Galenobismutite (PbBi$_{2}$S$_{4}$) Structure: A2BC4_oP28_62_2c_c_4c-001
| Prototype | Bi$_{2}$PbS$_{4}$ |
| AFLOW prototype label | A2BC4_oP28_62_2c_c_4c-001 |
| Mineral name | galenobismutite |
| ICSD | 158392 |
| CCDC | 1674904 |
| Pearson symbol | oP28 |
| Space group number | 62 |
| Space group symbol | $Pnma$ |
| AFLOW prototype command |
aflow --proto=A2BC4_oP28_62_2c_c_4c-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak x_{1}, \allowbreak z_{1}, \allowbreak x_{2}, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak z_{3}, \allowbreak x_{4}, \allowbreak z_{4}, \allowbreak x_{5}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak z_{6}, \allowbreak x_{7}, \allowbreak z_{7}$ |
Other compounds with this structure
(Cd$_{x}$Na$_{1-x}$)Rh$_{2}$O$_{4}$, Li(Fe, Ti)$_{2}$O$_{4}$, Na(Al, Ge)$_{2}$O$_{4}$, Na(Al, Si)$_{2}$O$_{4}$, Na(Fe$_{0.75}$, Sb$_{0.25}$)$_{2}$O$_{4}$, Na(Fe, Ru)$_{2}$O$_{4}$, Na(Fe, Sn)$_{2}$O$_{4}$, Na(Fe, Ti)$_{2}$O$_{4}$, Na(Sc, Hf)$_{2}$O$_{4}$, Na(Sc, Sn)$_{2}$O$_{4}$, Na(Sc, Ti)$_{2}$O$_{4}$, Na(Sc, Zr)$_{2}$O$_{4}$, Na(Sn, V)$_{2}$O$_{4}$, Sr(In, Yb)$_{2}$O$_{4}$, (Ba, Sr)Dy$_{2}$O$_{4}$, (Ba, Sr)Er$_{2}$O$_{4}$, (Ba, Sr)Eu$_{2}$O$_{4}$, (Ba, Sr)Gd$_{2}$O$_{4}$, (Ba, Sr)Ho$_{2}$O$_{4}$, (Ba, Sr)La$_{2}$O$_{4}$, (Ba, Sr)Lu$_{2}$O$_{4}$, (Ba, Sr)Nd$_{2}$O$_{4}$, (Ba, Sr)Sm$_{2}$O$_{4}$, (Ba, Sr)Tm$_{2}$O$_{4}$, (Ba, Sr)Y$_{2}$O$_{4}$, (Ba, Sr)Yb$_{2}$O$_{4}$, BaCe$_{2}$O$_{4}$, BaDy$_{2}$S$_{4}$, BaDy$_{2}$Se$_{4}$, BaDy$_{2}$Te$_{4}$, BaEr$_{2}$O$_{4}$, BaEr$_{2}$S$_{4}$, BaEr$_{2}$Se$_{4}$, BaEr$_{2}$Te$_{4}$, BaEu$_{2}$O$_{4}$, BaGd$_{2}$O$_{4}$, BaGd$_{2}$S$_{4}$, BaGd$_{2}$Se$_{4}$, BaGd$_{2}$Te$_{4}$, BaHo$_{2}$O$_{4}$, BaHo$_{2}$S$_{4}$, BaHo$_{2}$Te$_{4}$, BaLa$_{2}$O$_{4}$, BaLu$_{2}$O$_{4}$, BaLu$_{2}$S$_{4}$, BaLu$_{2}$Se$_{4}$, BaLu$_{2}$Te$_{4}$, BaNd$_{2}$O$_{4}$, BaNd$_{2}$S$_{4}$, BaPr$_{2}$O$_{4}$, BaSc$_{2}$Te$_{4}$, BaSm$_{2}$O$_{4}$, BaSm$_{2}$S$_{4}$, BaSm$_{2}$Se$_{4}$, BaSm$_{2}$Te$_{4}$, BaTb$_{2}$O$_{4}$, BaTb$_{2}$S$_{4}$, BaTb$_{2}$Te$_{4}$, BaTm$_{2}$O$_{4}$, BaTm$_{2}$S$_{4}$, BaTm$_{2}$Se$_{4}$, BaTm$_{2}$Te$_{4}$, BaY$_{2}$O$_{4}$, BaY$_{2}$S$_{4}$, BaY$_{2}$Se$_{4}$, BaY$_{2}$Te$_{4}$, BaYb$_{2}$O$_{4}$, BaYb$_{2}$S$_{4}$, BaYb$_{2}$Se$_{4}$, BiEu$_{2}$S$_{4}$, CaAl$_{2}$O$_{4}$, CaCo$_{2}$O$_{4}$, CaCr$_{2}$O$_{4}$ (Ellinaite), CaFe$_{2}$O$_{4}$, CaGa$_{2}$O$_{4}$, CaIn$_{2}$O$_{4}$, CaLu$_{2}$O$_{4}$, CaRh$_{2}$O$_{4}$, CaSc$_{2}$O$_{4}$, CaSc$_{2}$S$_{4}$, CaV$_{2}$O$_{4}$, CaYb$_{2}$O$_{4}$, CdRh$_{2}$O$_{4}$, EuBi$_{2}$S$_{4}$, EuBi$_{2}$Se$_{4}$, EuDy$_{2}$S$_{4}$, EuDy$_{2}$Se$_{4}$, EuEr$_{2}$S$_{4}$, EuEr$_{2}$Se$_{4}$, EuHo$_{2}$S$_{4}$, EuHo$_{2}$Se$_{4}$, EuLu$_{2}$O$_{4}$, EuLu$_{2}$Se$_{4}$, EuSb$_{2}$S$_{4}$, EuSb$_{2}$Se$_{4}$, EuSc$_{2}$Se$_{4}$, EuTb$_{2}$Se$_{4}$, EuTm$_{2}$Se$_{4}$, EuY$_{2}$Se$_{4}$, EuYb$_{2}$S$_{4}$, EuYb$_{2}$Se$_{4}$, FeCr$_{2}$O$_{4}$, FeNb$_{2}$S$_{4}$, FeSb$_{2}$S$_{4}$, LiMn$_{2}$O$_{4}$, LiRu$_{2}$O$_{4}$, LuPb$_{2}$S$_{4}$, MgAl$_{2}$O$_{4}$, MgSc$_{2}$O$_{4}$, MnCr$_{2}$S$_{4}$, MnSb$_{2}$S$_{4}$, NaCr$_{2}$O$_{4}$, NaMn$_{2}$O$_{4}$, NaRh$_{2}$O$_{4}$, NaRu$_{2}$O$_{4}$, NaTi$_{2}$O$_{4}$, NaV$_{2}$O$_{4}$, NiNb$_{2}$S$_{4}$, PbEr$_{2}$S$_{4}$, PbEr$_{2}$Se$_{4}$, PbHo$_{2}$S$_{4}$, PbIn$_{2}$S$_{4}$, PbLu$_{2}$S$_{4}$, PbLu$_{2}$Se$_{4}$, PbSc$_{2}$S$_{4}$, PbSc$_{2}$Se$_{4}$, PbTm$_{2}$S$_{4}$, PbTm$_{2}$Se$_{4}$, PbYb$_{2}$S$_{4}$, PbYb$_{2}$Se$_{4}$, SmTm$_{2}$O$_{4}$, SnCe$_{2}$Se$_{4}$, SrDy$_{2}$O$_{4}$, SrDy$_{2}$S$_{4}$, SrDy$_{2}$Se$_{4}$, SrEr$_{2}$O$_{4}$, SrEr$_{2}$S$_{4}$, SrEr$_{2}$Se$_{4}$, SrGd$_{2}$O$_{4}$, SrHo$_{2}$O$_{4}$, SrHo$_{2}$S$_{4}$, SrIn$_{2}$O$_{4}$, SrLu$_{2}$O$_{4}$, SrLu$_{2}$S$_{4}$, SrLu$_{2}$Se$_{4}$, SrSc$_{2}$O$_{4}$, SrSc$_{2}$S$_{4}$, SrTb$_{2}$O$_{4}$, SrTb$_{2}$S$_{4}$, SrTb$_{2}$Se$_{4}$, SrTl$_{2}$O$_{4}$, SrTm$_{2}$S$_{4}$, SrY$_{2}$O$_{4}$, SrY$_{2}$S$_{4}$, SrY$_{2}$Se$_{4}$, SrYb$_{2}$O$_{4}$, SrYb$_{2}$S$_{4}$, SrYb$_{2}$Se$_{4}$, YbBi$_{2}$S$_{4}$, YbSb$_{2}$S$_{4}$, YbSb$_{2}$Se$_{4}$
- This is the ternary form of the binary Eu$_{3}$O$_{4}$ and the quaternary FeSbBiS$_{4}$ structures.
- (Olson, 2007) put this structure in the $Pnam$ setting of space group #62. We used FINDSYM to transform this the standard $Pnma$ setting. We used the data taken at 1 atmosphere (100 kPa).
