Hemimorphite (Zn4Si2O7(OH)2·H2O, $S2_{2}$) Structure : A2B5CD2_oI40_44_2c_abcde_d_e

Picture of Structure; Click for Big Picture
Prototype : H2O5SiZn2
AFLOW prototype label : A2B5CD2_oI40_44_2c_abcde_d_e
Strukturbericht designation : $S2_{2}$
Pearson symbol : oI40
Space group number : 44
Space group symbol : $Imm2$
AFLOW prototype command : aflow --proto=A2B5CD2_oI40_44_2c_abcde_d_e
--params=
$a$,$b/a$,$c/a$,$z_{1}$,$z_{2}$,$x_{3}$,$z_{3}$,$x_{4}$,$z_{4}$,$x_{5}$,$z_{5}$,$y_{6}$,$z_{6}$,$y_{7}$,$z_{7}$,$x_{8}$,$y_{8}$,$z_{8}$,$x_{9}$,$y_{9}$,$z_{9}$


  • The original (Ito, 1932) determination of this structure did not locate the positions of the hydrogen atoms. (Hill, 1977) were able to do this, so we use the updated structure as the prototype.
  • (Hill, 1977) gives the $z$ coordinates of the atoms on the ($2c$) sites as 0.0190, 0.0643, and 0.0410, respectively, but this gives unrealistic H–O distances. Examination of the figures and distance tables shows that we should take $z_{2} = 0.190$, $z_{3} = 0.643$, and $z_{4} = 0.041$, a conclusion also reached by (Downs, 2003).

