# Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: ABC6D15_oC46_38_b_b_2a2d_2ab4d2e

• M. J. Mehl, D. Hicks, C. Toher, O. Levy, R. M. Hanson, G. L. W. Hart, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 1, Comp. Mat. Sci. 136, S1-S828 (2017). (doi=10.1016/j.commatsci.2017.01.017)
• D. Hicks, M. J. Mehl, E. Gossett, C. Toher, O. Levy, R. M. Hanson, G. L. W. Hart, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 2, Comp. Mat. Sci. 161, S1-S1011 (2019). (doi=10.1016/j.commatsci.2018.10.043)
• D. Hicks, M.J. Mehl, M. Esters, C. Oses, O. Levy, G.L.W. Hart, C. Toher, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 3, Comp. Mat. Sci. 199, 110450 (2021). (doi=10.1016/j.commatsci.2021.110450)

## NaNb6O15F Structure : ABC6D15_oC46_38_b_b_2a2d_2ab4d2e

 Prototype : FNaNb6O15 AFLOW prototype label : ABC6D15_oC46_38_b_b_2a2d_2ab4d2e Strukturbericht designation : None Pearson symbol : oC46 Space group number : 38 Space group symbol : $Amm2$ AFLOW prototype command : aflow --proto=ABC6D15_oC46_38_b_b_2a2d_2ab4d2e --params=$a$,$b/a$,$c/a$,$z_{1}$,$z_{2}$,$z_{3}$,$z_{4}$,$z_{5}$,$z_{6}$,$z_{7}$,$y_{8}$,$z_{8}$,$y_{9}$,$z_{9}$,$y_{10}$,$z_{10}$,$y_{11}$,$z_{11}$,$y_{12}$,$z_{12}$,$y_{13}$,$z_{13}$,$y_{14}$,$z_{14}$,$y_{15}$,$z_{15}$

### Other compounds with this structure

• NaNb6O15(OH)

• The x–ray scattering of an F ion is almost identical to that of O2–, and (Andersson, 1965) was not able to distinguish between them. He arbitrarily labeled the ($2b$) site he designated as O(1) 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. Presumably the same considerations hold for NaNb6O15(OH).
• Andersson sets $z_{4} = 0.159$ as the coordinate of what we label as O–II and he calls O(10), but this gives an unreasonably short distance between the Nb–II and O–II atoms, and the distances between the O–II atom and the other atoms in the structure do not agree with the distances given his paper. If we assume that the first two digits were transposed when printed, so that $z_{4} = 0.519$, then we get within 0.1% of Andersson's distances.

### Base-centered Orthorhombic primitive vectors:

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

Basis vectors:

$\begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & = & -z_{1} \, \mathbf{a}_{2} + z_{1} \, \mathbf{a}_{3} & = & z_{1}c \, \mathbf{\hat{z}} & \left(2a\right) & \text{Nb I} \\ \mathbf{B}_{2} & = & -z_{2} \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3} & = & z_{2}c \, \mathbf{\hat{z}} & \left(2a\right) & \text{Nb II} \\ \mathbf{B}_{3} & = & -z_{3} \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3} & = & z_{3}c \, \mathbf{\hat{z}} & \left(2a\right) & \text{O I} \\ \mathbf{B}_{4} & = & -z_{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & z_{4}c \, \mathbf{\hat{z}} & \left(2a\right) & \text{O II} \\ \mathbf{B}_{5} & = & \frac{1}{2} \, \mathbf{a}_{1}-z_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + z_{5}c \, \mathbf{\hat{z}} & \left(2b\right) & \text{F} \\ \mathbf{B}_{6} & = & \frac{1}{2} \, \mathbf{a}_{1}-z_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + z_{6}c \, \mathbf{\hat{z}} & \left(2b\right) & \text{Na} \\ \mathbf{B}_{7} & = & \frac{1}{2} \, \mathbf{a}_{1}-z_{7} \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + z_{7}c \, \mathbf{\hat{z}} & \left(2b\right) & \text{O III} \\ \mathbf{B}_{8} & = & \left(y_{8}-z_{8}\right) \, \mathbf{a}_{2} + \left(y_{8}+z_{8}\right) \, \mathbf{a}_{3} & = & y_{8}b \, \mathbf{\hat{y}} + z_{8}c \, \mathbf{\hat{z}} & \left(4d\right) & \text{Nb III} \\ \mathbf{B}_{9} & = & \left(-y_{8}-z_{8}\right) \, \mathbf{a}_{2} + \left(-y_{8}+z_{8}\right) \, \mathbf{a}_{3} & = & -y_{8}b \, \mathbf{\hat{y}} + z_{8}c \, \mathbf{\hat{z}} & \left(4d\right) & \text{Nb III} \\ \mathbf{B}_{10} & = & \left(y_{9}-z_{9}\right) \, \mathbf{a}_{2} + \left(y_{9}+z_{9}\right) \, \mathbf{a}_{3} & = & y_{9}b \, \mathbf{\hat{y}} + z_{9}c \, \mathbf{\hat{z}} & \left(4d\right) & \text{Nb IV} \\ \mathbf{B}_{11} & = & \left(-y_{9}-z_{9}\right) \, \mathbf{a}_{2} + \left(-y_{9}+z_{9}\right) \, \mathbf{a}_{3} & = & -y_{9}b \, \mathbf{\hat{y}} + z_{9}c \, \mathbf{\hat{z}} & \left(4d\right) & \text{Nb IV} \\ \mathbf{B}_{12} & = & \left(y_{10}-z_{10}\right) \, \mathbf{a}_{2} + \left(y_{10}+z_{10}\right) \, \mathbf{a}_{3} & = & y_{10}b \, \mathbf{\hat{y}} + z_{10}c \, \mathbf{\hat{z}} & \left(4d\right) & \text{O IV} \\ \mathbf{B}_{13} & = & \left(-y_{10}-z_{10}\right) \, \mathbf{a}_{2} + \left(-y_{10}+z_{10}\right) \, \mathbf{a}_{3} & = & -y_{10}b \, \mathbf{\hat{y}} + z_{10}c \, \mathbf{\hat{z}} & \left(4d\right) & \text{O IV} \\ \mathbf{B}_{14} & = & \left(y_{11}-z_{11}\right) \, \mathbf{a}_{2} + \left(y_{11}+z_{11}\right) \, \mathbf{a}_{3} & = & y_{11}b \, \mathbf{\hat{y}} + z_{11}c \, \mathbf{\hat{z}} & \left(4d\right) & \text{O V} \\ \mathbf{B}_{15} & = & \left(-y_{11}-z_{11}\right) \, \mathbf{a}_{2} + \left(-y_{11}+z_{11}\right) \, \mathbf{a}_{3} & = & -y_{11}b \, \mathbf{\hat{y}} + z_{11}c \, \mathbf{\hat{z}} & \left(4d\right) & \text{O V} \\ \mathbf{B}_{16} & = & \left(y_{12}-z_{12}\right) \, \mathbf{a}_{2} + \left(y_{12}+z_{12}\right) \, \mathbf{a}_{3} & = & y_{12}b \, \mathbf{\hat{y}} + z_{12}c \, \mathbf{\hat{z}} & \left(4d\right) & \text{O VI} \\ \mathbf{B}_{17} & = & \left(-y_{12}-z_{12}\right) \, \mathbf{a}_{2} + \left(-y_{12}+z_{12}\right) \, \mathbf{a}_{3} & = & -y_{12}b \, \mathbf{\hat{y}} + z_{12}c \, \mathbf{\hat{z}} & \left(4d\right) & \text{O VI} \\ \mathbf{B}_{18} & = & \left(y_{13}-z_{13}\right) \, \mathbf{a}_{2} + \left(y_{13}+z_{13}\right) \, \mathbf{a}_{3} & = & y_{13}b \, \mathbf{\hat{y}} + z_{13}c \, \mathbf{\hat{z}} & \left(4d\right) & \text{O VII} \\ \mathbf{B}_{19} & = & \left(-y_{13}-z_{13}\right) \, \mathbf{a}_{2} + \left(-y_{13}+z_{13}\right) \, \mathbf{a}_{3} & = & -y_{13}b \, \mathbf{\hat{y}} + z_{13}c \, \mathbf{\hat{z}} & \left(4d\right) & \text{O VII} \\ \mathbf{B}_{20} & = & \frac{1}{2} \, \mathbf{a}_{1} + \left(y_{14}-z_{14}\right) \, \mathbf{a}_{2} + \left(y_{14}+z_{14}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + y_{14}b \, \mathbf{\hat{y}} + z_{14}c \, \mathbf{\hat{z}} & \left(4e\right) & \text{O VIII} \\ \mathbf{B}_{21} & = & \frac{1}{2} \, \mathbf{a}_{1} + \left(-y_{14}-z_{14}\right) \, \mathbf{a}_{2} + \left(-y_{14}+z_{14}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}-y_{14}b \, \mathbf{\hat{y}} + z_{14}c \, \mathbf{\hat{z}} & \left(4e\right) & \text{O VIII} \\ \mathbf{B}_{22} & = & \frac{1}{2} \, \mathbf{a}_{1} + \left(y_{15}-z_{15}\right) \, \mathbf{a}_{2} + \left(y_{15}+z_{15}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + y_{15}b \, \mathbf{\hat{y}} + z_{15}c \, \mathbf{\hat{z}} & \left(4e\right) & \text{O IX} \\ \mathbf{B}_{23} & = & \frac{1}{2} \, \mathbf{a}_{1} + \left(-y_{15}-z_{15}\right) \, \mathbf{a}_{2} + \left(-y_{15}+z_{15}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}-y_{15}b \, \mathbf{\hat{y}} + z_{15}c \, \mathbf{\hat{z}} & \left(4e\right) & \text{O IX} \\ \end{array}$

### Prototype Generator

aflow --proto=ABC6D15_oC46_38_b_b_2a2d_2ab4d2e --params=