NaGdCu2F8 Structure: A2B8CD_tI24_97_d_k_a_b

Picture of Structure; Click for Big Picture
Prototype : NaGdCu2F8
AFLOW prototype label : A2B8CD_tI24_97_d_k_a_b
Strukturbericht designation : None
Pearson symbol : tI24
Space group number : 97
Space group symbol : $I422$
AFLOW prototype command : aflow --proto=A2B8CD_tI24_97_d_k_a_b
--params=
$a$,$c/a$,$x_{4}$,$y_{4}$,$z_{4}$


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} & = & 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{Gd} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} & = & \frac{1}{2}c \, \mathbf{\hat{z}} & \left(2b\right) & \mbox{Na} \\ \mathbf{B}_{3} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(4d\right) & \mbox{Cu} \\ \mathbf{B}_{4} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(4d\right) & \mbox{Cu} \\ \mathbf{B}_{5} & = & \left(y_{4}+z_{4}\right) \, \mathbf{a}_{1} + \left(x_{4}+z_{4}\right) \, \mathbf{a}_{2} + \left(x_{4}+y_{4}\right) \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + y_{4}a \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(16k\right) & \mbox{F} \\ \mathbf{B}_{6} & = & \left(-y_{4}+z_{4}\right) \, \mathbf{a}_{1} + \left(-x_{4}+z_{4}\right) \, \mathbf{a}_{2} + \left(-x_{4}-y_{4}\right) \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}}-y_{4}a \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(16k\right) & \mbox{F} \\ \mathbf{B}_{7} & = & \left(x_{4}+z_{4}\right) \, \mathbf{a}_{1} + \left(-y_{4}+z_{4}\right) \, \mathbf{a}_{2} + \left(x_{4}-y_{4}\right) \, \mathbf{a}_{3} & = & -y_{4}a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(16k\right) & \mbox{F} \\ \mathbf{B}_{8} & = & \left(-x_{4}+z_{4}\right) \, \mathbf{a}_{1} + \left(y_{4}+z_{4}\right) \, \mathbf{a}_{2} + \left(-x_{4}+y_{4}\right) \, \mathbf{a}_{3} & = & y_{4}a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(16k\right) & \mbox{F} \\ \mathbf{B}_{9} & = & \left(y_{4}-z_{4}\right) \, \mathbf{a}_{1} + \left(-x_{4}-z_{4}\right) \, \mathbf{a}_{2} + \left(-x_{4}+y_{4}\right) \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}} + y_{4}a \, \mathbf{\hat{y}}-z_{4}c \, \mathbf{\hat{z}} & \left(16k\right) & \mbox{F} \\ \mathbf{B}_{10} & = & \left(-y_{4}-z_{4}\right) \, \mathbf{a}_{1} + \left(x_{4}-z_{4}\right) \, \mathbf{a}_{2} + \left(x_{4}-y_{4}\right) \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}}-y_{4}a \, \mathbf{\hat{y}}-z_{4}c \, \mathbf{\hat{z}} & \left(16k\right) & \mbox{F} \\ \mathbf{B}_{11} & = & \left(x_{4}-z_{4}\right) \, \mathbf{a}_{1} + \left(y_{4}-z_{4}\right) \, \mathbf{a}_{2} + \left(x_{4}+y_{4}\right) \, \mathbf{a}_{3} & = & y_{4}a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}}-z_{4}c \, \mathbf{\hat{z}} & \left(16k\right) & \mbox{F} \\ \mathbf{B}_{12} & = & \left(-x_{4}-z_{4}\right) \, \mathbf{a}_{1} + \left(-y_{4}-z_{4}\right) \, \mathbf{a}_{2} + \left(-x_{4}-y_{4}\right) \, \mathbf{a}_{3} & = & -y_{4}a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}}-z_{4}c \, \mathbf{\hat{z}} & \left(16k\right) & \mbox{F} \\ \end{array} \]

References

  • C. De Nada"i, A. Demourgues, L. Lozano, P. Gravereau, and J. Grannec, Structural investigations of new copper fluorides NaRECu2F8 (RE3+ = Sm3+, Eu3+, Gd3+, Y3+, Er3+, Yb3+), J. Mater. Chem. 8, 2487–2491 (1998), doi:10.1039/A803015D.

Found in

  • P. Villars and K. Cenzual, Pearson's Crystal Data – Crystal Structure Database for Inorganic Compounds, ASM International (2013).

Geometry files


Prototype Generator

aflow --proto=A2B8CD_tI24_97_d_k_a_b --params=

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