Manganese–leonite [K2Mn(SO4)2·4H2O, $H4_{23}$] Structure : A8B2CD15E2_mC112_12_2i3j_j_ad_g4i5j_2i

Picture of Structure; Click for Big Picture
Prototype : H8K2MnO12S2
AFLOW prototype label : A8B2CD15E2_mC112_12_2i3j_j_ad_g4i5j_2i
Strukturbericht designation : $H4_{23}$
Pearson symbol : mC112
Space group number : 12
Space group symbol : $C2/m$
AFLOW prototype command : aflow --proto=A8B2CD15E2_mC112_12_2i3j_j_ad_g4i5j_2i
--params=
$a$,$b/a$,$c/a$,$\beta$,$y_{3}$,$x_{4}$,$z_{4}$,$x_{5}$,$z_{5}$,$x_{6}$,$z_{6}$,$x_{7}$,$z_{7}$,$x_{8}$,$z_{8}$,$x_{9}$,$z_{9}$,$x_{10}$,$z_{10}$,$x_{11}$,$z_{11}$,$x_{12}$,$y_{12}$,$z_{12}$,$x_{13}$,$y_{13}$,$z_{13}$,$x_{14}$,$y_{14}$,$z_{14}$,$x_{15}$,$y_{15}$,$z_{15}$,$x_{16}$,$y_{16}$,$z_{16}$,$x_{17}$,$y_{17}$,$z_{17}$,$x_{18}$,$y_{18}$,$z_{18}$,$x_{19}$,$y_{19}$,$z_{19}$,$x_{20}$,$y_{20}$,$z_{20}$


Other compounds with this structure

  • (NH2)2Co(SO4)2·4H2O, (NH2)2Cu(SO4)2·4H2O, (NH2)2Fe(SO4)2·4H2O, (NH2)2Mg(SO4)2·4H2O, (NH2)2Mn(SO4)2·4H2O, Cd2Co(SO4)2·4H2O, Cd2Cu(SO4)2·4H2O, Cd2Fe(SO4)2·4H2O, Cd2Mg(SO4)2·4H2O, Cd2Mn(SO4)2·4H2O, Cs2Co(SO4)2·4H2O, Cs2Cu(SO4)2·4H2O, Cs2Fe(SO4)2·4H2O, Cs2Mg(SO4)2·4H2O, Cs2Mn(SO4)2·4H2O, K2Co(SO4)2·4H2O, K2Cu(SO4)2·4H2O, K2Fe(SO4)2·4H2O (mereiterite), K2Mg(SO4)2·4H2O (leonite), Rb2Co(SO4)2·4H2O, Rb2Cu(SO4)2·4H2O, Rb2Fe(SO4)2·4H2O, Rb2Mg(SO4)2·4H2O, Rb2Mn(SO4)2·4H2O, Tl2Co(SO4)2·4H2O, Tl2Cu(SO4)2·4H2O, Tl2Fe(SO4)2·4H2O, Tl2Mg(SO4)2·4H2O, and Tl2Mn(SO4)2·4H2O

  • Properly, the prototype of leonite is K2Mg(SO4)2·4H2O, but (Herrmann, 1943) gives manganese–leonite Strukturbericht symbol $H4_{23}$, so we will use Mn–leonite as the prototype.
  • The room temperature leonite structure, shown here, is in space group $C2/m$ #12. It is characterized by the disorder of the second sulfate group, centered on atom S–II (Hertweck, 2001). The oxygen sites around S–II, labeled O–VII, O–VIII, and O–IX in our notation, are only occupied 50% of the time. (Anspach, 1939), who did the original determination of this structure, was not able to see the disorder, and so gives an ordered structure for both sulfates.
  • We use the structure determined by (Hertweck, 2001) at room temperature, 293 K. At lower temperatures, the leonites undergo phase transitions. The exact transition temperature depends on the compound.
  • At somewhat lower than room temperature (205 K for Mn–leonite) the sulfate group orders, doubling the size of the unit cell and changing the space group from $C2/m$ to $C2/c$ #15. At still lower temperatures (168 K for Mn–leonite) further ordering takes place and the structure transforms into the $P2_1/c$ #14 space group.

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} & = & 0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = & 0 \, \mathbf{\hat{x}} + 0 \, \mathbf{\hat{y}} + 0 \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Mn I} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \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}} & \left(2d\right) & \mbox{Mn II} \\ \mathbf{B}_{3} & = & -y_{3} \, \mathbf{a}_{1} + y_{3} \, \mathbf{a}_{2} & = & y_{3}b \, \mathbf{\hat{y}} & \left(4g\right) & \mbox{O I} \\ \mathbf{B}_{4} & = & y_{3} \, \mathbf{a}_{1}-y_{3} \, \mathbf{a}_{2} & = & -y_{3}b \, \mathbf{\hat{y}} & \left(4g\right) & \mbox{O I} \\ \mathbf{B}_{5} & = & 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{H I} \\ \mathbf{B}_{6} & = & -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{H I} \\ \mathbf{B}_{7} & = & 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{H II} \\ \mathbf{B}_{8} & = & -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{H II} \\ \mathbf{B}_{9} & = & 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{O II} \\ \mathbf{B}_{10} & = & -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{O II} \\ \mathbf{B}_{11} & = & x_{7} \, \mathbf{a}_{1} + x_{7} \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & \left(x_{7}a+z_{7}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{7}c\sin\beta \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{O III} \\ \mathbf{B}_{12} & = & -x_{7} \, \mathbf{a}_{1}-x_{7} \, \mathbf{a}_{2}-z_{7} \, \mathbf{a}_{3} & = & \left(-x_{7}a-z_{7}c\cos\beta\right) \, \mathbf{\hat{x}}-z_{7}c\sin\beta \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{O III} \\ \mathbf{B}_{13} & = & x_{8} \, \mathbf{a}_{1} + x_{8} \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & \left(x_{8}a+z_{8}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{8}c\sin\beta \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{O IV} \\ \mathbf{B}_{14} & = & -x_{8} \, \mathbf{a}_{1}-x_{8} \, \mathbf{a}_{2}-z_{8} \, \mathbf{a}_{3} & = & \left(-x_{8}a-z_{8}c\cos\beta\right) \, \mathbf{\hat{x}}-z_{8}c\sin\beta \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{O IV} \\ \mathbf{B}_{15} & = & x_{9} \, \mathbf{a}_{1} + x_{9} \, \mathbf{a}_{2} + z_{9} \, \mathbf{a}_{3} & = & \left(x_{9}a+z_{9}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{9}c\sin\beta \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{O V} \\ \mathbf{B}_{16} & = & -x_{9} \, \mathbf{a}_{1}-x_{9} \, \mathbf{a}_{2}-z_{9} \, \mathbf{a}_{3} & = & \left(-x_{9}a-z_{9}c\cos\beta\right) \, \mathbf{\hat{x}}-z_{9}c\sin\beta \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{O V} \\ \mathbf{B}_{17} & = & x_{10} \, \mathbf{a}_{1} + x_{10} \, \mathbf{a}_{2} + z_{10} \, \mathbf{a}_{3} & = & \left(x_{10}a+z_{10}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{10}c\sin\beta \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{S I} \\ \mathbf{B}_{18} & = & -x_{10} \, \mathbf{a}_{1}-x_{10} \, \mathbf{a}_{2}-z_{10} \, \mathbf{a}_{3} & = & \left(-x_{10}a-z_{10}c\cos\beta\right) \, \mathbf{\hat{x}}-z_{10}c\sin\beta \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{S I} \\ \mathbf{B}_{19} & = & x_{11} \, \mathbf{a}_{1} + x_{11} \, \mathbf{a}_{2} + z_{11} \, \mathbf{a}_{3} & = & \left(x_{11}a+z_{11}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{11}c\sin\beta \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{S II} \\ \mathbf{B}_{20} & = & -x_{11} \, \mathbf{a}_{1}-x_{11} \, \mathbf{a}_{2}-z_{11} \, \mathbf{a}_{3} & = & \left(-x_{11}a-z_{11}c\cos\beta\right) \, \mathbf{\hat{x}}-z_{11}c\sin\beta \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{S II} \\ \mathbf{B}_{21} & = & \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{H III} \\ \mathbf{B}_{22} & = & \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{H 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(-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{H III} \\ \mathbf{B}_{24} & = & \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{H III} \\ \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(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{H IV} \\ \mathbf{B}_{26} & = & \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{H IV} \\ \mathbf{B}_{27} & = & \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{H IV} \\ \mathbf{B}_{28} & = & \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{H IV} \\ \mathbf{B}_{29} & = & \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{H V} \\ \mathbf{B}_{30} & = & \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{H V} \\ \mathbf{B}_{31} & = & \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{H V} \\ \mathbf{B}_{32} & = & \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{H V} \\ \mathbf{B}_{33} & = & \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{K} \\ \mathbf{B}_{34} & = & \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{K} \\ \mathbf{B}_{35} & = & \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{K} \\ \mathbf{B}_{36} & = & \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{K} \\ \mathbf{B}_{37} & = & \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{O VI} \\ \mathbf{B}_{38} & = & \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{O VI} \\ \mathbf{B}_{39} & = & \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{O VI} \\ \mathbf{B}_{40} & = & \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{O VI} \\ \mathbf{B}_{41} & = & \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{O VII} \\ \mathbf{B}_{42} & = & \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{O VII} \\ \mathbf{B}_{43} & = & \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{O VII} \\ \mathbf{B}_{44} & = & \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{O VII} \\ \mathbf{B}_{45} & = & \left(x_{18}-y_{18}\right) \, \mathbf{a}_{1} + \left(x_{18}+y_{18}\right) \, \mathbf{a}_{2} + z_{18} \, \mathbf{a}_{3} & = & \left(x_{18}a+z_{18}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{18}b \, \mathbf{\hat{y}} + z_{18}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{O VIII} \\ \mathbf{B}_{46} & = & \left(-x_{18}-y_{18}\right) \, \mathbf{a}_{1} + \left(-x_{18}+y_{18}\right) \, \mathbf{a}_{2}-z_{18} \, \mathbf{a}_{3} & = & \left(-x_{18}a-z_{18}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{18}b \, \mathbf{\hat{y}}-z_{18}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{O VIII} \\ \mathbf{B}_{47} & = & \left(-x_{18}+y_{18}\right) \, \mathbf{a}_{1} + \left(-x_{18}-y_{18}\right) \, \mathbf{a}_{2}-z_{18} \, \mathbf{a}_{3} & = & \left(-x_{18}a-z_{18}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{18}b \, \mathbf{\hat{y}}-z_{18}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{O VIII} \\ \mathbf{B}_{48} & = & \left(x_{18}+y_{18}\right) \, \mathbf{a}_{1} + \left(x_{18}-y_{18}\right) \, \mathbf{a}_{2} + z_{18} \, \mathbf{a}_{3} & = & \left(x_{18}a+z_{18}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{18}b \, \mathbf{\hat{y}} + z_{18}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{O VIII} \\ \mathbf{B}_{49} & = & \left(x_{19}-y_{19}\right) \, \mathbf{a}_{1} + \left(x_{19}+y_{19}\right) \, \mathbf{a}_{2} + z_{19} \, \mathbf{a}_{3} & = & \left(x_{19}a+z_{19}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{19}b \, \mathbf{\hat{y}} + z_{19}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{O IX} \\ \mathbf{B}_{50} & = & \left(-x_{19}-y_{19}\right) \, \mathbf{a}_{1} + \left(-x_{19}+y_{19}\right) \, \mathbf{a}_{2}-z_{19} \, \mathbf{a}_{3} & = & \left(-x_{19}a-z_{19}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{19}b \, \mathbf{\hat{y}}-z_{19}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{O IX} \\ \mathbf{B}_{51} & = & \left(-x_{19}+y_{19}\right) \, \mathbf{a}_{1} + \left(-x_{19}-y_{19}\right) \, \mathbf{a}_{2}-z_{19} \, \mathbf{a}_{3} & = & \left(-x_{19}a-z_{19}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{19}b \, \mathbf{\hat{y}}-z_{19}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{O IX} \\ \mathbf{B}_{52} & = & \left(x_{19}+y_{19}\right) \, \mathbf{a}_{1} + \left(x_{19}-y_{19}\right) \, \mathbf{a}_{2} + z_{19} \, \mathbf{a}_{3} & = & \left(x_{19}a+z_{19}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{19}b \, \mathbf{\hat{y}} + z_{19}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{O IX} \\ \mathbf{B}_{53} & = & \left(x_{20}-y_{20}\right) \, \mathbf{a}_{1} + \left(x_{20}+y_{20}\right) \, \mathbf{a}_{2} + z_{20} \, \mathbf{a}_{3} & = & \left(x_{20}a+z_{20}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{20}b \, \mathbf{\hat{y}} + z_{20}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{O X} \\ \mathbf{B}_{54} & = & \left(-x_{20}-y_{20}\right) \, \mathbf{a}_{1} + \left(-x_{20}+y_{20}\right) \, \mathbf{a}_{2}-z_{20} \, \mathbf{a}_{3} & = & \left(-x_{20}a-z_{20}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{20}b \, \mathbf{\hat{y}}-z_{20}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{O X} \\ \mathbf{B}_{55} & = & \left(-x_{20}+y_{20}\right) \, \mathbf{a}_{1} + \left(-x_{20}-y_{20}\right) \, \mathbf{a}_{2}-z_{20} \, \mathbf{a}_{3} & = & \left(-x_{20}a-z_{20}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{20}b \, \mathbf{\hat{y}}-z_{20}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{O X} \\ \mathbf{B}_{56} & = & \left(x_{20}+y_{20}\right) \, \mathbf{a}_{1} + \left(x_{20}-y_{20}\right) \, \mathbf{a}_{2} + z_{20} \, \mathbf{a}_{3} & = & \left(x_{20}a+z_{20}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{20}b \, \mathbf{\hat{y}} + z_{20}c\sin\beta \, \mathbf{\hat{z}} & \left(8j\right) & \mbox{O X} \\ \end{array} \]

References

  • B. Hertweck, G. Giester, and E. Libowitzky, The crystal structures of the low–temperature phases of leonite–type compounds, K2$Me$(SO4)2·4H2O ($Me2+ = Mg, Mn, Fe), Am. Mineral. 86, 1282–1292 (2001), doi:10.2138/am-2001-1016.
  • H. Anspach, Die Struktur von Mn–Leonit, Zeitschrift für Kristallographie – Crystalline Materials 101, 39–77 (1939), doi:10.1524/zkri.1939.101.1.39.
  • K. Herrmann, ed., Strukturbericht Band VII 1939 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1943).

Geometry files


Prototype Generator

aflow --proto=A8B2CD15E2_mC112_12_2i3j_j_ad_g4i5j_2i --params=

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