Na2Ca6Si4O15 Structure : A6B2C15D4_mP54_7_6a_2a_15a_4a

Picture of Structure; Click for Big Picture
Prototype : Ca6Na2O15Si4
AFLOW prototype label : A6B2C15D4_mP54_7_6a_2a_15a_4a
Strukturbericht designation : None
Pearson symbol : mP54
Space group number : 7
Space group symbol : $Pc$
AFLOW prototype command : aflow --proto=A6B2C15D4_mP54_7_6a_2a_15a_4a
--params=
$a$,$b/a$,$c/a$,$\beta$,$x_{1}$,$y_{1}$,$z_{1}$,$x_{2}$,$y_{2}$,$z_{2}$,$x_{3}$,$y_{3}$,$z_{3}$,$x_{4}$,$y_{4}$,$z_{4}$,$x_{5}$,$y_{5}$,$z_{5}$,$x_{6}$,$y_{6}$,$z_{6}$,$x_{7}$,$y_{7}$,$z_{7}$,$x_{8}$,$y_{8}$,$z_{8}$,$x_{9}$,$y_{9}$,$z_{9}$,$x_{10}$,$y_{10}$,$z_{10}$,$x_{11}$,$y_{11}$,$z_{11}$,$x_{12}$,$y_{12}$,$z_{12}$,$x_{13}$,$y_{13}$,$z_{13}$,$x_{14}$,$y_{14}$,$z_{14}$,$x_{15}$,$y_{15}$,$z_{15}$,$x_{16}$,$y_{16}$,$z_{16}$,$x_{17}$,$y_{17}$,$z_{17}$,$x_{18}$,$y_{18}$,$z_{18}$,$x_{19}$,$y_{19}$,$z_{19}$,$x_{20}$,$y_{20}$,$z_{20}$,$x_{21}$,$y_{21}$,$z_{21}$,$x_{22}$,$y_{22}$,$z_{22}$,$x_{23}$,$y_{23}$,$z_{23}$,$x_{24}$,$y_{24}$,$z_{24}$,$x_{25}$,$y_{25}$,$z_{25}$,$x_{26}$,$y_{26}$,$z_{26}$,$x_{27}$,$y_{27}$,$z_{27}$


  • Although this structure was formed at 1300 °C, the data was taken after cooling to room temperature, 295 K.
  • The true composition of the Ca–I site is Ca0.84Na0.16, and the Na–I site has composition Na0.84Ca0.16.
  • The Si–III and Si–IV atoms share the O–$X$ atom between them, accounting for the missing oxygen atom.

Simple Monoclinic primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & x_{1} \, \mathbf{a}_{1} + y_{1} \, \mathbf{a}_{2} + z_{1} \, \mathbf{a}_{3} & = & \left(x_{1}a+z_{1}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{1}b \, \mathbf{\hat{y}} + z_{1}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Ca I} \\ \mathbf{B}_{2} & = & x_{1} \, \mathbf{a}_{1}-y_{1} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{1}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta +x_{1}a + z_{1}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{1}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{1}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Ca I} \\ \mathbf{B}_{3} & = & x_{2} \, \mathbf{a}_{1} + y_{2} \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3} & = & \left(x_{2}a+z_{2}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{2}b \, \mathbf{\hat{y}} + z_{2}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Ca II} \\ \mathbf{B}_{4} & = & x_{2} \, \mathbf{a}_{1}-y_{2} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta +x_{2}a + z_{2}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{2}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{2}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Ca II} \\ \mathbf{B}_{5} & = & x_{3} \, \mathbf{a}_{1} + y_{3} \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3} & = & \left(x_{3}a+z_{3}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{3}b \, \mathbf{\hat{y}} + z_{3}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Ca III} \\ \mathbf{B}_{6} & = & x_{3} \, \mathbf{a}_{1}-y_{3} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta +x_{3}a + z_{3}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{3}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{3}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Ca III} \\ \mathbf{B}_{7} & = & x_{4} \, \mathbf{a}_{1} + y_{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & \left(x_{4}a+z_{4}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{4}b \, \mathbf{\hat{y}} + z_{4}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Ca IV} \\ \mathbf{B}_{8} & = & x_{4} \, \mathbf{a}_{1}-y_{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta +x_{4}a + z_{4}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{4}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Ca IV} \\ \mathbf{B}_{9} & = & x_{5} \, \mathbf{a}_{1} + y_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & \left(x_{5}a+z_{5}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{5}b \, \mathbf{\hat{y}} + z_{5}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Ca V} \\ \mathbf{B}_{10} & = & x_{5} \, \mathbf{a}_{1}-y_{5} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta +x_{5}a + z_{5}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{5}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{5}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Ca V} \\ \mathbf{B}_{11} & = & x_{6} \, \mathbf{a}_{1} + y_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & \left(x_{6}a+z_{6}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{6}b \, \mathbf{\hat{y}} + z_{6}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Ca VI} \\ \mathbf{B}_{12} & = & x_{6} \, \mathbf{a}_{1}-y_{6} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta +x_{6}a + z_{6}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{6}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{6}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Ca VI} \\ \mathbf{B}_{13} & = & x_{7} \, \mathbf{a}_{1} + y_{7} \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & \left(x_{7}a+z_{7}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{7}b \, \mathbf{\hat{y}} + z_{7}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Na I} \\ \mathbf{B}_{14} & = & x_{7} \, \mathbf{a}_{1}-y_{7} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{7}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta +x_{7}a + z_{7}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{7}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{7}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Na I} \\ \mathbf{B}_{15} & = & x_{8} \, \mathbf{a}_{1} + y_{8} \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & \left(x_{8}a+z_{8}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{8}b \, \mathbf{\hat{y}} + z_{8}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Na II} \\ \mathbf{B}_{16} & = & x_{8} \, \mathbf{a}_{1}-y_{8} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{8}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta +x_{8}a + z_{8}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{8}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{8}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Na II} \\ \mathbf{B}_{17} & = & x_{9} \, \mathbf{a}_{1} + y_{9} \, \mathbf{a}_{2} + z_{9} \, \mathbf{a}_{3} & = & \left(x_{9}a+z_{9}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{9}b \, \mathbf{\hat{y}} + z_{9}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{O I} \\ \mathbf{B}_{18} & = & x_{9} \, \mathbf{a}_{1}-y_{9} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{9}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta +x_{9}a + z_{9}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{9}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{9}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{O I} \\ \mathbf{B}_{19} & = & x_{10} \, \mathbf{a}_{1} + y_{10} \, \mathbf{a}_{2} + z_{10} \, \mathbf{a}_{3} & = & \left(x_{10}a+z_{10}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{10}b \, \mathbf{\hat{y}} + z_{10}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{O II} \\ \mathbf{B}_{20} & = & x_{10} \, \mathbf{a}_{1}-y_{10} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{10}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta +x_{10}a + z_{10}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{10}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{10}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{O II} \\ \mathbf{B}_{21} & = & x_{11} \, \mathbf{a}_{1} + y_{11} \, \mathbf{a}_{2} + z_{11} \, \mathbf{a}_{3} & = & \left(x_{11}a+z_{11}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{11}b \, \mathbf{\hat{y}} + z_{11}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{O III} \\ \mathbf{B}_{22} & = & x_{11} \, \mathbf{a}_{1}-y_{11} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{11}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta +x_{11}a + z_{11}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{11}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{11}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{O III} \\ \mathbf{B}_{23} & = & x_{12} \, \mathbf{a}_{1} + y_{12} \, \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(2a\right) & \mbox{O IV} \\ \mathbf{B}_{24} & = & x_{12} \, \mathbf{a}_{1}-y_{12} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{12}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta +x_{12}a + z_{12}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{12}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{12}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{O IV} \\ \mathbf{B}_{25} & = & x_{13} \, \mathbf{a}_{1} + y_{13} \, \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(2a\right) & \mbox{O V} \\ \mathbf{B}_{26} & = & x_{13} \, \mathbf{a}_{1}-y_{13} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{13}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta +x_{13}a + z_{13}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{13}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{13}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{O V} \\ \mathbf{B}_{27} & = & x_{14} \, \mathbf{a}_{1} + y_{14} \, \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(2a\right) & \mbox{O VI} \\ \mathbf{B}_{28} & = & x_{14} \, \mathbf{a}_{1}-y_{14} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{14}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta +x_{14}a + z_{14}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{14}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{14}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{O VI} \\ \mathbf{B}_{29} & = & x_{15} \, \mathbf{a}_{1} + y_{15} \, \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(2a\right) & \mbox{O VII} \\ \mathbf{B}_{30} & = & x_{15} \, \mathbf{a}_{1}-y_{15} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{15}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta +x_{15}a + z_{15}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{15}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{15}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{O VII} \\ \mathbf{B}_{31} & = & x_{16} \, \mathbf{a}_{1} + y_{16} \, \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(2a\right) & \mbox{O VIII} \\ \mathbf{B}_{32} & = & x_{16} \, \mathbf{a}_{1}-y_{16} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{16}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta +x_{16}a + z_{16}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{16}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{16}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{O VIII} \\ \mathbf{B}_{33} & = & x_{17} \, \mathbf{a}_{1} + y_{17} \, \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(2a\right) & \mbox{O IX} \\ \mathbf{B}_{34} & = & x_{17} \, \mathbf{a}_{1}-y_{17} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{17}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta +x_{17}a + z_{17}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{17}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{17}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{O IX} \\ \mathbf{B}_{35} & = & x_{18} \, \mathbf{a}_{1} + y_{18} \, \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(2a\right) & \mbox{O X} \\ \mathbf{B}_{36} & = & x_{18} \, \mathbf{a}_{1}-y_{18} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{18}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta +x_{18}a + z_{18}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{18}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{18}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{O X} \\ \mathbf{B}_{37} & = & x_{19} \, \mathbf{a}_{1} + y_{19} \, \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(2a\right) & \mbox{O XI} \\ \mathbf{B}_{38} & = & x_{19} \, \mathbf{a}_{1}-y_{19} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{19}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta +x_{19}a + z_{19}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{19}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{19}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{O XI} \\ \mathbf{B}_{39} & = & x_{20} \, \mathbf{a}_{1} + y_{20} \, \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(2a\right) & \mbox{O XII} \\ \mathbf{B}_{40} & = & x_{20} \, \mathbf{a}_{1}-y_{20} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{20}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta +x_{20}a + z_{20}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{20}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{20}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{O XII} \\ \mathbf{B}_{41} & = & x_{21} \, \mathbf{a}_{1} + y_{21} \, \mathbf{a}_{2} + z_{21} \, \mathbf{a}_{3} & = & \left(x_{21}a+z_{21}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{21}b \, \mathbf{\hat{y}} + z_{21}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{O XIII} \\ \mathbf{B}_{42} & = & x_{21} \, \mathbf{a}_{1}-y_{21} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{21}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta +x_{21}a + z_{21}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{21}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{21}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{O XIII} \\ \mathbf{B}_{43} & = & x_{22} \, \mathbf{a}_{1} + y_{22} \, \mathbf{a}_{2} + z_{22} \, \mathbf{a}_{3} & = & \left(x_{22}a+z_{22}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{22}b \, \mathbf{\hat{y}} + z_{22}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{O XIV} \\ \mathbf{B}_{44} & = & x_{22} \, \mathbf{a}_{1}-y_{22} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{22}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta +x_{22}a + z_{22}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{22}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{22}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{O XIV} \\ \mathbf{B}_{45} & = & x_{23} \, \mathbf{a}_{1} + y_{23} \, \mathbf{a}_{2} + z_{23} \, \mathbf{a}_{3} & = & \left(x_{23}a+z_{23}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{23}b \, \mathbf{\hat{y}} + z_{23}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{O XV} \\ \mathbf{B}_{46} & = & x_{23} \, \mathbf{a}_{1}-y_{23} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{23}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta +x_{23}a + z_{23}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{23}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{23}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{O XV} \\ \mathbf{B}_{47} & = & x_{24} \, \mathbf{a}_{1} + y_{24} \, \mathbf{a}_{2} + z_{24} \, \mathbf{a}_{3} & = & \left(x_{24}a+z_{24}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{24}b \, \mathbf{\hat{y}} + z_{24}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Si I} \\ \mathbf{B}_{48} & = & x_{24} \, \mathbf{a}_{1}-y_{24} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{24}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta +x_{24}a + z_{24}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{24}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{24}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Si I} \\ \mathbf{B}_{49} & = & x_{25} \, \mathbf{a}_{1} + y_{25} \, \mathbf{a}_{2} + z_{25} \, \mathbf{a}_{3} & = & \left(x_{25}a+z_{25}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{25}b \, \mathbf{\hat{y}} + z_{25}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Si II} \\ \mathbf{B}_{50} & = & x_{25} \, \mathbf{a}_{1}-y_{25} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{25}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta +x_{25}a + z_{25}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{25}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{25}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Si II} \\ \mathbf{B}_{51} & = & x_{26} \, \mathbf{a}_{1} + y_{26} \, \mathbf{a}_{2} + z_{26} \, \mathbf{a}_{3} & = & \left(x_{26}a+z_{26}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{26}b \, \mathbf{\hat{y}} + z_{26}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Si III} \\ \mathbf{B}_{52} & = & x_{26} \, \mathbf{a}_{1}-y_{26} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{26}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta +x_{26}a + z_{26}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{26}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{26}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Si III} \\ \mathbf{B}_{53} & = & x_{27} \, \mathbf{a}_{1} + y_{27} \, \mathbf{a}_{2} + z_{27} \, \mathbf{a}_{3} & = & \left(x_{27}a+z_{27}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{27}b \, \mathbf{\hat{y}} + z_{27}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Si IV} \\ \mathbf{B}_{54} & = & x_{27} \, \mathbf{a}_{1}-y_{27} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{27}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}c\cos\beta +x_{27}a + z_{27}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{27}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{27}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Si IV} \\ \end{array} \]

References

  • V. Kahlenberg and M. Maier, On the existence of a high–temperature polymorph of Na2Ca6Si4O15–implications for the phase equilibria in the system Na2O–CaO–SiO2, Mineral. Petrol. 110, 905–915 (2016), doi:10.1007/s00710-016-0447-1.

Geometry files


Prototype Generator

aflow --proto=A6B2C15D4_mP54_7_6a_2a_15a_4a --params=

Species:

Running:

Output: