Jacutingaite (Pt2HgSe3) Structure : AB2C3_hP12_164_d_ae_i

Picture of Structure; Click for Big Picture
Prototype : HgPt2Se3
AFLOW prototype label : AB2C3_hP12_164_d_ae_i
Strukturbericht designation : None
Pearson symbol : hP12
Space group number : 164
Space group symbol : $P\bar{3}m1$
AFLOW prototype command : aflow --proto=AB2C3_hP12_164_d_ae_i
--params=
$a$,$c/a$,$z_{2}$,$x_{4}$,$z_{4}$


  • Table 4 of (Vymazalová, 2012) has a small error: the positions of the Hg(1) atoms should be written $(1/3, 2/3, 0.3507)$ rather than $(1/3, 1/3, 0.3507)$.

Trigonal Hexagonal primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{x}} - \frac{\sqrt3}2 \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac{\sqrt3}2 \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & c \, \mathbf{\hat{z}} \\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & 0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = & 0 \, \mathbf{\hat{x}} + 0 \, \mathbf{\hat{y}} + 0 \, \mathbf{\hat{z}} & \left(1a\right) & \mbox{Pt I} \\ \mathbf{B}_{2} & = & \frac{1}{3} \, \mathbf{a}_{1} + \frac{2}{3} \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + z_{2}c \, \mathbf{\hat{z}} & \left(2d\right) & \mbox{Hg} \\ \mathbf{B}_{3} & = & \frac{2}{3} \, \mathbf{a}_{1} + \frac{1}{3} \, \mathbf{a}_{2}-z_{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}}-z_{2}c \, \mathbf{\hat{z}} & \left(2d\right) & \mbox{Hg} \\ \mathbf{B}_{4} & = & \frac{1}{2} \, \mathbf{a}_{1} & = & \frac{1}{4}a \, \mathbf{\hat{x}}- \frac{\sqrt{3}}{4}a \, \mathbf{\hat{y}} & \left(3e\right) & \mbox{Pt II} \\ \mathbf{B}_{5} & = & \frac{1}{2} \, \mathbf{a}_{2} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{4}a \, \mathbf{\hat{y}} & \left(3e\right) & \mbox{Pt II} \\ \mathbf{B}_{6} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} & = & \frac{1}{2}a \, \mathbf{\hat{x}} & \left(3e\right) & \mbox{Pt II} \\ \mathbf{B}_{7} & = & x_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & -\sqrt{3}x_{4}a \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(6i\right) & \mbox{Se} \\ \mathbf{B}_{8} & = & x_{4} \, \mathbf{a}_{1} + 2x_{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & \frac{3}{2}x_{4}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{4}a \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(6i\right) & \mbox{Se} \\ \mathbf{B}_{9} & = & -2x_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & -\frac{3}{2}x_{4}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{4}a \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(6i\right) & \mbox{Se} \\ \mathbf{B}_{10} & = & -x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2}-z_{4} \, \mathbf{a}_{3} & = & \sqrt{3}x_{4}a \, \mathbf{\hat{y}}-z_{4}c \, \mathbf{\hat{z}} & \left(6i\right) & \mbox{Se} \\ \mathbf{B}_{11} & = & 2x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2}-z_{4} \, \mathbf{a}_{3} & = & \frac{3}{2}x_{4}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{4}a \, \mathbf{\hat{y}}-z_{4}c \, \mathbf{\hat{z}} & \left(6i\right) & \mbox{Se} \\ \mathbf{B}_{12} & = & -x_{4} \, \mathbf{a}_{1}-2x_{4} \, \mathbf{a}_{2}-z_{4} \, \mathbf{a}_{3} & = & -\frac{3}{2}x_{4}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{4}a \, \mathbf{\hat{y}}-z_{4}c \, \mathbf{\hat{z}} & \left(6i\right) & \mbox{Se} \\ \end{array} \]

References

  • A. Vymazalová, F. Laufek, M. Drábek, A. R. Cabral, J. Haloda, T. Sidorinová, B. Lehmann, H. F. Galbiatti, and J. Drahokoupil, Jacutingaite, Pt2HgSe3, A New Platinum–Group Mineral Species From the Cauê Iron–Ore Deposit, Itabira District, Minas Gerais, Brazil, Can. Mineral. 50, 431–440 (2012), doi:10.3749/canmin.50.2.431.

Found in

  • A. Marrazzo, N. Marzari, and M. Gibertini, Emergent dual topology in the three–dimensional Kane–Mele Pt2HgSe3, Phys. Rev. Research 2, 012063 (2020), doi:10.1103/PhysRevResearch.2.012063.

Geometry files


Prototype Generator

aflow --proto=AB2C3_hP12_164_d_ae_i --params=

Species:

Running:

Output: