Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: AB_tI16_141_e_e

  • 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)

MoB ($B_{g}$) Structure: AB_tI16_141_e_e

Picture of Structure; Click for Big Picture
Prototype : MoB
AFLOW prototype label : AB_tI16_141_e_e
Strukturbericht designation : $B_{g}$
Pearson symbol : tI16
Space group number : 141
Space group symbol : $\text{I4}_{1}\text{/amd}$
AFLOW prototype command : aflow --proto=AB_tI16_141_e_e
--params=
$a$,$c/a$,$z_{1}$,$z_{2}$


Other compounds with this structure

  • BCr, GaZr, B5Re3V2, Co3Er5Ni2, Ga3Hf2Sc

Body-centered Tetragonal primitive vectors:

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

Basis vectors:

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

References

Geometry files


Prototype Generator

aflow --proto=AB_tI16_141_e_e --params=

Species:

Running:

Output: