AFLOW Prototype: ABC3_hR10_167_a_b_e.CaCO3
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 | : | $\text{R}\bar{3}\text{c}$ |
AFLOW prototype command | : | aflow --proto=ABC3_hR10_167_a_b_e [--hex] --params=$a$,$c/a$,$x_{3}$ |
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{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) & \text{C} \\ \mathbf{B}_{2} & =& \frac34 \, \mathbf{a}_{1}+ \frac34 \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& =& \frac34 c \, \mathbf{\hat{z}}& \left(2a\right) & \text{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) & \text{Ca} \\ \mathbf{B}_{4} & =& \frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& =& \frac12 c \, \mathbf{\hat{z}}& \left(2b\right) & \text{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) & \text{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) & \text{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) & \text{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) & \text{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) & \text{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) & \text{O} \\ \end{array} \]