$\gamma$–Ag3SI (Low–temperature) Structure: A3BC_hR5_146_b_a_a

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Prototype : Ag3SI
AFLOW prototype label : A3BC_hR5_146_b_a_a
Strukturbericht designation : None
Pearson symbol : hR5
Space group number : 146
Space group symbol : $R3$
AFLOW prototype command : aflow --proto=A3BC_hR5_146_b_a_a [--hex]
--params=
$a$,$c/a$,$x_{1}$,$x_{2}$,$x_{3}$,$y_{3}$,$z_{3}$


Rhombohedral primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & ~ \frac12 \, a \, \mathbf{\hat{x}} - \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13 \, c \, \mathbf{\hat{z}} \\ \mathbf{a}_2 & = & \frac{1}{\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13 \, c \, \mathbf{\hat{z}} \\ \mathbf{a}_3 & = & - \frac12 \, a \, \mathbf{\hat{x}} - \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13 \, c \, \mathbf{\hat{z}} \\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & x_{1} \, \mathbf{a}_{1} + x_{1} \, \mathbf{a}_{2} + x_{1} \, \mathbf{a}_{3} & = & x_{1}c \, \mathbf{\hat{z}} & \left(1a\right) & \mbox{I} \\ \mathbf{B}_{2} & = & x_{2} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} + x_{2} \, \mathbf{a}_{3} & = & x_{2}c \, \mathbf{\hat{z}} & \left(1a\right) & \mbox{S} \\ \mathbf{B}_{3} & = & x_{3} \, \mathbf{a}_{1} + y_{3} \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{3}-z_{3}\right)a \, \mathbf{\hat{x}} + \left(-\frac{1}{2\sqrt{3}}x_{3}+\frac{1}{\sqrt{3}}y_{3}-\frac{1}{2\sqrt{3}}z_{3}\right)a \, \mathbf{\hat{y}} + \frac{1}{3}\left(x_{3}+y_{3}+z_{3}\right)c \, \mathbf{\hat{z}} & \left(3b\right) & \mbox{Ag} \\ \mathbf{B}_{4} & = & z_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + y_{3} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(-y_{3}+z_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{\sqrt{3}}x_{3}-\frac{1}{2\sqrt{3}}y_{3}-\frac{1}{2\sqrt{3}}z_{3}\right)a \, \mathbf{\hat{y}} + \frac{1}{3}\left(x_{3}+y_{3}+z_{3}\right)c \, \mathbf{\hat{z}} & \left(3b\right) & \mbox{Ag} \\ \mathbf{B}_{5} & = & y_{3} \, \mathbf{a}_{1} + z_{3} \, \mathbf{a}_{2} + x_{3} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(-x_{3}+y_{3}\right)a \, \mathbf{\hat{x}} + \left(-\frac{1}{2\sqrt{3}}x_{3}-\frac{1}{2\sqrt{3}}y_{3}+\frac{1}{\sqrt{3}}z_{3}\right)a \, \mathbf{\hat{y}} + \frac{1}{3}\left(x_{3}+y_{3}+z_{3}\right)c \, \mathbf{\hat{z}} & \left(3b\right) & \mbox{Ag} \\ \end{array} \]

References

  • S. Hoshino, T. Sakuma, and Y. Fujii, A Structural Phase Transition in Superionic Conductor Ag3SI, J. Phys. Soc. Jpn. 47, 1252–1259 (1979), doi:10.1143/JPSJ.47.1252.

Found in

  • P. Villars and K. Cenzual, Pearson's Crystal Data – Crystal Structure Database for Inorganic Compounds, ASM International (2013).

Geometry files


Prototype Generator

aflow --proto=A3BC_hR5_146_b_a_a --params=

Species:

Running:

Output: