Hulsite [(Fe$_{1.315}$Mg$_{0.56}$Sn$_{0.1}$)BO$_{5}$] Structure: A2B2C3D10E_mP18_10_m_ac_en_3m2n_g-001
| Prototype | BFe$_{1.315}$Mg$_{0.56}$O$_{5}$Sn$_{0.1}$ |
| AFLOW prototype label | A2B2C3D10E_mP18_10_m_ac_en_3m2n_g-001 |
| Mineral name | hulsite |
| ICSD | 12133 |
| Pearson symbol | mP18 |
| Space group number | 10 |
| Space group symbol | $P2/m$ |
| AFLOW prototype command |
aflow --proto=A2B2C3D10E_mP18_10_m_ac_en_3m2n_g-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak \beta, \allowbreak x_{5}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak z_{6}, \allowbreak x_{7}, \allowbreak z_{7}, \allowbreak x_{8}, \allowbreak z_{8}, \allowbreak x_{9}, \allowbreak z_{9}, \allowbreak x_{10}, \allowbreak z_{10}, \allowbreak x_{11}, \allowbreak z_{11}$ |
Other compounds with this structure
Na$_{2.57}$Sn$_{0.43}$BO$_{5}$
- As can be seen from the composition, the metallic atoms in this mineral are on mixed sites with many vacancies. The labels we have assigned to each site are purely for convenience.
- According to (Konnert, 1976), the composition of each site is:
- (1a) 50% Fe
- (1c) 50% Fe
- (1e) 36% Fe, 16% Mg (labeled Mg)
- (1g) 20% Sn, 27% Fe (labeled Sn here)
- Metallic (2n) 50% Fe, 48% Mg (labeled Mg).
- The boron and oxygen sites are fully occupied.
- We have switched the $a$ and $c$ axis from that defined by (Konnert, 1976). This swaps the (1a) and (1g) Wyckoff positions, while the (1d) Wyckoff postion becomes (1c) and (1f) becomes (1e).
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \cos{\beta} \,\mathbf{\hat{x}}+c \sin{\beta} \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (1a) | Fe I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \cos{\beta} \,\mathbf{\hat{x}}+\frac{1}{2}c \sin{\beta} \,\mathbf{\hat{z}}$ | (1c) | Fe II |
| $\mathbf{B_{3}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}$ | (1e) | Mg I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}\left(a + c \cos{\beta}\right) \,\mathbf{\hat{x}}+\frac{1}{2}c \sin{\beta} \,\mathbf{\hat{z}}$ | (1g) | Sn I |
| $\mathbf{B_{5}}$ | = | $x_{5} \, \mathbf{a}_{1}+z_{5} \, \mathbf{a}_{3}$ | = | $\left(a x_{5} + c z_{5} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{5} \sin{\beta} \,\mathbf{\hat{z}}$ | (2m) | B I |
| $\mathbf{B_{6}}$ | = | $- x_{5} \, \mathbf{a}_{1}- z_{5} \, \mathbf{a}_{3}$ | = | $- \left(a x_{5} + c z_{5} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{5} \sin{\beta} \,\mathbf{\hat{z}}$ | (2m) | B I |
| $\mathbf{B_{7}}$ | = | $x_{6} \, \mathbf{a}_{1}+z_{6} \, \mathbf{a}_{3}$ | = | $\left(a x_{6} + c z_{6} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{6} \sin{\beta} \,\mathbf{\hat{z}}$ | (2m) | O I |
| $\mathbf{B_{8}}$ | = | $- x_{6} \, \mathbf{a}_{1}- z_{6} \, \mathbf{a}_{3}$ | = | $- \left(a x_{6} + c z_{6} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{6} \sin{\beta} \,\mathbf{\hat{z}}$ | (2m) | O I |
| $\mathbf{B_{9}}$ | = | $x_{7} \, \mathbf{a}_{1}+z_{7} \, \mathbf{a}_{3}$ | = | $\left(a x_{7} + c z_{7} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{7} \sin{\beta} \,\mathbf{\hat{z}}$ | (2m) | O II |
| $\mathbf{B_{10}}$ | = | $- x_{7} \, \mathbf{a}_{1}- z_{7} \, \mathbf{a}_{3}$ | = | $- \left(a x_{7} + c z_{7} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{7} \sin{\beta} \,\mathbf{\hat{z}}$ | (2m) | O II |
| $\mathbf{B_{11}}$ | = | $x_{8} \, \mathbf{a}_{1}+z_{8} \, \mathbf{a}_{3}$ | = | $\left(a x_{8} + c z_{8} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{8} \sin{\beta} \,\mathbf{\hat{z}}$ | (2m) | O III |
| $\mathbf{B_{12}}$ | = | $- x_{8} \, \mathbf{a}_{1}- z_{8} \, \mathbf{a}_{3}$ | = | $- \left(a x_{8} + c z_{8} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{8} \sin{\beta} \,\mathbf{\hat{z}}$ | (2m) | O III |
| $\mathbf{B_{13}}$ | = | $x_{9} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $\left(a x_{9} + c z_{9} \cos{\beta}\right) \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}+c z_{9} \sin{\beta} \,\mathbf{\hat{z}}$ | (2n) | Mg II |
| $\mathbf{B_{14}}$ | = | $- x_{9} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ | = | $- \left(a x_{9} + c z_{9} \cos{\beta}\right) \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}- c z_{9} \sin{\beta} \,\mathbf{\hat{z}}$ | (2n) | Mg II |
| $\mathbf{B_{15}}$ | = | $x_{10} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $\left(a x_{10} + c z_{10} \cos{\beta}\right) \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}+c z_{10} \sin{\beta} \,\mathbf{\hat{z}}$ | (2n) | O IV |
| $\mathbf{B_{16}}$ | = | $- x_{10} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- z_{10} \, \mathbf{a}_{3}$ | = | $- \left(a x_{10} + c z_{10} \cos{\beta}\right) \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}- c z_{10} \sin{\beta} \,\mathbf{\hat{z}}$ | (2n) | O IV |
| $\mathbf{B_{17}}$ | = | $x_{11} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $\left(a x_{11} + c z_{11} \cos{\beta}\right) \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}+c z_{11} \sin{\beta} \,\mathbf{\hat{z}}$ | (2n) | O V |
| $\mathbf{B_{18}}$ | = | $- x_{11} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- z_{11} \, \mathbf{a}_{3}$ | = | $- \left(a x_{11} + c z_{11} \cos{\beta}\right) \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}- c z_{11} \sin{\beta} \,\mathbf{\hat{z}}$ | (2n) | O V |
References
- J. A. Konnert, D. E. Appleman, J. R. Clark, L. W. Finger, T. Kato, and Y. Miura, Crystal structure and cation distribution of hulsite, a tin-iron borate, Am. Mineral. 61, 116–122 (1976).
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=A2B2C3D10E_mP18_10_m_ac_en_3m2n_g --params=$a,b/a,c/a,\beta,x_{5},z_{5},x_{6},z_{6},x_{7},z_{7},x_{8},z_{8},x_{9},z_{9},x_{10},z_{10},x_{11},z_{11}$