NaMn$_{7}$O$_{12}$ Structure: A7BC12_cI40_204_bc_a

This is a double perovskite structure. It is stable above 3GBar and above room temperature, but is metastable under ambient conditions (Gilioli 2005ab). The actual composition of the measured sample is Na $_{0.95}$ Mn $_{7.05}$ O $_{12}$ , with the excess manganese displacing some of the sodium atoms on the (2a) site.
The (6b) and (6c) sites may be populated by two species of atoms. In that case we get the quaternary form of this structure, prototype CaCu $_{3}$ Mn $_{4}$ O $_{12}$ .

Body-centered Cubic primitive vectors

a_{1} a_{2} a_{3} = = = - \frac{1}{2} a \hat{x} + \frac{1}{2} a \hat{y} + \frac{1}{2} a \hat{z} \frac{1}{2} a \hat{x} - \frac{1}{2} a \hat{y} + \frac{1}{2} a \hat{z} \frac{1}{2} a \hat{x} + \frac{1}{2} a \hat{y} - \frac{1}{2} a \hat{z}

Picture of Structure; Click for Big Picture

Basis vectors

		Lattice coordinates		Cartesian coordinates	Wyckoff position	Atom type
$B_{1}$	=	$0$	=	$0$	(2a)	Na I
$B_{2}$	=	$\frac{1}{2} a_{2} + \frac{1}{2} a_{3}$	=	$\frac{1}{2} a \hat{x}$	(6b)	Mn I
$B_{3}$	=	$\frac{1}{2} a_{1} + \frac{1}{2} a_{3}$	=	$\frac{1}{2} a \hat{y}$	(6b)	Mn I
$B_{4}$	=	$\frac{1}{2} a_{1} + \frac{1}{2} a_{2}$	=	$\frac{1}{2} a \hat{z}$	(6b)	Mn I
$B_{5}$	=	$\frac{1}{2} a_{1} + \frac{1}{2} a_{2} + \frac{1}{2} a_{3}$	=	$\frac{1}{4} a \hat{x} + \frac{1}{4} a \hat{y} + \frac{1}{4} a \hat{z}$	(8c)	Mn II
$B_{6}$	=	$\frac{1}{2} a_{3}$	=	$\frac{1}{4} a \hat{x} + \frac{1}{4} a \hat{y} - \frac{1}{4} a \hat{z}$	(8c)	Mn II
$B_{7}$	=	$\frac{1}{2} a_{2}$	=	$\frac{1}{4} a \hat{x} - \frac{1}{4} a \hat{y} + \frac{1}{4} a \hat{z}$	(8c)	Mn II
$B_{8}$	=	$\frac{1}{2} a_{1}$	=	$- \frac{1}{4} a \hat{x} + \frac{1}{4} a \hat{y} + \frac{1}{4} a \hat{z}$	(8c)	Mn II
$B_{9}$	=	$(y_{4} + z_{4}) a_{1} + z_{4} a_{2} + y_{4} a_{3}$	=	$a y_{4} \hat{y} + a z_{4} \hat{z}$	(24g)	O I
$B_{10}$	=	$- (y_{4} - z_{4}) a_{1} + z_{4} a_{2} - y_{4} a_{3}$	=	$- a y_{4} \hat{y} + a z_{4} \hat{z}$	(24g)	O I
$B_{11}$	=	$(y_{4} - z_{4}) a_{1} - z_{4} a_{2} + y_{4} a_{3}$	=	$a y_{4} \hat{y} - a z_{4} \hat{z}$	(24g)	O I
$B_{12}$	=	$- (y_{4} + z_{4}) a_{1} - z_{4} a_{2} - y_{4} a_{3}$	=	$- a y_{4} \hat{y} - a z_{4} \hat{z}$	(24g)	O I
$B_{13}$	=	$y_{4} a_{1} + (y_{4} + z_{4}) a_{2} + z_{4} a_{3}$	=	$a z_{4} \hat{x} + a y_{4} \hat{z}$	(24g)	O I
$B_{14}$	=	$- y_{4} a_{1} - (y_{4} - z_{4}) a_{2} + z_{4} a_{3}$	=	$a z_{4} \hat{x} - a y_{4} \hat{z}$	(24g)	O I
$B_{15}$	=	$y_{4} a_{1} + (y_{4} - z_{4}) a_{2} - z_{4} a_{3}$	=	$- a z_{4} \hat{x} + a y_{4} \hat{z}$	(24g)	O I
$B_{16}$	=	$- y_{4} a_{1} - (y_{4} + z_{4}) a_{2} - z_{4} a_{3}$	=	$- a z_{4} \hat{x} - a y_{4} \hat{z}$	(24g)	O I
$B_{17}$	=	$z_{4} a_{1} + y_{4} a_{2} + (y_{4} + z_{4}) a_{3}$	=	$a y_{4} \hat{x} + a z_{4} \hat{y}$	(24g)	O I
$B_{18}$	=	$z_{4} a_{1} - y_{4} a_{2} - (y_{4} - z_{4}) a_{3}$	=	$- a y_{4} \hat{x} + a z_{4} \hat{y}$	(24g)	O I
$B_{19}$	=	$- z_{4} a_{1} + y_{4} a_{2} + (y_{4} - z_{4}) a_{3}$	=	$a y_{4} \hat{x} - a z_{4} \hat{y}$	(24g)	O I
$B_{20}$	=	$- z_{4} a_{1} - y_{4} a_{2} - (y_{4} + z_{4}) a_{3}$	=	$- a y_{4} \hat{x} - a z_{4} \hat{y}$	(24g)	O I

References

E. Gilioli, G. Calestani, F. Licci, A. Gauzzi, F. Bolzoni, A. Prodi, and M. Marezio, $P - T$ phase diagram and single crystal structural refinement of NaMn $_{7}$ O $_{12}$ , Solid State Sci. 7, 746–752 (2005), doi:10.1016/j.solidstatesciences.2004.11.020.

Found in

E. Gilioli, F. Licci, G. Calestani, A. Prodi, A. Gauzzi, and G. Salviati, Crystal growth and structural refinement of NaMn $_{7}$ O $_{12}$ , Crys. Res. Technol. 40, 1072–1075 (2005), doi:10.1002/crat.200410489.

Prototype	Mn $_{7}$ NaO $_{12}$
AFLOW prototype label	A7BC12_cI40_204_bc_a_g-001
ICSD	154189
Pearson symbol	cI40
Space group number	204
Space group symbol	$I m \overline{3}$
AFLOW prototype command	aflow --proto=A7BC12_cI40_204_bc_a_g-001 --params= $a, y_{4}, z_{4}$

Encyclopedia of Crystallographic Prototypes

NaMn $_{7}$ O $_{12}$ Structure: A7BC12_cI40_204_bc_a_g-001

Body-centered Cubic primitive vectors

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Encyclopedia of Crystallographic Prototypes

NaMn7​O12​ Structure: A7BC12_cI40_204_bc_a_g-001

Body-centered Cubic primitive vectors

References

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NaMn $_{7}$ O $_{12}$ Structure: A7BC12_cI40_204_bc_a_g-001