- The ICSD uses CaFe$_{2}$O$_{4}$ as the prototype for this structure.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{1} \, \mathbf{a}_{3}$ | = | $a x_{1} \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+c z_{1} \,\mathbf{\hat{z}}$ | (4c) | Bi I |
| $\mathbf{B_{2}}$ | = | $- \left(x_{1} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\left(z_{1} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{1} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{3}{4}b \,\mathbf{\hat{y}}+c \left(z_{1} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4c) | Bi I |
| $\mathbf{B_{3}}$ | = | $- x_{1} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{1} \, \mathbf{a}_{3}$ | = | $- a x_{1} \,\mathbf{\hat{x}}+\frac{3}{4}b \,\mathbf{\hat{y}}- c z_{1} \,\mathbf{\hat{z}}$ | (4c) | Bi I |
| $\mathbf{B_{4}}$ | = | $\left(x_{1} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}- \left(z_{1} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{1} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}- c \left(z_{1} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4c) | Bi I |
| $\mathbf{B_{5}}$ | = | $x_{2} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (4c) | Bi II |
| $\mathbf{B_{6}}$ | = | $- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\left(z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{3}{4}b \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4c) | Bi II |
| $\mathbf{B_{7}}$ | = | $- x_{2} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+\frac{3}{4}b \,\mathbf{\hat{y}}- c z_{2} \,\mathbf{\hat{z}}$ | (4c) | Bi II |
| $\mathbf{B_{8}}$ | = | $\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}- \left(z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}- c \left(z_{2} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4c) | Bi II |
| $\mathbf{B_{9}}$ | = | $x_{3} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (4c) | Pb I |
| $\mathbf{B_{10}}$ | = | $- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{3}{4}b \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4c) | Pb I |
| $\mathbf{B_{11}}$ | = | $- x_{3} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+\frac{3}{4}b \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (4c) | Pb I |
| $\mathbf{B_{12}}$ | = | $\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}- \left(z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}- c \left(z_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4c) | Pb I |
| $\mathbf{B_{13}}$ | = | $x_{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (4c) | S I |
| $\mathbf{B_{14}}$ | = | $- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{3}{4}b \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4c) | S I |
| $\mathbf{B_{15}}$ | = | $- x_{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+\frac{3}{4}b \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ | (4c) | S I |
| $\mathbf{B_{16}}$ | = | $\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}- \left(z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}- c \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4c) | S I |
| $\mathbf{B_{17}}$ | = | $x_{5} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (4c) | S II |
| $\mathbf{B_{18}}$ | = | $- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{3}{4}b \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4c) | S II |
| $\mathbf{B_{19}}$ | = | $- x_{5} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+\frac{3}{4}b \,\mathbf{\hat{y}}- c z_{5} \,\mathbf{\hat{z}}$ | (4c) | S II |
| $\mathbf{B_{20}}$ | = | $\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}- \left(z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}- c \left(z_{5} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4c) | S II |
| $\mathbf{B_{21}}$ | = | $x_{6} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (4c) | S III |
| $\mathbf{B_{22}}$ | = | $- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{3}{4}b \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4c) | S III |
| $\mathbf{B_{23}}$ | = | $- x_{6} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}+\frac{3}{4}b \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ | (4c) | S III |
| $\mathbf{B_{24}}$ | = | $\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}- c \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4c) | S III |
| $\mathbf{B_{25}}$ | = | $x_{7} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (4c) | S IV |
| $\mathbf{B_{26}}$ | = | $- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{3}{4}b \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4c) | S IV |
| $\mathbf{B_{27}}$ | = | $- x_{7} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}+\frac{3}{4}b \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ | (4c) | S IV |
| $\mathbf{B_{28}}$ | = | $\left(x_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}- \left(z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{7} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}- c \left(z_{7} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4c) | S IV |
References
- L. A. Olsen, T. Balic-Zunic, E. Makovicky, A. Ullrich, and R. Miletich, Hydrostatic compression of galenobismutite (PbBi$_{2}$S$_{4}$): elastic properties and high-pressure crystal chemistry, Phys. Chem. Minerals 34, 467–475 (2007), doi:10.1007/s00269-007-0163-9.
Found in
- R. T. Downs and M. Hall-Wallace, The American Mineralogist Crystal Structure Database, Am. Mineral. 88, 247–250 (2003).
First cited in
- H. Eckert, S. Divilov, M. J. Mehl, D. Hicks, A. C. Zettel, M. Esters, X. Campilongo, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 4, Comp. Mat. Sci. 240, 112988 (2024). (doi=10.1016/j.commatsci.2021.110450)
Geometry files
Prototype Generator
aflow --proto=A2BC4_oP28_62_2c_c_4c --params=$a,b/a,c/a,x_{1},z_{1},x_{2},z_{2},x_{3},z_{3},x_{4},z_{4},x_{5},z_{5},x_{6},z_{6},x_{7},z_{7}$