Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: A2B2C4D_tP18_132_e_i_o_b-001

This structure originally had the label A2B2C4D_tP18_132_e_i_o_d. Calls to that address will be redirected here.

If you are using this page, please cite:
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)

Links to this page

https://aflow.org/p/BD46
or https://aflow.org/p/A2B2C4D_tP18_132_e_i_o_b-001
or PDF Version

Rb$_{2}$TiCu$_{2}$S$_{4}$ Structure: A2B2C4D_tP18_132_e_i_o_b-001

Picture of Structure; Click for Big Picture
Prototype Cu$_{2}$Rb$_{2}$S$_{4}$Ti
AFLOW prototype label A2B2C4D_tP18_132_e_i_o_b-001
ICSD 280644
Pearson symbol tP18
Space group number 132
Space group symbol $P4_2/mcm$
AFLOW prototype command aflow --proto=A2B2C4D_tP18_132_e_i_o_b-001
--params=$a, \allowbreak c/a, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak z_{4}$

Other compounds with this structure

Cs$_{2}$TiAg$_{2}$S$_{4}$,  Cs$_{2}$TiCu$_{2}$Se$_{4}$


  • The atomic positions for this structure are not given in the main text. We take them from the ICSD Entry.

\[ \begin{array}{ccc} \mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}} \end{array}\]

Basis vectors

Lattice coordinates Cartesian coordinates Wyckoff position Atom type
$\mathbf{B_{1}}$ = $\frac{1}{4} \, \mathbf{a}_{3}$ = $\frac{1}{4}c \,\mathbf{\hat{z}}$ (2b) Ti I
$\mathbf{B_{2}}$ = $\frac{3}{4} \, \mathbf{a}_{3}$ = $\frac{3}{4}c \,\mathbf{\hat{z}}$ (2b) Ti I
$\mathbf{B_{3}}$ = $\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ (4e) Cu I
$\mathbf{B_{4}}$ = $\frac{1}{2} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ (4e) Cu I
$\mathbf{B_{5}}$ = $\frac{1}{2} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ (4e) Cu I
$\mathbf{B_{6}}$ = $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ (4e) Cu I
$\mathbf{B_{7}}$ = $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}$ = $a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}$ (4i) Rb I
$\mathbf{B_{8}}$ = $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}$ = $- a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}$ (4i) Rb I
$\mathbf{B_{9}}$ = $- x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ = $- a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ (4i) Rb I
$\mathbf{B_{10}}$ = $x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ = $a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ (4i) Rb I
$\mathbf{B_{11}}$ = $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ = $a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ (8o) S I
$\mathbf{B_{12}}$ = $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ = $- a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ (8o) S I
$\mathbf{B_{13}}$ = $- x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (8o) S I
$\mathbf{B_{14}}$ = $x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (8o) S I
$\mathbf{B_{15}}$ = $- x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}- \left(z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}- c \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (8o) S I
$\mathbf{B_{16}}$ = $x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- \left(z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}- c \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (8o) S I
$\mathbf{B_{17}}$ = $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ = $a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ (8o) S I
$\mathbf{B_{18}}$ = $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ = $- a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ (8o) S I

References

  • F. Q. Huang and J. A. Ibers, New Layered Materials:  Syntheses, Structures, and Optical Properties of K$_{2}$TiCu$_{2}$S$_{4}$, Rb$_{2}$TiCu$_{2}$S$_{4}$, Rb$_{2}$TiAg$_{2}$S$_{4}$, Cs$_{2}$TiAg$_{2}$S$_{4}$, and Cs$_{2}$TiCu$_{2}$Se$_{4}$, Inorg. Chem. 40, 2602–2607 (2001), doi:10.1021/ic001346d.

Prototype Generator

aflow --proto=A2B2C4D_tP18_132_e_i_o_b --params=$a,c/a,x_{3},x_{4},z_{4}$

Species:

Running:

Output: