Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: A2BC2_tI40_122_e_d_e-001

This structure originally had the label A2BC2_tI40_122_e_d_e. Calls to that address will be redirected here.

If you are using this page, please cite:
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)

Links to this page

https://aflow.org/p/05M4
or https://aflow.org/p/A2BC2_tI40_122_e_d_e-001
or PDF Version

Mercury Cyanide [Hg(CN)$_{2}$, $F1_{1}$] Structure: A2BC2_tI40_122_e_d_e-001

Picture of Structure; Click for Big Picture
Prototype C$_{2}$HgN$_{2}$
AFLOW prototype label A2BC2_tI40_122_e_d_e-001
Strukturbericht designation $F1_{1}$
Mineral name mercury cyanide
ICSD 412315
Pearson symbol tI40
Space group number 122
Space group symbol $I\overline{4}2d$
AFLOW prototype command aflow --proto=A2BC2_tI40_122_e_d_e-001
--params=$a, \allowbreak c/a, \allowbreak x_{1}, \allowbreak x_{2}, \allowbreak y_{2}, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak z_{3}$

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

Basis vectors

Lattice coordinates Cartesian coordinates Wyckoff position Atom type
$\mathbf{B_{1}}$ = $\frac{3}{8} \, \mathbf{a}_{1}+\left(x_{1} + \frac{1}{8}\right) \, \mathbf{a}_{2}+\left(x_{1} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $a x_{1} \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{8}c \,\mathbf{\hat{z}}$ (8d) Hg I
$\mathbf{B_{2}}$ = $\frac{7}{8} \, \mathbf{a}_{1}- \left(x_{1} - \frac{1}{8}\right) \, \mathbf{a}_{2}- \left(x_{1} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ = $- a x_{1} \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}+\frac{1}{8}c \,\mathbf{\hat{z}}$ (8d) Hg I
$\mathbf{B_{3}}$ = $- \left(x_{1} - \frac{7}{8}\right) \, \mathbf{a}_{1}+\frac{1}{8} \, \mathbf{a}_{2}- \left(x_{1} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- \frac{1}{4}a \,\mathbf{\hat{x}}- a \left(x_{1} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{3}{8}c \,\mathbf{\hat{z}}$ (8d) Hg I
$\mathbf{B_{4}}$ = $\left(x_{1} + \frac{7}{8}\right) \, \mathbf{a}_{1}+\frac{5}{8} \, \mathbf{a}_{2}+\left(x_{1} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ = $\frac{1}{4}a \,\mathbf{\hat{x}}+a \left(x_{1} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{3}{8}c \,\mathbf{\hat{z}}$ (8d) Hg I
$\mathbf{B_{5}}$ = $\left(y_{2} + z_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + z_{2}\right) \, \mathbf{a}_{2}+\left(x_{2} + y_{2}\right) \, \mathbf{a}_{3}$ = $a x_{2} \,\mathbf{\hat{x}}+a y_{2} \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ (16e) C I
$\mathbf{B_{6}}$ = $- \left(y_{2} - z_{2}\right) \, \mathbf{a}_{1}- \left(x_{2} - z_{2}\right) \, \mathbf{a}_{2}- \left(x_{2} + y_{2}\right) \, \mathbf{a}_{3}$ = $- a x_{2} \,\mathbf{\hat{x}}- a y_{2} \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ (16e) C I
$\mathbf{B_{7}}$ = $- \left(x_{2} + z_{2}\right) \, \mathbf{a}_{1}+\left(y_{2} - z_{2}\right) \, \mathbf{a}_{2}- \left(x_{2} - y_{2}\right) \, \mathbf{a}_{3}$ = $a y_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}- c z_{2} \,\mathbf{\hat{z}}$ (16e) C I
$\mathbf{B_{8}}$ = $\left(x_{2} - z_{2}\right) \, \mathbf{a}_{1}- \left(y_{2} + z_{2}\right) \, \mathbf{a}_{2}+\left(x_{2} - y_{2}\right) \, \mathbf{a}_{3}$ = $- a y_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}- c z_{2} \,\mathbf{\hat{z}}$ (16e) C I
$\mathbf{B_{9}}$ = $\left(y_{2} - z_{2} + \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(x_{2} + z_{2} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(- x_{2} + y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{2} \,\mathbf{\hat{x}}+a \left(y_{2} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (16e) C I
$\mathbf{B_{10}}$ = $- \left(y_{2} + z_{2} - \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(x_{2} - z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{2} - y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a x_{2} \,\mathbf{\hat{x}}- a \left(y_{2} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (16e) C I
$\mathbf{B_{11}}$ = $\left(- x_{2} + z_{2} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(- y_{2} + z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{2} + y_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a y_{2} \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (16e) C I
$\mathbf{B_{12}}$ = $\left(x_{2} + z_{2} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(y_{2} + z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{2} + y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a y_{2} \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (16e) C I
$\mathbf{B_{13}}$ = $\left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} + y_{3}\right) \, \mathbf{a}_{3}$ = $a x_{3} \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ (16e) N I
$\mathbf{B_{14}}$ = $- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} - z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} + y_{3}\right) \, \mathbf{a}_{3}$ = $- a x_{3} \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ (16e) N I
$\mathbf{B_{15}}$ = $- \left(x_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(y_{3} - z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} - y_{3}\right) \, \mathbf{a}_{3}$ = $a y_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ (16e) N I
$\mathbf{B_{16}}$ = $\left(x_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} - y_{3}\right) \, \mathbf{a}_{3}$ = $- a y_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ (16e) N I
$\mathbf{B_{17}}$ = $\left(y_{3} - z_{3} + \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(x_{3} + z_{3} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(- x_{3} + y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{3} \,\mathbf{\hat{x}}+a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (16e) N I
$\mathbf{B_{18}}$ = $- \left(y_{3} + z_{3} - \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(x_{3} - z_{3} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{3} - y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a x_{3} \,\mathbf{\hat{x}}- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (16e) N I
$\mathbf{B_{19}}$ = $\left(- x_{3} + z_{3} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(- y_{3} + z_{3} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{3} + y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a y_{3} \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (16e) N I
$\mathbf{B_{20}}$ = $\left(x_{3} + z_{3} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(y_{3} + z_{3} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{3} + y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a y_{3} \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (16e) N I

References

  • O. Reckeweg and A. Simon, X-Ray and Raman Investigations on Cyanides ofMono- and DivalentMetals and Synthesis, Crystal Structure and Raman Spectrum of Tl$_{5}$(CO$_{3}$)$_{2}$(CN), Z. f. Naturf. B 57, 895–900 (2002), doi:10.1515/znb-2002-0809.

Found in

  • P. Villars, Hg(CN)2 (Hg[CN]2) Crystal Structure (2016). PAULING FILE in: Inorganic Solid Phases, SpringerMaterials (online database).

Prototype Generator

aflow --proto=A2BC2_tI40_122_e_d_e --params=$a,c/a,x_{1},x_{2},y_{2},z_{2},x_{3},y_{3},z_{3}$

Species:

Running:

Output: