Sylvanite (AgAuTe4, $E1_{b}$) Structure: ABC4_mP12_13_e_a_2g

Picture of Structure; Click for Big Picture
Prototype : AgAuTe4
AFLOW prototype label : ABC4_mP12_13_e_a_2g
Strukturbericht designation : $E1_{b}$
Pearson symbol : mP12
Space group number : 13
Space group symbol : $\mbox{P2/c}$
AFLOW prototype command : aflow --proto=ABC4_mP12_13_e_a_2g
--params=
$a$,$b/a$,$c/a$,$\beta$,$y_2$,$x_3$,$y_3$,$z_3$,$x_4$,$y_4$,$z_4$


Simple Monoclinic primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & a \, \mathbf{\hat{x}} \\ \mathbf{a}_2 & = & b \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & c \cos\beta \, \mathbf{\hat{x}} + c \sin\beta \, \mathbf{\hat{z}} \end{array} \]

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(2a\right) & \mbox{Au} \\ \mathbf{B_2} & = & \frac12 \, \mathbf{a}_{3}& = & \frac12 \, c \cos\beta \, \mathbf{\hat{x}} + \frac12 \, c \sin\beta\, \mathbf{\hat{z}}& \left(2a\right) & \mbox{Au} \\ \mathbf{B_3} & = & y_2 \, \mathbf{a}_{2} + \frac14 \, \mathbf{a}_{3} & = &\frac14 \, c \cos\beta \, \mathbf{\hat{x}} + y_2 \, b \, \mathbf{\hat{y}} +\frac14 \, c \sin\beta \, \mathbf{\hat{z}}& \left(2e\right) & \mbox{Ag} \\ \mathbf{B_4} & = & - y_2 \, \mathbf{a}_{2} + \frac34 \, \mathbf{a}_{3} & = &\frac34 \, c \cos\beta \, \mathbf{\hat{x}} - y_2 \, b \, \mathbf{\hat{y}} +\frac34 \, c \sin\beta \, \mathbf{\hat{z}}& \left(2e\right) & \mbox{Ag} \\ \mathbf{B_5} & = &x_3 \, \mathbf{a}_{1} + y_3 \, \mathbf{a}_{2} + z_3 \, \mathbf{a}_{3}& = &\left(x_3 \, a + z_3 \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_3 \, b \, \mathbf{\hat{y}}+ z_3 \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4g\right) & \mbox{Te I} \\ \mathbf{B_6} & = &-x_3 \, \mathbf{a}_{1} + y_3 \, \mathbf{a}_{2} + \left(\frac12 - z_3\right) \, \mathbf{a}_{3}& = &\left(-x_3 \, a + \left(\frac12 - z_3\right) \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_3 \, b \, \mathbf{\hat{y}}+ \left(\frac12 - z_3\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4g\right) & \mbox{Te I} \\ \mathbf{B_7} & = &- x_3 \, \mathbf{a}_{1} - y_3 \, \mathbf{a}_{2} - z_3 \, \mathbf{a}_{3}& = &- \left(x_3 \, a + z_3 \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- y_3 \, b \, \mathbf{\hat{y}}- z_3 \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4g\right) & \mbox{Te I} \\ \mathbf{B_8} & = &x_3 \, \mathbf{a}_{1} - y_3 \, \mathbf{a}_{2} + \left(\frac12 + z_3\right) \, \mathbf{a}_{3}& = &\left(x_3 \, a + \left(\frac12 + z_3\right) \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- y_3 \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_3\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4g\right) & \mbox{Te I} \\ \mathbf{B_9} & = &x_4 \, \mathbf{a}_{1} + y_4 \, \mathbf{a}_{2} + z_4 \, \mathbf{a}_{3}& = &\left(x_4 \, a + z_4 \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_4 \, b \, \mathbf{\hat{y}}+ z_4 \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4g\right) & \mbox{Te II} \\ \mathbf{B}_{10} & = &-x_4 \, \mathbf{a}_{1} + y_4 \, \mathbf{a}_{2} + \left(\frac12 - z_4\right) \, \mathbf{a}_{3}& = &\left(-x_4 \, a + \left(\frac12 - z_4\right) \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_4 \, b \, \mathbf{\hat{y}}+ \left(\frac12 - z_4\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4g\right) & \mbox{Te II} \\ \mathbf{B}_{11} & = &- x_4 \, \mathbf{a}_{1} - y_4 \, \mathbf{a}_{2} - z_4 \, \mathbf{a}_{3}& = &- \left(x_4 \, a + z_4 \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- y_4 \, b \, \mathbf{\hat{y}}- z_4 \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4g\right) & \mbox{Te II} \\ \mathbf{B}_{12} & = &x_4 \, \mathbf{a}_{1} - y_4 \, \mathbf{a}_{2} + \left(\frac12 + z_4\right) \, \mathbf{a}_{3}& = &\left(x_4 \, a + \left(\frac12 + z_4\right) \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- y_4 \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_4\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4g\right) & \mbox{Te II} \\ \end{array} \]

References

  • F. Pertlik, Kristallchemie natürlicher Telluride I: Verfeinerung der Kristallstruktur des Sylvanits, AuAgTe4, Tschermaks mineralogische und petrographische Mitteilungen 33, 203–212 (1984), doi:10.1007/BF01081381.

Found in

  • P. Villars, Material Phases Data System ((MPDS), CH–6354 Vitznau, Switzerland, 2014). Accessed through the Springer Materials site.

Geometry files


Prototype Generator

aflow --proto=ABC4_mP12_13_e_a_2g --params=

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