Mn12Th ($D2_{b}$) Structure: A12B_tI26_139_fij_a

Picture of Structure; Click for Big Picture
Prototype : Mn12Th
AFLOW prototype label : A12B_tI26_139_fij_a
Strukturbericht designation : $D2_{b}$
Pearson symbol : tI26
Space group number : 139
Space group symbol : $\mbox{I4/mmm}$
AFLOW prototype command : aflow --proto=A12B_tI26_139_fij_a
--params=
$a$,$c/a$,$x_{3}$,$x_{4}$


Other compounds with this structure

  • AgBe12, Al8Cr4Er, Fe4Mn8, Fe7Mn5, others.

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} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{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(2a\right) & \mbox{Th} \\ \mathbf{B}_{2} & =&\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& =&\frac14 \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{y}}+ \frac14 \, c \, \mathbf{\hat{z}}& \left(8f\right) & \mbox{Mn I} \\ \mathbf{B}_{3} & =&\frac12 \, \mathbf{a}_{3}& =&\frac14 \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{y}}+ \frac34 \, c \, \mathbf{\hat{z}}& \left(8f\right) & \mbox{Mn I} \\ \mathbf{B}_{4} & =&\frac12 \, \mathbf{a}_{1}& =&\frac34 \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{y}}+ \frac14 \, c \, \mathbf{\hat{z}}& \left(8f\right) & \mbox{Mn I} \\ \mathbf{B}_{5} & =&\frac12 \, \mathbf{a}_{2}& =&\frac14 \, a \, \mathbf{\hat{x}}+ \frac34 \, a \, \mathbf{\hat{y}}+ \frac14 \, c \, \mathbf{\hat{z}}& \left(8f\right) & \mbox{Mn I} \\ \mathbf{B}_{6} & =&x_{3} \, \mathbf{a}_{2}+ x_{3} \, \mathbf{a}_{3}& =&x_{3} \, a \, \mathbf{\hat{x}}& \left(8i\right) & \mbox{Mn II} \\ \mathbf{B}_{7} & =&- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}& =&- x_{3} \, a \, \mathbf{\hat{x}}& \left(8i\right) & \mbox{Mn II} \\ \mathbf{B}_{8} & =&x_{3} \, \mathbf{a}_{1}+ x_{3} \, \mathbf{a}_{3}& =&x_{3} \, a \, \mathbf{\hat{y}}& \left(8i\right) & \mbox{Mn II} \\ \mathbf{B}_{9} & =&- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{3}& =&- x_{3} \, a \, \mathbf{\hat{y}}& \left(8i\right) & \mbox{Mn II} \\ \mathbf{B}_{10} & =&\frac12 \, \mathbf{a}_{1}+ x_{4} \, \mathbf{a}_{2}+ \left(\frac12 + x_{4}\right) \, \mathbf{a}_{3}& =&x_{4} \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}& \left(8j\right) & \mbox{Mn III} \\ \mathbf{B}_{11} & =&\frac12 \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+ \left( \frac12 - x_{4} \right) \, \mathbf{a}_{3}& =&- x_{4} \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}& \left(8j\right) & \mbox{Mn III} \\ \mathbf{B}_{12} & =&x_{4} \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ \left( \frac12 + x_{4} \right) \, \mathbf{a}_{3}& =&\frac12 \, a \, \mathbf{\hat{x}}+ x_{4} \, a \, \mathbf{\hat{y}}& \left(8j\right) & \mbox{Mn III} \\ \mathbf{B}_{13} & =&- x_{4} \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ \left( \frac12 - x_{4} \right) \, \mathbf{a}_{3}& =&\frac12 \, a \, \mathbf{\hat{x}}- x_{4} \, a \, \mathbf{\hat{y}}& \left(8j\right) & \mbox{Mn III} \\ \end{array} \]

References

  • J. V. Florio, R. E. Rundle, and A. I. Snow, Compounds of thorium with transition metals. I. The thorium–manganese system, Acta Cryst. 5, 449–457 (1952), doi:10.1107/S0365110X52001337.

Found in

  • P. Villars and L. Calvert, Pearson's Handbook of Crystallographic Data for Intermetallic Phases (ASM International, Materials Park, OH, 1991), 2nd edn., pp. 4396.

Geometry files


Prototype Generator

aflow --proto=A12B_tI26_139_fij_a --params=

Species:

Running:

Output: