Bromocarnallite (KMg(H2O)6(Cl,Br)3, $E2_{6}$) Structure : A3B6CD_tP44_85_bcg_3g_ac_e

Picture of Structure; Click for Big Picture
Prototype : (Br,Cl)3(H2O)6KMg
AFLOW prototype label : A3B6CD_tP44_85_bcg_3g_ac_e
Strukturbericht designation : $E2_{6}$
Pearson symbol : tP44
Space group number : 85
Space group symbol : $P4/n$
AFLOW prototype command : aflow --proto=A3B6CD_tP44_85_bcg_3g_ac_e
--params=
$a$,$c/a$,$z_{3}$,$z_{4}$,$x_{6}$,$y_{6}$,$z_{6}$,$x_{7}$,$y_{7}$,$z_{7}$,$x_{8}$,$y_{8}$,$z_{8}$,$x_{9}$,$y_{9}$,$z_{9}$


  • (Andreß, 1939) first determined the structure of bromocarnallite, using a sample with 75% bromine on the halide site. They were unable to locate the hydrogen atoms, and placed the compound in space group $P4/n$ #85. The data was given by (Hermann, 1939) in setting 1 of this group, but we used FINDSYM to place it in the standard setting 2.
  • (Hermann, 1939) assigned this compound the Strukturbericht symbol $E2_{6}$.
  • (Schlemper, 1985) re–examined the structure for the pure chlorine version, carnallite. They located the hydrogen atoms and placed the system in space group $Pnna$ #52. We present this structure in the carnallite structure page.

Simple Tetragonal primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{3}{4}a \, \mathbf{\hat{y}} & \left(2a\right) & \mbox{K I} \\ \mathbf{B}_{2} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} & \left(2a\right) & \mbox{K I} \\ \mathbf{B}_{3} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{3}{4}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(2b\right) & \mbox{Br I} \\ \mathbf{B}_{4} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(2b\right) & \mbox{Br I} \\ \mathbf{B}_{5} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(2c\right) & \mbox{Br II} \\ \mathbf{B}_{6} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2}-z_{3} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \frac{3}{4}a \, \mathbf{\hat{y}}-z_{3}c \, \mathbf{\hat{z}} & \left(2c\right) & \mbox{Br II} \\ \mathbf{B}_{7} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(2c\right) & \mbox{K II} \\ \mathbf{B}_{8} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2}-z_{4} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \frac{3}{4}a \, \mathbf{\hat{y}}-z_{4}c \, \mathbf{\hat{z}} & \left(2c\right) & \mbox{K II} \\ \mathbf{B}_{9} & = & \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}c \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{Mg} \\ \mathbf{B}_{10} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{Mg} \\ \mathbf{B}_{11} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{Mg} \\ \mathbf{B}_{12} & = & \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{Mg} \\ \mathbf{B}_{13} & = & x_{6} \, \mathbf{a}_{1} + y_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & x_{6}a \, \mathbf{\hat{x}} + y_{6}a \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{Br III} \\ \mathbf{B}_{14} & = & \left(\frac{1}{2} - x_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{6}\right) \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{6}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-y_{6}\right)a \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{Br III} \\ \mathbf{B}_{15} & = & \left(\frac{1}{2} - y_{6}\right) \, \mathbf{a}_{1} + x_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-y_{6}\right)a \, \mathbf{\hat{x}} + x_{6}a \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{Br III} \\ \mathbf{B}_{16} & = & y_{6} \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{6}\right) \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & y_{6}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{6}\right)a \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{Br III} \\ \mathbf{B}_{17} & = & -x_{6} \, \mathbf{a}_{1}-y_{6} \, \mathbf{a}_{2}-z_{6} \, \mathbf{a}_{3} & = & -x_{6}a \, \mathbf{\hat{x}}-y_{6}a \, \mathbf{\hat{y}}-z_{6}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{Br III} \\ \mathbf{B}_{18} & = & \left(\frac{1}{2} +x_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{6}\right) \, \mathbf{a}_{2}-z_{6} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{6}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{6}\right)a \, \mathbf{\hat{y}}-z_{6}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{Br III} \\ \mathbf{B}_{19} & = & \left(\frac{1}{2} +y_{6}\right) \, \mathbf{a}_{1}-x_{6} \, \mathbf{a}_{2}-z_{6} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +y_{6}\right)a \, \mathbf{\hat{x}}-x_{6}a \, \mathbf{\hat{y}}-z_{6}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{Br III} \\ \mathbf{B}_{20} & = & -y_{6} \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{6}\right) \, \mathbf{a}_{2}-z_{6} \, \mathbf{a}_{3} & = & -y_{6}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{6}\right)a \, \mathbf{\hat{y}}-z_{6}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{Br III} \\ \mathbf{B}_{21} & = & x_{7} \, \mathbf{a}_{1} + y_{7} \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & x_{7}a \, \mathbf{\hat{x}} + y_{7}a \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{H$_{2}$O I} \\ \mathbf{B}_{22} & = & \left(\frac{1}{2} - x_{7}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{7}\right) \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{7}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-y_{7}\right)a \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{H$_{2}$O I} \\ \mathbf{B}_{23} & = & \left(\frac{1}{2} - y_{7}\right) \, \mathbf{a}_{1} + x_{7} \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-y_{7}\right)a \, \mathbf{\hat{x}} + x_{7}a \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{H$_{2}$O I} \\ \mathbf{B}_{24} & = & y_{7} \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{7}\right) \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & y_{7}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{7}\right)a \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{H$_{2}$O I} \\ \mathbf{B}_{25} & = & -x_{7} \, \mathbf{a}_{1}-y_{7} \, \mathbf{a}_{2}-z_{7} \, \mathbf{a}_{3} & = & -x_{7}a \, \mathbf{\hat{x}}-y_{7}a \, \mathbf{\hat{y}}-z_{7}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{H$_{2}$O I} \\ \mathbf{B}_{26} & = & \left(\frac{1}{2} +x_{7}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{7}\right) \, \mathbf{a}_{2}-z_{7} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{7}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{7}\right)a \, \mathbf{\hat{y}}-z_{7}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{H$_{2}$O I} \\ \mathbf{B}_{27} & = & \left(\frac{1}{2} +y_{7}\right) \, \mathbf{a}_{1}-x_{7} \, \mathbf{a}_{2}-z_{7} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +y_{7}\right)a \, \mathbf{\hat{x}}-x_{7}a \, \mathbf{\hat{y}}-z_{7}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{H$_{2}$O I} \\ \mathbf{B}_{28} & = & -y_{7} \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{7}\right) \, \mathbf{a}_{2}-z_{7} \, \mathbf{a}_{3} & = & -y_{7}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{7}\right)a \, \mathbf{\hat{y}}-z_{7}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{H$_{2}$O I} \\ \mathbf{B}_{29} & = & x_{8} \, \mathbf{a}_{1} + y_{8} \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & x_{8}a \, \mathbf{\hat{x}} + y_{8}a \, \mathbf{\hat{y}} + z_{8}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{H$_{2}$O II} \\ \mathbf{B}_{30} & = & \left(\frac{1}{2} - x_{8}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{8}\right) \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{8}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-y_{8}\right)a \, \mathbf{\hat{y}} + z_{8}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{H$_{2}$O II} \\ \mathbf{B}_{31} & = & \left(\frac{1}{2} - y_{8}\right) \, \mathbf{a}_{1} + x_{8} \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-y_{8}\right)a \, \mathbf{\hat{x}} + x_{8}a \, \mathbf{\hat{y}} + z_{8}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{H$_{2}$O II} \\ \mathbf{B}_{32} & = & y_{8} \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{8}\right) \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & y_{8}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{8}\right)a \, \mathbf{\hat{y}} + z_{8}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{H$_{2}$O II} \\ \mathbf{B}_{33} & = & -x_{8} \, \mathbf{a}_{1}-y_{8} \, \mathbf{a}_{2}-z_{8} \, \mathbf{a}_{3} & = & -x_{8}a \, \mathbf{\hat{x}}-y_{8}a \, \mathbf{\hat{y}}-z_{8}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{H$_{2}$O II} \\ \mathbf{B}_{34} & = & \left(\frac{1}{2} +x_{8}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{8}\right) \, \mathbf{a}_{2}-z_{8} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{8}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{8}\right)a \, \mathbf{\hat{y}}-z_{8}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{H$_{2}$O II} \\ \mathbf{B}_{35} & = & \left(\frac{1}{2} +y_{8}\right) \, \mathbf{a}_{1}-x_{8} \, \mathbf{a}_{2}-z_{8} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +y_{8}\right)a \, \mathbf{\hat{x}}-x_{8}a \, \mathbf{\hat{y}}-z_{8}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{H$_{2}$O II} \\ \mathbf{B}_{36} & = & -y_{8} \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{8}\right) \, \mathbf{a}_{2}-z_{8} \, \mathbf{a}_{3} & = & -y_{8}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{8}\right)a \, \mathbf{\hat{y}}-z_{8}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{H$_{2}$O II} \\ \mathbf{B}_{37} & = & x_{9} \, \mathbf{a}_{1} + y_{9} \, \mathbf{a}_{2} + z_{9} \, \mathbf{a}_{3} & = & x_{9}a \, \mathbf{\hat{x}} + y_{9}a \, \mathbf{\hat{y}} + z_{9}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{H$_{2}$O III} \\ \mathbf{B}_{38} & = & \left(\frac{1}{2} - x_{9}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{9}\right) \, \mathbf{a}_{2} + z_{9} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{9}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-y_{9}\right)a \, \mathbf{\hat{y}} + z_{9}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{H$_{2}$O III} \\ \mathbf{B}_{39} & = & \left(\frac{1}{2} - y_{9}\right) \, \mathbf{a}_{1} + x_{9} \, \mathbf{a}_{2} + z_{9} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-y_{9}\right)a \, \mathbf{\hat{x}} + x_{9}a \, \mathbf{\hat{y}} + z_{9}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{H$_{2}$O III} \\ \mathbf{B}_{40} & = & y_{9} \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{9}\right) \, \mathbf{a}_{2} + z_{9} \, \mathbf{a}_{3} & = & y_{9}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{9}\right)a \, \mathbf{\hat{y}} + z_{9}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{H$_{2}$O III} \\ \mathbf{B}_{41} & = & -x_{9} \, \mathbf{a}_{1}-y_{9} \, \mathbf{a}_{2}-z_{9} \, \mathbf{a}_{3} & = & -x_{9}a \, \mathbf{\hat{x}}-y_{9}a \, \mathbf{\hat{y}}-z_{9}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{H$_{2}$O III} \\ \mathbf{B}_{42} & = & \left(\frac{1}{2} +x_{9}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{9}\right) \, \mathbf{a}_{2}-z_{9} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{9}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{9}\right)a \, \mathbf{\hat{y}}-z_{9}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{H$_{2}$O III} \\ \mathbf{B}_{43} & = & \left(\frac{1}{2} +y_{9}\right) \, \mathbf{a}_{1}-x_{9} \, \mathbf{a}_{2}-z_{9} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +y_{9}\right)a \, \mathbf{\hat{x}}-x_{9}a \, \mathbf{\hat{y}}-z_{9}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{H$_{2}$O III} \\ \mathbf{B}_{44} & = & -y_{9} \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{9}\right) \, \mathbf{a}_{2}-z_{9} \, \mathbf{a}_{3} & = & -y_{9}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{9}\right)a \, \mathbf{\hat{y}}-z_{9}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{H$_{2}$O III} \\ \end{array} \]

References

  • K. R. Andreß and O. Saffe, Röntgenographische Untersuchung der Mischkristallreihe Karnallit–Bromkarnallit, Zeitschrift für Kristallographie – Crystalline Materials 101, 451–469 (1939), doi:10.1524/zkri.1939.101.1.451.
  • E. O. Schlemper, P. K. Sen Gupta, and T. Zoltai, Refinement of the structure of carnallite, Mg(H2O)6KCl3, Am. Mineral. 70, 1309–1313 (1985).

Found in

  • K. Herrmann, ed., Strukturbericht Band VII 1939 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1943).

Geometry files


Prototype Generator

aflow --proto=A3B6CD_tP44_85_bcg_3g_ac_e --params=

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