$\sigma$–CrFe ($D8_{b}$) Structure: sigma_tP30_136_bf2ij

Picture of Structure; Click for Big Picture
Prototype : $\sigma$–CrFe
AFLOW prototype label : sigma_tP30_136_bf2ij
Strukturbericht designation : $D8_{b}$
Pearson symbol : tP30
Space group number : 136
Space group symbol : $\mbox{P4}_{2}\mbox{/mnm}$
AFLOW prototype command : aflow --proto=sigma_tP30_136_bf2ij
--params=
$a$,$c/a$,$x_{2}$,$x_{3}$,$y_{3}$,$x_{4}$,$y_{4}$,$x_{5}$,$z_{5}$


Other compounds with this structure

  • Al3CoNb6, AlCrNb3, Co2Mo3, Ta3V7, PdTa3, IrMo2, IrW3, many others.

  • The atoms in this lattice are completely disordered, that is, the Cr and Fe atoms are distributed randomly on the sites in the unit cell. This seems to be the case for all of the compounds listed below. We have chosen several of the atoms near Fe and Cr in the periodic table to color the above pictures. Except for a shift of the origin, this structure is crystallographically equivalent to $\beta$–U (Ab). Due to an origin shift, literature may list different Wyckoff designations. For instance, the structure in (Berne, 2001) lists a different Wyckoff sequence of af2ij; however, it is structurally equivalent to this prototype and can be verified with AFLOW-XtalFinder. Previously, the Pd-Rh distance was too short. This is the corrected version. We thank Brandon Bocklund for pointing this out.

Simple Tetragonal primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & =&\frac12 \, \mathbf{a}_{3} & =&\frac12 c \, \mathbf{\hat{z}} & \left(2b\right) & \mbox{M I} \\ \mathbf{B}_{2} & =&\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}& =&\frac12 \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}& \left(2b\right) & \mbox{M I} \\ \mathbf{B}_{3} & =&x_{2} \, \mathbf{a}_{1}+ x_{2} \, \mathbf{a}_{2}& =&x_{2} \, a \, \mathbf{\hat{x}}+ x_{2} \, a \, \mathbf{\hat{y}}& \left(4f\right) & \mbox{M II} \\ \mathbf{B}_{4} & =&- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}& =&- x_{2} \, a \, \mathbf{\hat{x}}- x_{2} \, a \, \mathbf{\hat{y}}& \left(4f\right) & \mbox{M II} \\ \mathbf{B}_{5} & =&\left(\frac12 - x_{2}\right) \, \mathbf{a}_{1}+ \left(\frac12 + x_{2}\right) \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& =&\left(\frac12 - x_{2}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 + x_{2}\right) \, a \, \mathbf{\hat{y}}+ \frac12 \, c \, \mathbf{\hat{z}}& \left(4f\right) & \mbox{M II} \\ \mathbf{B}_{6} & =&\left(\frac12 + x_{2}\right) \, \mathbf{a}_{1}+ \left(\frac12 - x_{2}\right) \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& =&\left(\frac12 + x_{2}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 - x_{2}\right) \, a \, \mathbf{\hat{y}}+ \frac12 \, c \, \mathbf{\hat{z}}& \left(4f\right) & \mbox{M II} \\ \mathbf{B}_{7} & =&x_{3} \, \mathbf{a}_{1}+ y_{3} \, \mathbf{a}_{2}& =&x_{3} \, a \, \mathbf{\hat{x}}+ y_{3} \, a \, \mathbf{\hat{y}}& \left(8i\right) & \mbox{M III} \\ \mathbf{B}_{8} & =&- x_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}& =&- x_{3} \, a \, \mathbf{\hat{x}}- y_{3} \, a \, \mathbf{\hat{y}}& \left(8i\right) & \mbox{M III} \\ \mathbf{B}_{9} & =&\left(\frac12 - y_{3}\right) \, \mathbf{a}_{1}+ \left(\frac12 + x_{3}\right) \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& =&\left(\frac12 - y_{3}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 + x_{3}\right) \, a \, \mathbf{\hat{y}}+ \frac12 \, c \, \mathbf{\hat{z}}& \left(8i\right) & \mbox{M III} \\ \mathbf{B}_{10} & =&\left(\frac12 + y_{3}\right) \, \mathbf{a}_{1}+ \left(\frac12 - x_{3}\right) \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& =&\left(\frac12 + y_{3}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 - x_{3}\right) \, a \, \mathbf{\hat{y}}+ \frac12 \, c \, \mathbf{\hat{z}}& \left(8i\right) & \mbox{M III} \\ \mathbf{B}_{11} & =&\left(\frac12 - x_{3}\right) \, \mathbf{a}_{1}+ \left(\frac12 + y_{3}\right) \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& =&\left(\frac12 - x_{3}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 + y_{3}\right) \, a \, \mathbf{\hat{y}}+ \frac12 \, c \, \mathbf{\hat{z}}& \left(8i\right) & \mbox{M III} \\ \mathbf{B}_{12} & =&\left(\frac12 + x_{3}\right) \, \mathbf{a}_{1}+ \left(\frac12 - y_{3}\right) \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& =&\left(\frac12 + x_{3}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 - y_{3}\right) \, a \, \mathbf{\hat{y}}+ \frac12 \, c \, \mathbf{\hat{z}}& \left(8i\right) & \mbox{M III} \\ \mathbf{B}_{13} & =&y_{3} \, \mathbf{a}_{1}+ x_{3} \, \mathbf{a}_{2}& =&y_{3} \, a \, \mathbf{\hat{x}}+ x_{3} \, a \, \mathbf{\hat{y}}& \left(8i\right) & \mbox{M III} \\ \mathbf{B}_{14} & =&- y_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}& =&- y_{3} \, a \, \mathbf{\hat{x}}- x_{3} \, a \, \mathbf{\hat{y}}& \left(8i\right) & \mbox{M III} \\ \mathbf{B}_{15} & =&x_{4} \, \mathbf{a}_{1}+ y_{4} \, \mathbf{a}_{2}& =&x_{4} \, a \, \mathbf{\hat{x}}+ y_{4} \, a \, \mathbf{\hat{y}}& \left(8i\right) & \mbox{M IV} \\ \mathbf{B}_{16} & =&- x_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}& =&- x_{4} \, a \, \mathbf{\hat{x}}- y_{4} \, a \, \mathbf{\hat{y}}& \left(8i\right) & \mbox{M IV} \\ \mathbf{B}_{17} & =&\left(\frac12 - y_{4}\right) \, \mathbf{a}_{1}+ \left(\frac12 + x_{4}\right) \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& =&\left(\frac12 - y_{4}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 + x_{4}\right) \, a \, \mathbf{\hat{y}}+ \frac12 \, c \, \mathbf{\hat{z}}& \left(8i\right) & \mbox{M IV} \\ \mathbf{B}_{18} & =&\left(\frac12 + y_{4}\right) \, \mathbf{a}_{1}+ \left(\frac12 - x_{4}\right) \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& =&\left(\frac12 + y_{4}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 - x_{4}\right) \, a \, \mathbf{\hat{y}}+ \frac12 \, c \, \mathbf{\hat{z}}& \left(8i\right) & \mbox{M IV} \\ \mathbf{B}_{19} & =&\left(\frac12 - x_{4}\right) \, \mathbf{a}_{1}+ \left(\frac12 + y_{4}\right) \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& =&\left(\frac12 - x_{4}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 + y_{4}\right) \, a \, \mathbf{\hat{y}}+ \frac12 \, c \, \mathbf{\hat{z}}& \left(8i\right) & \mbox{M IV} \\ \mathbf{B}_{20} & =&\left(\frac12 + x_{4}\right) \, \mathbf{a}_{1}+ \left(\frac12 - y_{4}\right) \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& =&\left(\frac12 + x_{4}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 - y_{4}\right) \, a \, \mathbf{\hat{y}}+ \frac12 \, c \, \mathbf{\hat{z}}& \left(8i\right) & \mbox{M IV} \\ \mathbf{B}_{21} & =&y_{4} \, \mathbf{a}_{1}+ x_{4} \, \mathbf{a}_{2}& =&y_{4} \, a \, \mathbf{\hat{x}}+ x_{4} \, a \, \mathbf{\hat{y}}& \left(8i\right) & \mbox{M IV} \\ \mathbf{B}_{22} & =&- y_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}& =&- y_{4} \, a \, \mathbf{\hat{x}}- x_{4} \, a \, \mathbf{\hat{y}}& \left(8i\right) & \mbox{M IV} \\ \mathbf{B}_{23} & =&x_{5} \, \mathbf{a}_{1}+ x_{5} \, \mathbf{a}_{2}+ z_{5} \, \mathbf{a}_{3}& =&x_{5} \, a \, \mathbf{\hat{x}}+ x_{5} \, a \, \mathbf{\hat{y}}+ z_{5} \, c \, \mathbf{\hat{z}}& \left(8j\right) & \mbox{M V} \\ \mathbf{B}_{24} & =&- x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}+ z_{5} \, \mathbf{a}_{3}& =&- x_{5} \, a \, \mathbf{\hat{x}}- x_{5} \, a \, \mathbf{\hat{y}}+ z_{5} \, c \, \mathbf{\hat{z}}& \left(8j\right) & \mbox{M V} \\ \mathbf{B}_{25} & =&\left(\frac12 - x_{5}\right) \, \mathbf{a}_{1}+ \left(\frac12 + x_{5}\right) \, \mathbf{a}_{2}+ \left(\frac12 + z_{5}\right) \, \mathbf{a}_{3}& =&\left(\frac12 - x_{5}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 + x_{5}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac12 + z_{5}\right) \, c \, \mathbf{\hat{z}}& \left(8j\right) & \mbox{M V} \\ \mathbf{B}_{26} & =&\left(\frac12 + x_{5}\right) \, \mathbf{a}_{1}+ \left(\frac12 - x_{5}\right) \, \mathbf{a}_{2}+ \left(\frac12 + z_{5}\right) \, \mathbf{a}_{3}& =&\left(\frac12 + x_{5}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 - x_{5}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac12 + z_{5}\right) \, c \, \mathbf{\hat{z}}& \left(8j\right) & \mbox{M V} \\ \mathbf{B}_{27} & =&\left(\frac12 - x_{5}\right) \, \mathbf{a}_{1}+ \left(\frac12 + x_{5}\right) \, \mathbf{a}_{2}+ \left(\frac12 - z_{5}\right) \, \mathbf{a}_{3}& =&\left(\frac12 - x_{5}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 + x_{5}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac12 - z_{5}\right) \, c \, \mathbf{\hat{z}}& \left(8j\right) & \mbox{M V} \\ \mathbf{B}_{28} & =&\left(\frac12 + x_{5}\right) \, \mathbf{a}_{1}+ \left(\frac12 - x_{5}\right) \, \mathbf{a}_{2}+ \left(\frac12 - z_{5}\right) \, \mathbf{a}_{3}& =&\left(\frac12 + x_{5}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 - x_{5}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac12 - z_{5}\right) \, c \, \mathbf{\hat{z}}& \left(8j\right) & \mbox{M V} \\ \mathbf{B}_{29} & =&x_{5} \, \mathbf{a}_{1}+ x_{5} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}& =&x_{5} \, a \, \mathbf{\hat{x}}+ x_{5} \, a \, \mathbf{\hat{y}}- z_{5} \, c \, \mathbf{\hat{z}}& \left(8j\right) & \mbox{M V} \\ \mathbf{B}_{30} & =&- x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}& =&- x_{5} \, a \, \mathbf{\hat{x}}- x_{5} \, a \, \mathbf{\hat{y}}- z_{5} \, c \, \mathbf{\hat{z}}& \left(8j\right) & \mbox{M V} \\ \end{array} \]

References

  • H. L. Yakel, Atom distributions in sigma phases. I. Fe and Cr atom distributions in a binary sigma phase equilibrated at 1063, 1013 and 923 K, Acta Crystallogr. Sect. B Struct. Sci. B39, 20–28 (1983), doi:10.1107/S0108768183001974.

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. 2639.

Geometry files


Prototype Generator

aflow --proto=sigma_tP30_136_bf2ij --params=

Species:

Running:

Output: