Calcite (CaCO3, $G0_{1}$) Structure: ABC3_hR10_167_a_b_e

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Prototype : CaCO3
AFLOW prototype label : ABC3_hR10_167_a_b_e
Strukturbericht designation : $G0_{1}$
Pearson symbol : hR10
Space group number : 167
Space group symbol : $\mbox{R}\bar{3}\mbox{c}$
AFLOW prototype command : aflow --proto=ABC3_hR10_167_a_b_e [--hex]
--params=
$a$,$c/a$,$x_{3}$


Other compounds with this structure

  • AlBO3, (Ca,Mn)CO3 (kutnohorite, rhodocrosite), CdCO3 (otavite), (Cd,Mg)CO3 (otavite), CoCO3 (spherocobaltite), CuCO3, FeCO3 (siderite), (La,Na)O3 (loparite), LaNiO3, MgCO3 (magnesite), MnCO3 (rhodochrosite), NaNO3 (nitratine), NiCO3 (gaspeite), ZnCO3 (smithsonite)

  • Strukturbericht Band I, (Ewald, 1931), 292-295, gives this the designation G1, but the index in Band II, (Hermann, 1937) lists this as G01. Note that paraelectric LiNbO_3 (ABC3_hR10_167_a_b_e, LiNbO3) and calcite (ABC3_hR10_167_a_b_e, CaCO3) have the same AFLOW prototype label. They are generated by the same symmetry operations with different sets of parameters (––params) specified in their corresponding CIF files. Hexagonal settings of this structure can be obtained with the option ––hex.

Rhombohedral primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & ~ \frac12 \, a \, \mathbf{\hat{x}} - \frac1{2\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13 \, c \, \mathbf{\hat{z}} \\ \mathbf{a}_2 & = & \frac1{\sqrt3} \, a \, \mathbf{\hat{y}} + \frac13 \, c \, \mathbf{\hat{z}} \\ \mathbf{a}_3 & = & - \frac12 \, a \, \mathbf{\hat{x}} - \frac1{2\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13 \, c \, \mathbf{\hat{z}} \\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & =& \frac14 \, \mathbf{a}_{1}+ \frac14 \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& =& \frac14 c \, \mathbf{\hat{z}}& \left(2a\right) & \mbox{C} \\ \mathbf{B}_{2} & =& \frac34 \, \mathbf{a}_{1}+ \frac34 \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& =& \frac34 c \, \mathbf{\hat{z}}& \left(2a\right) & \mbox{C} \\ \mathbf{B}_{3} & =&0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & =&0 \mathbf{\hat{x}} + 0 \mathbf{\hat{y}} + 0 \mathbf{\hat{z}} & \left(2b\right) & \mbox{Ca} \\ \mathbf{B}_{4} & =& \frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& =& \frac12 c \, \mathbf{\hat{z}}& \left(2b\right) & \mbox{Ca} \\ \mathbf{B}_{5} & =&x_{3} \, \mathbf{a}_{1}+ \left(\frac12 - x_{3}\right) \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& =&- \frac18 \left(1 - 4 x_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt{3}}{8} \left(1 - 4 x_{3}\right) \, a \mathbf{\hat{y}}+ \frac14 \, c \, \mathbf{\hat{z}}& \left(6e\right) & \mbox{O} \\ \mathbf{B}_{6} & =&\frac14 \, \mathbf{a}_{1}+ x_{3} \, \mathbf{a}_{2}+ \left(\frac12 - x_{3}\right) \, \mathbf{a}_{3}& =&- \frac18 \left(1 - 4 x_{3}\right) \, a \, \mathbf{\hat{x}}- \frac{\sqrt{3}}{8} \left(1 - 4 x_{3}\right) \, a \mathbf{\hat{y}}+ \frac14 \, c \, \mathbf{\hat{z}}& \left(6e\right) & \mbox{O} \\ \mathbf{B}_{7} & =&\left(\frac12 - x_{3}\right) \, \mathbf{a}_{1}+ \frac14 \, \mathbf{a}_{2}+ x_{3} \, \mathbf{a}_{3}& =&\frac14 \left(1 - 4 x_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac14 \, c \, \mathbf{\hat{z}}& \left(6e\right) & \mbox{O} \\ \mathbf{B}_{8} & =&- x_{3} \, \mathbf{a}_{1}+ \left(\frac12 + x_{3}\right) \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& =&- \frac18 \left(3 + 4 x_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac1{8\sqrt3} \left(1 + 12 x_{3}\right) \, a \mathbf{\hat{y}}+ \frac5{12} \, c \, \mathbf{\hat{z}}& \left(6e\right) & \mbox{O} \\ \mathbf{B}_{9} & =&\frac34 \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+ \left(\frac12 + x_{3}\right) \, \mathbf{a}_{3}& =&\frac18 \left(1 - 4 x_{3}\right) \, a \, \mathbf{\hat{x}}- \frac1{8\sqrt3} \left(5 + 12 x_{3}\right) \, a \mathbf{\hat{y}}+ \frac5{12} \, c \, \mathbf{\hat{z}}& \left(6e\right) & \mbox{O} \\ \mathbf{B}_{10} & =&\left(\frac12 + x_{3}\right) \, \mathbf{a}_{1}+ \frac34 \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}& =&\frac14 \left(1 + 4 x_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac1{2\sqrt3} \, a \mathbf{\hat{y}}+ \frac5{12} \, c \, \mathbf{\hat{z}}& \left(6e\right) & \mbox{O} \\ \end{array} \]

References

  • S. A. Markgraf and R. J. Reeder, High–temperature structure refinements of calcite and magnesite, Am. Mineral. 70, 590–600 (1985).
  • P. P. Ewald and C. Hermann, Strukturbericht Band I, 1913–1928 (Akademsiche Verlagsgesellschaft M. B. H., Leipzig, 1931).
  • C. Hermann, O. Lohrmann, and H. Philipp, Strukturbericht Band II, 1928–1932 (Akademsiche Verlagsgesellschaft M. B. H., Leipzig, 1937).

Found in

  • R. T. Downs and M. Hall–Wallace, The American Mineralogist Crystal Structure Database, Am. Mineral. 88, 247–250 (2003).

Geometry files


Prototype Generator

aflow --proto=ABC3_hR10_167_a_b_e --params=

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