High–Temperature Cryolite (Na3AlF6) Structure : AB6C3_oI20_71_a_in_cj

Picture of Structure; Click for Big Picture
Prototype : AlF6Na3
AFLOW prototype label : AB6C3_oI20_71_a_in_cj
Strukturbericht designation : None
Pearson symbol : oI20
Space group number : 71
Space group symbol : $Immm$
AFLOW prototype command : aflow --proto=AB6C3_oI20_71_a_in_cj
--params=
$a$,$b/a$,$c/a$,$z_{3}$,$z_{4}$,$x_{5}$,$y_{5}$



Body-centered Orthorhombic primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & 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(2a\right) & \mbox{Al} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} & = & \frac{1}{2}c \, \mathbf{\hat{z}} & \left(2c\right) & \mbox{Na I} \\ \mathbf{B}_{3} & = & z_{3} \, \mathbf{a}_{1} + z_{3} \, \mathbf{a}_{2} & = & z_{3}c \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{F I} \\ \mathbf{B}_{4} & = & -z_{3} \, \mathbf{a}_{1}-z_{3} \, \mathbf{a}_{2} & = & -z_{3}c \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{F I} \\ \mathbf{B}_{5} & = & z_{4} \, \mathbf{a}_{1} + \left(\frac{1}{2} +z_{4}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + z_{4}c \, \mathbf{\hat{z}} & \left(4j\right) & \mbox{Na II} \\ \mathbf{B}_{6} & = & -z_{4} \, \mathbf{a}_{1} + \left(\frac{1}{2} - z_{4}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}-z_{4}c \, \mathbf{\hat{z}} & \left(4j\right) & \mbox{Na II} \\ \mathbf{B}_{7} & = & y_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} + \left(x_{5}+y_{5}\right) \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}} + y_{5}b \, \mathbf{\hat{y}} & \left(8n\right) & \mbox{F II} \\ \mathbf{B}_{8} & = & -y_{5} \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2} + \left(-x_{5}-y_{5}\right) \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}}-y_{5}b \, \mathbf{\hat{y}} & \left(8n\right) & \mbox{F II} \\ \mathbf{B}_{9} & = & y_{5} \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2} + \left(-x_{5}+y_{5}\right) \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}} + y_{5}b \, \mathbf{\hat{y}} & \left(8n\right) & \mbox{F II} \\ \mathbf{B}_{10} & = & -y_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} + \left(x_{5}-y_{5}\right) \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}}-y_{5}b \, \mathbf{\hat{y}} & \left(8n\right) & \mbox{F II} \\ \end{array} \]

References

  • H. Yang, S. Ghose, and D. M. Hatch, Ferroelastic phase transition in cryolite, Na3AlF6, a mixed fluoride perovskite: High temperature single crystal X–ray diffraction study and symmetry analysis of the transition mechanism, Phys. Chem. Miner. 19, 528–544 (1993), doi:10.1007/BF00203053.

Found in

  • R. T. Downs and M. Hall–Wallace, The American Mineralogist Crystal Structure Database, Am. Mineral. 88, 247–250 (2003).

Geometry files


Prototype Generator

aflow --proto=AB6C3_oI20_71_a_in_cj --params=

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