Krennerite (AuTe2, $C46$) Structure: AB2_oP24_28_acd_2c3d

Picture of Structure; Click for Big Picture
Prototype : AuTe2
AFLOW prototype label : AB2_oP24_28_acd_2c3d
Strukturbericht designation : $C46$
Pearson symbol : oP24
Space group number : 28
Space group symbol : $\mbox{Pma2}$
AFLOW prototype command : aflow --proto=AB2_oP24_28_acd_2c3d
--params=
$a$,$b/a$,$c/a$,$z_{1}$,$y_{2}$,$z_{2}$,$y_{3}$,$z_{3}$,$y_{4}$,$z_{4}$,$x_{5}$,$y_{5}$,$z_{5}$,$x_{6}$,$y_{6}$,$z_{6}$,$x_{7}$,$y_{7}$,$z_{7}$,$x_{8}$,$y_{8}$,$z_{8}$


  • The sample studied had composition (Au0.88,Ag0.12)Te2. For simplicity we make all of the Au/Ag sites Au. (Pearson, 1972) states that this is a distortion of the trigonal $\omega$ phase. Note that AuTe2 also exists in the C34 structure.

Simple Orthorhombic primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & =& z_{1} \, \mathbf{a}_{3}& =& z_{1} \, c \, \mathbf{\hat{z}}& \left(2a\right) & \mbox{Au I} \\ \mathbf{B}_{2} & =& \frac12 \, \mathbf{a}_{1} + z_{1} \, \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} + z_{1} \, c \, \mathbf{\hat{z}}& \left(2a\right) & \mbox{Au I} \\ \mathbf{B}_{3} & =& \frac14 \, \mathbf{a}_{1} + y_{2} \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3}& =& \frac14 \, a \, \mathbf{\hat{x}} + y_{2} \, b \, \mathbf{\hat{y}}+ z_{2} \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{Au II} \\ \mathbf{B}_{4} & =& \frac34 \, \mathbf{a}_{1} - y_{2} \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3}& =& \frac34 \, a \, \mathbf{\hat{x}} - y_{2} \, b \, \mathbf{\hat{y}}+ z_{2} \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{Au II} \\ \mathbf{B}_{5} & =& \frac14 \, \mathbf{a}_{1} + y_{3} \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3}& =& \frac14 \, a \, \mathbf{\hat{x}} + y_{3} \, b \, \mathbf{\hat{y}}+ z_{3} \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{Te I} \\ \mathbf{B}_{6} & =& \frac34 \, \mathbf{a}_{1} - y_{3} \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3}& =& \frac34 \, a \, \mathbf{\hat{x}} - y_{3} \, b \, \mathbf{\hat{y}}+ z_{3} \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{Te I} \\ \mathbf{B}_{7} & =& \frac14 \, \mathbf{a}_{1} + y_{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3}& =& \frac14 \, a \, \mathbf{\hat{x}} + y_{4} \, b \, \mathbf{\hat{y}}+ z_{4} \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{Te II} \\ \mathbf{B}_{8} & =& \frac34 \, \mathbf{a}_{1} - y_{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3}& =& \frac34 \, a \, \mathbf{\hat{x}} - y_{4} \, b \, \mathbf{\hat{y}}+ z_{4} \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{Te II} \\ \mathbf{B}_{9} & =& x_{5} \, \mathbf{a}_{1} + y_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3}& =& x_{5} \, a \, \mathbf{\hat{x}} + y_{5} \, b \, \mathbf{\hat{y}}+ z_{5} \, c \, \mathbf{\hat{z}}& \left(4d\right) & \mbox{Au III} \\ \mathbf{B}_{10} & =& - x_{5} \, \mathbf{a}_{1} - y_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3}& =& - x_{5} \, a \, \mathbf{\hat{x}} - y_{5} \, b \, \mathbf{\hat{y}}+ z_{5} \, c \, \mathbf{\hat{z}}& \left(4d\right) & \mbox{Au III} \\ \mathbf{B}_{11} & =& \left(\frac12 + x_{5}\right) \, \mathbf{a}_{1} - y_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3}& =& \left(\frac12 + x_{5}\right) \, a \, \mathbf{\hat{x}} - y_{5} \, b \, \mathbf{\hat{y}}+ z_{5} \, c \, \mathbf{\hat{z}}& \left(4d\right) & \mbox{Au III} \\ \mathbf{B}_{12} & =& \left(\frac12 - x_{5}\right) \, \mathbf{a}_{1} + y_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3}& =& \left(\frac12 - x_{5}\right) \, a \, \mathbf{\hat{x}} + y_{5} \, b \, \mathbf{\hat{y}}+ z_{5} \, c \, \mathbf{\hat{z}}& \left(4d\right) & \mbox{Au III} \\ \mathbf{B}_{13} & =& x_{6} \, \mathbf{a}_{1} + y_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3}& =& x_{6} \, a \, \mathbf{\hat{x}} + y_{6} \, b \, \mathbf{\hat{y}}+ z_{6} \, c \, \mathbf{\hat{z}}& \left(4d\right) & \mbox{Te III} \\ \mathbf{B}_{14} & =& - x_{6} \, \mathbf{a}_{1} - y_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3}& =& - x_{6} \, a \, \mathbf{\hat{x}} - y_{6} \, b \, \mathbf{\hat{y}}+ z_{6} \, c \, \mathbf{\hat{z}}& \left(4d\right) & \mbox{Te III} \\ \mathbf{B}_{15} & =& \left(\frac12 + x_{6}\right) \, \mathbf{a}_{1} - y_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3}& =& \left(\frac12 + x_{6}\right) \, a \, \mathbf{\hat{x}} - y_{6} \, b \, \mathbf{\hat{y}}+ z_{6} \, c \, \mathbf{\hat{z}}& \left(4d\right) & \mbox{Te III} \\ \mathbf{B}_{16} & =& \left(\frac12 - x_{6}\right) \, \mathbf{a}_{1} + y_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3}& =& \left(\frac12 - x_{6}\right) \, a \, \mathbf{\hat{x}} + y_{6} \, b \, \mathbf{\hat{y}}+ z_{6} \, c \, \mathbf{\hat{z}}& \left(4d\right) & \mbox{Te III} \\ \mathbf{B}_{17} & =& x_{7} \, \mathbf{a}_{1} + y_{7} \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3}& =& x_{7} \, a \, \mathbf{\hat{x}} + y_{7} \, b \, \mathbf{\hat{y}}+ z_{7} \, c \, \mathbf{\hat{z}}& \left(4d\right) & \mbox{Te IV} \\ \mathbf{B}_{18} & =& - x_{7} \, \mathbf{a}_{1} - y_{7} \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3}& =& - x_{7} \, a \, \mathbf{\hat{x}} - y_{7} \, b \, \mathbf{\hat{y}}+ z_{7} \, c \, \mathbf{\hat{z}}& \left(4d\right) & \mbox{Te IV} \\ \mathbf{B}_{19} & =& \left(\frac12 + x_{7}\right) \, \mathbf{a}_{1} - y_{7} \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3}& =& \left(\frac12 + x_{7}\right) \, a \, \mathbf{\hat{x}} - y_{7} \, b \, \mathbf{\hat{y}}+ z_{7} \, c \, \mathbf{\hat{z}}& \left(4d\right) & \mbox{Te IV} \\ \mathbf{B}_{20} & =& \left(\frac12 - x_{7}\right) \, \mathbf{a}_{1} + y_{7} \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3}& =& \left(\frac12 - x_{7}\right) \, a \, \mathbf{\hat{x}} + y_{7} \, b \, \mathbf{\hat{y}}+ z_{7} \, c \, \mathbf{\hat{z}}& \left(4d\right) & \mbox{Te IV} \\ \mathbf{B}_{21} & =& x_{8} \, \mathbf{a}_{1} + y_{8} \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3}& =& x_{8} \, a \, \mathbf{\hat{x}} + y_{8} \, b \, \mathbf{\hat{y}}+ z_{8} \, c \, \mathbf{\hat{z}}& \left(4d\right) & \mbox{Te V} \\ \mathbf{B}_{22} & =& - x_{8} \, \mathbf{a}_{1} - y_{8} \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3}& =& - x_{8} \, a \, \mathbf{\hat{x}} - y_{8} \, b \, \mathbf{\hat{y}}+ z_{8} \, c \, \mathbf{\hat{z}}& \left(4d\right) & \mbox{Te V} \\ \mathbf{B}_{23} & =& \left(\frac12 + x_{8}\right) \, \mathbf{a}_{1} - y_{8} \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3}& =& \left(\frac12 + x_{8}\right) \, a \, \mathbf{\hat{x}} - y_{8} \, b \, \mathbf{\hat{y}}+ z_{8} \, c \, \mathbf{\hat{z}}& \left(4d\right) & \mbox{Te V} \\ \mathbf{B}_{24} & =& \left(\frac12 - x_{8}\right) \, \mathbf{a}_{1} + y_{8} \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3}& =& \left(\frac12 - x_{8}\right) \, a \, \mathbf{\hat{x}} + y_{8} \, b \, \mathbf{\hat{y}}+ z_{8} \, c \, \mathbf{\hat{z}}& \left(4d\right) & \mbox{Te V} \\ \end{array} \]

References

  • G. Tunell and K. J. Murata, The Atomic Arrangement and Chemical Composition of Krennerite, The American Mineralogist 35, 959–984 (1950).
  • W. B. Pearson, The Crystal Chemistry and Physics of Metals and Alloys (Wiley– Interscience, New York, London, Sydney, Toronto, 1972).

Geometry files


Prototype Generator

aflow --proto=AB2_oP24_28_acd_2c3d --params=

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