Boracite (Mg3B7ClO13) Structure: A7BC3D13_cF192_219_de_b_c_ah

Picture of Structure; Click for Big Picture
Prototype : Mg3B7ClO13
AFLOW prototype label : A7BC3D13_cF192_219_de_b_c_ah
Strukturbericht designation : None
Pearson symbol : cF192
Space group number : 219
Space group symbol : $F\bar{4}3c$
AFLOW prototype command : aflow --proto=A7BC3D13_cF192_219_de_b_c_ah
--params=
$a$,$x_{5}$,$x_{6}$,$y_{6}$,$z_{6}$


Other compounds with this structure

  • M3B7O13X; M = Mg, Cr, Mn, Fe, Co; X = Cl, Br, I

  • Experimental data was obtained at 400° C.

Face-centered Cubic primitive vectors:

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

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(8a\right) & \mbox{O 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}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(8a\right) & \mbox{O I} \\ \mathbf{B}_{3} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{Cl} \\ \mathbf{B}_{4} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \frac{3}{4}a \, \mathbf{\hat{y}} + \frac{3}{4}a \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{Cl} \\ \mathbf{B}_{5} & = & \frac{1}{2} \, \mathbf{a}_{1} & = & \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(24c\right) & \mbox{Mg} \\ \mathbf{B}_{6} & = & \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(24c\right) & \mbox{Mg} \\ \mathbf{B}_{7} & = & \frac{1}{2} \, \mathbf{a}_{2} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(24c\right) & \mbox{Mg} \\ \mathbf{B}_{8} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(24c\right) & \mbox{Mg} \\ \mathbf{B}_{9} & = & \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} & \left(24c\right) & \mbox{Mg} \\ \mathbf{B}_{10} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(24c\right) & \mbox{Mg} \\ \mathbf{B}_{11} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{B I} \\ \mathbf{B}_{12} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{B I} \\ \mathbf{B}_{13} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{B I} \\ \mathbf{B}_{14} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{3}{4}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{B I} \\ \mathbf{B}_{15} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{B I} \\ \mathbf{B}_{16} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{3}{4}a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{B I} \\ \mathbf{B}_{17} & = & x_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} + x_{5} \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}} + x_{5}a \, \mathbf{\hat{y}} + x_{5}a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{B II} \\ \mathbf{B}_{18} & = & x_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2}-3x_{5} \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}}-x_{5}a \, \mathbf{\hat{y}} + x_{5}a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{B II} \\ \mathbf{B}_{19} & = & x_{5} \, \mathbf{a}_{1}-3x_{5} \, \mathbf{a}_{2} + x_{5} \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}} + x_{5}a \, \mathbf{\hat{y}}-x_{5}a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{B II} \\ \mathbf{B}_{20} & = & -3x_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} + x_{5} \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}}-x_{5}a \, \mathbf{\hat{y}}-x_{5}a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{B II} \\ \mathbf{B}_{21} & = & \left(\frac{1}{2} +x_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{5}\right)a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{B II} \\ \mathbf{B}_{22} & = & \left(\frac{1}{2} +x_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - 3x_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - x_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - x_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{5}\right)a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{B II} \\ \mathbf{B}_{23} & = & \left(\frac{1}{2} - 3x_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - x_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - x_{5}\right)a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{B II} \\ \mathbf{B}_{24} & = & \left(\frac{1}{2} +x_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - 3x_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - x_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - x_{5}\right)a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{B II} \\ \mathbf{B}_{25} & = & \left(-x_{6}+y_{6}+z_{6}\right) \, \mathbf{a}_{1} + \left(x_{6}-y_{6}+z_{6}\right) \, \mathbf{a}_{2} + \left(x_{6}+y_{6}-z_{6}\right) \, \mathbf{a}_{3} & = & x_{6}a \, \mathbf{\hat{x}} + y_{6}a \, \mathbf{\hat{y}} + z_{6}a \, \mathbf{\hat{z}} & \left(96h\right) & \mbox{O II} \\ \mathbf{B}_{26} & = & \left(x_{6}-y_{6}+z_{6}\right) \, \mathbf{a}_{1} + \left(-x_{6}+y_{6}+z_{6}\right) \, \mathbf{a}_{2} + \left(-x_{6}-y_{6}-z_{6}\right) \, \mathbf{a}_{3} & = & -x_{6}a \, \mathbf{\hat{x}}-y_{6}a \, \mathbf{\hat{y}} + z_{6}a \, \mathbf{\hat{z}} & \left(96h\right) & \mbox{O II} \\ \mathbf{B}_{27} & = & \left(x_{6}+y_{6}-z_{6}\right) \, \mathbf{a}_{1} + \left(-x_{6}-y_{6}-z_{6}\right) \, \mathbf{a}_{2} + \left(-x_{6}+y_{6}+z_{6}\right) \, \mathbf{a}_{3} & = & -x_{6}a \, \mathbf{\hat{x}} + y_{6}a \, \mathbf{\hat{y}}-z_{6}a \, \mathbf{\hat{z}} & \left(96h\right) & \mbox{O II} \\ \mathbf{B}_{28} & = & \left(-x_{6}-y_{6}-z_{6}\right) \, \mathbf{a}_{1} + \left(x_{6}+y_{6}-z_{6}\right) \, \mathbf{a}_{2} + \left(x_{6}-y_{6}+z_{6}\right) \, \mathbf{a}_{3} & = & x_{6}a \, \mathbf{\hat{x}}-y_{6}a \, \mathbf{\hat{y}}-z_{6}a \, \mathbf{\hat{z}} & \left(96h\right) & \mbox{O II} \\ \mathbf{B}_{29} & = & \left(x_{6}+y_{6}-z_{6}\right) \, \mathbf{a}_{1} + \left(-x_{6}+y_{6}+z_{6}\right) \, \mathbf{a}_{2} + \left(x_{6}-y_{6}+z_{6}\right) \, \mathbf{a}_{3} & = & z_{6}a \, \mathbf{\hat{x}} + x_{6}a \, \mathbf{\hat{y}} + y_{6}a \, \mathbf{\hat{z}} & \left(96h\right) & \mbox{O II} \\ \mathbf{B}_{30} & = & \left(-x_{6}-y_{6}-z_{6}\right) \, \mathbf{a}_{1} + \left(x_{6}-y_{6}+z_{6}\right) \, \mathbf{a}_{2} + \left(-x_{6}+y_{6}+z_{6}\right) \, \mathbf{a}_{3} & = & z_{6}a \, \mathbf{\hat{x}}-x_{6}a \, \mathbf{\hat{y}}-y_{6}a \, \mathbf{\hat{z}} & \left(96h\right) & \mbox{O II} \\ \mathbf{B}_{31} & = & \left(-x_{6}+y_{6}+z_{6}\right) \, \mathbf{a}_{1} + \left(x_{6}+y_{6}-z_{6}\right) \, \mathbf{a}_{2} + \left(-x_{6}-y_{6}-z_{6}\right) \, \mathbf{a}_{3} & = & -z_{6}a \, \mathbf{\hat{x}}-x_{6}a \, \mathbf{\hat{y}} + y_{6}a \, \mathbf{\hat{z}} & \left(96h\right) & \mbox{O II} \\ \mathbf{B}_{32} & = & \left(x_{6}-y_{6}+z_{6}\right) \, \mathbf{a}_{1} + \left(-x_{6}-y_{6}-z_{6}\right) \, \mathbf{a}_{2} + \left(x_{6}+y_{6}-z_{6}\right) \, \mathbf{a}_{3} & = & -z_{6}a \, \mathbf{\hat{x}} + x_{6}a \, \mathbf{\hat{y}}-y_{6}a \, \mathbf{\hat{z}} & \left(96h\right) & \mbox{O II} \\ \mathbf{B}_{33} & = & \left(x_{6}-y_{6}+z_{6}\right) \, \mathbf{a}_{1} + \left(x_{6}+y_{6}-z_{6}\right) \, \mathbf{a}_{2} + \left(-x_{6}+y_{6}+z_{6}\right) \, \mathbf{a}_{3} & = & y_{6}a \, \mathbf{\hat{x}} + z_{6}a \, \mathbf{\hat{y}} + x_{6}a \, \mathbf{\hat{z}} & \left(96h\right) & \mbox{O II} \\ \mathbf{B}_{34} & = & \left(-x_{6}+y_{6}+z_{6}\right) \, \mathbf{a}_{1} + \left(-x_{6}-y_{6}-z_{6}\right) \, \mathbf{a}_{2} + \left(x_{6}-y_{6}+z_{6}\right) \, \mathbf{a}_{3} & = & -y_{6}a \, \mathbf{\hat{x}} + z_{6}a \, \mathbf{\hat{y}}-x_{6}a \, \mathbf{\hat{z}} & \left(96h\right) & \mbox{O II} \\ \mathbf{B}_{35} & = & \left(-x_{6}-y_{6}-z_{6}\right) \, \mathbf{a}_{1} + \left(-x_{6}+y_{6}+z_{6}\right) \, \mathbf{a}_{2} + \left(x_{6}+y_{6}-z_{6}\right) \, \mathbf{a}_{3} & = & y_{6}a \, \mathbf{\hat{x}}-z_{6}a \, \mathbf{\hat{y}}-x_{6}a \, \mathbf{\hat{z}} & \left(96h\right) & \mbox{O II} \\ \mathbf{B}_{36} & = & \left(x_{6}+y_{6}-z_{6}\right) \, \mathbf{a}_{1} + \left(x_{6}-y_{6}+z_{6}\right) \, \mathbf{a}_{2} + \left(-x_{6}-y_{6}-z_{6}\right) \, \mathbf{a}_{3} & = & -y_{6}a \, \mathbf{\hat{x}}-z_{6}a \, \mathbf{\hat{y}} + x_{6}a \, \mathbf{\hat{z}} & \left(96h\right) & \mbox{O II} \\ \mathbf{B}_{37} & = & \left(\frac{1}{2} +x_{6} - y_{6} + z_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{6} + y_{6} - z_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +y_{6}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{6}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{6}\right)a \, \mathbf{\hat{z}} & \left(96h\right) & \mbox{O II} \\ \mathbf{B}_{38} & = & \left(\frac{1}{2} - x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{6} - y_{6} + z_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{6} - y_{6} - z_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - y_{6}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - x_{6}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{6}\right)a \, \mathbf{\hat{z}} & \left(96h\right) & \mbox{O II} \\ \mathbf{B}_{39} & = & \left(\frac{1}{2} - x_{6} - y_{6} - z_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{6} + y_{6} - z_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +y_{6}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - x_{6}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{6}\right)a \, \mathbf{\hat{z}} & \left(96h\right) & \mbox{O II} \\ \mathbf{B}_{40} & = & \left(\frac{1}{2} +x_{6} + y_{6} - z_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{6} - y_{6} - z_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{6} - y_{6} + z_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - y_{6}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{6}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{6}\right)a \, \mathbf{\hat{z}} & \left(96h\right) & \mbox{O II} \\ \mathbf{B}_{41} & = & \left(\frac{1}{2} - x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{6} + y_{6} - z_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{6} - y_{6} + z_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{6}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +z_{6}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +y_{6}\right)a \, \mathbf{\hat{z}} & \left(96h\right) & \mbox{O II} \\ \mathbf{B}_{42} & = & \left(\frac{1}{2} +x_{6} - y_{6} + z_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{6} - y_{6} - z_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - x_{6}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +z_{6}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - y_{6}\right)a \, \mathbf{\hat{z}} & \left(96h\right) & \mbox{O II} \\ \mathbf{B}_{43} & = & \left(\frac{1}{2} +x_{6} + y_{6} - z_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{6} - y_{6} - z_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - x_{6}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - z_{6}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +y_{6}\right)a \, \mathbf{\hat{z}} & \left(96h\right) & \mbox{O II} \\ \mathbf{B}_{44} & = & \left(\frac{1}{2} - x_{6} - y_{6} - z_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{6} - y_{6} + z_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{6} + y_{6} - z_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{6}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - z_{6}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - y_{6}\right)a \, \mathbf{\hat{z}} & \left(96h\right) & \mbox{O II} \\ \mathbf{B}_{45} & = & \left(\frac{1}{2} +x_{6} + y_{6} - z_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{6} - y_{6} + z_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +z_{6}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{6}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{6}\right)a \, \mathbf{\hat{z}} & \left(96h\right) & \mbox{O II} \\ \mathbf{B}_{46} & = & \left(\frac{1}{2} - x_{6} - y_{6} - z_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{6} - y_{6} + z_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +z_{6}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - y_{6}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - x_{6}\right)a \, \mathbf{\hat{z}} & \left(96h\right) & \mbox{O II} \\ \mathbf{B}_{47} & = & \left(\frac{1}{2} - x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{6} - y_{6} - z_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{6} + y_{6} - z_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - z_{6}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{6}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - x_{6}\right)a \, \mathbf{\hat{z}} & \left(96h\right) & \mbox{O II} \\ \mathbf{B}_{48} & = & \left(\frac{1}{2} +x_{6} - y_{6} + z_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{6} + y_{6} - z_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{6} - y_{6} - z_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - z_{6}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - y_{6}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{6}\right)a \, \mathbf{\hat{z}} & \left(96h\right) & \mbox{O II} \\ \end{array} \]

References

  • S. Sueno, J. R. Clark, J. J. Papike, and J. A. Konnert, Crystal–Structure Refinement of Cubic Boracite, Am. Mineral. 58, 691–697 (1973).

Geometry files


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