LiNb6O15F Structure : ABC6D15_oP46_51_f_d_2e2i_aef4i2j

Picture of Structure; Click for Big Picture
Prototype : FLiNb6O15
AFLOW prototype label : ABC6D15_oP46_51_f_d_2e2i_aef4i2j
Strukturbericht designation : None
Pearson symbol : oP46
Space group number : 51
Space group symbol : $Pmma$
AFLOW prototype command : aflow --proto=ABC6D15_oP46_51_f_d_2e2i_aef4i2j
--params=
$a$,$b/a$,$c/a$,$z_{3}$,$z_{4}$,$z_{5}$,$z_{6}$,$z_{7}$,$x_{8}$,$z_{8}$,$x_{9}$,$z_{9}$,$x_{10}$,$z_{10}$,$x_{11}$,$z_{11}$,$x_{12}$,$z_{12}$,$x_{13}$,$z_{13}$,$x_{14}$,$z_{14}$,$x_{15}$,$z_{15}$


  • (Lundberg, 1965) suggests that the lithium atoms are either on the ($2d$) site or are statistically distributed on a ($4j$) site with approximate coordinates (0.08,1/2,0.10). For simplicity we place the atoms on the ($2d$) site.
  • The x–ray scattering of a F ion is almost identical to that of O2–, and Lundberg was not able to distinguish between them. She arbitrarily designated the ($2f$) site she also called O4 as the location of the fluorine ion and we follow this, but in reality we have no idea if the F ions are located on this site, are ordered on another site, or are statistically distributed on the oxygen sites.

Simple Orthorhombic primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & 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{O I} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{1} & = & \frac{1}{2}a \, \mathbf{\hat{x}} & \left(2a\right) & \mbox{O I} \\ \mathbf{B}_{3} & = & \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}b \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(2d\right) & \mbox{Li} \\ \mathbf{B}_{4} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}b \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(2d\right) & \mbox{Li} \\ \mathbf{B}_{5} & = & \frac{1}{4} \, \mathbf{a}_{1} + z_{3} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + z_{3}c \, \mathbf{\hat{z}} & \left(2e\right) & \mbox{Nb I} \\ \mathbf{B}_{6} & = & \frac{3}{4} \, \mathbf{a}_{1}-z_{3} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}}-z_{3}c \, \mathbf{\hat{z}} & \left(2e\right) & \mbox{Nb I} \\ \mathbf{B}_{7} & = & \frac{1}{4} \, \mathbf{a}_{1} + z_{4} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + z_{4}c \, \mathbf{\hat{z}} & \left(2e\right) & \mbox{Nb II} \\ \mathbf{B}_{8} & = & \frac{3}{4} \, \mathbf{a}_{1}-z_{4} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}}-z_{4}c \, \mathbf{\hat{z}} & \left(2e\right) & \mbox{Nb II} \\ \mathbf{B}_{9} & = & \frac{1}{4} \, \mathbf{a}_{1} + z_{5} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + z_{5}c \, \mathbf{\hat{z}} & \left(2e\right) & \mbox{O II} \\ \mathbf{B}_{10} & = & \frac{3}{4} \, \mathbf{a}_{1}-z_{5} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}}-z_{5}c \, \mathbf{\hat{z}} & \left(2e\right) & \mbox{O II} \\ \mathbf{B}_{11} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{2}b \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(2f\right) & \mbox{F} \\ \mathbf{B}_{12} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2}-z_{6} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \frac{1}{2}b \, \mathbf{\hat{y}}-z_{6}c \, \mathbf{\hat{z}} & \left(2f\right) & \mbox{F} \\ \mathbf{B}_{13} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{2}b \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(2f\right) & \mbox{O III} \\ \mathbf{B}_{14} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2}-z_{7} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \frac{1}{2}b \, \mathbf{\hat{y}}-z_{7}c \, \mathbf{\hat{z}} & \left(2f\right) & \mbox{O III} \\ \mathbf{B}_{15} & = & x_{8} \, \mathbf{a}_{1} + z_{8} \, \mathbf{a}_{3} & = & x_{8}a \, \mathbf{\hat{x}} + z_{8}c \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{Nb III} \\ \mathbf{B}_{16} & = & \left(\frac{1}{2} - x_{8}\right) \, \mathbf{a}_{1} + z_{8} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{8}\right)a \, \mathbf{\hat{x}} + z_{8}c \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{Nb III} \\ \mathbf{B}_{17} & = & -x_{8} \, \mathbf{a}_{1}-z_{8} \, \mathbf{a}_{3} & = & -x_{8}a \, \mathbf{\hat{x}}-z_{8}c \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{Nb III} \\ \mathbf{B}_{18} & = & \left(\frac{1}{2} +x_{8}\right) \, \mathbf{a}_{1}-z_{8} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{8}\right)a \, \mathbf{\hat{x}}-z_{8}c \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{Nb III} \\ \mathbf{B}_{19} & = & x_{9} \, \mathbf{a}_{1} + z_{9} \, \mathbf{a}_{3} & = & x_{9}a \, \mathbf{\hat{x}} + z_{9}c \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{Nb IV} \\ \mathbf{B}_{20} & = & \left(\frac{1}{2} - x_{9}\right) \, \mathbf{a}_{1} + z_{9} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{9}\right)a \, \mathbf{\hat{x}} + z_{9}c \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{Nb IV} \\ \mathbf{B}_{21} & = & -x_{9} \, \mathbf{a}_{1}-z_{9} \, \mathbf{a}_{3} & = & -x_{9}a \, \mathbf{\hat{x}}-z_{9}c \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{Nb IV} \\ \mathbf{B}_{22} & = & \left(\frac{1}{2} +x_{9}\right) \, \mathbf{a}_{1}-z_{9} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{9}\right)a \, \mathbf{\hat{x}}-z_{9}c \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{Nb IV} \\ \mathbf{B}_{23} & = & x_{10} \, \mathbf{a}_{1} + z_{10} \, \mathbf{a}_{3} & = & x_{10}a \, \mathbf{\hat{x}} + z_{10}c \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{O IV} \\ \mathbf{B}_{24} & = & \left(\frac{1}{2} - x_{10}\right) \, \mathbf{a}_{1} + z_{10} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{10}\right)a \, \mathbf{\hat{x}} + z_{10}c \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{O IV} \\ \mathbf{B}_{25} & = & -x_{10} \, \mathbf{a}_{1}-z_{10} \, \mathbf{a}_{3} & = & -x_{10}a \, \mathbf{\hat{x}}-z_{10}c \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{O IV} \\ \mathbf{B}_{26} & = & \left(\frac{1}{2} +x_{10}\right) \, \mathbf{a}_{1}-z_{10} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{10}\right)a \, \mathbf{\hat{x}}-z_{10}c \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{O IV} \\ \mathbf{B}_{27} & = & x_{11} \, \mathbf{a}_{1} + z_{11} \, \mathbf{a}_{3} & = & x_{11}a \, \mathbf{\hat{x}} + z_{11}c \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{O V} \\ \mathbf{B}_{28} & = & \left(\frac{1}{2} - x_{11}\right) \, \mathbf{a}_{1} + z_{11} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{11}\right)a \, \mathbf{\hat{x}} + z_{11}c \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{O V} \\ \mathbf{B}_{29} & = & -x_{11} \, \mathbf{a}_{1}-z_{11} \, \mathbf{a}_{3} & = & -x_{11}a \, \mathbf{\hat{x}}-z_{11}c \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{O V} \\ \mathbf{B}_{30} & = & \left(\frac{1}{2} +x_{11}\right) \, \mathbf{a}_{1}-z_{11} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{11}\right)a \, \mathbf{\hat{x}}-z_{11}c \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{O V} \\ \mathbf{B}_{31} & = & x_{12} \, \mathbf{a}_{1} + z_{12} \, \mathbf{a}_{3} & = & x_{12}a \, \mathbf{\hat{x}} + z_{12}c \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{O VI} \\ \mathbf{B}_{32} & = & \left(\frac{1}{2} - x_{12}\right) \, \mathbf{a}_{1} + z_{12} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{12}\right)a \, \mathbf{\hat{x}} + z_{12}c \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{O VI} \\ \mathbf{B}_{33} & = & -x_{12} \, \mathbf{a}_{1}-z_{12} \, \mathbf{a}_{3} & = & -x_{12}a \, \mathbf{\hat{x}}-z_{12}c \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{O VI} \\ \mathbf{B}_{34} & = & \left(\frac{1}{2} +x_{12}\right) \, \mathbf{a}_{1}-z_{12} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{12}\right)a \, \mathbf{\hat{x}}-z_{12}c \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{O VI} \\ \mathbf{B}_{35} & = & x_{13} \, \mathbf{a}_{1} + z_{13} \, \mathbf{a}_{3} & = & x_{13}a \, \mathbf{\hat{x}} + z_{13}c \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{O VII} \\ \mathbf{B}_{36} & = & \left(\frac{1}{2} - x_{13}\right) \, \mathbf{a}_{1} + z_{13} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{13}\right)a \, \mathbf{\hat{x}} + z_{13}c \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{O VII} \\ \mathbf{B}_{37} & = & -x_{13} \, \mathbf{a}_{1}-z_{13} \, \mathbf{a}_{3} & = & -x_{13}a \, \mathbf{\hat{x}}-z_{13}c \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{O VII} \\ \mathbf{B}_{38} & = & \left(\frac{1}{2} +x_{13}\right) \, \mathbf{a}_{1}-z_{13} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{13}\right)a \, \mathbf{\hat{x}}-z_{13}c \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{O VII} \\ \mathbf{B}_{39} & = & x_{14} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + z_{14} \, \mathbf{a}_{3} & = & x_{14}a \, \mathbf{\hat{x}} + \frac{1}{2}b \, \mathbf{\hat{y}} + z_{14}c \, \mathbf{\hat{z}} & \left(4j\right) & \mbox{O VIII} \\ \mathbf{B}_{40} & = & \left(\frac{1}{2} - x_{14}\right) \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + z_{14} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{14}\right)a \, \mathbf{\hat{x}} + \frac{1}{2}b \, \mathbf{\hat{y}} + z_{14}c \, \mathbf{\hat{z}} & \left(4j\right) & \mbox{O VIII} \\ \mathbf{B}_{41} & = & -x_{14} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2}-z_{14} \, \mathbf{a}_{3} & = & -x_{14}a \, \mathbf{\hat{x}} + \frac{1}{2}b \, \mathbf{\hat{y}}-z_{14}c \, \mathbf{\hat{z}} & \left(4j\right) & \mbox{O VIII} \\ \mathbf{B}_{42} & = & \left(\frac{1}{2} +x_{14}\right) \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2}-z_{14} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{14}\right)a \, \mathbf{\hat{x}} + \frac{1}{2}b \, \mathbf{\hat{y}}-z_{14}c \, \mathbf{\hat{z}} & \left(4j\right) & \mbox{O VIII} \\ \mathbf{B}_{43} & = & x_{15} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + z_{15} \, \mathbf{a}_{3} & = & x_{15}a \, \mathbf{\hat{x}} + \frac{1}{2}b \, \mathbf{\hat{y}} + z_{15}c \, \mathbf{\hat{z}} & \left(4j\right) & \mbox{O IX} \\ \mathbf{B}_{44} & = & \left(\frac{1}{2} - x_{15}\right) \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + z_{15} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{15}\right)a \, \mathbf{\hat{x}} + \frac{1}{2}b \, \mathbf{\hat{y}} + z_{15}c \, \mathbf{\hat{z}} & \left(4j\right) & \mbox{O IX} \\ \mathbf{B}_{45} & = & -x_{15} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2}-z_{15} \, \mathbf{a}_{3} & = & -x_{15}a \, \mathbf{\hat{x}} + \frac{1}{2}b \, \mathbf{\hat{y}}-z_{15}c \, \mathbf{\hat{z}} & \left(4j\right) & \mbox{O IX} \\ \mathbf{B}_{46} & = & \left(\frac{1}{2} +x_{15}\right) \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2}-z_{15} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{15}\right)a \, \mathbf{\hat{x}} + \frac{1}{2}b \, \mathbf{\hat{y}}-z_{15}c \, \mathbf{\hat{z}} & \left(4j\right) & \mbox{O IX} \\ \end{array} \]

References

Geometry files


Prototype Generator

aflow --proto=ABC6D15_oP46_51_f_d_2e2i_aef4i2j --params=

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