γ-Ag$_{3}$SI (Low-Temperature) Structure: A3BC_hR5_146_b_a_a-001
| Prototype | Ag$_{3}$IS |
| AFLOW prototype label | A3BC_hR5_146_b_a_a-001 |
| ICSD | 174095 |
| Pearson symbol | hR5 |
| Space group number | 146 |
| Space group symbol | $R3$ |
| AFLOW prototype command |
aflow --proto=A3BC_hR5_146_b_a_a-001
--params=$a, \allowbreak c/a, \allowbreak x_{1}, \allowbreak x_{2}, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak z_{3}$ |
Other compounds with this structure
CsGeCl$_{3}$
- $\gamma$–Ag$_{3}$SI is the low temperature structure. Above 157K it transforms into $\beta$–Ag$_{3}$SI, a variation of the cubic perovskite ($E2_{1}$) structure.
- Space group $R3$ #146 allows an arbitary placement of the origin of the $z$-axis. We use this freedom to place a sulfur atom at the origin, $z_{2} = 0$.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{\sqrt{3}}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}+x_{1} \, \mathbf{a}_{3}$ | = | $c x_{1} \,\mathbf{\hat{z}}$ | (1a) | I I |
| $\mathbf{B_{2}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $c x_{2} \,\mathbf{\hat{z}}$ | (1a) | S I |
| $\mathbf{B_{3}}$ | = | $x_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{3} - z_{3}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{3} - 2 y_{3} + z_{3}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{3} + y_{3} + z_{3}\right) \,\mathbf{\hat{z}}$ | (3b) | Ag I |
| $\mathbf{B_{4}}$ | = | $z_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+y_{3} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(y_{3} - z_{3}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(2 x_{3} - y_{3} - z_{3}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{3} + y_{3} + z_{3}\right) \,\mathbf{\hat{z}}$ | (3b) | Ag I |
| $\mathbf{B_{5}}$ | = | $y_{3} \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{3} - y_{3}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{3} + y_{3} - 2 z_{3}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{3} + y_{3} + z_{3}\right) \,\mathbf{\hat{z}}$ | (3b) | Ag I |
References
- S. Hoshino, T. Sakuma, and Y. Fujii, A Structural Phase Transition in Superionic Conductor Ag$_{3}$SI, 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 (2013). ASM International.
Prototype Generator
aflow --proto=A3BC_hR5_146_b_a_a --params=$a,c/a,x_{1},x_{2},x_{3},y_{3},z_{3}$