$\gamma$–Y2Si2O7 Structure : A4BC_mP24_14_4e_e_e

Picture of Structure; Click for Big Picture
Prototype : O7Si2Y2
AFLOW prototype label : A4BC_mP24_14_4e_e_e
Strukturbericht designation : None
Pearson symbol : mP24
Space group number : 14
Space group symbol : $P2_{1}/c$
AFLOW prototype command : aflow --proto=A4BC_mP24_14_4e_e_e
--params=
$a$,$b/a$,$c/a$,$\beta$,$x_{1}$,$y_{1}$,$z_{1}$,$x_{2}$,$y_{2}$,$z_{2}$,$x_{3}$,$y_{3}$,$z_{3}$,$x_{4}$,$y_{4}$,$z_{4}$,$x_{5}$,$y_{5}$,$z_{5}$,$x_{6}$,$y_{6}$,$z_{6}$


Other compounds with this structure

  • $\gamma$–Er2Si2O7 and $\gamma$–Ho2Si2O7

  • The O–III site is only 50% occupied. The Jmol image shows the two possible sites as a pair of very closely spaced oxygen atoms.
  • (Christensen, 1997) refer to this as $D$–Y2Si2O7, but we follow the classification of the $RE$2Si2O7 structures in (Becerro, 2004) and refer to this as $\gamma$–Y2Si2O7.

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(4e\right) & \mbox{O I} \\ \mathbf{B}_{2} & = & -x_{1} \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{1}\right) \, \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}} + \left(\frac{1}{2} +y_{1}\right)b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{1}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{O I} \\ \mathbf{B}_{3} & = & -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(4e\right) & \mbox{O I} \\ \mathbf{B}_{4} & = & x_{1} \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{1}\right) \, \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}} + \left(\frac{1}{2}-y_{1}\right)b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{1}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{O I} \\ \mathbf{B}_{5} & = & 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(4e\right) & \mbox{O II} \\ \mathbf{B}_{6} & = & -x_{2} \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{2}\right) \, \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}} + \left(\frac{1}{2} +y_{2}\right)b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{2}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{O II} \\ \mathbf{B}_{7} & = & -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(4e\right) & \mbox{O II} \\ \mathbf{B}_{8} & = & x_{2} \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{2}\right) \, \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}} + \left(\frac{1}{2}-y_{2}\right)b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{2}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{O II} \\ \mathbf{B}_{9} & = & 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(4e\right) & \mbox{O III} \\ \mathbf{B}_{10} & = & -x_{3} \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{3}\right) \, \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}} + \left(\frac{1}{2} +y_{3}\right)b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{3}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{O III} \\ \mathbf{B}_{11} & = & -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(4e\right) & \mbox{O III} \\ \mathbf{B}_{12} & = & x_{3} \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{3}\right) \, \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}} + \left(\frac{1}{2}-y_{3}\right)b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{3}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{O III} \\ \mathbf{B}_{13} & = & 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(4e\right) & \mbox{O IV} \\ \mathbf{B}_{14} & = & -x_{4} \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{4}\right) \, \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}} + \left(\frac{1}{2} +y_{4}\right)b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{4}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{O IV} \\ \mathbf{B}_{15} & = & -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(4e\right) & \mbox{O IV} \\ \mathbf{B}_{16} & = & x_{4} \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{4}\right) \, \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}} + \left(\frac{1}{2}-y_{4}\right)b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{4}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{O IV} \\ \mathbf{B}_{17} & = & 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(4e\right) & \mbox{Si} \\ \mathbf{B}_{18} & = & -x_{5} \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{5}\right) \, \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}} + \left(\frac{1}{2} +y_{5}\right)b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{5}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{Si} \\ \mathbf{B}_{19} & = & -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(4e\right) & \mbox{Si} \\ \mathbf{B}_{20} & = & x_{5} \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{5}\right) \, \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}} + \left(\frac{1}{2}-y_{5}\right)b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{5}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{Si} \\ \mathbf{B}_{21} & = & 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(4e\right) & \mbox{Y} \\ \mathbf{B}_{22} & = & -x_{6} \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{6}\right) \, \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}} + \left(\frac{1}{2} +y_{6}\right)b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{6}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{Y} \\ \mathbf{B}_{23} & = & -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(4e\right) & \mbox{Y} \\ \mathbf{B}_{24} & = & x_{6} \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{6}\right) \, \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}} + \left(\frac{1}{2}-y_{6}\right)b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{6}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{Y} \\ \end{array} \]

References

  • A. N. Christensen, R. G. Hazell, and A. W. Hewat, Synthesis, Crystal Growth and Structure Investigations of Rare–Earth Disilicates and Rare–Earth Oxyapatites, Acta Chem. Scand. 51, 37–43 (1997), doi:10.3891/acta.chem.scand.51-0037.

Found in

  • A. I. Becerro and A. Escudero, Revision of the crystallographic data of polymorphic Y2Si2O7 and Y2SiO5 compounds, Phase Transit. 77, 1093–1102 (2004), doi:10.1080/01411590412331282814.

Geometry files


Prototype Generator

aflow --proto=A4BC_mP24_14_4e_e_e --params=

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