ZrNiAl Structure : ABC_hP9_189_g_ad_f

Picture of Structure; Click for Big Picture
Prototype : AlNiZr
AFLOW prototype label : ABC_hP9_189_g_ad_f
Strukturbericht designation : None
Pearson symbol : hP9
Space group number : 189
Space group symbol : $P\bar{6}2m$
AFLOW prototype command : aflow --proto=ABC_hP9_189_g_ad_f
--params=
$a$,$c/a$,$x_{3}$,$x_{4}$


Other compounds with this structure

  • AgAsCa, AgSiYb, AlCoPu, AlCuTm, AlNiTb, DyNiIn, DyNiSn, ErNiAl, FeGaU, FeNiP, GdNiIn, GdNiSn, HoNiIn, RhSnZr, RuSiZr, ScIrP, TbNiIn, and BSi2Ni6

  • This is the ternary form of the Fe2P structure. In the former case the origin was placed so that the potassium atoms were on the ($1b$) and ($2c$) Wyckoff positions, while here we follow (Shved, 2019) and place the nickel atoms on the ($1a$) and ($2d$) sites. This is merely a shift in the origin by $1/2\, c\, \hat{z}$. If the structures have a common origin then they are nearly identical.
  • (Shved, 2019) found evidence of 6–10% mixing between the Ni–II ($2d$) and Al ($3g$) sites.

Hexagonal primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{x}} - \frac{\sqrt3}2 \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac{\sqrt3}2 \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & c \, \mathbf{\hat{z}} \\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & 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{Ni I} \\ \mathbf{B}_{2} & = & \frac{1}{3} \, \mathbf{a}_{1} + \frac{2}{3} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(2d\right) & \mbox{Ni II} \\ \mathbf{B}_{3} & = & \frac{2}{3} \, \mathbf{a}_{1} + \frac{1}{3} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(2d\right) & \mbox{Ni II} \\ \mathbf{B}_{4} & = & x_{3} \, \mathbf{a}_{1} & = & \frac{1}{2}x_{3}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{3}a \, \mathbf{\hat{y}} & \left(3f\right) & \mbox{Zr} \\ \mathbf{B}_{5} & = & x_{3} \, \mathbf{a}_{2} & = & \frac{1}{2}x_{3}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{3}a \, \mathbf{\hat{y}} & \left(3f\right) & \mbox{Zr} \\ \mathbf{B}_{6} & = & -x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2} & = & -x_{3}a \, \mathbf{\hat{x}} & \left(3f\right) & \mbox{Zr} \\ \mathbf{B}_{7} & = & x_{4} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}x_{4}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{4}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(3g\right) & \mbox{Al} \\ \mathbf{B}_{8} & = & x_{4} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}x_{4}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{4}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(3g\right) & \mbox{Al} \\ \mathbf{B}_{9} & = & -x_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(3g\right) & \mbox{Al} \\ \end{array} \]

References

  • O. Shved, L. P. Salamakha, S. Mudry, O. Sologub, P. F. Rogl, and E. Bauer, Zr–based nickel aluminides: crystal structure and electronic properties, J. Alloys\ Compd. 821, 153326 (2020), doi:10.1016/j.jallcom.2019.153326.

Geometry files


Prototype Generator

aflow --proto=ABC_hP9_189_g_ad_f --params=

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