Ni3Sn ($D0_{19}$) Structure: A3B_hP8_194_h_c

Picture of Structure; Click for Big Picture
Prototype : Ni3Sn
AFLOW prototype label : A3B_hP8_194_h_c
Strukturbericht designation : $D0_{19}$
Pearson symbol : hP8
Space group number : 194
Space group symbol : $\mbox{P6}_{3}\mbox{/mmc}$
AFLOW prototype command : aflow --proto=A3B_hP8_194_h_c
--params=
$a$,$c/a$,$x_{2}$


Other compounds with this structure

  • Ti3Sn, Ti3Al, Mn3Sn, Cd3Mg, Mg3In, Hg3Y

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}& = &\frac13 \, \mathbf{a}_{1}+ \frac23 \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ \frac14 \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{Sn} \\ \mathbf{B}_{2}& = &\frac23 \, \mathbf{a}_{1}+ \frac13 \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ \frac34 \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{Sn} \\ \mathbf{B}_{3}& = &x_{2} \, \mathbf{a}_{1}+ 2 \, x_{2} \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& = &\frac32 \, x_{2} \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}{2} \, x_{2} \, a \, \mathbf{\hat{y}}+ \frac14 \, c \, \mathbf{\hat{z}}& \left(6h\right) & \mbox{Ni} \\ \mathbf{B}_{4}& = &- 2 \, x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& = &- \frac32 \, x_{2} \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}{2} \, x_{2} \, a \, \mathbf{\hat{y}}+ \frac14 \, c \, \mathbf{\hat{z}}& \left(6h\right) & \mbox{Ni} \\ \mathbf{B}_{5}& = &x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& = &- \sqrt3 \, x_{2} \, a \, \mathbf{\hat{y}}+ \frac14 \, c \, \mathbf{\hat{z}}& \left(6h\right) & \mbox{Ni} \\ \mathbf{B}_{6}& = &- x_{2} \, \mathbf{a}_{1}- 2 \, x_{2} \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& = &- \frac32 \, x_{2} \, a \, \mathbf{\hat{x}}- \frac{\sqrt3}{2} \, x_{2} \, a \, \mathbf{\hat{y}}+ \frac34 \, c \, \mathbf{\hat{z}}& \left(6h\right) & \mbox{Ni} \\ \mathbf{B}_{7}& = &2 \, x_{2} \, \mathbf{a}_{1}+ x_{2} \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& = &\frac32 \, x_{2} \, a \, \mathbf{\hat{x}}- \frac{\sqrt3}{2} \, x_{2} \, a \, \mathbf{\hat{y}}+ \frac34 \, c \, \mathbf{\hat{z}}& \left(6h\right) & \mbox{Ni} \\ \mathbf{B}_{8}& = &- x_{2} \, \mathbf{a}_{1}+ x_{2} \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& = &+ \sqrt3 \, x_{2} \, a \, \mathbf{\hat{y}}+ \frac34 \, c \, \mathbf{\hat{z}}& \left(6h\right) & \mbox{Ni} \\ \end{array} \]

References

  • A. L. Lyubimtsev, A. I. Baranov, A. Fischer, L. Kloo, and B. A. Popovkin, The structure and bonding of Ni3Sn, J. Alloys Compd. 340, 167–172 (2002), doi:10.1016/S0925-8388(02)00047-6.

Geometry files


Prototype Generator

aflow --proto=A3B_hP8_194_h_c --params=

Species:

Running:

Output: