Diopside [CaMg(SiO3)2, $S4_{1}$] Structure : ABC6D2_mC40_15_e_e_3f_f

Picture of Structure; Click for Big Picture
Prototype : CaMgO6Si2
AFLOW prototype label : ABC6D2_mC40_15_e_e_3f_f
Strukturbericht designation : $S4_{1}$
Pearson symbol : mC40
Space group number : 15
Space group symbol : $C2/c$
AFLOW prototype command : aflow --proto=ABC6D2_mC40_15_e_e_3f_f
--params=
$a$,$b/a$,$c/a$,$\beta$,$y_{1}$,$y_{2}$,$x_{3}$,$y_{3}$,$z_{3}$,$x_{4}$,$y_{4}$,$z_{4}$,$x_{5}$,$y_{5}$,$z_{5}$,$x_{6}$,$y_{6}$,$z_{6}$


Other compounds with this structure

  • (Ca,Na)(Mg,Fe,Al,Ti)(Si,Al)2O6 (augite)

  • (Finger, 1976) list the two ($4e$) positions as 'M1' and 'M2', and both are mixtures of calcium and magnesium. For visual clarity we desigated the first ($4e$) position as calcium and the second as magnesium.
  • This structure has the same AFLOW label as Esseneite. The structures are generated by the same symmetry operations with different sets of parameters (\texttt––params) specified in their corresponding CIF files.

Base-centered Monoclinic primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{x}} - \frac12 \, b \, \mathbf{\hat{y}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, b \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & c \cos\beta \, \mathbf{\hat{x}} + c \sin\beta \, \mathbf{\hat{z}} \\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & -y_{1} \, \mathbf{a}_{1} + y_{1} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}c\cos\beta \, \mathbf{\hat{x}} + y_{1}b \, \mathbf{\hat{y}} + \frac{1}{4}c\sin\beta \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{Ca} \\ \mathbf{B}_{2} & = & y_{1} \, \mathbf{a}_{1}-y_{1} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{3}{4}c\cos\beta \, \mathbf{\hat{x}}-y_{1}b \, \mathbf{\hat{y}} + \frac{3}{4}c\sin\beta \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{Ca} \\ \mathbf{B}_{3} & = & -y_{2} \, \mathbf{a}_{1} + y_{2} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}c\cos\beta \, \mathbf{\hat{x}} + y_{2}b \, \mathbf{\hat{y}} + \frac{1}{4}c\sin\beta \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{Mg} \\ \mathbf{B}_{4} & = & y_{2} \, \mathbf{a}_{1}-y_{2} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{3}{4}c\cos\beta \, \mathbf{\hat{x}}-y_{2}b \, \mathbf{\hat{y}} + \frac{3}{4}c\sin\beta \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{Mg} \\ \mathbf{B}_{5} & = & \left(x_{3}-y_{3}\right) \, \mathbf{a}_{1} + \left(x_{3}+y_{3}\right) \, \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(8f\right) & \mbox{O I} \\ \mathbf{B}_{6} & = & \left(-x_{3}-y_{3}\right) \, \mathbf{a}_{1} + \left(-x_{3}+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}} + y_{3}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{3}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{O I} \\ \mathbf{B}_{7} & = & \left(-x_{3}+y_{3}\right) \, \mathbf{a}_{1} + \left(-x_{3}-y_{3}\right) \, \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(8f\right) & \mbox{O I} \\ \mathbf{B}_{8} & = & \left(x_{3}+y_{3}\right) \, \mathbf{a}_{1} + \left(x_{3}-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}}-y_{3}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{3}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{O I} \\ \mathbf{B}_{9} & = & \left(x_{4}-y_{4}\right) \, \mathbf{a}_{1} + \left(x_{4}+y_{4}\right) \, \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(8f\right) & \mbox{O II} \\ \mathbf{B}_{10} & = & \left(-x_{4}-y_{4}\right) \, \mathbf{a}_{1} + \left(-x_{4}+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}} + y_{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{4}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{O II} \\ \mathbf{B}_{11} & = & \left(-x_{4}+y_{4}\right) \, \mathbf{a}_{1} + \left(-x_{4}-y_{4}\right) \, \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(8f\right) & \mbox{O II} \\ \mathbf{B}_{12} & = & \left(x_{4}+y_{4}\right) \, \mathbf{a}_{1} + \left(x_{4}-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}}-y_{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{4}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{O II} \\ \mathbf{B}_{13} & = & \left(x_{5}-y_{5}\right) \, \mathbf{a}_{1} + \left(x_{5}+y_{5}\right) \, \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(8f\right) & \mbox{O III} \\ \mathbf{B}_{14} & = & \left(-x_{5}-y_{5}\right) \, \mathbf{a}_{1} + \left(-x_{5}+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}} + y_{5}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{5}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{O III} \\ \mathbf{B}_{15} & = & \left(-x_{5}+y_{5}\right) \, \mathbf{a}_{1} + \left(-x_{5}-y_{5}\right) \, \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(8f\right) & \mbox{O III} \\ \mathbf{B}_{16} & = & \left(x_{5}+y_{5}\right) \, \mathbf{a}_{1} + \left(x_{5}-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}}-y_{5}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{5}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{O III} \\ \mathbf{B}_{17} & = & \left(x_{6}-y_{6}\right) \, \mathbf{a}_{1} + \left(x_{6}+y_{6}\right) \, \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(8f\right) & \mbox{Si} \\ \mathbf{B}_{18} & = & \left(-x_{6}-y_{6}\right) \, \mathbf{a}_{1} + \left(-x_{6}+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}} + y_{6}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{6}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{Si} \\ \mathbf{B}_{19} & = & \left(-x_{6}+y_{6}\right) \, \mathbf{a}_{1} + \left(-x_{6}-y_{6}\right) \, \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(8f\right) & \mbox{Si} \\ \mathbf{B}_{20} & = & \left(x_{6}+y_{6}\right) \, \mathbf{a}_{1} + \left(x_{6}-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}}-y_{6}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{6}\right)c\sin\beta \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{Si} \\ \end{array} \]

References

  • L. W. Finger and Y. Ohashi, The thermal expansion of diopside to 800°C and a refinement of the crystal structure at 700°C, Am. Mineral. 61, 303–310 (1976).

Geometry files


Prototype Generator

aflow --proto=ABC6D2_mC40_15_e_e_3f_f --params=

Species:

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