Chrysotile [Mg$_{3}$Si$_{2}$O$_{5}$(OH)$_{4}$] Structure: A3B5C4D2_mC56_9_3a_5a_4a_2a-001
| Prototype | Mg$_{3}$O$_{5}$(OH)$_{4}$Si$_{2}$ |
| AFLOW prototype label | A3B5C4D2_mC56_9_3a_5a_4a_2a-001 |
| Mineral name | chrysotile |
| ICSD | 413633 |
| Pearson symbol | mC56 |
| Space group number | 9 |
| Space group symbol | $Cc$ |
| AFLOW prototype command |
aflow --proto=A3B5C4D2_mC56_9_3a_5a_4a_2a-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak \beta, \allowbreak x_{1}, \allowbreak y_{1}, \allowbreak z_{1}, \allowbreak x_{2}, \allowbreak y_{2}, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak z_{3}, \allowbreak x_{4}, \allowbreak y_{4}, \allowbreak z_{4}, \allowbreak x_{5}, \allowbreak y_{5}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak y_{6}, \allowbreak z_{6}, \allowbreak x_{7}, \allowbreak y_{7}, \allowbreak z_{7}, \allowbreak x_{8}, \allowbreak y_{8}, \allowbreak z_{8}, \allowbreak x_{9}, \allowbreak y_{9}, \allowbreak z_{9}, \allowbreak x_{10}, \allowbreak y_{10}, \allowbreak z_{10}, \allowbreak x_{11}, \allowbreak y_{11}, \allowbreak z_{11}, \allowbreak x_{12}, \allowbreak y_{12}, \allowbreak z_{12}, \allowbreak x_{13}, \allowbreak y_{13}, \allowbreak z_{13}, \allowbreak x_{14}, \allowbreak y_{14}, \allowbreak z_{14}$ |
- Chrysotile is more commonly known as
white asbestos.
Chrysotile sheets typically curl into tubular fibers and the crystal structure is difficult to determine. (Yada, 1967) has a partial list of the experiments performed to determine this structure. - This structure differs from (Warren, 1931), $S4_{5}$, halving the size of the unit cell and removing the inversion site.
- For this prototype the OH molecules are centered on (4a) Wyckoff positions.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \cos{\beta} \,\mathbf{\hat{x}}+c \sin{\beta} \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\left(x_{1} - y_{1}\right) \, \mathbf{a}_{1}+\left(x_{1} + y_{1}\right) \, \mathbf{a}_{2}+z_{1} \, \mathbf{a}_{3}$ | = | $\left(a x_{1} + c z_{1} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{1} \,\mathbf{\hat{y}}+c z_{1} \sin{\beta} \,\mathbf{\hat{z}}$ | (4a) | Mg I |
| $\mathbf{B_{2}}$ | = | $\left(x_{1} + y_{1}\right) \, \mathbf{a}_{1}+\left(x_{1} - y_{1}\right) \, \mathbf{a}_{2}+\left(z_{1} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{1} + c \left(z_{1} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{1} \,\mathbf{\hat{y}}+c \left(z_{1} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (4a) | Mg I |
| $\mathbf{B_{3}}$ | = | $\left(x_{2} - y_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + y_{2}\right) \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $\left(a x_{2} + c z_{2} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{2} \,\mathbf{\hat{y}}+c z_{2} \sin{\beta} \,\mathbf{\hat{z}}$ | (4a) | Mg II |
| $\mathbf{B_{4}}$ | = | $\left(x_{2} + y_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} - y_{2}\right) \, \mathbf{a}_{2}+\left(z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{2} + c \left(z_{2} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{2} \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (4a) | Mg II |
| $\mathbf{B_{5}}$ | = | $\left(x_{3} - y_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} + y_{3}\right) \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\left(a x_{3} + c z_{3} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{3} \,\mathbf{\hat{y}}+c z_{3} \sin{\beta} \,\mathbf{\hat{z}}$ | (4a) | Mg III |
| $\mathbf{B_{6}}$ | = | $\left(x_{3} + y_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} - y_{3}\right) \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{3} + c \left(z_{3} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{3} \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (4a) | Mg III |
| $\mathbf{B_{7}}$ | = | $\left(x_{4} - y_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + y_{4}\right) \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $\left(a x_{4} + c z_{4} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{4} \,\mathbf{\hat{y}}+c z_{4} \sin{\beta} \,\mathbf{\hat{z}}$ | (4a) | O I |
| $\mathbf{B_{8}}$ | = | $\left(x_{4} + y_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} - y_{4}\right) \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{4} + c \left(z_{4} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{4} \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (4a) | O I |
| $\mathbf{B_{9}}$ | = | $\left(x_{5} - y_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} + y_{5}\right) \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $\left(a x_{5} + c z_{5} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{5} \,\mathbf{\hat{y}}+c z_{5} \sin{\beta} \,\mathbf{\hat{z}}$ | (4a) | O II |
| $\mathbf{B_{10}}$ | = | $\left(x_{5} + y_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} - y_{5}\right) \, \mathbf{a}_{2}+\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{5} + c \left(z_{5} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{5} \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (4a) | O II |
| $\mathbf{B_{11}}$ | = | $\left(x_{6} - y_{6}\right) \, \mathbf{a}_{1}+\left(x_{6} + y_{6}\right) \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $\left(a x_{6} + c z_{6} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{6} \,\mathbf{\hat{y}}+c z_{6} \sin{\beta} \,\mathbf{\hat{z}}$ | (4a) | O III |
| $\mathbf{B_{12}}$ | = | $\left(x_{6} + y_{6}\right) \, \mathbf{a}_{1}+\left(x_{6} - y_{6}\right) \, \mathbf{a}_{2}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{6} + c \left(z_{6} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{6} \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (4a) | O III |
| $\mathbf{B_{13}}$ | = | $\left(x_{7} - y_{7}\right) \, \mathbf{a}_{1}+\left(x_{7} + y_{7}\right) \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $\left(a x_{7} + c z_{7} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{7} \,\mathbf{\hat{y}}+c z_{7} \sin{\beta} \,\mathbf{\hat{z}}$ | (4a) | O IV |
| $\mathbf{B_{14}}$ | = | $\left(x_{7} + y_{7}\right) \, \mathbf{a}_{1}+\left(x_{7} - y_{7}\right) \, \mathbf{a}_{2}+\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{7} + c \left(z_{7} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{7} \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (4a) | O IV |
| $\mathbf{B_{15}}$ | = | $\left(x_{8} - y_{8}\right) \, \mathbf{a}_{1}+\left(x_{8} + y_{8}\right) \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $\left(a x_{8} + c z_{8} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{8} \,\mathbf{\hat{y}}+c z_{8} \sin{\beta} \,\mathbf{\hat{z}}$ | (4a) | O V |
| $\mathbf{B_{16}}$ | = | $\left(x_{8} + y_{8}\right) \, \mathbf{a}_{1}+\left(x_{8} - y_{8}\right) \, \mathbf{a}_{2}+\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{8} + c \left(z_{8} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{8} \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (4a) | O V |
| $\mathbf{B_{17}}$ | = | $\left(x_{9} - y_{9}\right) \, \mathbf{a}_{1}+\left(x_{9} + y_{9}\right) \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $\left(a x_{9} + c z_{9} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{9} \,\mathbf{\hat{y}}+c z_{9} \sin{\beta} \,\mathbf{\hat{z}}$ | (4a) | OH I |
| $\mathbf{B_{18}}$ | = | $\left(x_{9} + y_{9}\right) \, \mathbf{a}_{1}+\left(x_{9} - y_{9}\right) \, \mathbf{a}_{2}+\left(z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{9} + c \left(z_{9} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{9} \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (4a) | OH I |
| $\mathbf{B_{19}}$ | = | $\left(x_{10} - y_{10}\right) \, \mathbf{a}_{1}+\left(x_{10} + y_{10}\right) \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $\left(a x_{10} + c z_{10} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{10} \,\mathbf{\hat{y}}+c z_{10} \sin{\beta} \,\mathbf{\hat{z}}$ | (4a) | OH II |
