$D0_{7}$ (CrO3) (obsolete) Structure : AB3_oC16_20_a_bc
| Prototype | : | CrO3 |
| AFLOW prototype label | : | AB3_oC16_20_a_bc |
| Strukturbericht designation | : | $D0_{7}$ |
| Pearson symbol | : | oC16 |
| Space group number | : | 20 |
| Space group symbol | : | $C222_{1}$ |
| AFLOW prototype command | : | aflow --proto=AB3_oC16_20_a_bc --params=$a$,$b/a$,$c/a$,$x_{1}$,$y_{2}$,$x_{3}$,$y_{3}$,$z_{3}$ |
- This is the determination of the orthorhombic structure of CrO3 given the $D0_{7}$ designation by (Hermann, 1937). This structure is superceded by the one found by (Byström, 1950), which we call the
orthorhombic CrO3 phase,
. The current structure has the Cr atom at the center of a distorted oxygen octahedron, while the newer structure has the Cr atom at center of a distorted tetrahedron.
Base-centered Orthorhombic primitive vectors:
\[ \begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{x}} - \frac12 \, b \, \mathbf{\hat{y}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, b \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & c \, \mathbf{\hat{z}} \\ \end{array} \]
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & = & x_{1} \, \mathbf{a}_{1} + x_{1} \, \mathbf{a}_{2} & = & x_{1}a \, \mathbf{\hat{x}} & \left(4a\right) & \text{Cr} \\ \mathbf{B}_{2} & = & -x_{1} \, \mathbf{a}_{1}-x_{1} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & -x_{1}a \, \mathbf{\hat{x}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(4a\right) & \text{Cr} \\ \mathbf{B}_{3} & = & -y_{2} \, \mathbf{a}_{1} + y_{2} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & y_{2}b \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(4b\right) & \text{O I} \\ \mathbf{B}_{4} & = & y_{2} \, \mathbf{a}_{1}-y_{2} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & -y_{2}b \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(4b\right) & \text{O I} \\ \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} & = & x_{3}a \, \mathbf{\hat{x}} + y_{3}b \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(8c\right) & \text{O II} \\ \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} & = & -x_{3}a \, \mathbf{\hat{x}}-y_{3}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{3}\right)c \, \mathbf{\hat{z}} & \left(8c\right) & \text{O II} \\ \mathbf{B}_{7} & = & \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} & = & -x_{3}a \, \mathbf{\hat{x}} + y_{3}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{3}\right)c \, \mathbf{\hat{z}} & \left(8c\right) & \text{O II} \\ \mathbf{B}_{8} & = & \left(x_{3}+y_{3}\right) \, \mathbf{a}_{1} + \left(x_{3}-y_{3}\right) \, \mathbf{a}_{2}-z_{3} \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}}-y_{3}b \, \mathbf{\hat{y}}-z_{3}c \, \mathbf{\hat{z}} & \left(8c\right) & \text{O II} \\ \end{array} \]References
- H. Bräkken, Die Kristallstrukturen der Trioxyde von Chrom, Molybdän und Wolfram, Zeitschrift für Kristallographie – Crystalline Materials 78, 484–488 (1931), doi:10.1524/zkri.1931.78.1.484.
- C. Hermann, O. Lohrmann, and H. Philipp, eds., Strukturebericht Band II, 1928–1932 (Akademsiche Verlagsgesellschaft M. B. H, Leipzig, 1937).
Found in
- A. Byström and K.–A. Wilhelmi, The Crystal Structure of Chromium Trioxide, Acta Chem. Scand. 4, 1131–1141 (1950), doi:10.3891/acta.chem.scand.04-1131.