Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: A2BC3_mC24_12_acg_h_ij-002

If you are using this page, please cite:
H. Eckert, S. Divilov, M. J. Mehl, D. Hicks, A. C. Zettel, M. Esters. X. Campilongo and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 4. Submitted to Computational Materials Science.

Links to this page

https://aflow.org/p/R3L4
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Li$_{2}$MnO$_{3}$ Structure: A2BC3_mC24_12_acg_h_ij-002

Picture of Structure; Click for Big Picture
Prototype Li$_{2}$MnO$_{3}$
AFLOW prototype label A2BC3_mC24_12_acg_h_ij-002
ICSD 202639
Pearson symbol mC24
Space group number 12
Space group symbol $C2/m$
AFLOW prototype command aflow --proto=A2BC3_mC24_12_acg_h_ij-002
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak \beta, \allowbreak y_{3}, \allowbreak y_{4}, \allowbreak x_{5}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak y_{6}, \allowbreak z_{6}$

Other compounds with this structure

Li$_{2}$IrO$_{3}$,  Li$_{2}$PtO$_{3}$,  Na$_{2}$IrO$_{3}$


  • This seems to be the consensus structure for these compounds. Others place them in space group $C2/c$ #15, possibly with a doubled unit cell.

\[ \begin{array}{ccc} \mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \cos{\beta} \,\mathbf{\hat{x}}+c \sin{\beta} \,\mathbf{\hat{z}} \end{array}\]

Basis vectors

Lattice coordinates Cartesian coordinates Wyckoff position Atom type
$\mathbf{B_{1}}$ = $0$ = $0$ (2a) Li I
$\mathbf{B_{2}}$ = $\frac{1}{2} \, \mathbf{a}_{3}$ = $\frac{1}{2}c \cos{\beta} \,\mathbf{\hat{x}}+\frac{1}{2}c \sin{\beta} \,\mathbf{\hat{z}}$ (2c) Li II
$\mathbf{B_{3}}$ = $- y_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}$ = $b y_{3} \,\mathbf{\hat{y}}$ (4g) Li III
$\mathbf{B_{4}}$ = $y_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}$ = $- b y_{3} \,\mathbf{\hat{y}}$ (4g) Li III
$\mathbf{B_{5}}$ = $- y_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ = $\frac{1}{2}c \cos{\beta} \,\mathbf{\hat{x}}+b y_{4} \,\mathbf{\hat{y}}+\frac{1}{2}c \sin{\beta} \,\mathbf{\hat{z}}$ (4h) Mn I
$\mathbf{B_{6}}$ = $y_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ = $\frac{1}{2}c \cos{\beta} \,\mathbf{\hat{x}}- b y_{4} \,\mathbf{\hat{y}}+\frac{1}{2}c \sin{\beta} \,\mathbf{\hat{z}}$ (4h) Mn I
$\mathbf{B_{7}}$ = $x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ = $\left(a x_{5} + c z_{5} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{5} \sin{\beta} \,\mathbf{\hat{z}}$ (4i) O I
$\mathbf{B_{8}}$ = $- x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ = $- \left(a x_{5} + c z_{5} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{5} \sin{\beta} \,\mathbf{\hat{z}}$ (4i) O I
$\mathbf{B_{9}}$ = $\left(x_{6} - y_{6}\right) \, \mathbf{a}_{1}+\left(x_{6} + y_{6}\right) \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ = $\left(a x_{6} + c z_{6} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{6} \,\mathbf{\hat{y}}+c z_{6} \sin{\beta} \,\mathbf{\hat{z}}$ (8j) O II
$\mathbf{B_{10}}$ = $- \left(x_{6} + y_{6}\right) \, \mathbf{a}_{1}- \left(x_{6} - y_{6}\right) \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ = $- \left(a x_{6} + c z_{6} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{6} \,\mathbf{\hat{y}}- c z_{6} \sin{\beta} \,\mathbf{\hat{z}}$ (8j) O II
$\mathbf{B_{11}}$ = $- \left(x_{6} - y_{6}\right) \, \mathbf{a}_{1}- \left(x_{6} + y_{6}\right) \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ = $- \left(a x_{6} + c z_{6} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{6} \,\mathbf{\hat{y}}- c z_{6} \sin{\beta} \,\mathbf{\hat{z}}$ (8j) O II
$\mathbf{B_{12}}$ = $\left(x_{6} + y_{6}\right) \, \mathbf{a}_{1}+\left(x_{6} - y_{6}\right) \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ = $\left(a x_{6} + c z_{6} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{6} \,\mathbf{\hat{y}}+c z_{6} \sin{\beta} \,\mathbf{\hat{z}}$ (8j) O II

References

  • P. Strobel and B. Lambert-Andron, Crystallographic and Magnetic Structure of Li$_{2}$MnO$_{3}$, J. Solid State Chem. 75, 90–98 (1988), doi:10.1016/0022-4596(88)90305-2.

Prototype Generator

aflow --proto=A2BC3_mC24_12_acg_h_ij --params=$a,b/a,c/a,\beta,y_{3},y_{4},x_{5},z_{5},x_{6},y_{6},z_{6}$

Species:

Running:

Output: