Albite (NaAlSi3O8, $S6_{8}$) Structure : ABC8D3_aP26_2_i_i_8i_3i

Picture of Structure; Click for Big Picture
Prototype : AlNaO8Si3
AFLOW prototype label : ABC8D3_aP26_2_i_i_8i_3i
Strukturbericht designation : $S6_{8}$
Pearson symbol : aP26
Space group number : 2
Space group symbol : $P\bar{1}$
AFLOW prototype command : aflow --proto=ABC8D3_aP26_2_i_i_8i_3i
--params=
$a$,$b/a$,$c/a$,$\alpha$,$\beta$,$\gamma$,$x_{1}$,$y_{1}$,$z_{1}$,$x_{2}$,$y_{2}$,$z_{2}$,$x_{3}$,$y_{3}$,$z_{3}$,$x_{4}$,$y_{4}$,$z_{4}$,$x_{5}$,$y_{5}$,$z_{5}$,$x_{6}$,$y_{6}$,$z_{6}$,$x_{7}$,$y_{7}$,$z_{7}$,$x_{8}$,$y_{8}$,$z_{8}$,$x_{9}$,$y_{9}$,$z_{9}$,$x_{10}$,$y_{10}$,$z_{10}$,$x_{11}$,$y_{11}$,$z_{11}$,$x_{12}$,$y_{12}$,$z_{12}$,$x_{13}$,$y_{13}$,$z_{13}$


  • We used the 13 K data from (Smith, 1986), however they present their data in space group $C\overline{1}$, which doubles the primitive unit cell compared to the standard space group $P\overline{1}$ #2. We used FINDSYM to convert from the presented cell to the conventional cell. This involved a rotation of the cell, e.g., the original $c$ axis is the $a$ axis in our standard primitive cell.
  • Technically this is low albite. In high albite the silicon and aluminum atoms are mixed over all four sites, as in sandine ($S6_{7}$). Indeed, under some conditions albite crystals are seen in the sandine structure (Winter, 1979). See the albite entry in (Downs, 2003) for other experimental work.

Triclinic primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & a \mathbf{\hat{x}} \\ \mathbf{a}_2 & = & b \cos\gamma \, \mathbf{\hat{x}} + b \sin\gamma \,\mathbf{\hat{y}} \\ \mathbf{a}_3 & = & c_x \mathbf{\hat{x}} + c_y \, \mathbf{\hat{y}} + c_z \, \mathbf{\hat{z}}\\\\ c_x & = & c \, \cos\beta \\ c_y & = & c \, (\cos\alpha -\cos\beta \cos\gamma)/\sin\gamma \\ c_z & = & \sqrt{c^2-c_x^2-c_y^2} \end{array} \]

