δ-V$_{4}$D$_{3}$ Structure: A3B4_oP14_49_ej_2q-001
| Prototype | H$_{3}$V$_{4}$ |
| AFLOW prototype label | A3B4_oP14_49_ej_2q-001 |
| ICSD | 42434 |
| Pearson symbol | oP14 |
| Space group number | 49 |
| Space group symbol | $Pccm$ |
| AFLOW prototype command |
aflow --proto=A3B4_oP14_49_ej_2q-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak x_{2}, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak x_{4}, \allowbreak y_{4}$ |
- $\delta$–V$_{4}$D$_{3}$ is the only completely ordered structure in the Vanadium-Hydrogen/Deuterium system (Asano, 1973). Even then, the deuterium sites are only 98% occupied.
- The data for this structure was obtained at 88K.
- While (Asano, 1973) placed this in space group $Pcc2$ #27, (Cenzual, 1991) showed that the published coordinates placed the system in space group $Pccm$ #49.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}c \,\mathbf{\hat{z}}$ | (2e) | D I |
| $\mathbf{B_{2}}$ | = | $\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}c \,\mathbf{\hat{z}}$ | (2e) | D I |
| $\mathbf{B_{3}}$ | = | $x_{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4j) | D II |
| $\mathbf{B_{4}}$ | = | $- x_{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4j) | D II |
| $\mathbf{B_{5}}$ | = | $- x_{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (4j) | D II |
| $\mathbf{B_{6}}$ | = | $x_{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (4j) | D II |
| $\mathbf{B_{7}}$ | = | $x_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}$ | = | $a x_{3} \,\mathbf{\hat{x}}+b y_{3} \,\mathbf{\hat{y}}$ | (4q) | V I |
| $\mathbf{B_{8}}$ | = | $- x_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- b y_{3} \,\mathbf{\hat{y}}$ | (4q) | V I |
| $\mathbf{B_{9}}$ | = | $- x_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+b y_{3} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4q) | V I |
| $\mathbf{B_{10}}$ | = | $x_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}- b y_{3} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4q) | V I |
| $\mathbf{B_{11}}$ | = | $x_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}$ | = | $a x_{4} \,\mathbf{\hat{x}}+b y_{4} \,\mathbf{\hat{y}}$ | (4q) | V II |
| $\mathbf{B_{12}}$ | = | $- x_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- b y_{4} \,\mathbf{\hat{y}}$ | (4q) | V II |
| $\mathbf{B_{13}}$ | = | $- x_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+b y_{4} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4q) | V II |
| $\mathbf{B_{14}}$ | = | $x_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}- b y_{4} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4q) | V II |
References
- H. Asano and M. Hirabayashi, Interstitial superstructures of vanadium deuterides, phys. stat. sol. (a) 15, 267–279 (1973), doi:10.1002/pssa.2210150130.
Found in
- K. Cenzual, L. M. Gelato, M. Penzo, and E. Parthé, Inorganic structure types with revised space groups. I, Acta Crystallogr. Sect. B 47, 433–439 (1991), doi:10.1107/S0108768191000903.
Prototype Generator
aflow --proto=A3B4_oP14_49_ej_2q --params=$a,b/a,c/a,x_{2},x_{3},y_{3},x_{4},y_{4}$