High–pressure cI16 Li Structure: A_cI16_220_c

Picture of Structure; Click for Big Picture
Prototype : Li
AFLOW prototype label : A_cI16_220_c
Strukturbericht designation : None
Pearson symbol : cI16
Space group number : 220
Space group symbol : $\mbox{I}\bar{4}\mbox{3d}$
AFLOW prototype command : aflow --proto=A_cI16_220_c
--params=
$a$,$x_{1}$


Other compounds with this structure

  • Na (under pressure)

  • This is a high-pressure phase of lithium. We use the data from (Hanfland, 2000) at 38.9 GPa. When $x_{1}$ = 0 this becomes a body-centered cubic (A2) system. We have used the fact that all vectors of the form $( \pm a/2 \mathbf{\hat{x}} \pm a/2 \mathbf{\hat{y}} \pm a/2 \mathbf{\hat{z}} )$ are primitive vectors of the body-centered cubic lattice to simplify the positions of some atoms in both lattice and Cartesian coordinates.

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(16c\right) & \mbox{Li} \\ \mathbf{B}_{2} & = &\frac12 \, \mathbf{a}_{1}+ \left(\frac12 - 2 x_{1}\right) \, \mathbf{a}_{3}& = &- x_{1} \, a \, \mathbf{\hat{x}}+ \left(\frac12 - x_{1}\right) \, a \, \mathbf{\hat{y}}+ x_{1} \, a \, \mathbf{\hat{z}}& \left(16c\right) & \mbox{Li} \\ \mathbf{B}_{3} & = &\left(\frac12 - 2 x_{1}\right) \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\left(\frac12 - x_{1}\right) \, a \, \mathbf{\hat{x}}+ x_{1} \, a \, \mathbf{\hat{y}}- x_{1} \, a \, \mathbf{\hat{z}}& \left(16c\right) & \mbox{Li} \\ \mathbf{B}_{4} & = &\left(\frac12 - 2 x_{1}\right) \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}& = &+ x_{1} \, a \, \mathbf{\hat{x}}- x_{1} \, a \, \mathbf{\hat{y}}\left(\frac12 - x_{1}\right) \, a \, \mathbf{\hat{z}}& \left(16c\right) & \mbox{Li} \\ \mathbf{B}_{5} & = &\left(\frac12 + 2 x_{1}\right) \, \mathbf{a}_{1}+ \left(\frac12 + 2 x_{1}\right) \, \mathbf{a}_{2}+ \left(\frac12 + 2 x_{1}\right) \, \mathbf{a}_{3}& = &\left(\frac14 + x_{1}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac14 + x_{1}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac14 + x_{1}\right) \, a \, \mathbf{\hat{z}}& \left(16c\right) & \mbox{Li} \\ \mathbf{B}_{6} & = &\frac12 \, \mathbf{a}_{1}- 2 x_{1} \, \mathbf{a}_{3}& = &\left(\frac34 - x_{1}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac14 - x_{1}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac14 + x_{1}\right) \, a \, \mathbf{\hat{z}}& \left(16c\right) & \mbox{Li} \\ \mathbf{B}_{7} & = &- 2 x_{1} \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}& = &\left(\frac14 + x_{1}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac34 - x_{1}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac14 - x_{1}\right) \, a \, \mathbf{\hat{z}}& \left(16c\right) & \mbox{Li} \\ \mathbf{B}_{8} & = &- 2 x_{1} \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\left(\frac14 - x_{1}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac14 + x_{1}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac34 - x_{1}\right) \, a \, \mathbf{\hat{z}}& \left(16c\right) & \mbox{Li} \\ \end{array} \]

References

  • M. Hanfland, K. Syassen, N. E. Christensen, and D. L. Novikov, New high–pressure phases of lithium, Nature 408, 174–178 (2000), doi:10.1038/35041515.

Geometry files


Prototype Generator

aflow --proto=A_cI16_220_c --params=

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