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+y_{1}b\cos\gamma+z_{1}c_{x}\right) \, \mathbf{\hat{x}} + \left(y_{1}b\sin\gamma+z_{1}c_{y}\right) \, \mathbf{\hat{y}} + z_{1}c_{z} \, \mathbf{\hat{z}} & \left(2i\right) & \mbox{Al} \\ \mathbf{B}_{2} & = & -x_{1} \, \mathbf{a}_{1}-y_{1} \, \mathbf{a}_{2}-z_{1} \, \mathbf{a}_{3} & = & \left(-x_{1}a-y_{1}b\cos\gamma-z_{1}c_{x}\right) \, \mathbf{\hat{x}} + \left(-y_{1}b\sin\gamma-z_{1}c_{y}\right) \, \mathbf{\hat{y}}-z_{1}c_{z} \, \mathbf{\hat{z}} & \left(2i\right) & \mbox{Al} \\ \mathbf{B}_{3} & = & x_{2} \, \mathbf{a}_{1} + y_{2} \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3} & = & \left(x_{2}a+y_{2}b\cos\gamma+z_{2}c_{x}\right) \, \mathbf{\hat{x}} + \left(y_{2}b\sin\gamma+z_{2}c_{y}\right) \, \mathbf{\hat{y}} + z_{2}c_{z} \, \mathbf{\hat{z}} & \left(2i\right) & \mbox{Na} \\ \mathbf{B}_{4} & = & -x_{2} \, \mathbf{a}_{1}-y_{2} \, \mathbf{a}_{2}-z_{2} \, \mathbf{a}_{3} & = & \left(-x_{2}a-y_{2}b\cos\gamma-z_{2}c_{x}\right) \, \mathbf{\hat{x}} + \left(-y_{2}b\sin\gamma-z_{2}c_{y}\right) \, \mathbf{\hat{y}}-z_{2}c_{z} \, \mathbf{\hat{z}} & \left(2i\right) & \mbox{Na} \\ \mathbf{B}_{5} & = & x_{3} \, \mathbf{a}_{1} + y_{3} \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3} & = & \left(x_{3}a+y_{3}b\cos\gamma+z_{3}c_{x}\right) \, \mathbf{\hat{x}} + \left(y_{3}b\sin\gamma+z_{3}c_{y}\right) \, \mathbf{\hat{y}} + z_{3}c_{z} \, \mathbf{\hat{z}} & \left(2i\right) & \mbox{O I} \\ \mathbf{B}_{6} & = & -x_{3} \, \mathbf{a}_{1}-y_{3} \, \mathbf{a}_{2}-z_{3} \, \mathbf{a}_{3} & = & \left(-x_{3}a-y_{3}b\cos\gamma-z_{3}c_{x}\right) \, \mathbf{\hat{x}} + \left(-y_{3}b\sin\gamma-z_{3}c_{y}\right) \, \mathbf{\hat{y}}-z_{3}c_{z} \, \mathbf{\hat{z}} & \left(2i\right) & \mbox{O I} \\ \mathbf{B}_{7} & = & x_{4} \, \mathbf{a}_{1} + y_{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & \left(x_{4}a+y_{4}b\cos\gamma+z_{4}c_{x}\right) \, \mathbf{\hat{x}} + \left(y_{4}b\sin\gamma+z_{4}c_{y}\right) \, \mathbf{\hat{y}} + z_{4}c_{z} \, \mathbf{\hat{z}} & \left(2i\right) & \mbox{O II} \\ \mathbf{B}_{8} & = & -x_{4} \, \mathbf{a}_{1}-y_{4} \, \mathbf{a}_{2}-z_{4} \, \mathbf{a}_{3} & = & \left(-x_{4}a-y_{4}b\cos\gamma-z_{4}c_{x}\right) \, \mathbf{\hat{x}} + \left(-y_{4}b\sin\gamma-z_{4}c_{y}\right) \, \mathbf{\hat{y}}-z_{4}c_{z} \, \mathbf{\hat{z}} & \left(2i\right) & \mbox{O II} \\ \mathbf{B}_{9} & = & x_{5} \, \mathbf{a}_{1} + y_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & \left(x_{5}a+y_{5}b\cos\gamma+z_{5}c_{x}\right) \, \mathbf{\hat{x}} + \left(y_{5}b\sin\gamma+z_{5}c_{y}\right) \, \mathbf{\hat{y}} + z_{5}c_{z} \, \mathbf{\hat{z}} & \left(2i\right) & \mbox{O III} \\ \mathbf{B}_{10} & = & -x_{5} \, \mathbf{a}_{1}-y_{5} \, \mathbf{a}_{2}-z_{5} \, \mathbf{a}_{3} & = & \left(-x_{5}a-y_{5}b\cos\gamma-z_{5}c_{x}\right) \, \mathbf{\hat{x}} + \left(-y_{5}b\sin\gamma-z_{5}c_{y}\right) \, \mathbf{\hat{y}}-z_{5}c_{z} \, \mathbf{\hat{z}} & \left(2i\right) & \mbox{O III} \\ \mathbf{B}_{11} & = & x_{6} \, \mathbf{a}_{1} + y_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & \left(x_{6}a+y_{6}b\cos\gamma+z_{6}c_{x}\right) \, \mathbf{\hat{x}} + \left(y_{6}b\sin\gamma+z_{6}c_{y}\right) \, \mathbf{\hat{y}} + z_{6}c_{z} \, \mathbf{\hat{z}} & \left(2i\right) & \mbox{O IV} \\ \mathbf{B}_{12} & = & -x_{6} \, \mathbf{a}_{1}-y_{6} \, \mathbf{a}_{2}-z_{6} \, \mathbf{a}_{3} & = & \left(-x_{6}a-y_{6}b\cos\gamma-z_{6}c_{x}\right) \, \mathbf{\hat{x}} + \left(-y_{6}b\sin\gamma-z_{6}c_{y}\right) \, \mathbf{\hat{y}}-z_{6}c_{z} \, \mathbf{\hat{z}} & \left(2i\right) & \mbox{O IV} \\ \mathbf{B}_{13} & = & x_{7} \, \mathbf{a}_{1} + y_{7} \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & \left(x_{7}a+y_{7}b\cos\gamma+z_{7}c_{x}\right) \, \mathbf{\hat{x}} + \left(y_{7}b\sin\gamma+z_{7}c_{y}\right) \, \mathbf{\hat{y}} + z_{7}c_{z} \, \mathbf{\hat{z}} & \left(2i\right) & \mbox{O V} \\ \mathbf{B}_{14} & = & -x_{7} \, \mathbf{a}_{1}-y_{7} \, \mathbf{a}_{2}-z_{7} \, \mathbf{a}_{3} & = & \left(-x_{7}a-y_{7}b\cos\gamma-z_{7}c_{x}\right) \, \mathbf{\hat{x}} + \left(-y_{7}b\sin\gamma-z_{7}c_{y}\right) \, \mathbf{\hat{y}}-z_{7}c_{z} \, \mathbf{\hat{z}} & \left(2i\right) & \mbox{O V} \\ \mathbf{B}_{15} & = & x_{8} \, \mathbf{a}_{1} + y_{8} \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & \left(x_{8}a+y_{8}b\cos\gamma+z_{8}c_{x}\right) \, \mathbf{\hat{x}} + \left(y_{8}b\sin\gamma+z_{8}c_{y}\right) \, \mathbf{\hat{y}} + z_{8}c_{z} \, \mathbf{\hat{z}} & \left(2i\right) & \mbox{O VI} \\ \mathbf{B}_{16} & = & -x_{8} \, \mathbf{a}_{1}-y_{8} \, \mathbf{a}_{2}-z_{8} \, \mathbf{a}_{3} & = & \left(-x_{8}a-y_{8}b\cos\gamma-z_{8}c_{x}\right) \, \mathbf{\hat{x}} + \left(-y_{8}b\sin\gamma-z_{8}c_{y}\right) \, \mathbf{\hat{y}}-z_{8}c_{z} \, \mathbf{\hat{z}} & \left(2i\right) & \mbox{O VI} \\ \mathbf{B}_{17} & = & x_{9} \, \mathbf{a}_{1} + y_{9} \, \mathbf{a}_{2} + z_{9} \, \mathbf{a}_{3} & = & \left(x_{9}a+y_{9}b\cos\gamma+z_{9}c_{x}\right) \, \mathbf{\hat{x}} + \left(y_{9}b\sin\gamma+z_{9}c_{y}\right) \, \mathbf{\hat{y}} + z_{9}c_{z} \, \mathbf{\hat{z}} & \left(2i\right) & \mbox{O VII} \\ \mathbf{B}_{18} & = & -x_{9} \, \mathbf{a}_{1}-y_{9} \, \mathbf{a}_{2}-z_{9} \, \mathbf{a}_{3} & = & \left(-x_{9}a-y_{9}b\cos\gamma-z_{9}c_{x}\right) \, \mathbf{\hat{x}} + \left(-y_{9}b\sin\gamma-z_{9}c_{y}\right) \, \mathbf{\hat{y}}-z_{9}c_{z} \, \mathbf{\hat{z}} & \left(2i\right) & \mbox{O VII} \\ \mathbf{B}_{19} & = & x_{10} \, \mathbf{a}_{1} + y_{10} \, \mathbf{a}_{2} + z_{10} \, \mathbf{a}_{3} & = & \left(x_{10}a+y_{10}b\cos\gamma+z_{10}c_{x}\right) \, \mathbf{\hat{x}} + \left(y_{10}b\sin\gamma+z_{10}c_{y}\right) \, \mathbf{\hat{y}} + z_{10}c_{z} \, \mathbf{\hat{z}} & \left(2i\right) & \mbox{O VIII} \\ \mathbf{B}_{20} & = & -x_{10} \, \mathbf{a}_{1}-y_{10} \, \mathbf{a}_{2}-z_{10} \, \mathbf{a}_{3} & = & \left(-x_{10}a-y_{10}b\cos\gamma-z_{10}c_{x}\right) \, \mathbf{\hat{x}} + \left(-y_{10}b\sin\gamma-z_{10}c_{y}\right) \, \mathbf{\hat{y}}-z_{10}c_{z} \, \mathbf{\hat{z}} & \left(2i\right) & \mbox{O VIII} \\ \mathbf{B}_{21} & = & x_{11} \, \mathbf{a}_{1} + y_{11} \, \mathbf{a}_{2} + z_{11} \, \mathbf{a}_{3} & = & \left(x_{11}a+y_{11}b\cos\gamma+z_{11}c_{x}\right) \, \mathbf{\hat{x}} + \left(y_{11}b\sin\gamma+z_{11}c_{y}\right) \, \mathbf{\hat{y}} + z_{11}c_{z} \, \mathbf{\hat{z}} & \left(2i\right) & \mbox{Si I} \\ \mathbf{B}_{22} & = & -x_{11} \, \mathbf{a}_{1}-y_{11} \, \mathbf{a}_{2}-z_{11} \, \mathbf{a}_{3} & = & \left(-x_{11}a-y_{11}b\cos\gamma-z_{11}c_{x}\right) \, \mathbf{\hat{x}} + \left(-y_{11}b\sin\gamma-z_{11}c_{y}\right) \, \mathbf{\hat{y}}-z_{11}c_{z} \, \mathbf{\hat{z}} & \left(2i\right) & \mbox{Si I} \\ \mathbf{B}_{23} & = & x_{12} \, \mathbf{a}_{1} + y_{12} \, \mathbf{a}_{2} + z_{12} \, \mathbf{a}_{3} & = & \left(x_{12}a+y_{12}b\cos\gamma+z_{12}c_{x}\right) \, \mathbf{\hat{x}} + \left(y_{12}b\sin\gamma+z_{12}c_{y}\right) \, \mathbf{\hat{y}} + z_{12}c_{z} \, \mathbf{\hat{z}} & \left(2i\right) & \mbox{Si II} \\ \mathbf{B}_{24} & = & -x_{12} \, \mathbf{a}_{1}-y_{12} \, \mathbf{a}_{2}-z_{12} \, \mathbf{a}_{3} & = & \left(-x_{12}a-y_{12}b\cos\gamma-z_{12}c_{x}\right) \, \mathbf{\hat{x}} + \left(-y_{12}b\sin\gamma-z_{12}c_{y}\right) \, \mathbf{\hat{y}}-z_{12}c_{z} \, \mathbf{\hat{z}} & \left(2i\right) & \mbox{Si II} \\ \mathbf{B}_{25} & = & x_{13} \, \mathbf{a}_{1} + y_{13} \, \mathbf{a}_{2} + z_{13} \, \mathbf{a}_{3} & = & \left(x_{13}a+y_{13}b\cos\gamma+z_{13}c_{x}\right) \, \mathbf{\hat{x}} + \left(y_{13}b\sin\gamma+z_{13}c_{y}\right) \, \mathbf{\hat{y}} + z_{13}c_{z} \, \mathbf{\hat{z}} & \left(2i\right) & \mbox{Si III} \\ \mathbf{B}_{26} & = & -x_{13} \, \mathbf{a}_{1}-y_{13} \, \mathbf{a}_{2}-z_{13} \, \mathbf{a}_{3} & = & \left(-x_{13}a-y_{13}b\cos\gamma-z_{13}c_{x}\right) \, \mathbf{\hat{x}} + \left(-y_{13}b\sin\gamma-z_{13}c_{y}\right) \, \mathbf{\hat{y}}-z_{13}c_{z} \, \mathbf{\hat{z}} & \left(2i\right) & \mbox{Si III} \\ \end{array} \]

References

  • J. V. Smith, G. Artioli, and Å. Kvick, Low albite, NaAlSi3O8: Neutron diffraction study of crystal structure at 13 K, Am. Mineral. 71, 727–733 (1986).
  • R. T. Downs and M. Hall–Wallace, The American Mineralogist Crystal Structure Database, Am. Mineral. 88, 247–250 (2003).
  • J. K. Winter, F. P. Okamura, and S. Ghose, A high–temperature structural study of high albite, monalbite, and the analbite $\rightarrow$ monalbite phase transition, Am. Mineral. 64, 409–423 (1979).

Geometry files


Prototype Generator

aflow --proto=ABC8D3_aP26_2_i_i_8i_3i --params=

Species:

Running:

Output: