Proustite (Ag$_{3}$AsS$_{3}$) Structure: A3BC3_hR14_161_b_a_b-001
| Prototype | Ag$_{3}$AsS$_{3}$ |
| AFLOW prototype label | A3BC3_hR14_161_b_a_b-001 |
| Mineral name | proustite |
| ICSD | 27841 |
| Pearson symbol | hR14 |
| Space group number | 161 |
| Space group symbol | $R3c$ |
| AFLOW prototype command |
aflow --proto=A3BC3_hR14_161_b_a_b-001
--params=$a, \allowbreak c/a, \allowbreak x_{1}, \allowbreak x_{2}, \allowbreak y_{2}, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak z_{3}$ |
Other compounds with this structure
Ag$_{3}$AsSe$_{3}$, Ag$_{3}$SbS$_{3}$ (pyrargyrite)
- Ag$_{3}$AsS$_{3}$ can also be found in the monoclinic xanthoconite structure. (Villars, 2018) shows phase diagrams with xanthoconite at 150°C and proustite at 350°C, but (Engel, 1968) state that
[xanthoconite] is obviously more unstable than proustite.
- Space group $R3c$ #161 allows an arbitrary choice of the origin of the $z$-axis. Here we set $z_{1} = 0$ for the arsenic atom.
- Hexagonal settings of this structure can be obtained with the option
--hex.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{\sqrt{3}}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}+x_{1} \, \mathbf{a}_{3}$ | = | $c x_{1} \,\mathbf{\hat{z}}$ | (2a) | As I |
| $\mathbf{B_{2}}$ | = | $\left(x_{1} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{1} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{1} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $c \left(x_{1} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2a) | As I |
| $\mathbf{B_{3}}$ | = | $x_{2} \, \mathbf{a}_{1}+y_{2} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{2} - z_{2}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{2} - 2 y_{2} + z_{2}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{2} + y_{2} + z_{2}\right) \,\mathbf{\hat{z}}$ | (6b) | Ag I |
| $\mathbf{B_{4}}$ | = | $z_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+y_{2} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(y_{2} - z_{2}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(2 x_{2} - y_{2} - z_{2}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{2} + y_{2} + z_{2}\right) \,\mathbf{\hat{z}}$ | (6b) | Ag I |
| $\mathbf{B_{5}}$ | = | $y_{2} \, \mathbf{a}_{1}+z_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{2} - y_{2}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{2} + y_{2} - 2 z_{2}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{2} + y_{2} + z_{2}\right) \,\mathbf{\hat{z}}$ | (6b) | Ag I |
| $\mathbf{B_{6}}$ | = | $\left(z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{2} - z_{2}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{2} - 2 y_{2} + z_{2}\right) \,\mathbf{\hat{y}}+\frac{1}{6}c \left(2 x_{2} + 2 y_{2} + 2 z_{2} + 3\right) \,\mathbf{\hat{z}}$ | (6b) | Ag I |
| $\mathbf{B_{7}}$ | = | $\left(y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(y_{2} - z_{2}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(2 x_{2} - y_{2} - z_{2}\right) \,\mathbf{\hat{y}}+\frac{1}{6}c \left(2 x_{2} + 2 y_{2} + 2 z_{2} + 3\right) \,\mathbf{\hat{z}}$ | (6b) | Ag I |
| $\mathbf{B_{8}}$ | = | $\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{2} - y_{2}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{2} + y_{2} - 2 z_{2}\right) \,\mathbf{\hat{y}}+\frac{1}{6}c \left(2 x_{2} + 2 y_{2} + 2 z_{2} + 3\right) \,\mathbf{\hat{z}}$ | (6b) | Ag I |
| $\mathbf{B_{9}}$ | = | $x_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{3} - z_{3}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{3} - 2 y_{3} + z_{3}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{3} + y_{3} + z_{3}\right) \,\mathbf{\hat{z}}$ | (6b) | S I |
| $\mathbf{B_{10}}$ | = | $z_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+y_{3} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(y_{3} - z_{3}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(2 x_{3} - y_{3} - z_{3}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{3} + y_{3} + z_{3}\right) \,\mathbf{\hat{z}}$ | (6b) | S I |
| $\mathbf{B_{11}}$ | = | $y_{3} \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{3} - y_{3}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{3} + y_{3} - 2 z_{3}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{3} + y_{3} + z_{3}\right) \,\mathbf{\hat{z}}$ | (6b) | S I |
| $\mathbf{B_{12}}$ | = | $\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{3} - z_{3}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{3} - 2 y_{3} + z_{3}\right) \,\mathbf{\hat{y}}+\frac{1}{6}c \left(2 x_{3} + 2 y_{3} + 2 z_{3} + 3\right) \,\mathbf{\hat{z}}$ | (6b) | S I |
| $\mathbf{B_{13}}$ | = | $\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(y_{3} - z_{3}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(2 x_{3} - y_{3} - z_{3}\right) \,\mathbf{\hat{y}}+\frac{1}{6}c \left(2 x_{3} + 2 y_{3} + 2 z_{3} + 3\right) \,\mathbf{\hat{z}}$ | (6b) | S I |
| $\mathbf{B_{14}}$ | = | $\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{3} - y_{3}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{3} + y_{3} - 2 z_{3}\right) \,\mathbf{\hat{y}}+\frac{1}{6}c \left(2 x_{3} + 2 y_{3} + 2 z_{3} + 3\right) \,\mathbf{\hat{z}}$ | (6b) | S I |
References
- D. Harker, The Application of the Three‐Dimensional Patterson Method and the Crystal Structures of Proustite, Ag$_{3}$AsS$_{3}$, and Pyrargyrite, Ag$_{3}$SbS$_{3}$, J. Chem. Phys. 4, 381–390 (1936), doi:10.1063/1.1749863.
- P. Villars, H. Okamoto, and K. Cenzual, eds., ASM Alloy Phase Diagram Database (ASM International, 2018), chap. 1988 Schmid Fetzer R. (Silver-Arsenic-Sulfur). Copyright © 2006-2018 ASM International.
Found in
- R. T. Downs and M. Hall-Wallace, The American Mineralogist Crystal Structure Database, Am. Mineral. 88, 247–250 (2003).
Prototype Generator
aflow --proto=A3BC3_hR14_161_b_a_b --params=$a,c/a,x_{1},x_{2},y_{2},z_{2},x_{3},y_{3},z_{3}$