Ga4Ni Structure: A4B_cI40_197_cde_c

Picture of Structure; Click for Big Picture
Prototype : Ga4Ni
AFLOW prototype label : A4B_cI40_197_cde_c
Strukturbericht designation : None
Pearson symbol : cI40
Space group number : 197
Space group symbol : $\mbox{I23}$
AFLOW prototype command : aflow --proto=A4B_cI40_197_cde_c
--params=
$a$,$x_{1}$,$x_{2}$,$x_{3}$,$x_{4}$


Body-centered Cubic primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = &2 x_{1} \, \mathbf{a}_{1}+ 2 x_{1} \, \mathbf{a}_{2}+ 2 x_{1} \, \mathbf{a}_{3}& = &x_{1} \, a \, \mathbf{\hat{x}}+ x_{1} \, a \, \mathbf{\hat{y}}+ x_{1} \, a \, \mathbf{\hat{z}}& \left(8c\right) & \mbox{Ga I} \\ \mathbf{B}_{2} & = &- 2 x_{1} \, \mathbf{a}_{3}& = &- x_{1} \, a \, \mathbf{\hat{x}}- x_{1} \, a \, \mathbf{\hat{y}}+ x_{1} \, a \, \mathbf{\hat{z}}& \left(8c\right) & \mbox{Ga I} \\ \mathbf{B}_{3} & = &- 2 x_{1} \, \mathbf{a}_{2}& = &- x_{1} \, a \, \mathbf{\hat{x}}+ x_{1} \, a \, \mathbf{\hat{y}}- x_{1} \, a \, \mathbf{\hat{z}}& \left(8c\right) & \mbox{Ga I} \\ \mathbf{B}_{4} & = &- 2 x_{1} \, \mathbf{a}_{1}& = &x_{1} \, a \, \mathbf{\hat{x}}- x_{1} \, a \, \mathbf{\hat{y}}- x_{1} \, a \, \mathbf{\hat{z}}& \left(8c\right) & \mbox{Ga I} \\ \mathbf{B}_{5} & = &2 x_{2} \, \mathbf{a}_{1}+ 2 x_{2} \, \mathbf{a}_{2}+ 2 x_{2} \, \mathbf{a}_{3}& = &x_{2} \, a \, \mathbf{\hat{x}}+ x_{2} \, a \, \mathbf{\hat{y}}+ x_{2} \, a \, \mathbf{\hat{z}}& \left(8c\right) & \mbox{Ni} \\ \mathbf{B}_{6} & = &- 2 x_{2} \, \mathbf{a}_{3}& = &- x_{2} \, a \, \mathbf{\hat{x}}- x_{2} \, a \, \mathbf{\hat{y}}+ x_{2} \, a \, \mathbf{\hat{z}}& \left(8c\right) & \mbox{Ni} \\ \mathbf{B}_{7} & = &- 2 x_{2} \, \mathbf{a}_{2}& = &- x_{2} \, a \, \mathbf{\hat{x}}+ x_{2} \, a \, \mathbf{\hat{y}}- x_{2} \, a \, \mathbf{\hat{z}}& \left(8c\right) & \mbox{Ni} \\ \mathbf{B}_{8} & = &- 2 x_{2} \, \mathbf{a}_{1}& = &x_{2} \, a \, \mathbf{\hat{x}}- x_{2} \, a \, \mathbf{\hat{y}}- x_{2} \, a \, \mathbf{\hat{z}}& \left(8c\right) & \mbox{Ni} \\ \mathbf{B}_{9} & = &x_{3} \, \mathbf{a}_{2}+ x_{3} \, \mathbf{a}_{3}& = &x_{3} \, a \, \mathbf{\hat{x}}& \left(12d\right) & \mbox{Ga II} \\ \mathbf{B}_{10} & = &x_{3} \, \mathbf{a}_{1}+ x_{3} \, \mathbf{a}_{3}& = &x_{3} \, a \, \mathbf{\hat{y}}& \left(12d\right) & \mbox{Ga II} \\ \mathbf{B}_{11} & = &x_{3} \, \mathbf{a}_{1}+ x_{3} \, \mathbf{a}_{2}& = &x_{3} \, a \, \mathbf{\hat{z}}& \left(12d\right) & \mbox{Ga II} \\ \mathbf{B}_{12} & = &- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}& = &- x_{3} \, a \, \mathbf{\hat{x}}& \left(12d\right) & \mbox{Ga II} \\ \mathbf{B}_{13} & = &- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{3}& = &- x_{3} \, a \, \mathbf{\hat{y}}& \left(12d\right) & \mbox{Ga II} \\ \mathbf{B}_{14} & = &- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}& = &- x_{3} \, a \, \mathbf{\hat{z}}& \left(12d\right) & \mbox{Ga II} \\ \mathbf{B}_{15} & = &\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(12e\right) & \mbox{Ga III} \\ \mathbf{B}_{16} & = &\left(\frac12 + x_{4}\right) \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ x_{4} \, \mathbf{a}_{3}& = &x_{4} \, a \, \mathbf{\hat{y}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(12e\right) & \mbox{Ga III} \\ \mathbf{B}_{17} & = &x_{4} \, \mathbf{a}_{1}+ \left(\frac12 + x_{4}\right) \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ x_{4} \, a \, \mathbf{\hat{z}}& \left(12e\right) & \mbox{Ga III} \\ \mathbf{B}_{18} & = &\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(12e\right) & \mbox{Ga III} \\ \mathbf{B}_{19} & = &\left(\frac12 - x_{4}\right) \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}& = &- x_{4} \, a \, \mathbf{\hat{y}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(12e\right) & \mbox{Ga III} \\ \mathbf{B}_{20} & = &- x_{4} \, \mathbf{a}_{1}+ \left(\frac12 - x_{4}\right) \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}- x_{4} \, a \, \mathbf{\hat{z}}& \left(12e\right) & \mbox{Ga III} \\ \end{array} \]

References

  • L. Jingkui and X. Sishen, The Structure of NiGa4 Crystal – A New Vacancy Controlled gamma–Brass Phase, Scientia Sinica, Series A: Mathematical, Physical, Astronomical and Technical Sciences, English Edition 26, 1305–1313 (1983).

Found in

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

Geometry files


Prototype Generator

aflow --proto=A4B_cI40_197_cde_c --params=

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