Esseneite (CaFeSi$_{2}$O$_{6}$) Structure: ABC6D2_mC40_15_e_e_3f_f

Picture of Structure; Click for Big Picture
Prototype : CaFeO6Si2
AFLOW prototype label : ABC6D2_mC40_15_e_e_3f_f
Strukturbericht designation : None
Pearson symbol : mC40
Space group number : 15
Space group symbol : $\mbox{C2/c}$
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

  • CaFeSi2O6 (hedenbergite), CaFeSi2O6 (hedenbergite), CaMgSi2O6 (diopside), CaMnGe2O6, CaMnSi2O6 (johannsenite), CaMnSi2O6 (johannsenite), CaScSi2O6 (davisite), CaTiSi2O6 (grossmanite), CaVSi2O6 (burnettite), LiAlSi2O6 (spodumene), NaAlSi2O6 (jadeite), NaCrSi2O6 (ureyite), NaFeSi2O6 (acmite/aegirine), and NaScSi2O6 (jervisite)

  • Named for University of Michigan geologist Eric Essene (1939-2010). (Cosca, 1987) gives the composition as (Ca0.97Fe0.03)(Fe0.58Al0.42)O6(Si0.54Al0.46)2. We will use the majority atom at each site to draw the structure. Esseneite is one of the class of “clinopyroxene” materials, composition $XY$Si$_{2}$O$_{6}$, where in general $X$ is an alkaline or alkaline earth metal and $Y$ is a transition metal. In addition, the silicon may be partially or wholly replaced by another element. Clinopyroxenes are in the space group $C2/c$ #15, distinguishing them from orthopyroxenes, which are in space group $Pbca$ #61 and the atoms $X$ and $Y$ are both small radius cations. Most of the structures listed are stable at room temperature and above.

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} + \frac14 \, \mathbf{a}_{3}& = &\frac14 \, c \, \cos\beta \, \mathbf{\hat{x}}+ y_{1} \, b \, \mathbf{\hat{y}}+ \frac14 \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4e\right) & \mbox{Ca} \\ \mathbf{B}_{2} & =& y_{1} \, \mathbf{a}_{1} - y_{1} \, \mathbf{a}_{2} + \frac34 \, \mathbf{a}_{3}& = &\frac34 \, c \, \cos\beta \, \mathbf{\hat{x}}- y_{1} \, b \, \mathbf{\hat{y}}+ \frac34 \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4e\right) & \mbox{Ca} \\ \mathbf{B}_{3} & =& - y_{2} \, \mathbf{a}_{1} + y_{2} \, \mathbf{a}_{2} + \frac14 \, \mathbf{a}_{3}& = &\frac14 \, c \, \cos\beta \, \mathbf{\hat{x}}+ y_{2} \, b \, \mathbf{\hat{y}}+ \frac14 \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4e\right) & \mbox{Fe} \\ \mathbf{B}_{4} & =& y_{2} \, \mathbf{a}_{1} - y_{2} \, \mathbf{a}_{2} + \frac34 \, \mathbf{a}_{3}& = &\frac34 \, c \, \cos\beta \, \mathbf{\hat{x}}- y_{2} \, b \, \mathbf{\hat{y}}+ \frac34 \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4e\right) & \mbox{Fe} \\ \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(y_{3} - x_{3}\right) \, \mathbf{a}_{2}+ \left(\frac12 - z_{3}\right) \, \mathbf{a}_{3}& = &\left( - x_{3} \, a + \left(\frac12 - z_{3}\right) \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{3} \, b \, \mathbf{\hat{y}}+ \left(\frac12 - z_{3}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(8f\right) & \mbox{O I} \\ \mathbf{B}_{7} & =&\left(y_{3} - x_{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(\frac12 + z_{3}\right) \, \mathbf{a}_{3}& = &\left(x_{3} \, a + \left(\frac12 + z_{3}\right) \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- y_{3} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + 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(y_{4} - x_{4}\right) \, \mathbf{a}_{2}+ \left(\frac12 - z_{4}\right) \, \mathbf{a}_{3}& = &\left( - x_{4} \, a + \left(\frac12 - z_{4}\right) \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{4} \, b \, \mathbf{\hat{y}}+ \left(\frac12 - z_{4}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(8f\right) & \mbox{O II} \\ \mathbf{B}_{11} & =&\left(y_{4} - x_{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(\frac12 + z_{4}\right) \, \mathbf{a}_{3}& = &\left(x_{4} \, a + \left(\frac12 + z_{4}\right) \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- y_{4} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + 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(y_{5} - x_{5}\right) \, \mathbf{a}_{2}+ \left(\frac12 - z_{5}\right) \, \mathbf{a}_{3}& = &\left( - x_{5} \, a + \left(\frac12 - z_{5}\right) \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{5} \, b \, \mathbf{\hat{y}}+ \left(\frac12 - z_{5}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(8f\right) & \mbox{O III} \\ \mathbf{B}_{15} & =&\left(y_{5} - x_{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(\frac12 + z_{5}\right) \, \mathbf{a}_{3}& = &\left(x_{5} \, a + \left(\frac12 + z_{5}\right) \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- y_{5} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + 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(y_{6} - x_{6}\right) \, \mathbf{a}_{2}+ \left(\frac12 - z_{6}\right) \, \mathbf{a}_{3}& = &\left( - x_{6} \, a + \left(\frac12 - z_{6}\right) \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{6} \, b \, \mathbf{\hat{y}}+ \left(\frac12 - z_{6}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(8f\right) & \mbox{Si} \\ \mathbf{B}_{19} & =&\left(y_{6} - x_{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(\frac12 + z_{6}\right) \, \mathbf{a}_{3}& = &\left(x_{6} \, a + \left(\frac12 + z_{6}\right) \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- y_{6} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{6}\right) \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(8f\right) & \mbox{Si} \\ \end{array} \]

References

  • M. A. Cosca and D. R. Peacor, Chemistry and structure of esseneite (CaFe3+AlSiO6), a new pyroxene produced by pyrometamorphism, Am. Mineral. 72, 148–156 (1987).

Geometry files


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