Body-centered Orthorhombic primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & z_{1} \, \mathbf{a}_{1} + z_{1} \, \mathbf{a}_{2} & = & z_{1}c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{O I} \\ \mathbf{B}_{2} & = & \left(\frac{1}{2} +z_{2}\right) \, \mathbf{a}_{1} + z_{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}b \, \mathbf{\hat{y}} + z_{2}c \, \mathbf{\hat{z}} & \left(2b\right) & \mbox{O II} \\ \mathbf{B}_{3} & = & z_{3} \, \mathbf{a}_{1} + \left(x_{3}+z_{3}\right) \, \mathbf{a}_{2} + x_{3} \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}} + z_{3}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{H I} \\ \mathbf{B}_{4} & = & z_{3} \, \mathbf{a}_{1} + \left(-x_{3}+z_{3}\right) \, \mathbf{a}_{2}-x_{3} \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}} + z_{3}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{H I} \\ \mathbf{B}_{5} & = & z_{4} \, \mathbf{a}_{1} + \left(x_{4}+z_{4}\right) \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + z_{4}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{H II} \\ \mathbf{B}_{6} & = & z_{4} \, \mathbf{a}_{1} + \left(-x_{4}+z_{4}\right) \, \mathbf{a}_{2}-x_{4} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}} + z_{4}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{H II} \\ \mathbf{B}_{7} & = & z_{5} \, \mathbf{a}_{1} + \left(x_{5}+z_{5}\right) \, \mathbf{a}_{2} + x_{5} \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}} + z_{5}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{O III} \\ \mathbf{B}_{8} & = & z_{5} \, \mathbf{a}_{1} + \left(-x_{5}+z_{5}\right) \, \mathbf{a}_{2}-x_{5} \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}} + z_{5}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{O III} \\ \mathbf{B}_{9} & = & \left(y_{6}+z_{6}\right) \, \mathbf{a}_{1} + z_{6} \, \mathbf{a}_{2} + y_{6} \, \mathbf{a}_{3} & = & y_{6}b \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(4d\right) & \mbox{O IV} \\ \mathbf{B}_{10} & = & \left(-y_{6}+z_{6}\right) \, \mathbf{a}_{1} + z_{6} \, \mathbf{a}_{2}-y_{6} \, \mathbf{a}_{3} & = & -y_{6}b \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(4d\right) & \mbox{O IV} \\ \mathbf{B}_{11} & = & \left(y_{7}+z_{7}\right) \, \mathbf{a}_{1} + z_{7} \, \mathbf{a}_{2} + y_{7} \, \mathbf{a}_{3} & = & y_{7}b \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(4d\right) & \mbox{Si} \\ \mathbf{B}_{12} & = & \left(-y_{7}+z_{7}\right) \, \mathbf{a}_{1} + z_{7} \, \mathbf{a}_{2}-y_{7} \, \mathbf{a}_{3} & = & -y_{7}b \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(4d\right) & \mbox{Si} \\ \mathbf{B}_{13} & = & \left(y_{8}+z_{8}\right) \, \mathbf{a}_{1} + \left(x_{8}+z_{8}\right) \, \mathbf{a}_{2} + \left(x_{8}+y_{8}\right) \, \mathbf{a}_{3} & = & x_{8}a \, \mathbf{\hat{x}} + y_{8}b \, \mathbf{\hat{y}} + z_{8}c \, \mathbf{\hat{z}} & \left(8e\right) & \mbox{O V} \\ \mathbf{B}_{14} & = & \left(-y_{8}+z_{8}\right) \, \mathbf{a}_{1} + \left(-x_{8}+z_{8}\right) \, \mathbf{a}_{2} + \left(-x_{8}-y_{8}\right) \, \mathbf{a}_{3} & = & -x_{8}a \, \mathbf{\hat{x}}-y_{8}b \, \mathbf{\hat{y}} + z_{8}c \, \mathbf{\hat{z}} & \left(8e\right) & \mbox{O V} \\ \mathbf{B}_{15} & = & \left(-y_{8}+z_{8}\right) \, \mathbf{a}_{1} + \left(x_{8}+z_{8}\right) \, \mathbf{a}_{2} + \left(x_{8}-y_{8}\right) \, \mathbf{a}_{3} & = & x_{8}a \, \mathbf{\hat{x}}-y_{8}b \, \mathbf{\hat{y}} + z_{8}c \, \mathbf{\hat{z}} & \left(8e\right) & \mbox{O V} \\ \mathbf{B}_{16} & = & \left(y_{8}+z_{8}\right) \, \mathbf{a}_{1} + \left(-x_{8}+z_{8}\right) \, \mathbf{a}_{2} + \left(-x_{8}+y_{8}\right) \, \mathbf{a}_{3} & = & -x_{8}a \, \mathbf{\hat{x}} + y_{8}b \, \mathbf{\hat{y}} + z_{8}c \, \mathbf{\hat{z}} & \left(8e\right) & \mbox{O V} \\ \mathbf{B}_{17} & = & \left(y_{9}+z_{9}\right) \, \mathbf{a}_{1} + \left(x_{9}+z_{9}\right) \, \mathbf{a}_{2} + \left(x_{9}+y_{9}\right) \, \mathbf{a}_{3} & = & x_{9}a \, \mathbf{\hat{x}} + y_{9}b \, \mathbf{\hat{y}} + z_{9}c \, \mathbf{\hat{z}} & \left(8e\right) & \mbox{Zn} \\ \mathbf{B}_{18} & = & \left(-y_{9}+z_{9}\right) \, \mathbf{a}_{1} + \left(-x_{9}+z_{9}\right) \, \mathbf{a}_{2} + \left(-x_{9}-y_{9}\right) \, \mathbf{a}_{3} & = & -x_{9}a \, \mathbf{\hat{x}}-y_{9}b \, \mathbf{\hat{y}} + z_{9}c \, \mathbf{\hat{z}} & \left(8e\right) & \mbox{Zn} \\ \mathbf{B}_{19} & = & \left(-y_{9}+z_{9}\right) \, \mathbf{a}_{1} + \left(x_{9}+z_{9}\right) \, \mathbf{a}_{2} + \left(x_{9}-y_{9}\right) \, \mathbf{a}_{3} & = & x_{9}a \, \mathbf{\hat{x}}-y_{9}b \, \mathbf{\hat{y}} + z_{9}c \, \mathbf{\hat{z}} & \left(8e\right) & \mbox{Zn} \\ \mathbf{B}_{20} & = & \left(y_{9}+z_{9}\right) \, \mathbf{a}_{1} + \left(-x_{9}+z_{9}\right) \, \mathbf{a}_{2} + \left(-x_{9}+y_{9}\right) \, \mathbf{a}_{3} & = & -x_{9}a \, \mathbf{\hat{x}} + y_{9}b \, \mathbf{\hat{y}} + z_{9}c \, \mathbf{\hat{z}} & \left(8e\right) & \mbox{Zn} \\ \end{array} \]

References

  • R. J. Hill, G. V. Gibbs, J. R. Craig, F. K. Ross, and J. M. Williams, A neutron–diffraction study of hemimorphite, Zeitschrift für Kristallographie – Crystalline Materials 146, 241–259 (1977), doi:10.1524/zkri.1978.146.16.241.
  • T. Ito and J. West, The Structure of Hemimorphite (H2Zn2SiO5), Zeitschrift für Kristallographie – Crystalline Materials 83, 1–8 (1932), doi:10.1524/zkri.1932.83.1.1.

Found in

  • R. T. Downs and M. Hall–Wallace, The American Mineralogist Crystal Structure Database, Am. Mineral. 88, 247–250 (2003).

Geometry files


Prototype Generator

aflow --proto=A2B5CD2_oI40_44_2c_abcde_d_e --params=

Species:

Running:

Output: