Chrysotile (H4Mg3Si2O9, $S4_{5}$) Structure : AB6C11D6E4_mC112_12_e_gi2j_i5j_2i2j_2j

Picture of Structure; Click for Big Picture
Prototype : (H2O)(OH)6O11Mg6Si4
AFLOW prototype label : AB6C11D6E4_mC112_12_e_gi2j_i5j_2i2j_2j
Strukturbericht designation : $S4_{5}$
Pearson symbol : mC112
Space group number : 12
Space group symbol : $C2/m$
AFLOW prototype command : aflow --proto=AB6C11D6E4_mC112_12_e_gi2j_i5j_2i2j_2j
--params=
$a$,$b/a$,$c/a$,$\beta$,$y_{2}$,$x_{3}$,$z_{3}$,$x_{4}$,$z_{4}$,$x_{5}$,$z_{5}$,$x_{6}$,$z_{6}$,$x_{7}$,$y_{7}$,$z_{7}$,$x_{8}$,$y_{8}$,$z_{8}$,$x_{9}$,$y_{9}$,$z_{9}$,$x_{10}$,$y_{10}$,$z_{10}$,$x_{11}$,$y_{11}$,$z_{11}$,$x_{12}$,$y_{12}$,$z_{12}$,$x_{13}$,$y_{13}$,$z_{13}$,$x_{14}$,$y_{14}$,$z_{14}$,$x_{15}$,$y_{15}$,$z_{15}$,$x_{16}$,$y_{16}$,$z_{16}$,$x_{17}$,$y_{17}$,$z_{17}$


  • 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. The current structure was given the Strukturbericht designation $S4_{5}$ by (Hermann, 1937). It doubles the unit cell of our other chrysotile structure, by (Falini, 2004) and includes an inversion site.
  • The structure was originally given in the $I2/m$ setting of space group #12. We used FINDSYM to place it in the standard $C2/m$ setting.

Base-centered Monoclinic primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{x}} - \frac12 \, b \, \mathbf{\hat{y}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, b \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & c \cos\beta \, \mathbf{\hat{x}} + c \sin\beta \, \mathbf{\hat{z}} \\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & \frac{1}{2} \, \mathbf{a}_{2} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} & \left(4e\right) & \mbox{H$_{2}$O} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{1} & = & \frac{1}{4}a \, \mathbf{\hat{x}}- \frac{1}{4}b \, \mathbf{\hat{y}} & \left(4e\right) & \mbox{H$_{2}$O} \\ \mathbf{B}_{3} & = & -y_{2} \, \mathbf{a}_{1} + y_{2} \, \mathbf{a}_{2} & = & y_{2}b \, \mathbf{\hat{y}} & \left(4g\right) & \mbox{Mg I} \\ \mathbf{B}_{4} & = & y_{2} \, \mathbf{a}_{1}-y_{2} \, \mathbf{a}_{2} & = & -y_{2}b \, \mathbf{\hat{y}} & \left(4g\right) & \mbox{Mg I} \\ \mathbf{B}_{5} & = & x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3} & = & \left(x_{3}a+z_{3}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{3}c\sin\beta \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{Mg II} \\ \mathbf{B}_{6} & = & -x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2}-z_{3} \, \mathbf{a}_{3} & = & \left(-x_{3}a-z_{3}c\cos\beta\right) \, \mathbf{\hat{x}}-z_{3}c\sin\beta \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{Mg II} \\ \mathbf{B}_{7} & = & x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & \left(x_{4}a+z_{4}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{4}c\sin\beta \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{O I} \\ \mathbf{B}_{8} & = & -x_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2}-z_{4} \, \mathbf{a}_{3} & = & \left(-x_{4}a-z_{4}c\cos\beta\right) \, \mathbf{\hat{x}}-z_{4}c\sin\beta \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{O I} \\ \mathbf{B}_{9} & = & x_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & \left(x_{5}a+z_{5}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{5}c\sin\beta \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{OH I} \\ \mathbf{B}_{10} & = & -x_{5} \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2}-z_{5} \, \mathbf{a}_{3} & = & \left(-x_{5}a-z_{5}c\cos\beta\right) \, \mathbf{\hat{x}}-z_{5}c\sin\beta \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{OH I} \\ \mathbf{B}_{11} & = & x_{6} \, \mathbf{a}_{1} + x_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & \left(x_{6}a+z_{6}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{6}c\sin\beta \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{OH II} \\ \mathbf{B}_{12} & = & -x_{6} \, \mathbf{a}_{1}-x_{6} \, \mathbf{a}_{2}-z_{6} \, \mathbf{a}_{3} & = & \left(-x_{6}a-z_{6}c\cos\beta\right) \, \mathbf{\hat{x}}-z_{6}c\sin\beta \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{OH II} \\ \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(x_{7}a+z_{7}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{7}b \, \mathbf{\hat{y}} + z_{7}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{Mg III} \\ \mathbf{B}_{14} & = & \left(-x_{7}-y_{7}\right) \, \mathbf{a}_{1} + \left(-x_{7}+y_{7}\right) \, \mathbf{a}_{2}-z_{7} \, \mathbf{a}_{3} & = & \left(-x_{7}a-z_{7}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{7}b \, \mathbf{\hat{y}}-z_{7}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{Mg III} \\ \mathbf{B}_{15} & = & \left(-x_{7}+y_{7}\right) \, \mathbf{a}_{1} + \left(-x_{7}-y_{7}\right) \, \mathbf{a}_{2}-z_{7} \, \mathbf{a}_{3} & = & \left(-x_{7}a-z_{7}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{7}b \, \mathbf{\hat{y}}-z_{7}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{Mg III} \\ \mathbf{B}_{16} & = & \left(x_{7}+y_{7}\right) \, \mathbf{a}_{1} + \left(x_{7}-y_{7}\right) \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & \left(x_{7}a+z_{7}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{7}b \, \mathbf{\hat{y}} + z_{7}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{Mg III} \\ \mathbf{B}_{17} & = & \left(x_{8}-y_{8}\right) \, \mathbf{a}_{1} + \left(x_{8}+y_{8}\right) \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & \left(x_{8}a+z_{8}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{8}b \, \mathbf{\hat{y}} + z_{8}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{Mg IV} \\ \mathbf{B}_{18} & = & \left(-x_{8}-y_{8}\right) \, \mathbf{a}_{1} + \left(-x_{8}+y_{8}\right) \, \mathbf{a}_{2}-z_{8} \, \mathbf{a}_{3} & = & \left(-x_{8}a-z_{8}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{8}b \, \mathbf{\hat{y}}-z_{8}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{Mg IV} \\ \mathbf{B}_{19} & = & \left(-x_{8}+y_{8}\right) \, \mathbf{a}_{1} + \left(-x_{8}-y_{8}\right) \, \mathbf{a}_{2}-z_{8} \, \mathbf{a}_{3} & = & \left(-x_{8}a-z_{8}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{8}b \, \mathbf{\hat{y}}-z_{8}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{Mg IV} \\ \mathbf{B}_{20} & = & \left(x_{8}+y_{8}\right) \, \mathbf{a}_{1} + \left(x_{8}-y_{8}\right) \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & \left(x_{8}a+z_{8}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{8}b \, \mathbf{\hat{y}} + z_{8}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{Mg IV} \\ \mathbf{B}_{21} & = & \left(x_{9}-y_{9}\right) \, \mathbf{a}_{1} + \left(x_{9}+y_{9}\right) \, \mathbf{a}_{2} + z_{9} \, \mathbf{a}_{3} & = & \left(x_{9}a+z_{9}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{9}b \, \mathbf{\hat{y}} + z_{9}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{O II} \\ \mathbf{B}_{22} & = & \left(-x_{9}-y_{9}\right) \, \mathbf{a}_{1} + \left(-x_{9}+y_{9}\right) \, \mathbf{a}_{2}-z_{9} \, \mathbf{a}_{3} & = & \left(-x_{9}a-z_{9}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{9}b \, \mathbf{\hat{y}}-z_{9}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{O II} \\ \mathbf{B}_{23} & = & \left(-x_{9}+y_{9}\right) \, \mathbf{a}_{1} + \left(-x_{9}-y_{9}\right) \, \mathbf{a}_{2}-z_{9} \, \mathbf{a}_{3} & = & \left(-x_{9}a-z_{9}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{9}b \, \mathbf{\hat{y}}-z_{9}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{O II} \\ \mathbf{B}_{24} & = & \left(x_{9}+y_{9}\right) \, \mathbf{a}_{1} + \left(x_{9}-y_{9}\right) \, \mathbf{a}_{2} + z_{9} \, \mathbf{a}_{3} & = & \left(x_{9}a+z_{9}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{9}b \, \mathbf{\hat{y}} + z_{9}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{O II} \\ \mathbf{B}_{25} & = & \left(x_{10}-y_{10}\right) \, \mathbf{a}_{1} + \left(x_{10}+y_{10}\right) \, \mathbf{a}_{2} + z_{10} \, \mathbf{a}_{3} & = & \left(x_{10}a+z_{10}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{10}b \, \mathbf{\hat{y}} + z_{10}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{O III} \\ \mathbf{B}_{26} & = & \left(-x_{10}-y_{10}\right) \, \mathbf{a}_{1} + \left(-x_{10}+y_{10}\right) \, \mathbf{a}_{2}-z_{10} \, \mathbf{a}_{3} & = & \left(-x_{10}a-z_{10}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{10}b \, \mathbf{\hat{y}}-z_{10}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{O III} \\ \mathbf{B}_{27} & = & \left(-x_{10}+y_{10}\right) \, \mathbf{a}_{1} + \left(-x_{10}-y_{10}\right) \, \mathbf{a}_{2}-z_{10} \, \mathbf{a}_{3} & = & \left(-x_{10}a-z_{10}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{10}b \, \mathbf{\hat{y}}-z_{10}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{O III} \\ \mathbf{B}_{28} & = & \left(x_{10}+y_{10}\right) \, \mathbf{a}_{1} + \left(x_{10}-y_{10}\right) \, \mathbf{a}_{2} + z_{10} \, \mathbf{a}_{3} & = & \left(x_{10}a+z_{10}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{10}b \, \mathbf{\hat{y}} + z_{10}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{O III} \\ \mathbf{B}_{29} & = & \left(x_{11}-y_{11}\right) \, \mathbf{a}_{1} + \left(x_{11}+y_{11}\right) \, \mathbf{a}_{2} + z_{11} \, \mathbf{a}_{3} & = & \left(x_{11}a+z_{11}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{11}b \, \mathbf{\hat{y}} + z_{11}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{O IV} \\ \mathbf{B}_{30} & = & \left(-x_{11}-y_{11}\right) \, \mathbf{a}_{1} + \left(-x_{11}+y_{11}\right) \, \mathbf{a}_{2}-z_{11} \, \mathbf{a}_{3} & = & \left(-x_{11}a-z_{11}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{11}b \, \mathbf{\hat{y}}-z_{11}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{O IV} \\ \mathbf{B}_{31} & = & \left(-x_{11}+y_{11}\right) \, \mathbf{a}_{1} + \left(-x_{11}-y_{11}\right) \, \mathbf{a}_{2}-z_{11} \, \mathbf{a}_{3} & = & \left(-x_{11}a-z_{11}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{11}b \, \mathbf{\hat{y}}-z_{11}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{O IV} \\ \mathbf{B}_{32} & = & \left(x_{11}+y_{11}\right) \, \mathbf{a}_{1} + \left(x_{11}-y_{11}\right) \, \mathbf{a}_{2} + z_{11} \, \mathbf{a}_{3} & = & \left(x_{11}a+z_{11}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{11}b \, \mathbf{\hat{y}} + z_{11}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{O IV} \\ \mathbf{B}_{33} & = & \left(x_{12}-y_{12}\right) \, \mathbf{a}_{1} + \left(x_{12}+y_{12}\right) \, \mathbf{a}_{2} + z_{12} \, \mathbf{a}_{3} & = & \left(x_{12}a+z_{12}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{12}b \, \mathbf{\hat{y}} + z_{12}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{O V} \\ \mathbf{B}_{34} & = & \left(-x_{12}-y_{12}\right) \, \mathbf{a}_{1} + \left(-x_{12}+y_{12}\right) \, \mathbf{a}_{2}-z_{12} \, \mathbf{a}_{3} & = & \left(-x_{12}a-z_{12}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{12}b \, \mathbf{\hat{y}}-z_{12}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{O V} \\ \mathbf{B}_{35} & = & \left(-x_{12}+y_{12}\right) \, \mathbf{a}_{1} + \left(-x_{12}-y_{12}\right) \, \mathbf{a}_{2}-z_{12} \, \mathbf{a}_{3} & = & \left(-x_{12}a-z_{12}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{12}b \, \mathbf{\hat{y}}-z_{12}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{O V} \\ \mathbf{B}_{36} & = & \left(x_{12}+y_{12}\right) \, \mathbf{a}_{1} + \left(x_{12}-y_{12}\right) \, \mathbf{a}_{2} + z_{12} \, \mathbf{a}_{3} & = & \left(x_{12}a+z_{12}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{12}b \, \mathbf{\hat{y}} + z_{12}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{O V} \\ \mathbf{B}_{37} & = & \left(x_{13}-y_{13}\right) \, \mathbf{a}_{1} + \left(x_{13}+y_{13}\right) \, \mathbf{a}_{2} + z_{13} \, \mathbf{a}_{3} & = & \left(x_{13}a+z_{13}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{13}b \, \mathbf{\hat{y}} + z_{13}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{O VI} \\ \mathbf{B}_{38} & = & \left(-x_{13}-y_{13}\right) \, \mathbf{a}_{1} + \left(-x_{13}+y_{13}\right) \, \mathbf{a}_{2}-z_{13} \, \mathbf{a}_{3} & = & \left(-x_{13}a-z_{13}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{13}b \, \mathbf{\hat{y}}-z_{13}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{O VI} \\ \mathbf{B}_{39} & = & \left(-x_{13}+y_{13}\right) \, \mathbf{a}_{1} + \left(-x_{13}-y_{13}\right) \, \mathbf{a}_{2}-z_{13} \, \mathbf{a}_{3} & = & \left(-x_{13}a-z_{13}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{13}b \, \mathbf{\hat{y}}-z_{13}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{O VI} \\ \mathbf{B}_{40} & = & \left(x_{13}+y_{13}\right) \, \mathbf{a}_{1} + \left(x_{13}-y_{13}\right) \, \mathbf{a}_{2} + z_{13} \, \mathbf{a}_{3} & = & \left(x_{13}a+z_{13}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{13}b \, \mathbf{\hat{y}} + z_{13}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{O VI} \\ \mathbf{B}_{41} & = & \left(x_{14}-y_{14}\right) \, \mathbf{a}_{1} + \left(x_{14}+y_{14}\right) \, \mathbf{a}_{2} + z_{14} \, \mathbf{a}_{3} & = & \left(x_{14}a+z_{14}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{14}b \, \mathbf{\hat{y}} + z_{14}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{OH III} \\ \mathbf{B}_{42} & = & \left(-x_{14}-y_{14}\right) \, \mathbf{a}_{1} + \left(-x_{14}+y_{14}\right) \, \mathbf{a}_{2}-z_{14} \, \mathbf{a}_{3} & = & \left(-x_{14}a-z_{14}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{14}b \, \mathbf{\hat{y}}-z_{14}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{OH III} \\ \mathbf{B}_{43} & = & \left(-x_{14}+y_{14}\right) \, \mathbf{a}_{1} + \left(-x_{14}-y_{14}\right) \, \mathbf{a}_{2}-z_{14} \, \mathbf{a}_{3} & = & \left(-x_{14}a-z_{14}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{14}b \, \mathbf{\hat{y}}-z_{14}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{OH III} \\ \mathbf{B}_{44} & = & \left(x_{14}+y_{14}\right) \, \mathbf{a}_{1} + \left(x_{14}-y_{14}\right) \, \mathbf{a}_{2} + z_{14} \, \mathbf{a}_{3} & = & \left(x_{14}a+z_{14}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{14}b \, \mathbf{\hat{y}} + z_{14}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{OH III} \\ \mathbf{B}_{45} & = & \left(x_{15}-y_{15}\right) \, \mathbf{a}_{1} + \left(x_{15}+y_{15}\right) \, \mathbf{a}_{2} + z_{15} \, \mathbf{a}_{3} & = & \left(x_{15}a+z_{15}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{15}b \, \mathbf{\hat{y}} + z_{15}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{OH IV} \\ \mathbf{B}_{46} & = & \left(-x_{15}-y_{15}\right) \, \mathbf{a}_{1} + \left(-x_{15}+y_{15}\right) \, \mathbf{a}_{2}-z_{15} \, \mathbf{a}_{3} & = & \left(-x_{15}a-z_{15}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{15}b \, \mathbf{\hat{y}}-z_{15}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{OH IV} \\ \mathbf{B}_{47} & = & \left(-x_{15}+y_{15}\right) \, \mathbf{a}_{1} + \left(-x_{15}-y_{15}\right) \, \mathbf{a}_{2}-z_{15} \, \mathbf{a}_{3} & = & \left(-x_{15}a-z_{15}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{15}b \, \mathbf{\hat{y}}-z_{15}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{OH IV} \\ \mathbf{B}_{48} & = & \left(x_{15}+y_{15}\right) \, \mathbf{a}_{1} + \left(x_{15}-y_{15}\right) \, \mathbf{a}_{2} + z_{15} \, \mathbf{a}_{3} & = & \left(x_{15}a+z_{15}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{15}b \, \mathbf{\hat{y}} + z_{15}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{OH IV} \\ \mathbf{B}_{49} & = & \left(x_{16}-y_{16}\right) \, \mathbf{a}_{1} + \left(x_{16}+y_{16}\right) \, \mathbf{a}_{2} + z_{16} \, \mathbf{a}_{3} & = & \left(x_{16}a+z_{16}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{16}b \, \mathbf{\hat{y}} + z_{16}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{Si I} \\ \mathbf{B}_{50} & = & \left(-x_{16}-y_{16}\right) \, \mathbf{a}_{1} + \left(-x_{16}+y_{16}\right) \, \mathbf{a}_{2}-z_{16} \, \mathbf{a}_{3} & = & \left(-x_{16}a-z_{16}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{16}b \, \mathbf{\hat{y}}-z_{16}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{Si I} \\ \mathbf{B}_{51} & = & \left(-x_{16}+y_{16}\right) \, \mathbf{a}_{1} + \left(-x_{16}-y_{16}\right) \, \mathbf{a}_{2}-z_{16} \, \mathbf{a}_{3} & = & \left(-x_{16}a-z_{16}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{16}b \, \mathbf{\hat{y}}-z_{16}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{Si I} \\ \mathbf{B}_{52} & = & \left(x_{16}+y_{16}\right) \, \mathbf{a}_{1} + \left(x_{16}-y_{16}\right) \, \mathbf{a}_{2} + z_{16} \, \mathbf{a}_{3} & = & \left(x_{16}a+z_{16}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{16}b \, \mathbf{\hat{y}} + z_{16}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{Si I} \\ \mathbf{B}_{53} & = & \left(x_{17}-y_{17}\right) \, \mathbf{a}_{1} + \left(x_{17}+y_{17}\right) \, \mathbf{a}_{2} + z_{17} \, \mathbf{a}_{3} & = & \left(x_{17}a+z_{17}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{17}b \, \mathbf{\hat{y}} + z_{17}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{Si II} \\ \mathbf{B}_{54} & = & \left(-x_{17}-y_{17}\right) \, \mathbf{a}_{1} + \left(-x_{17}+y_{17}\right) \, \mathbf{a}_{2}-z_{17} \, \mathbf{a}_{3} & = & \left(-x_{17}a-z_{17}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{17}b \, \mathbf{\hat{y}}-z_{17}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{Si II} \\ \mathbf{B}_{55} & = & \left(-x_{17}+y_{17}\right) \, \mathbf{a}_{1} + \left(-x_{17}-y_{17}\right) \, \mathbf{a}_{2}-z_{17} \, \mathbf{a}_{3} & = & \left(-x_{17}a-z_{17}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{17}b \, \mathbf{\hat{y}}-z_{17}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{Si II} \\ \mathbf{B}_{56} & = & \left(x_{17}+y_{17}\right) \, \mathbf{a}_{1} + \left(x_{17}-y_{17}\right) \, \mathbf{a}_{2} + z_{17} \, \mathbf{a}_{3} & = & \left(x_{17}a+z_{17}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{17}b \, \mathbf{\hat{y}} + z_{17}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{Si II} \\ \end{array} \]

References

  • B. E. Warren and W. L. Bragg, The Structure of Chrysotile H4Mg3Si2O9, Zeitschrift für Kristallographie – Crystalline Materials 76, 201–210 (1931), doi:10.1524/zkri.1931.76.1.201.
  • K. Yada, Study of Chrysotile Asbestos by a High Resolution Electron Microscope, Acta Cryst. 23, 704–707 (1967), doi:10.1107/S0365110X67003524.

Found in

  • C. Hermann, O. Lohrmann, and H. Philipp, eds., Strukturbericht Band II 1928–1932 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1937).

Geometry files


Prototype Generator

aflow --proto=AB6C11D6E4_mC112_12_e_gi2j_i5j_2i2j_2j --params=

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