Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: A3B4_mC14_12_ai_2i-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/17US
or https://aflow.org/p/A3B4_mC14_12_ai_2i-002
or PDF Version

Brezinaite (Cr$_{3}$S$_{4}$) Structure: A3B4_mC14_12_ai_2i-002

Picture of Structure; Click for Big Picture
Prototype Cr$_{3}$S$_{4}$
AFLOW prototype label A3B4_mC14_12_ai_2i-002
Mineral name brezinaite
ICSD 16722
Pearson symbol mC14
Space group number 12
Space group symbol $C2/m$
AFLOW prototype command aflow --proto=A3B4_mC14_12_ai_2i-002
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak \beta, \allowbreak x_{2}, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak z_{3}, \allowbreak x_{4}, \allowbreak z_{4}$

Other compounds with this structure

Co$_{3}$Se$_{4}$,  Cr$_{3}$Te$_{4}$,  Fe$_{3}$Se$_{4}$,  Re$_{3}$P$_{4}$,  V$_{3}$S$_{4}$,  V$_{3}$Te$_{4}$,  FeCr$_{2}$Se$_{4}$,  MnCr$_{2}$Se$_{4}$,  NiCr$_{2}$S$_{4}$,  NiTi$_{2}$Se$_{4}$,  VCr$_{2}$S$_{4}$


  • (Jellinek, 1957) gives this structure in the $I2/m$ setting of space group #12. We used FINDSYM to change this to the standard $C2/m$ setting. When doing this the shape of the conventional cell changes from that found in the original paper, but of course the Wigner-Seitz cells are identical.
  • Cr$_{3}$Sn$_{4}$ and $\delta$–Ni$_{3}$Sn$_{4}$ ($D7_{a}$) have the same AFLOW prototype label, A3B4_mC14_12_ai_2i. They are generated by the same symmetry operations with different sets of parameters (--params) specified in their corresponding CIF files.

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

Basis vectors

Lattice coordinates Cartesian coordinates Wyckoff position Atom type
$\mathbf{B_{1}}$ = $0$ = $0$ (2a) Cr I
$\mathbf{B_{2}}$ = $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ = $\left(a x_{2} + c z_{2} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{2} \sin{\beta} \,\mathbf{\hat{z}}$ (4i) Cr II
$\mathbf{B_{3}}$ = $- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}$ = $- \left(a x_{2} + c z_{2} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{2} \sin{\beta} \,\mathbf{\hat{z}}$ (4i) Cr II
$\mathbf{B_{4}}$ = $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ = $\left(a x_{3} + c z_{3} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{3} \sin{\beta} \,\mathbf{\hat{z}}$ (4i) S I
$\mathbf{B_{5}}$ = $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ = $- \left(a x_{3} + c z_{3} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{3} \sin{\beta} \,\mathbf{\hat{z}}$ (4i) S I
$\mathbf{B_{6}}$ = $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ = $\left(a x_{4} + c z_{4} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{4} \sin{\beta} \,\mathbf{\hat{z}}$ (4i) S II
$\mathbf{B_{7}}$ = $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ = $- \left(a x_{4} + c z_{4} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{4} \sin{\beta} \,\mathbf{\hat{z}}$ (4i) S II

References

Found in

  • R. T. Downs and M. Hall-Wallace, The American Mineralogist Crystal Structure Database, Am. Mineral. 88, 247–250 (2003).

Prototype Generator

aflow --proto=A3B4_mC14_12_ai_2i --params=$a,b/a,c/a,\beta,x_{2},z_{2},x_{3},z_{3},x_{4},z_{4}$

Species:

Running:

Output: