Murataite [(Y,Na)6(Zn,Fe)5Ti12O29(O,F)10F4] Structure : A16B40C12D6E5_cF316_216_eh_e2g2h_h_f_be

Picture of Structure; Click for Big Picture
Prototype : F16O40Ti12Y6Zn5
AFLOW prototype label : A16B40C12D6E5_cF316_216_eh_e2g2h_h_f_be
Strukturbericht designation : None
Pearson symbol : cF316
Space group number : 216
Space group symbol : $F\bar{4}3m$
AFLOW prototype command : aflow --proto=A16B40C12D6E5_cF316_216_eh_e2g2h_h_f_be
--params=
$a$,$x_{2}$,$x_{3}$,$x_{4}$,$x_{5}$,$x_{6}$,$x_{7}$,$x_{8}$,$z_{8}$,$x_{9}$,$z_{9}$,$x_{10}$,$z_{10}$,$x_{11}$,$z_{11}$


  • Most of the sites in this structure are somewhat disordered. The nominal composition is given as F16O40Ti12Y6Zn5 by (Ercit, 1995), but as the CIF in (Downs, 2003) shows, even these labels are not quite correct. In our listing we label each Wyckoff position by the type of atom that has the largest concentration on that site. Following (Downs, 2003):
    • Site Zn–I has the composition Zn0.89Si0.11.
    • Site F–I has the composition F0.55O0.45.
    • Site O–I is pure oxygen.
    • Site Zn–II has the composition Zn0.48Fe0.25Na0.16Ti0.11.
    • Site Y has the composition Y0.37Na0.35Mn0.03HREE0.25, where HREE is a mixture of heavy Rare Earth elements.
    • Site O–II is pure oxygen, but only 8.3333% of the sites are occupied.
    • Site O–III has the composition O0.7F0.3.
    • Site O–IV is pure oxygen.
    • Site O–V is pure oxygen, but only 87% of the sites are occupied.
    • Site F–II is pure fluorine, but only 33.333% of the sites are occupied.
    • Site Ti has the composition Ti0.76Nb0.13Na0.11.

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} & = & \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(4b\right) & \mbox{Zn I} \\ \mathbf{B}_{2} & = & x_{2} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} + x_{2} \, \mathbf{a}_{3} & = & x_{2}a \, \mathbf{\hat{x}} + x_{2}a \, \mathbf{\hat{y}} + x_{2}a \, \mathbf{\hat{z}} & \left(16e\right) & \mbox{F I} \\ \mathbf{B}_{3} & = & x_{2} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2}-3x_{2} \, \mathbf{a}_{3} & = & -x_{2}a \, \mathbf{\hat{x}}-x_{2}a \, \mathbf{\hat{y}} + x_{2}a \, \mathbf{\hat{z}} & \left(16e\right) & \mbox{F I} \\ \mathbf{B}_{4} & = & x_{2} \, \mathbf{a}_{1}-3x_{2} \, \mathbf{a}_{2} + x_{2} \, \mathbf{a}_{3} & = & -x_{2}a \, \mathbf{\hat{x}} + x_{2}a \, \mathbf{\hat{y}}-x_{2}a \, \mathbf{\hat{z}} & \left(16e\right) & \mbox{F I} \\ \mathbf{B}_{5} & = & -3x_{2} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} + x_{2} \, \mathbf{a}_{3} & = & x_{2}a \, \mathbf{\hat{x}}-x_{2}a \, \mathbf{\hat{y}}-x_{2}a \, \mathbf{\hat{z}} & \left(16e\right) & \mbox{F I} \\ \mathbf{B}_{6} & = & x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + x_{3} \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}} + x_{3}a \, \mathbf{\hat{y}} + x_{3}a \, \mathbf{\hat{z}} & \left(16e\right) & \mbox{O I} \\ \mathbf{B}_{7} & = & x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2}-3x_{3} \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}}-x_{3}a \, \mathbf{\hat{y}} + x_{3}a \, \mathbf{\hat{z}} & \left(16e\right) & \mbox{O I} \\ \mathbf{B}_{8} & = & x_{3} \, \mathbf{a}_{1}-3x_{3} \, \mathbf{a}_{2} + x_{3} \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}} + x_{3}a \, \mathbf{\hat{y}}-x_{3}a \, \mathbf{\hat{z}} & \left(16e\right) & \mbox{O I} \\ \mathbf{B}_{9} & = & -3x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + x_{3} \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}}-x_{3}a \, \mathbf{\hat{y}}-x_{3}a \, \mathbf{\hat{z}} & \left(16e\right) & \mbox{O I} \\ \mathbf{B}_{10} & = & x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}} + x_{4}a \, \mathbf{\hat{z}} & \left(16e\right) & \mbox{Zn II} \\ \mathbf{B}_{11} & = & x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2}-3x_{4} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}} + x_{4}a \, \mathbf{\hat{z}} & \left(16e\right) & \mbox{Zn II} \\ \mathbf{B}_{12} & = & x_{4} \, \mathbf{a}_{1}-3x_{4} \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}}-x_{4}a \, \mathbf{\hat{z}} & \left(16e\right) & \mbox{Zn II} \\ \mathbf{B}_{13} & = & -3x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}}-x_{4}a \, \mathbf{\hat{z}} & \left(16e\right) & \mbox{Zn II} \\ \mathbf{B}_{14} & = & -x_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} + x_{5} \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}} & \left(24f\right) & \mbox{Y} \\ \mathbf{B}_{15} & = & x_{5} \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2}-x_{5} \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}} & \left(24f\right) & \mbox{Y} \\ \mathbf{B}_{16} & = & x_{5} \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2} + x_{5} \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{y}} & \left(24f\right) & \mbox{Y} \\ \mathbf{B}_{17} & = & -x_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2}-x_{5} \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{y}} & \left(24f\right) & \mbox{Y} \\ \mathbf{B}_{18} & = & x_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2}-x_{5} \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{z}} & \left(24f\right) & \mbox{Y} \\ \mathbf{B}_{19} & = & -x_{5} \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2} + x_{5} \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{z}} & \left(24f\right) & \mbox{Y} \\ \mathbf{B}_{20} & = & \left(\frac{1}{2} - x_{6}\right) \, \mathbf{a}_{1} + x_{6} \, \mathbf{a}_{2} + x_{6} \, \mathbf{a}_{3} & = & x_{6}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{O II} \\ \mathbf{B}_{21} & = & x_{6} \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{6}\right)a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{O II} \\ \mathbf{B}_{22} & = & x_{6} \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{6}\right) \, \mathbf{a}_{2} + x_{6} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + x_{6}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{O II} \\ \mathbf{B}_{23} & = & \left(\frac{1}{2} - x_{6}\right) \, \mathbf{a}_{1} + x_{6} \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{6}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{6}\right)a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{O II} \\ \mathbf{B}_{24} & = & x_{6} \, \mathbf{a}_{1} + x_{6} \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{6}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + x_{6}a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{O II} \\ \mathbf{B}_{25} & = & \left(\frac{1}{2} - x_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{6}\right) \, \mathbf{a}_{2} + x_{6} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-x_{6}\right)a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{O II} \\ \mathbf{B}_{26} & = & \left(\frac{1}{2} - x_{7}\right) \, \mathbf{a}_{1} + x_{7} \, \mathbf{a}_{2} + x_{7} \, \mathbf{a}_{3} & = & x_{7}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{O III} \\ \mathbf{B}_{27} & = & x_{7} \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{7}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{7}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{7}\right)a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{O III} \\ \mathbf{B}_{28} & = & x_{7} \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{7}\right) \, \mathbf{a}_{2} + x_{7} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + x_{7}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{O III} \\ \mathbf{B}_{29} & = & \left(\frac{1}{2} - x_{7}\right) \, \mathbf{a}_{1} + x_{7} \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{7}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{7}\right)a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{O III} \\ \mathbf{B}_{30} & = & x_{7} \, \mathbf{a}_{1} + x_{7} \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{7}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + x_{7}a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{O III} \\ \mathbf{B}_{31} & = & \left(\frac{1}{2} - x_{7}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{7}\right) \, \mathbf{a}_{2} + x_{7} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-x_{7}\right)a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{O III} \\ \mathbf{B}_{32} & = & z_{8} \, \mathbf{a}_{1} + z_{8} \, \mathbf{a}_{2} + \left(2x_{8}-z_{8}\right) \, \mathbf{a}_{3} & = & x_{8}a \, \mathbf{\hat{x}} + x_{8}a \, \mathbf{\hat{y}} + z_{8}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{F II} \\ \mathbf{B}_{33} & = & z_{8} \, \mathbf{a}_{1} + z_{8} \, \mathbf{a}_{2} + \left(-2x_{8}-z_{8}\right) \, \mathbf{a}_{3} & = & -x_{8}a \, \mathbf{\hat{x}}-x_{8}a \, \mathbf{\hat{y}} + z_{8}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{F II} \\ \mathbf{B}_{34} & = & \left(2x_{8}-z_{8}\right) \, \mathbf{a}_{1} + \left(-2x_{8}-z_{8}\right) \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & -x_{8}a \, \mathbf{\hat{x}} + x_{8}a \, \mathbf{\hat{y}}-z_{8}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{F II} \\ \mathbf{B}_{35} & = & \left(-2x_{8}-z_{8}\right) \, \mathbf{a}_{1} + \left(2x_{8}-z_{8}\right) \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & x_{8}a \, \mathbf{\hat{x}}-x_{8}a \, \mathbf{\hat{y}}-z_{8}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{F II} \\ \mathbf{B}_{36} & = & \left(2x_{8}-z_{8}\right) \, \mathbf{a}_{1} + z_{8} \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & z_{8}a \, \mathbf{\hat{x}} + x_{8}a \, \mathbf{\hat{y}} + x_{8}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{F II} \\ \mathbf{B}_{37} & = & \left(-2x_{8}-z_{8}\right) \, \mathbf{a}_{1} + z_{8} \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & z_{8}a \, \mathbf{\hat{x}}-x_{8}a \, \mathbf{\hat{y}}-x_{8}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{F II} \\ \mathbf{B}_{38} & = & z_{8} \, \mathbf{a}_{1} + \left(2x_{8}-z_{8}\right) \, \mathbf{a}_{2} + \left(-2x_{8}-z_{8}\right) \, \mathbf{a}_{3} & = & -z_{8}a \, \mathbf{\hat{x}}-x_{8}a \, \mathbf{\hat{y}} + x_{8}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{F II} \\ \mathbf{B}_{39} & = & z_{8} \, \mathbf{a}_{1} + \left(-2x_{8}-z_{8}\right) \, \mathbf{a}_{2} + \left(2x_{8}-z_{8}\right) \, \mathbf{a}_{3} & = & -z_{8}a \, \mathbf{\hat{x}} + x_{8}a \, \mathbf{\hat{y}}-x_{8}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{F II} \\ \mathbf{B}_{40} & = & z_{8} \, \mathbf{a}_{1} + \left(2x_{8}-z_{8}\right) \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & x_{8}a \, \mathbf{\hat{x}} + z_{8}a \, \mathbf{\hat{y}} + x_{8}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{F II} \\ \mathbf{B}_{41} & = & z_{8} \, \mathbf{a}_{1} + \left(-2x_{8}-z_{8}\right) \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & -x_{8}a \, \mathbf{\hat{x}} + z_{8}a \, \mathbf{\hat{y}}-x_{8}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{F II} \\ \mathbf{B}_{42} & = & \left(-2x_{8}-z_{8}\right) \, \mathbf{a}_{1} + z_{8} \, \mathbf{a}_{2} + \left(2x_{8}-z_{8}\right) \, \mathbf{a}_{3} & = & x_{8}a \, \mathbf{\hat{x}}-z_{8}a \, \mathbf{\hat{y}}-x_{8}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{F II} \\ \mathbf{B}_{43} & = & \left(2x_{8}-z_{8}\right) \, \mathbf{a}_{1} + z_{8} \, \mathbf{a}_{2} + \left(-2x_{8}-z_{8}\right) \, \mathbf{a}_{3} & = & -x_{8}a \, \mathbf{\hat{x}}-z_{8}a \, \mathbf{\hat{y}} + x_{8}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{F II} \\ \mathbf{B}_{44} & = & z_{9} \, \mathbf{a}_{1} + z_{9} \, \mathbf{a}_{2} + \left(2x_{9}-z_{9}\right) \, \mathbf{a}_{3} & = & x_{9}a \, \mathbf{\hat{x}} + x_{9}a \, \mathbf{\hat{y}} + z_{9}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{O IV} \\ \mathbf{B}_{45} & = & z_{9} \, \mathbf{a}_{1} + z_{9} \, \mathbf{a}_{2} + \left(-2x_{9}-z_{9}\right) \, \mathbf{a}_{3} & = & -x_{9}a \, \mathbf{\hat{x}}-x_{9}a \, \mathbf{\hat{y}} + z_{9}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{O IV} \\ \mathbf{B}_{46} & = & \left(2x_{9}-z_{9}\right) \, \mathbf{a}_{1} + \left(-2x_{9}-z_{9}\right) \, \mathbf{a}_{2} + z_{9} \, \mathbf{a}_{3} & = & -x_{9}a \, \mathbf{\hat{x}} + x_{9}a \, \mathbf{\hat{y}}-z_{9}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{O IV} \\ \mathbf{B}_{47} & = & \left(-2x_{9}-z_{9}\right) \, \mathbf{a}_{1} + \left(2x_{9}-z_{9}\right) \, \mathbf{a}_{2} + z_{9} \, \mathbf{a}_{3} & = & x_{9}a \, \mathbf{\hat{x}}-x_{9}a \, \mathbf{\hat{y}}-z_{9}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{O IV} \\ \mathbf{B}_{48} & = & \left(2x_{9}-z_{9}\right) \, \mathbf{a}_{1} + z_{9} \, \mathbf{a}_{2} + z_{9} \, \mathbf{a}_{3} & = & z_{9}a \, \mathbf{\hat{x}} + x_{9}a \, \mathbf{\hat{y}} + x_{9}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{O IV} \\ \mathbf{B}_{49} & = & \left(-2x_{9}-z_{9}\right) \, \mathbf{a}_{1} + z_{9} \, \mathbf{a}_{2} + z_{9} \, \mathbf{a}_{3} & = & z_{9}a \, \mathbf{\hat{x}}-x_{9}a \, \mathbf{\hat{y}}-x_{9}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{O IV} \\ \mathbf{B}_{50} & = & z_{9} \, \mathbf{a}_{1} + \left(2x_{9}-z_{9}\right) \, \mathbf{a}_{2} + \left(-2x_{9}-z_{9}\right) \, \mathbf{a}_{3} & = & -z_{9}a \, \mathbf{\hat{x}}-x_{9}a \, \mathbf{\hat{y}} + x_{9}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{O IV} \\ \mathbf{B}_{51} & = & z_{9} \, \mathbf{a}_{1} + \left(-2x_{9}-z_{9}\right) \, \mathbf{a}_{2} + \left(2x_{9}-z_{9}\right) \, \mathbf{a}_{3} & = & -z_{9}a \, \mathbf{\hat{x}} + x_{9}a \, \mathbf{\hat{y}}-x_{9}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{O IV} \\ \mathbf{B}_{52} & = & z_{9} \, \mathbf{a}_{1} + \left(2x_{9}-z_{9}\right) \, \mathbf{a}_{2} + z_{9} \, \mathbf{a}_{3} & = & x_{9}a \, \mathbf{\hat{x}} + z_{9}a \, \mathbf{\hat{y}} + x_{9}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{O IV} \\ \mathbf{B}_{53} & = & z_{9} \, \mathbf{a}_{1} + \left(-2x_{9}-z_{9}\right) \, \mathbf{a}_{2} + z_{9} \, \mathbf{a}_{3} & = & -x_{9}a \, \mathbf{\hat{x}} + z_{9}a \, \mathbf{\hat{y}}-x_{9}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{O IV} \\ \mathbf{B}_{54} & = & \left(-2x_{9}-z_{9}\right) \, \mathbf{a}_{1} + z_{9} \, \mathbf{a}_{2} + \left(2x_{9}-z_{9}\right) \, \mathbf{a}_{3} & = & x_{9}a \, \mathbf{\hat{x}}-z_{9}a \, \mathbf{\hat{y}}-x_{9}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{O IV} \\ \mathbf{B}_{55} & = & \left(2x_{9}-z_{9}\right) \, \mathbf{a}_{1} + z_{9} \, \mathbf{a}_{2} + \left(-2x_{9}-z_{9}\right) \, \mathbf{a}_{3} & = & -x_{9}a \, \mathbf{\hat{x}}-z_{9}a \, \mathbf{\hat{y}} + x_{9}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{O IV} \\ \mathbf{B}_{56} & = & z_{10} \, \mathbf{a}_{1} + z_{10} \, \mathbf{a}_{2} + \left(2x_{10}-z_{10}\right) \, \mathbf{a}_{3} & = & x_{10}a \, \mathbf{\hat{x}} + x_{10}a \, \mathbf{\hat{y}} + z_{10}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{O V} \\ \mathbf{B}_{57} & = & z_{10} \, \mathbf{a}_{1} + z_{10} \, \mathbf{a}_{2} + \left(-2x_{10}-z_{10}\right) \, \mathbf{a}_{3} & = & -x_{10}a \, \mathbf{\hat{x}}-x_{10}a \, \mathbf{\hat{y}} + z_{10}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{O V} \\ \mathbf{B}_{58} & = & \left(2x_{10}-z_{10}\right) \, \mathbf{a}_{1} + \left(-2x_{10}-z_{10}\right) \, \mathbf{a}_{2} + z_{10} \, \mathbf{a}_{3} & = & -x_{10}a \, \mathbf{\hat{x}} + x_{10}a \, \mathbf{\hat{y}}-z_{10}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{O V} \\ \mathbf{B}_{59} & = & \left(-2x_{10}-z_{10}\right) \, \mathbf{a}_{1} + \left(2x_{10}-z_{10}\right) \, \mathbf{a}_{2} + z_{10} \, \mathbf{a}_{3} & = & x_{10}a \, \mathbf{\hat{x}}-x_{10}a \, \mathbf{\hat{y}}-z_{10}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{O V} \\ \mathbf{B}_{60} & = & \left(2x_{10}-z_{10}\right) \, \mathbf{a}_{1} + z_{10} \, \mathbf{a}_{2} + z_{10} \, \mathbf{a}_{3} & = & z_{10}a \, \mathbf{\hat{x}} + x_{10}a \, \mathbf{\hat{y}} + x_{10}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{O V} \\ \mathbf{B}_{61} & = & \left(-2x_{10}-z_{10}\right) \, \mathbf{a}_{1} + z_{10} \, \mathbf{a}_{2} + z_{10} \, \mathbf{a}_{3} & = & z_{10}a \, \mathbf{\hat{x}}-x_{10}a \, \mathbf{\hat{y}}-x_{10}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{O V} \\ \mathbf{B}_{62} & = & z_{10} \, \mathbf{a}_{1} + \left(2x_{10}-z_{10}\right) \, \mathbf{a}_{2} + \left(-2x_{10}-z_{10}\right) \, \mathbf{a}_{3} & = & -z_{10}a \, \mathbf{\hat{x}}-x_{10}a \, \mathbf{\hat{y}} + x_{10}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{O V} \\ \mathbf{B}_{63} & = & z_{10} \, \mathbf{a}_{1} + \left(-2x_{10}-z_{10}\right) \, \mathbf{a}_{2} + \left(2x_{10}-z_{10}\right) \, \mathbf{a}_{3} & = & -z_{10}a \, \mathbf{\hat{x}} + x_{10}a \, \mathbf{\hat{y}}-x_{10}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{O V} \\ \mathbf{B}_{64} & = & z_{10} \, \mathbf{a}_{1} + \left(2x_{10}-z_{10}\right) \, \mathbf{a}_{2} + z_{10} \, \mathbf{a}_{3} & = & x_{10}a \, \mathbf{\hat{x}} + z_{10}a \, \mathbf{\hat{y}} + x_{10}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{O V} \\ \mathbf{B}_{65} & = & z_{10} \, \mathbf{a}_{1} + \left(-2x_{10}-z_{10}\right) \, \mathbf{a}_{2} + z_{10} \, \mathbf{a}_{3} & = & -x_{10}a \, \mathbf{\hat{x}} + z_{10}a \, \mathbf{\hat{y}}-x_{10}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{O V} \\ \mathbf{B}_{66} & = & \left(-2x_{10}-z_{10}\right) \, \mathbf{a}_{1} + z_{10} \, \mathbf{a}_{2} + \left(2x_{10}-z_{10}\right) \, \mathbf{a}_{3} & = & x_{10}a \, \mathbf{\hat{x}}-z_{10}a \, \mathbf{\hat{y}}-x_{10}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{O V} \\ \mathbf{B}_{67} & = & \left(2x_{10}-z_{10}\right) \, \mathbf{a}_{1} + z_{10} \, \mathbf{a}_{2} + \left(-2x_{10}-z_{10}\right) \, \mathbf{a}_{3} & = & -x_{10}a \, \mathbf{\hat{x}}-z_{10}a \, \mathbf{\hat{y}} + x_{10}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{O V} \\ \mathbf{B}_{68} & = & z_{11} \, \mathbf{a}_{1} + z_{11} \, \mathbf{a}_{2} + \left(2x_{11}-z_{11}\right) \, \mathbf{a}_{3} & = & x_{11}a \, \mathbf{\hat{x}} + x_{11}a \, \mathbf{\hat{y}} + z_{11}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{Ti} \\ \mathbf{B}_{69} & = & z_{11} \, \mathbf{a}_{1} + z_{11} \, \mathbf{a}_{2} + \left(-2x_{11}-z_{11}\right) \, \mathbf{a}_{3} & = & -x_{11}a \, \mathbf{\hat{x}}-x_{11}a \, \mathbf{\hat{y}} + z_{11}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{Ti} \\ \mathbf{B}_{70} & = & \left(2x_{11}-z_{11}\right) \, \mathbf{a}_{1} + \left(-2x_{11}-z_{11}\right) \, \mathbf{a}_{2} + z_{11} \, \mathbf{a}_{3} & = & -x_{11}a \, \mathbf{\hat{x}} + x_{11}a \, \mathbf{\hat{y}}-z_{11}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{Ti} \\ \mathbf{B}_{71} & = & \left(-2x_{11}-z_{11}\right) \, \mathbf{a}_{1} + \left(2x_{11}-z_{11}\right) \, \mathbf{a}_{2} + z_{11} \, \mathbf{a}_{3} & = & x_{11}a \, \mathbf{\hat{x}}-x_{11}a \, \mathbf{\hat{y}}-z_{11}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{Ti} \\ \mathbf{B}_{72} & = & \left(2x_{11}-z_{11}\right) \, \mathbf{a}_{1} + z_{11} \, \mathbf{a}_{2} + z_{11} \, \mathbf{a}_{3} & = & z_{11}a \, \mathbf{\hat{x}} + x_{11}a \, \mathbf{\hat{y}} + x_{11}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{Ti} \\ \mathbf{B}_{73} & = & \left(-2x_{11}-z_{11}\right) \, \mathbf{a}_{1} + z_{11} \, \mathbf{a}_{2} + z_{11} \, \mathbf{a}_{3} & = & z_{11}a \, \mathbf{\hat{x}}-x_{11}a \, \mathbf{\hat{y}}-x_{11}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{Ti} \\ \mathbf{B}_{74} & = & z_{11} \, \mathbf{a}_{1} + \left(2x_{11}-z_{11}\right) \, \mathbf{a}_{2} + \left(-2x_{11}-z_{11}\right) \, \mathbf{a}_{3} & = & -z_{11}a \, \mathbf{\hat{x}}-x_{11}a \, \mathbf{\hat{y}} + x_{11}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{Ti} \\ \mathbf{B}_{75} & = & z_{11} \, \mathbf{a}_{1} + \left(-2x_{11}-z_{11}\right) \, \mathbf{a}_{2} + \left(2x_{11}-z_{11}\right) \, \mathbf{a}_{3} & = & -z_{11}a \, \mathbf{\hat{x}} + x_{11}a \, \mathbf{\hat{y}}-x_{11}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{Ti} \\ \mathbf{B}_{76} & = & z_{11} \, \mathbf{a}_{1} + \left(2x_{11}-z_{11}\right) \, \mathbf{a}_{2} + z_{11} \, \mathbf{a}_{3} & = & x_{11}a \, \mathbf{\hat{x}} + z_{11}a \, \mathbf{\hat{y}} + x_{11}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{Ti} \\ \mathbf{B}_{77} & = & z_{11} \, \mathbf{a}_{1} + \left(-2x_{11}-z_{11}\right) \, \mathbf{a}_{2} + z_{11} \, \mathbf{a}_{3} & = & -x_{11}a \, \mathbf{\hat{x}} + z_{11}a \, \mathbf{\hat{y}}-x_{11}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{Ti} \\ \mathbf{B}_{78} & = & \left(-2x_{11}-z_{11}\right) \, \mathbf{a}_{1} + z_{11} \, \mathbf{a}_{2} + \left(2x_{11}-z_{11}\right) \, \mathbf{a}_{3} & = & x_{11}a \, \mathbf{\hat{x}}-z_{11}a \, \mathbf{\hat{y}}-x_{11}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{Ti} \\ \mathbf{B}_{79} & = & \left(2x_{11}-z_{11}\right) \, \mathbf{a}_{1} + z_{11} \, \mathbf{a}_{2} + \left(-2x_{11}-z_{11}\right) \, \mathbf{a}_{3} & = & -x_{11}a \, \mathbf{\hat{x}}-z_{11}a \, \mathbf{\hat{y}} + x_{11}a \, \mathbf{\hat{z}} & \left(48h\right) & \mbox{Ti} \\ \end{array} \]

References

  • T. S. Ercit and F. C. Hawthorne, Murataite, A UB12 derivative structure with condensed Keggin molecules, Can. Mineral. 33, 1233–1229 (1995).
  • 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=A16B40C12D6E5_cF316_216_eh_e2g2h_h_f_be --params=

Species:

Running:

Output: