V$_{13}$O$_{16}$ Structure: A16B13_tI116_141_2hi_a2fh-001
| Prototype | O$_{16}$V$_{13}$ |
| AFLOW prototype label | A16B13_tI116_141_2hi_a2fh-001 |
| ICSD | 77708 |
| Pearson symbol | tI116 |
| Space group number | 141 |
| Space group symbol | $I4_1/amd$ |
| AFLOW prototype command |
aflow --proto=A16B13_tI116_141_2hi_a2fh-001
--params=$a, \allowbreak c/a, \allowbreak x_{2}, \allowbreak x_{3}, \allowbreak y_{4}, \allowbreak z_{4}, \allowbreak y_{5}, \allowbreak z_{5}, \allowbreak y_{6}, \allowbreak z_{6}, \allowbreak x_{7}, \allowbreak y_{7}, \allowbreak z_{7}$ |
- There are serveral problems with this structure:
- It is not clear if (Andersson, 1970) put this in the first (4a site at the origin) or second (inversion site at the origin) setting of space group $I4_{1}/amd$ #141.
- Furthermore, they give values for x and z for the (16h) positions, even though the standard definition is (0 y z) in both settings.
- The ICSD entry assumes the first setting, and that the authors meant
y
rather thanx
for the first coordinate, but kept x asx
for the other Wyckoff positions. - We follow this convention, using AFLOW to convert that structure to the standard second setting. The result is shown here.
- However, (Andersson, 1970) call this structure a distorted rock salt ($B1$) structure with vacancies on the vanadium sites and interstitial vanadium atoms on the (4a) sites, and our structure look nothing like this.
- Furthermore, the (presumably relaxed) structure found on the Materials Project page (Jain, 2013) has the same symmetry and occupied Wyckoff positions, but is actually much different than this structure.
- We fill investigate this further. If updates are necessary we will revise this page.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{7}{8} \, \mathbf{a}_{1}+\frac{1}{8} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{y}}+\frac{1}{8}c \,\mathbf{\hat{z}}$ | (4a) | V I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{8} \, \mathbf{a}_{1}+\frac{7}{8} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{4}a \,\mathbf{\hat{y}}+\frac{3}{8}c \,\mathbf{\hat{z}}$ | (4a) | V I |
| $\mathbf{B_{3}}$ | = | $x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}$ | (16f) | V II |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}$ | (16f) | V II |
| $\mathbf{B_{5}}$ | = | $x_{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (16f) | V II |
| $\mathbf{B_{6}}$ | = | $- x_{2} \, \mathbf{a}_{1}- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- \frac{1}{4}c \,\mathbf{\hat{z}}$ | (16f) | V II |
| $\mathbf{B_{7}}$ | = | $- x_{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}$ | (16f) | V II |
| $\mathbf{B_{8}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}$ | (16f) | V II |
| $\mathbf{B_{9}}$ | = | $- x_{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (16f) | V II |
| $\mathbf{B_{10}}$ | = | $x_{2} \, \mathbf{a}_{1}+\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- \frac{1}{4}c \,\mathbf{\hat{z}}$ | (16f) | V II |
| $\mathbf{B_{11}}$ | = | $x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}$ | (16f) | V III |
| $\mathbf{B_{12}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}$ | (16f) | V III |
| $\mathbf{B_{13}}$ | = | $x_{3} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (16f) | V III |
| $\mathbf{B_{14}}$ | = | $- x_{3} \, \mathbf{a}_{1}- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- \frac{1}{4}c \,\mathbf{\hat{z}}$ | (16f) | V III |
| $\mathbf{B_{15}}$ | = | $- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}$ | (16f) | V III |
| $\mathbf{B_{16}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}$ | (16f) | V III |
| $\mathbf{B_{17}}$ | = | $- x_{3} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (16f) | V III |
| $\mathbf{B_{18}}$ | = | $x_{3} \, \mathbf{a}_{1}+\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- \frac{1}{4}c \,\mathbf{\hat{z}}$ | (16f) | V III |
| $\mathbf{B_{19}}$ | = | $\left(y_{4} + z_{4}\right) \, \mathbf{a}_{1}+z_{4} \, \mathbf{a}_{2}+y_{4} \, \mathbf{a}_{3}$ | = | $a y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (16h) | O I |
| $\mathbf{B_{20}}$ | = | $\left(- y_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{4} \, \mathbf{a}_{2}- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (16h) | O I |
| $\mathbf{B_{21}}$ | = | $z_{4} \, \mathbf{a}_{1}+\left(- y_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}- y_{4} \, \mathbf{a}_{3}$ | = | $- a \left(y_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- \frac{1}{4}a \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16h) | O I |
| $\mathbf{B_{22}}$ | = | $z_{4} \, \mathbf{a}_{1}+\left(y_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+c \left(z_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16h) | O I |
| $\mathbf{B_{23}}$ | = | $\left(y_{4} - z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{2}+\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ | (16h) | O I |
| $\mathbf{B_{24}}$ | = | $- \left(y_{4} + z_{4}\right) \, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{2}- y_{4} \, \mathbf{a}_{3}$ | = | $- a y_{4} \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ | (16h) | O I |
| $\mathbf{B_{25}}$ | = | $- z_{4} \, \mathbf{a}_{1}+\left(y_{4} - z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+y_{4} \, \mathbf{a}_{3}$ | = | $a \left(y_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- \frac{1}{4}a \,\mathbf{\hat{y}}- c \left(z_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16h) | O I |
| $\mathbf{B_{26}}$ | = | $- z_{4} \, \mathbf{a}_{1}- \left(y_{4} + z_{4}\right) \, \mathbf{a}_{2}- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}- c \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16h) | O I |
| $\mathbf{B_{27}}$ | = | $\left(y_{5} + z_{5}\right) \, \mathbf{a}_{1}+z_{5} \, \mathbf{a}_{2}+y_{5} \, \mathbf{a}_{3}$ | = | $a y_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (16h) | O II |
| $\mathbf{B_{28}}$ | = | $\left(- y_{5} + z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{5} \, \mathbf{a}_{2}- \left(y_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{5} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (16h) | O II |
| $\mathbf{B_{29}}$ | = | $z_{5} \, \mathbf{a}_{1}+\left(- y_{5} + z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}- y_{5} \, \mathbf{a}_{3}$ | = | $- a \left(y_{5} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- \frac{1}{4}a \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16h) | O II |
| $\mathbf{B_{30}}$ | = | $z_{5} \, \mathbf{a}_{1}+\left(y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(y_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{5} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+c \left(z_{5} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16h) | O II |
| $\mathbf{B_{31}}$ | = | $\left(y_{5} - z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{5} \, \mathbf{a}_{2}+\left(y_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{5} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{5} \,\mathbf{\hat{z}}$ | (16h) | O II |
| $\mathbf{B_{32}}$ | = | $- \left(y_{5} + z_{5}\right) \, \mathbf{a}_{1}- z_{5} \, \mathbf{a}_{2}- y_{5} \, \mathbf{a}_{3}$ | = | $- a y_{5} \,\mathbf{\hat{y}}- c z_{5} \,\mathbf{\hat{z}}$ | (16h) | O II |
| $\mathbf{B_{33}}$ | = | $- z_{5} \, \mathbf{a}_{1}+\left(y_{5} - z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}+y_{5} \, \mathbf{a}_{3}$ | = | $a \left(y_{5} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- \frac{1}{4}a \,\mathbf{\hat{y}}- c \left(z_{5} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16h) | O II |
| $\mathbf{B_{34}}$ | = | $- z_{5} \, \mathbf{a}_{1}- \left(y_{5} + z_{5}\right) \, \mathbf{a}_{2}- \left(y_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{5} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}- c \left(z_{5} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16h) | O II |
| $\mathbf{B_{35}}$ | = | $\left(y_{6} + z_{6}\right) \, \mathbf{a}_{1}+z_{6} \, \mathbf{a}_{2}+y_{6} \, \mathbf{a}_{3}$ | = | $a y_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (16h) | V IV |
| $\mathbf{B_{36}}$ | = | $\left(- y_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{6} \, \mathbf{a}_{2}- \left(y_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (16h) | V IV |
| $\mathbf{B_{37}}$ | = | $z_{6} \, \mathbf{a}_{1}+\left(- y_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}- y_{6} \, \mathbf{a}_{3}$ | = | $- a \left(y_{6} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- \frac{1}{4}a \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16h) | V IV |
| $\mathbf{B_{38}}$ | = | $z_{6} \, \mathbf{a}_{1}+\left(y_{6} + z_{6}\right) \, \mathbf{a}_{2}+\left(y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{6} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+c \left(z_{6} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16h) | V IV |
| $\mathbf{B_{39}}$ | = | $\left(y_{6} - z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{6} \, \mathbf{a}_{2}+\left(y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ | (16h) | V IV |
| $\mathbf{B_{40}}$ | = | $- \left(y_{6} + z_{6}\right) \, \mathbf{a}_{1}- z_{6} \, \mathbf{a}_{2}- y_{6} \, \mathbf{a}_{3}$ | = | $- a y_{6} \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ | (16h) | V IV |
| $\mathbf{B_{41}}$ | = | $- z_{6} \, \mathbf{a}_{1}+\left(y_{6} - z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}+y_{6} \, \mathbf{a}_{3}$ | = | $a \left(y_{6} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- \frac{1}{4}a \,\mathbf{\hat{y}}- c \left(z_{6} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16h) | V IV |
| $\mathbf{B_{42}}$ | = | $- z_{6} \, \mathbf{a}_{1}- \left(y_{6} + z_{6}\right) \, \mathbf{a}_{2}- \left(y_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{6} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}- c \left(z_{6} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16h) | V IV |
| $\mathbf{B_{43}}$ | = | $\left(y_{7} + z_{7}\right) \, \mathbf{a}_{1}+\left(x_{7} + z_{7}\right) \, \mathbf{a}_{2}+\left(x_{7} + y_{7}\right) \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}+a y_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (32i) | O III |
| $\mathbf{B_{44}}$ | = | $\left(- y_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{7} - z_{7}\right) \, \mathbf{a}_{2}- \left(x_{7} + y_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}- a \left(y_{7} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (32i) | O III |
| $\mathbf{B_{45}}$ | = | $\left(x_{7} + z_{7}\right) \, \mathbf{a}_{1}+\left(- y_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{7} - y_{7}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{7} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{7} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32i) | O III |
| $\mathbf{B_{46}}$ | = | $- \left(x_{7} - z_{7}\right) \, \mathbf{a}_{1}+\left(y_{7} + z_{7}\right) \, \mathbf{a}_{2}+\left(- x_{7} + y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{7} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{7} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{7} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32i) | O III |
| $\mathbf{B_{47}}$ | = | $\left(y_{7} - z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{7} + z_{7}\right) \, \mathbf{a}_{2}+\left(- x_{7} + y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}+a \left(y_{7} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ | (32i) | O III |
| $\mathbf{B_{48}}$ | = | $- \left(y_{7} + z_{7}\right) \, \mathbf{a}_{1}+\left(x_{7} - z_{7}\right) \, \mathbf{a}_{2}+\left(x_{7} - y_{7}\right) \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}- a y_{7} \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ | (32i) | O III |
| $\mathbf{B_{49}}$ | = | $\left(x_{7} - z_{7}\right) \, \mathbf{a}_{1}+\left(y_{7} - z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{7} + y_{7}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{7} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{7} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- c \left(z_{7} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32i) | O III |
| $\mathbf{B_{50}}$ | = | $- \left(x_{7} + z_{7}\right) \, \mathbf{a}_{1}- \left(y_{7} + z_{7}\right) \, \mathbf{a}_{2}- \left(x_{7} + y_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{7} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{7} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- c \left(z_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32i) | O III |
| $\mathbf{B_{51}}$ | = | $- \left(y_{7} + z_{7}\right) \, \mathbf{a}_{1}- \left(x_{7} + z_{7}\right) \, \mathbf{a}_{2}- \left(x_{7} + y_{7}\right) \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}- a y_{7} \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ | (32i) | O III |
| $\mathbf{B_{52}}$ | = | $\left(y_{7} - z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{7} - z_{7}\right) \, \mathbf{a}_{2}+\left(x_{7} + y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}+a \left(y_{7} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ | (32i) | O III |
| $\mathbf{B_{53}}$ | = | $- \left(x_{7} + z_{7}\right) \, \mathbf{a}_{1}+\left(y_{7} - z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{7} - y_{7}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{7} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{7} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- c \left(z_{7} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32i) | O III |
| $\mathbf{B_{54}}$ | = | $\left(x_{7} - z_{7}\right) \, \mathbf{a}_{1}- \left(y_{7} + z_{7}\right) \, \mathbf{a}_{2}+\left(x_{7} - y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{7} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{7} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- c \left(z_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32i) | O III |
| $\mathbf{B_{55}}$ | = | $\left(- y_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{7} + z_{7}\right) \, \mathbf{a}_{2}+\left(x_{7} - y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}- a \left(y_{7} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (32i) | O III |
| $\mathbf{B_{56}}$ | = | $\left(y_{7} + z_{7}\right) \, \mathbf{a}_{1}- \left(x_{7} - z_{7}\right) \, \mathbf{a}_{2}- \left(x_{7} - y_{7}\right) \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}+a y_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (32i) | O III |
| $\mathbf{B_{57}}$ | = | $- \left(x_{7} - z_{7}\right) \, \mathbf{a}_{1}+\left(- y_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{7} + y_{7}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{7} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{7} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32i) | O III |
| $\mathbf{B_{58}}$ | = | $\left(x_{7} + z_{7}\right) \, \mathbf{a}_{1}+\left(y_{7} + z_{7}\right) \, \mathbf{a}_{2}+\left(x_{7} + y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{7} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{7} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{7} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32i) | O III |
References
- B. Andersson and J. Gj\onnes, Ordered Phases in the Monoxide Region of the Vanadium-Oxygen System, Acta Chem. Scand. 24, 2250–2252 (1970), doi:10.3891/acta.chem.scand.24-2250.
Found in
- A. Jain, S. Ping, G. Hautier, W. Chen, W. D. Richards, S. Dacek, S. Cholia, D. Gunter, D. Skinner, G. Ceder, and K. A. Persson, Commentary: The Materials Project: A materials genome approach to accelerating materials innovation}, APL Materials 1, 011002 (2013), doi:10.1063/1.4812323. V$_{13}$O$_{16$, mp-30065.
Prototype Generator
aflow --proto=A16B13_tI116_141_2hi_a2fh --params=$a,c/a,x_{2},x_{3},y_{4},z_{4},y_{5},z_{5},y_{6},z_{6},x_{7},y_{7},z_{7}$