B}_{11} & =&- x_{3} \, \mathbf{a}_{1}+ \frac34 \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}& =&- x_{3} \, a \, \mathbf{\hat{x}}+ \frac34 \, b \, \mathbf{\hat{y}}- z_{3} \, c \, \mathbf{\hat{z}}& \left(4c\right) & \text{Mg} \\ \mathbf{B}_{12} & =&\left(\frac12 + x_{3}\right) \, \mathbf{a}_{1}+ \frac14 \, \mathbf{a}_{2}+ \left(\frac12 - z_{3}\right) \, \mathbf{a}_{3}& =&\left(\frac12 + x_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac14 \, b \, \mathbf{\hat{y}}+ \left(\frac12 - z_{3}\right) \, c \, \mathbf{\hat{z}}& \left(4c\right) & \text{Mg} \\ \mathbf{B}_{13} & =&x_{4} \, \mathbf{a}_{1}+ y_{4} \, \mathbf{a}_{2}+ z_{4} \, \mathbf{a}_{3}& =&x_{4} \, a \, \mathbf{\hat{x}}+ y_{4} \, b \, \mathbf{\hat{y}}+ z_{4} \, c \, \mathbf{\hat{z}}& \left(8d\right) & \text{B III} \\ \mathbf{B}_{14} & =&\left(\frac12 - x_{4}\right) \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}+ \left(\frac12 + z_{4}\right) \, \mathbf{a}_{3}& =&\left(\frac12 - x_{4}\right) \, a \, \mathbf{\hat{x}}- y_{4} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{4}\right) \, c \, \mathbf{\hat{z}}& \left(8d\right) & \text{B III} \\ \mathbf{B}_{15} & =&- x_{4} \, \mathbf{a}_{1}+ \left(\frac12 + y_{4}\right) \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}& =&- x_{4} \, a \, \mathbf{\hat{x}}+ \left(\frac12 + y_{4}\right) \, b \, \mathbf{\hat{y}}- z_{4} \, c \, \mathbf{\hat{z}}& \left(8d\right) & \text{B III} \\ \mathbf{B}_{16} & =&\left(\frac12 + x_{4}\right) \, \mathbf{a}_{1}+ \left(\frac12 - y_{4}\right) \, \mathbf{a}_{2}+ \left(\frac12 - z_{4}\right) \, \mathbf{a}_{3}& =&\left(\frac12 + x_{4}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 - y_{4}\right) \, b \, \mathbf{\hat{y}}+ \left(\frac12 - z_{4}\right) \, c \, \mathbf{\hat{z}}& \left(8d\right) & \text{B III} \\ \mathbf{B}_{17} & =&- x_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}& =&- x_{4} \, a \, \mathbf{\hat{x}}- y_{4} \, b \, \mathbf{\hat{y}}- z_{4} \, c \, \mathbf{\hat{z}}& \left(8d\right) & \text{B III} \\ \mathbf{B}_{18} & =&\left(\frac12 + x_{4}\right) \, \mathbf{a}_{1}+ y_{4} \, \mathbf{a}_{2}+ \left(\frac12 - z_{4}\right) \, \mathbf{a}_{3}& =&\left(\frac12 + x_{4}\right) \, a \, \mathbf{\hat{x}}+ y_{4} \, b \, \mathbf{\hat{y}}+ \left(\frac12 - z_{4}\right) \, c \, \mathbf{\hat{z}}& \left(8d\right) & \text{B III} \\ \mathbf{B}_{19} & =&x_{4} \, \mathbf{a}_{1}+ \left(\frac12 - y_{4}\right) \, \mathbf{a}_{2}+ z_{4} \, \mathbf{a}_{3}& =&x_{4} \, a \, \mathbf{\hat{x}}+ \left(\frac12 - y_{4}\right) \, b \, \mathbf{\hat{y}}+ z_{4} \, c \, \mathbf{\hat{z}}& \left(8d\right) & \text{B III} \\ \mathbf{B}_{20} & =&\left(\frac12 - x_{4}\right) \, \mathbf{a}_{1}+ \left(\frac12 + y_{4}\right) \, \mathbf{a}_{2}+ \left(\frac12 + z_{4}\right) \, \mathbf{a}_{3}& =&\left(\frac12 - x_{4}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 + y_{4}\right) \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{4}\right) \, c \, \mathbf{\hat{z}}& \left(8d\right) & \text{B III} \\ \end{array} \]

References

  • R. Naslain, A. Guette, and M. Barret, Sur le diborure et le tétraborure de magnésium. Considérations cristallochimiques sur les tétraborures, J. Solid State Chem. 8, 68–85 (1973), doi:10.1016/0022-4596(73)90022-4.

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=A4B_oP20_62_2cd_c --params=

Species:

Running:

Output: