Parkerite (Ni$_{3}$Bi$_{2}$S$_{4}$) Structure: AB2C_oP8_51_e_be_f-001
| Prototype | Bi$_{2}$Ni$_{3}$S$_{2}$ |
| AFLOW prototype label | AB2C_oP8_51_e_be_f-001 |
| Mineral name | parkerite |
| ICSD | 70052 |
| Pearson symbol | oP8 |
| Space group number | 51 |
| Space group symbol | $Pmma$ |
| AFLOW prototype command |
aflow --proto=AB2C_oP8_51_e_be_f-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak z_{2}, \allowbreak z_{3}, \allowbreak z_{4}$ |
Other compounds with this structure
Ni$_{3}$(Bi, Pb)$_{2}$S$_{4}$
- (Fleet, 1973) states that parkerite is a derivative of the shandite (Ni$_{3}$Pb$_{2}$S$_{2}$) structure, and changes to shandite if more than 4% of the bismuth is replaced by lead.
- The Ni-II (2e) site is occupied 50% of the time, given the observed stoichiometry.
- Earlier sources give parkerite a monoclinic structure. This may be due to an ordering of the nickel atoms at lower temperature. We follow (Downs, 2003) and use the orthorhombic structure.
- (Fleet, 1973) describes the structure in the $Pmam$ setting of space group #51. We used FINDSYM to transform it to the standard $Pmma$ setting.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}b \,\mathbf{\hat{y}}$ | (2b) | Ni I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}$ | (2b) | Ni I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+z_{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+c z_{2} \,\mathbf{\hat{z}}$ | (2e) | Bi I |
| $\mathbf{B_{4}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}- z_{2} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}- c z_{2} \,\mathbf{\hat{z}}$ | (2e) | Bi I |
| $\mathbf{B_{5}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+c z_{3} \,\mathbf{\hat{z}}$ | (2e) | Ni II |
| $\mathbf{B_{6}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}- c z_{3} \,\mathbf{\hat{z}}$ | (2e) | Ni II |
| $\mathbf{B_{7}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (2f) | S I |
| $\mathbf{B_{8}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ | (2f) | S I |
References
- M. E. Fleet, The Crystal Structure of Parkerite (Ni$_{3}$Bi$_{2}$S$_{4}$), Am. Mineral. 58, 435–439 (1973).
- R. T. Downs and M. Hall-Wallace, The American Mineralogist Crystal Structure Database, Am. Mineral. 88, 247–250 (2003).
Prototype Generator
aflow --proto=AB2C_oP8_51_e_be_f --params=$a,b/a,c/a,z_{2},z_{3},z_{4}$