$\beta$–Sn ($A5$) Structure: A_tI4_141_a

Picture of Structure; Click for Big Picture
Prototype : $\beta$–Sn
AFLOW prototype label : A_tI4_141_a
Strukturbericht designation : $A5$
Pearson symbol : tI4
Space group number : 141
Space group symbol : $\mbox{I4}_{1}\mbox{/amd}$
AFLOW prototype command : aflow --proto=A_tI4_141_a
--params=
$a$,$c/a$


  • When $c/a = \sqrt2$ this structure is equivalent to diamond (A4).

Body-centered Tetragonal primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & =&\frac78 \, \mathbf{a}_{1}+ \frac18 \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& =&\frac34 \, a \, \mathbf{\hat{y}}+ \frac18 \, c \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Sn} \\ \mathbf{B}_{2} & =&\frac18 \, \mathbf{a}_{1}+ \frac78 \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& =&\frac12 \, a \, \mathbf{\hat{x}}+ \frac34 \, a \, \mathbf{\hat{y}}+ \frac38 \, c \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Sn} \\ \end{array} \]

References

Found in

  • M. Winter, WebElements: the periodic table on the WWW (1993–2015). The University of Sheffield and WebElements Ltd.

Geometry files


Prototype Generator

aflow --proto=A_tI4_141_a --params=

Species:

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