Fe7W6 ($D8_{5}$) $\mu$–phase: A7B6_hR13_166_ah_3c

Picture of Structure; Click for Big Picture
Prototype : Fe7W6
AFLOW prototype label : A7B6_hR13_166_ah_3c
Strukturbericht designation : $D8_{5}$
Pearson symbol : hR13
Space group number : 166
Space group symbol : $\mbox{R}\bar{3}\mbox{m}$
AFLOW prototype command : aflow --proto=A7B6_hR13_166_ah_3c [--hex]
--params=
$a$,$c/a$,$x_{2}$,$x_{3}$,$x_{4}$,$x_{5}$,$z_{5}$


Other compounds with this structure

  • Co7Mo6, Co6Mo7, Co7W6, Co6Re6Si, Fe6Ta7, Fe7Nb6, Fe7Mo6, Fe7Ta6, Ta6Zn7, Mn6Si7, etc.

  • For more information on the $\mu$-phase, see (Pearson, 1972) 664. There it is referred to as a tetrahedrally close-packed Frank–Kasper structure. We have been unable to obtain a copy of the original reference for this structure, (Arnfeldt, 1935), so we use the structure from (Villars, 1991) 3415, which itself is taken from a secondary reference. Hexagonal settings of this structure can be obtained with the option ––hex.

Rhombohedral primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & ~ \frac12 \, a \, \mathbf{\hat{x}} - \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13 \, c \, \mathbf{\hat{z}} \\ \mathbf{a}_2 & = & \frac{1}{\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13 \, c \, \mathbf{\hat{z}} \\ \mathbf{a}_3 & = & - \frac12 \, a \, \mathbf{\hat{x}} - \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13 \, c \, \mathbf{\hat{z}} \\ \end{array} \]

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(1a\right) & \mbox{Fe I} \\ \mathbf{B}_{2} & =&x_{2} \, \mathbf{a}_{1}+ x_{2} \, \mathbf{a}_{2}+ x_{2} \, \mathbf{a}_{3}& =&x_{2} \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{W I} \\ \mathbf{B}_{3} & =&- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}& =&- x_{2} \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{W I} \\ \mathbf{B}_{4} & =&x_{3} \, \mathbf{a}_{1}+ x_{3} \, \mathbf{a}_{2}+ x_{3} \, \mathbf{a}_{3}& =&x_{3} \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{W II} \\ \mathbf{B}_{5} & =&- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}& =&- x_{3} \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{W II} \\ \mathbf{B}_{6} & =&x_{4} \, \mathbf{a}_{1}+ x_{4} \, \mathbf{a}_{2}+ x_{4} \, \mathbf{a}_{3}& =&x_{4} \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{W III} \\ \mathbf{B}_{7} & =&- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}& =&- x_{4} \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{W III} \\ \mathbf{B}_{8} & =&x_{5} \, \mathbf{a}_{1}+ x_{5} \, \mathbf{a}_{2}+ z_{5} \, \mathbf{a}_{3}& =&\frac12 \, \left(x_{5} - z_{5}\right) \, a \, \mathbf{\hat{x}}+ \frac1{2\sqrt3} \left(x_{5} - z_{5}\right) \, a \, \mathbf{\hat{y}}+ \frac13 \, \left(2 x_{5} + z_{5}\right) \, c \, \mathbf{\hat{z}}& \left(6h\right) & \mbox{Fe II} \\ \mathbf{B}_{9} & =&z_{5} \, \mathbf{a}_{1}+ x_{5} \, \mathbf{a}_{2}+ x_{5} \, \mathbf{a}_{3}& =&\frac12 \, \left(z_{5} - x_{5}\right) \, a \, \mathbf{\hat{x}}+ \frac1{2\sqrt3} \left(x_{5} - z_{5}\right) \, a \, \mathbf{\hat{y}}+ \frac13 \, \left(2 x_{5} + z_{5}\right) \, c \, \mathbf{\hat{z}}& \left(6h\right) & \mbox{Fe II} \\ \mathbf{B}_{10} & =&x_{5} \, \mathbf{a}_{1}+ z_{5} \, \mathbf{a}_{2}+ x_{5} \, \mathbf{a}_{3}& =&\frac1{\sqrt3} \left(z_{5} - x_{5}\right) \, a \, \mathbf{\hat{y}}+ \frac13 \, \left(2 x_{5} + z_{5}\right) \, c \, \mathbf{\hat{z}}& \left(6h\right) & \mbox{Fe II} \\ \mathbf{B}_{11} & =&- x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}& =&\frac12 \, \left(z_{5} - x_{5}\right) \, a \, \mathbf{\hat{x}}+ \frac1{2\sqrt3} \left(z_{5} - x_{5}\right) \, a \, \mathbf{\hat{y}}- \frac13 \, \left(2 x_{5} + z_{5}\right) \, c \, \mathbf{\hat{z}}& \left(6h\right) & \mbox{Fe II} \\ \mathbf{B}_{12} & =&- z_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}& =&\frac12 \, \left(x_{5} - z_{5}\right) \, a \, \mathbf{\hat{x}}+ \frac1{2\sqrt3} \left(z_{5} - x_{5}\right) \, a \, \mathbf{\hat{y}}- \frac13 \, \left(2 x_{5} + z_{5}\right) \, c \, \mathbf{\hat{z}}& \left(6h\right) & \mbox{Fe II} \\ \mathbf{B}_{13} & =&- x_{5} \, \mathbf{a}_{1}- z_{5} \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}& =&\frac1{\sqrt3} \left(x_{5} - z_{5}\right) \, a \, \mathbf{\hat{y}}- \frac13 \, \left(2 x_{5} + z_{5}\right) \, c \, \mathbf{\hat{z}}& \left(6h\right) & \mbox{Fe II} \\ \end{array} \]

References

  • H. Arnfelt, Crystal Structure of Fe7W6, Jernkontorets Annaler 119, 185–187 (1935).
  • W. B. Pearson, The Crystal Chemistry and Physics of Metals and Alloys (Wiley– Interscience, New York, London, Sydney, Toronto, 1972).

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. 3415.

Geometry files


Prototype Generator

aflow --proto=A7B6_hR13_166_ah_3c --params=

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