| $\mathbf{B_{20}}$ | = | $\left(x_{10} + y_{10}\right) \, \mathbf{a}_{1}+\left(x_{10} - y_{10}\right) \, \mathbf{a}_{2}+\left(z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{10} + c \left(z_{10} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{10} \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (4a) | OH II |
| $\mathbf{B_{21}}$ | = | $\left(x_{11} - y_{11}\right) \, \mathbf{a}_{1}+\left(x_{11} + y_{11}\right) \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $\left(a x_{11} + c z_{11} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{11} \,\mathbf{\hat{y}}+c z_{11} \sin{\beta} \,\mathbf{\hat{z}}$ | (4a) | OH III |
| $\mathbf{B_{22}}$ | = | $\left(x_{11} + y_{11}\right) \, \mathbf{a}_{1}+\left(x_{11} - y_{11}\right) \, \mathbf{a}_{2}+\left(z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{11} + c \left(z_{11} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{11} \,\mathbf{\hat{y}}+c \left(z_{11} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (4a) | OH III |
| $\mathbf{B_{23}}$ | = | $\left(x_{12} - y_{12}\right) \, \mathbf{a}_{1}+\left(x_{12} + y_{12}\right) \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ | = | $\left(a x_{12} + c z_{12} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{12} \,\mathbf{\hat{y}}+c z_{12} \sin{\beta} \,\mathbf{\hat{z}}$ | (4a) | OH IV |
| $\mathbf{B_{24}}$ | = | $\left(x_{12} + y_{12}\right) \, \mathbf{a}_{1}+\left(x_{12} - y_{12}\right) \, \mathbf{a}_{2}+\left(z_{12} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{12} + c \left(z_{12} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{12} \,\mathbf{\hat{y}}+c \left(z_{12} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (4a) | OH IV |
| $\mathbf{B_{25}}$ | = | $\left(x_{13} - y_{13}\right) \, \mathbf{a}_{1}+\left(x_{13} + y_{13}\right) \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ | = | $\left(a x_{13} + c z_{13} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{13} \,\mathbf{\hat{y}}+c z_{13} \sin{\beta} \,\mathbf{\hat{z}}$ | (4a) | Si I |
| $\mathbf{B_{26}}$ | = | $\left(x_{13} + y_{13}\right) \, \mathbf{a}_{1}+\left(x_{13} - y_{13}\right) \, \mathbf{a}_{2}+\left(z_{13} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{13} + c \left(z_{13} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{13} \,\mathbf{\hat{y}}+c \left(z_{13} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (4a) | Si I |
| $\mathbf{B_{27}}$ | = | $\left(x_{14} - y_{14}\right) \, \mathbf{a}_{1}+\left(x_{14} + y_{14}\right) \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ | = | $\left(a x_{14} + c z_{14} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{14} \,\mathbf{\hat{y}}+c z_{14} \sin{\beta} \,\mathbf{\hat{z}}$ | (4a) | Si II |
| $\mathbf{B_{28}}$ | = | $\left(x_{14} + y_{14}\right) \, \mathbf{a}_{1}+\left(x_{14} - y_{14}\right) \, \mathbf{a}_{2}+\left(z_{14} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{14} + c \left(z_{14} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{14} \,\mathbf{\hat{y}}+c \left(z_{14} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (4a) | Si II |
References
- G. Falini, E. Foresti, M. Gazzano, A. F. Gualtieri, M. Leoni, I. G. Lesci, and N. Roveri, Tubular-Shaped Stoichiometric Chrysotile Nanocrystals, Chem. Eur. J. 10, 3043–3049 (2004), doi:10.1002/chem.200305685.
- K. Yada, Study of Chrysotile Asbestos by a High Resolution Electron Microscope, Acta Cryst. 23, 704–707 (1967), doi:10.1107/S0365110X67003524.
- B. E. Warren and W. L. Bragg, The Structure of Chrysotile H$_{4}$Mg$_{3}$Si$_{2}$O$_{9}$, Z. Krystallogr. 76, 201–210 (1931), doi:10.1524/zkri.1931.76.1.201.
Prototype Generator
aflow --proto=A3B5C4D2_mC56_9_3a_5a_4a_2a --params=$a,b/a,c/a,\beta,x_{1},y_{1},z_{1},x_{2},y_{2},z_{2},x_{3},y_{3},z_{3},x_{4},y_{4},z_{4},x_{5},y_{5},z_{5},x_{6},y_{6},z_{6},x_{7},y_{7},z_{7},x_{8},y_{8},z_{8},x_{9},y_{9},z_{9},x_{10},y_{10},z_{10},x_{11},y_{11},z_{11},x_{12},y_{12},z_{12},x_{13},y_{13},z_{13},x_{14},y_{14},z_{14}$