Ga4Ni3 Structure: A4B3_cI112_230_af_g

Picture of Structure; Click for Big Picture
Prototype : Ga4Ni3
AFLOW prototype label : A4B3_cI112_230_af_g
Strukturbericht designation : None
Pearson symbol : cI112
Space group number : 230
Space group symbol : $\mbox{Ia}\bar{3}\mbox{d}$
AFLOW prototype command : aflow --proto=A4B3_cI112_230_af_g
--params=
$a$,$x_{2}$,$y_{3}$


  • This is a simple defect superstructure of the CsCl (B2) structure. If a GaNi B2 structure is expanded into a 128 atom supercell, we can describe it using space group Ia3d (#230), with Ga atoms on the (16a) and (48f) Wyckoff sites and Ni atoms on the (16b) and (48g) sites. Removing the Ni atoms from the (16b) sites yields this structure.

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} & = &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(16a\right) & \mbox{Ga I} \\ \mathbf{B}_{2} & = &\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{y}}& \left(16a\right) & \mbox{Ga I} \\ \mathbf{B}_{3} & = &\frac12 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}& \left(16a\right) & \mbox{Ga I} \\ \mathbf{B}_{4} & = &\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}& = &\frac12 \, a \, \mathbf{\hat{z}}& \left(16a\right) & \mbox{Ga I} \\ \mathbf{B}_{5} & = &\frac12 \, \mathbf{a}_{1}& = &\frac34 \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{y}}+ \frac14 \, a \, \mathbf{\hat{z}}& \left(16a\right) & \mbox{Ga I} \\ \mathbf{B}_{6} & = &\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\frac14 \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{y}}+ \frac14 \, a \, \mathbf{\hat{z}}& \left(16a\right) & \mbox{Ga I} \\ \mathbf{B}_{7} & = &\frac12 \, \mathbf{a}_{3}& = &\frac14 \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{y}}+ \frac34 \, a \, \mathbf{\hat{z}}& \left(16a\right) & \mbox{Ga I} \\ \mathbf{B}_{8} & = &\frac12 \, \mathbf{a}_{2}& = &\frac14 \, a \, \mathbf{\hat{x}}+ \frac34 \, a \, \mathbf{\hat{y}}+ \frac14 \, a \, \mathbf{\hat{z}}& \left(16a\right) & \mbox{Ga I} \\ \mathbf{B}_{9} & = &\frac14 \, \mathbf{a}_{1}+ \left(\frac14 + x_{2}\right) \, \mathbf{a}_{2}+ x_{2} \, \mathbf{a}_{3}& = &x_{2} \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{z}}& \left(48f\right) & \mbox{Ga II} \\ \mathbf{B}_{10} & = &\frac34 \, \mathbf{a}_{1}+ \left(\frac14 - x_{2}\right) \, \mathbf{a}_{2}+ \left(\frac12 - x_{2}\right) \, \mathbf{a}_{3}& = &- x_{2} \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}+ \frac14 \, a \, \mathbf{\hat{z}}& \left(48f\right) & \mbox{Ga II} \\ \mathbf{B}_{11} & = &x_{2} \, \mathbf{a}_{1}+ \frac14 \, \mathbf{a}_{2}+ \left(\frac14 + x_{2}\right) \, \mathbf{a}_{3}& = &\frac14 \, a \, \mathbf{\hat{x}}+ x_{2} \, a \, \mathbf{\hat{y}}& \left(48f\right) & \mbox{Ga II} \\ \mathbf{B}_{12} & = &\left(\frac12 - x_{2}\right) \, \mathbf{a}_{1}+ \frac34 \, \mathbf{a}_{2}+ \left(\frac14 - x_{2}\right) \, \mathbf{a}_{3}& = &\frac14 \, a \, \mathbf{\hat{x}}- x_{2} \, a \, \mathbf{\hat{y}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(48f\right) & \mbox{Ga II} \\ \mathbf{B}_{13} & = &\left(\frac14 + x_{2}\right) \, \mathbf{a}_{1}+ x_{2} \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& = &\frac14 \, a \, \mathbf{\hat{y}}+ x_{2} \, a \, \mathbf{\hat{z}}& \left(48f\right) & \mbox{Ga II} \\ \mathbf{B}_{14} & = &\left(\frac14 - x_{2}\right) \, \mathbf{a}_{1}+ \left(\frac12 - x_{2}\right) \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}\frac14 \, a \, \mathbf{\hat{y}}- x_{2} \, a \, \mathbf{\hat{z}}& \left(48f\right) & \mbox{Ga II} \\ \mathbf{B}_{15} & = &\left(\frac14 + x_{2}\right) \, \mathbf{a}_{1}+ \frac34 \, \mathbf{a}_{2}+ x_{2} \, \mathbf{a}_{3}& = &\frac14 \, a \, \mathbf{\hat{x}}+ \left(\frac34 + x_{2}\right) \, a \, \mathbf{\hat{y}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(48f\right) & \mbox{Ga II} \\ \mathbf{B}_{16} & = &\left(\frac14 - x_{2}\right) \, \mathbf{a}_{1}+ \frac14 \, \mathbf{a}_{2}+ \left(\frac12 - x_{2}\right) \, \mathbf{a}_{3}& = &\frac14 \, a \, \mathbf{\hat{x}}+ \left(\frac14 - x_{2}\right) \, a \, \mathbf{\hat{y}}& \left(48f\right) & \mbox{Ga II} \\ \mathbf{B}_{17} & = &\frac34 \, \mathbf{a}_{1}+ x_{2} \, \mathbf{a}_{2}+ \left(\frac14 + x_{2}\right) \, \mathbf{a}_{3}& = &\left(\frac34 + x_{2}\right) \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}+ \frac14 \, a \, \mathbf{\hat{z}}& \left(48f\right) & \mbox{Ga II} \\ \mathbf{B}_{18} & = &\frac14 \, \mathbf{a}_{1}+ \left(\frac12 - x_{2}\right) \, \mathbf{a}_{2}+ \left(\frac14 - x_{2}\right) \, \mathbf{a}_{3}& = &\left(\frac14 - x_{2}\right) \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{z}}& \left(48f\right) & \mbox{Ga II} \\ \mathbf{B}_{19} & = &\left(\frac12 - x_{2}\right) \, \mathbf{a}_{1}+ \left(\frac14 - x_{2}\right) \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& = &\frac14 \, a \, \mathbf{\hat{y}}+ \left(\frac14 - x_{2}\right) \, a \, \mathbf{\hat{z}}& \left(48f\right) & \mbox{Ga II} \\ \mathbf{B}_{20} & = &x_{2} \, \mathbf{a}_{1}+ \left(\frac14 + x_{2}\right) \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}\frac14 \, a \, \mathbf{\hat{y}}+ \left(\frac34 + x_{2}\right) \, a \, \mathbf{\hat{z}}& \left(48f\right) & \mbox{Ga II} \\ \mathbf{B}_{21} & = &\frac34 \, \mathbf{a}_{1}+ \left(\frac34 - x_{2}\right) \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}& = &- x_{2} \, a \, \mathbf{\hat{x}}+ \frac34 \, a \, \mathbf{\hat{z}}& \left(48f\right) & \mbox{Ga II} \\ \mathbf{B}_{22} & = &\frac14 \, \mathbf{a}_{1}+ \left(x_{2} + \frac34\right) \, \mathbf{a}_{2}+ \left(\frac12 + x_{2}\right) \, \mathbf{a}_{3}& = &\left(\frac12 + x_{2}\right) \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{z}}& \left(48f\right) & \mbox{Ga II} \\ \mathbf{B}_{23} & = &- x_{2} \, \mathbf{a}_{1}+ \frac34 \, \mathbf{a}_{2}+ \left(\frac34 - x_{2}\right) \, \mathbf{a}_{3}& = &\frac34 \, a \, \mathbf{\hat{x}}- x_{2} \, a \, \mathbf{\hat{y}}& \left(48f\right) & \mbox{Ga II} \\ \mathbf{B}_{24} & = &\left(\frac12 + x_{2}\right) \, \mathbf{a}_{1}+ \frac14 \, \mathbf{a}_{2}+ \left(x_{2} + \frac34\right) \, \mathbf{a}_{3}& = &\frac14 \, a \, \mathbf{\hat{x}}+ \left(\frac12 + x_{2}\right) \, a \, \mathbf{\hat{y}}& \left(48f\right) & \mbox{Ga II} \\ \mathbf{B}_{25} & = &\left(\frac34 - x_{2}\right) \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& = &\frac34 \, a \, \mathbf{\hat{y}}- x_{2} \, a \, \mathbf{\hat{z}}& \left(48f\right) & \mbox{Ga II} \\ \mathbf{B}_{26} & = &\left(x_{2} + \frac34\right) \, \mathbf{a}_{1}+ \left(\frac12 + x_{2}\right) \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& = &\frac14 \, a \, \mathbf{\hat{y}}+ \left(\frac12 + x_{2}\right) \, a \, \mathbf{\hat{z}}& \left(48f\right) & \mbox{Ga II} \\ \mathbf{B}_{27} & = &\left(\frac34 - x_{2}\right) \, \mathbf{a}_{1}+ \frac14 \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}& = &\frac34 \, a \, \mathbf{\hat{x}}+ \left(\frac14 - x_{2}\right) \, a \, \mathbf{\hat{y}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(48f\right) & \mbox{Ga II} \\ \mathbf{B}_{28} & = &\left(x_{2} + \frac34\right) \, \mathbf{a}_{1}+ \frac34 \, \mathbf{a}_{2}+ \left(\frac12 + x_{2}\right) \, \mathbf{a}_{3}& = &\frac14 \, a \, \mathbf{\hat{x}}+ \left(\frac14 + x_{2}\right) \, a \, \mathbf{\hat{y}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(48f\right) & \mbox{Ga II} \\ \mathbf{B}_{29} & = &\frac14 \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+ \left(\frac34 - x_{2}\right) \, \mathbf{a}_{3}& = &\left(\frac14 - x_{2}\right) \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}+ \frac34 \, a \, \mathbf{\hat{z}}& \left(48f\right) & \mbox{Ga II} \\ \mathbf{B}_{30} & = &\frac34 \, \mathbf{a}_{1}+ \left(\frac12 + x_{2}\right) \, \mathbf{a}_{2}+ \left(x_{2} + \frac34\right) \, \mathbf{a}_{3}& = &\left(\frac14 + x_{2}\right) \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}+ \frac14 \, a \, \mathbf{\hat{z}}& \left(48f\right) & \mbox{Ga II} \\ \mathbf{B}_{31} & = &\left(\frac12 + x_{2}\right) \, \mathbf{a}_{1}+ \left(x_{2} + \frac34\right) \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{y}}+ \left(\frac14 + x_{2}\right) \, a \, \mathbf{\hat{z}}& \left(48f\right) & \mbox{Ga II} \\ \mathbf{B}_{32} & = &- x_{2} \, \mathbf{a}_{1}+ \left(\frac34 - x_{2}\right) \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}\frac34 \, a \, \mathbf{\hat{y}}+ \left(\frac14 - x_{2}\right) \, a \, \mathbf{\hat{z}}& \left(48f\right) & \mbox{Ga II} \\ \mathbf{B}_{33} & = &\frac14 \, \mathbf{a}_{1}+ \left(\frac38 - y_{3}\right) \, \mathbf{a}_{2}+ \left(\frac18 + y_{3}\right) \, \mathbf{a}_{3}& = &\frac18 \, a \, \mathbf{\hat{x}}+ y_{3} \, a \, \mathbf{\hat{y}}+ \left(\frac14 - y_{3}\right) \, a \, \mathbf{\hat{z}}& \left(48g\right) & \mbox{Ni} \\ \mathbf{B}_{34} & = &\left(\frac34 - 2 y_{3}\right) \, \mathbf{a}_{1}+ \left(\frac18 - y_{3}\right) \, \mathbf{a}_{2}+ \left(\frac38 - y_{3}\right) \, \mathbf{a}_{3}& = &\frac78 \, a \, \mathbf{\hat{x}}+ \left(\frac12 - y_{3}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac14 - y_{3}\right) \, a \, \mathbf{\hat{z}}& \left(48g\right) & \mbox{Ni} \\ \mathbf{B}_{35} & = &\left(2 y_{3} + \frac34\right) \, \mathbf{a}_{1}+ \left(\frac18 + y_{3}\right) \, \mathbf{a}_{2}+ \left(\frac38 + y_{3}\right) \, \mathbf{a}_{3}& = &\frac78 \, a \, \mathbf{\hat{x}}+ \left(\frac12 + y_{3}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac14 + y_{3}\right) \, a \, \mathbf{\hat{z}}& \left(48g\right) & \mbox{Ni} \\ \mathbf{B}_{36} & = &\frac14 \, \mathbf{a}_{1}+ \left(\frac38 + y_{3}\right) \, \mathbf{a}_{2}+ \left(\frac18 - y_{3}\right) \, \mathbf{a}_{3}& = &\frac18 \, a \, \mathbf{\hat{x}}- y_{3} \, a \, \mathbf{\hat{y}}+ \left(\frac14 + y_{3}\right) \, a \, \mathbf{\hat{z}}& \left(48g\right) & \mbox{Ni} \\ \mathbf{B}_{37} & = &\left(\frac18 + y_{3}\right) \, \mathbf{a}_{1}+ \frac14 \, \mathbf{a}_{2}+ \left(\frac38 - y_{3}\right) \, \mathbf{a}_{3}& = &\left(\frac14 - y_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac18 \, a \, \mathbf{\hat{y}}+ y_{3} \, a \, \mathbf{\hat{z}}& \left(48g\right) & \mbox{Ni} \\ \mathbf{B}_{38} & = &\left(\frac38 - y_{3}\right) \, \mathbf{a}_{1}+ \left(\frac34 - 2 y_{3}\right) \, \mathbf{a}_{2}+ \left(\frac18 - y_{3}\right) \, \mathbf{a}_{3}& = &\left(\frac14 - y_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac78 \, a \, \mathbf{\hat{y}}+ \left(\frac12 - y_{3}\right) \, a \, \mathbf{\hat{z}}& \left(48g\right) & \mbox{Ni} \\ \mathbf{B}_{39} & = &\left(\frac38 + y_{3}\right) \, \mathbf{a}_{1}+ \left(2 y_{3} + \frac34\right) \, \mathbf{a}_{2}+ \left(\frac18 + y_{3}\right) \, \mathbf{a}_{3}& = &\left(\frac14 + y_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac78 \, a \, \mathbf{\hat{y}}+ \left(\frac12 + y_{3}\right) \, a \, \mathbf{\hat{z}}& \left(48g\right) & \mbox{Ni} \\ \mathbf{B}_{40} & = &\left(\frac18 - y_{3}\right) \, \mathbf{a}_{1}+ \frac14 \, \mathbf{a}_{2}+ \left(\frac38 + y_{3}\right) \, \mathbf{a}_{3}& = &\left(\frac14 + y_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac18 \, a \, \mathbf{\hat{y}}- y_{3} \, a \, \mathbf{\hat{z}}& \left(48g\right) & \mbox{Ni} \\ \mathbf{B}_{41} & = &\left(\frac38 - y_{3}\right) \, \mathbf{a}_{1}+ \left(\frac18 + y_{3}\right) \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& = &y_{3} \, a \, \mathbf{\hat{x}}+ \left(\frac14 - y_{3}\right) \, a \, \mathbf{\hat{y}}+ \frac18 \, a \, \mathbf{\hat{z}}& \left(48g\right) & \mbox{Ni} \\ \mathbf{B}_{42} & = &\left(\frac18 - y_{3}\right) \, \mathbf{a}_{1}+ \left(\frac38 - y_{3}\right) \, \mathbf{a}_{2}+ \left(\frac34 - 2 y_{3}\right) \, \mathbf{a}_{3}& = &\left(\frac12 - y_{3}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac14 - y_{3}\right) \, a \, \mathbf{\hat{y}}+ \frac78 \, a \, \mathbf{\hat{z}}& \left(48g\right) & \mbox{Ni} \\ \mathbf{B}_{43} & = &\left(\frac18 + y_{3}\right) \, \mathbf{a}_{1}+ \left(\frac38 + y_{3}\right) \, \mathbf{a}_{2}+ \left(2 y_{3} + \frac34\right) \, \mathbf{a}_{3}& = &\left(\frac12 + y_{3}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac14 + y_{3}\right) \, a \, \mathbf{\hat{y}}+ \frac78 \, a \, \mathbf{\hat{z}}& \left(48g\right) & \mbox{Ni} \\ \mathbf{B}_{44} & = &\left(\frac38 + y_{3}\right) \, \mathbf{a}_{1}+ \left(\frac18 - y_{3}\right) \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& = &- y_{3} \, a \, \mathbf{\hat{x}}+ \left(\frac14 + y_{3}\right) \, a \, \mathbf{\hat{y}}+ \frac18 \, a \, \mathbf{\hat{z}}& \left(48g\right) & \mbox{Ni} \\ \mathbf{B}_{45} & = &\frac34 \, \mathbf{a}_{1}+ \left(\frac58 + y_{3}\right) \, \mathbf{a}_{2}+ \left(\frac78 - y_{3}\right) \, \mathbf{a}_{3}& = &\frac38 \, a \, \mathbf{\hat{x}}+ \left(\frac12 - y_{3}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac14 + y_{3}\right) \, a \, \mathbf{\hat{z}}& \left(48g\right) & \mbox{Ni} \\ \mathbf{B}_{46} & = &\left(\frac14 + 2 y_{3}\right) \, \mathbf{a}_{1}+ \left(\frac78 + y_{3}\right) \, \mathbf{a}_{2}+ \left(\frac58 + y_{3}\right) \, \mathbf{a}_{3}& = &\frac58 \, a \, \mathbf{\hat{x}}+ y_{3} \, a \, \mathbf{\hat{y}}+ \left(\frac14 + y_{3}\right) \, a \, \mathbf{\hat{z}}& \left(48g\right) & \mbox{Ni} \\ \mathbf{B}_{47} & = &\left(\frac14 - 2 y_{3}\right) \, \mathbf{a}_{1}+ \left(\frac78 - y_{3}\right) \, \mathbf{a}_{2}+ \left(\frac58 - y_{3}\right) \, \mathbf{a}_{3}& = &\frac58 \, a \, \mathbf{\hat{x}}- y_{3} \, a \, \mathbf{\hat{y}}+ \left(\frac14 - y_{3}\right) \, a \, \mathbf{\hat{z}}& \left(48g\right) & \mbox{Ni} \\ \mathbf{B}_{48} & = &\frac34 \, \mathbf{a}_{1}+ \left(\frac58 - y_{3}\right) \, \mathbf{a}_{2}+ \left(y_{3} + \frac78\right) \, \mathbf{a}_{3}& = &\frac38 \, a \, \mathbf{\hat{x}}+ \left(\frac12 + y_{3}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac14 - y_{3}\right) \, a \, \mathbf{\hat{z}}& \left(48g\right) & \mbox{Ni} \\ \mathbf{B}_{49} & = &\left(\frac78 - y_{3}\right) \, \mathbf{a}_{1}+ \frac34 \, \mathbf{a}_{2}+ \left(\frac58 + y_{3}\right) \, \mathbf{a}_{3}& = &\left(\frac14 + y_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac38 \, a \, \mathbf{\hat{y}}+ \left(\frac12- y_{3}\right) \, a \, \mathbf{\hat{z}}& \left(48g\right) & \mbox{Ni} \\ \mathbf{B}_{50} & = &\left(y_{3} + \frac58\right) \, \mathbf{a}_{1}+ \left(\frac14 + 2 y_{3}\right) \, \mathbf{a}_{2}+ \left(\frac78 + y_{3}\right) \, \mathbf{a}_{3}& = &\left(\frac14 + y_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac58 \, a \, \mathbf{\hat{y}}+ y_{3} \, a \, \mathbf{\hat{z}}& \left(48g\right) & \mbox{Ni} \\ \mathbf{B}_{51} & = &\left(\frac58 - y_{3}\right) \, \mathbf{a}_{1}+ \left(\frac14 - 2 y_{3}\right) \, \mathbf{a}_{2}+ \left(\frac78 - y_{3}\right) \, \mathbf{a}_{3}& = &\left(\frac14 - y_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac58 \, a \, \mathbf{\hat{y}}- y_{3} \, a \, \mathbf{\hat{z}}& \left(48g\right) & \mbox{Ni} \\ \mathbf{B}_{52} & = &\left(y_{3} + \frac78\right) \, \mathbf{a}_{1}+ \frac34 \, \mathbf{a}_{2}+ \left(\frac58 - y_{3}\right) \, \mathbf{a}_{3}& = &\left(\frac14 - y_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac38 \, a \, \mathbf{\hat{y}}+ \left(\frac12 + y_{3}\right) \, a \, \mathbf{\hat{z}}& \left(48g\right) & \mbox{Ni} \\ \mathbf{B}_{53} & = &\left(\frac58 + y_{3}\right) \, \mathbf{a}_{1}+ \left(\frac78 - y_{3}\right) \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& = &\left(\frac12 - y_{3}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac14 + y_{3}\right) \, a \, \mathbf{\hat{y}}+ \frac38 \, a \, \mathbf{\hat{z}}& \left(48g\right) & \mbox{Ni} \\ \mathbf{B}_{54} & = &\left(\frac78 + y_{3}\right) \, \mathbf{a}_{1}+ \left(y_{3} + \frac58\right) \, \mathbf{a}_{2}+ \left(\frac14 + 2 y_{3}\right) \, \mathbf{a}_{3}& = &y_{3} \, a \, \mathbf{\hat{x}}+ \left(\frac14 + y_{3}\right) \, a \, \mathbf{\hat{y}}+ \frac58 \, a \, \mathbf{\hat{z}}& \left(48g\right) & \mbox{Ni} \\ \mathbf{B}_{55} & = &\left(\frac78 - y_{3}\right) \, \mathbf{a}_{1}+ \left(\frac58 - y_{3}\right) \, \mathbf{a}_{2}+ \left(\frac14 - 2 y_{3}\right) \, \mathbf{a}_{3}& = &- y_{3} \, a \, \mathbf{\hat{x}}+ \left(\frac14 - y_{3}\right) \, a \, \mathbf{\hat{y}}+ \frac58 \, a \, \mathbf{\hat{z}}& \left(48g\right) & \mbox{Ni} \\ \mathbf{B}_{56} & = &\left(\frac58 - y_{3}\right) \, \mathbf{a}_{1}+ \left(y_{3} + \frac78\right) \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& = &\left(\frac12 + y_{3}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac14 - y_{3}\right) \, a \, \mathbf{\hat{y}}+ \frac38 \, a \, \mathbf{\hat{z}}& \left(48g\right) & \mbox{Ni} \\ \end{array} \]

References

Found in

  • P. Villars and K. Cenzual, Landolt–Börnstein – Group III Condensed Matter (Springer–Verlag Berlin Heidelberg, 2004). Accessed through the Springer Materials site. end{thebibliography}

Geometry files


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aflow --proto=A4B3_cI112_230_af_g --params=

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