β-V$_{2}$N ($L'3_{2}$) Structure: AB2_hP9_162_ad_k-001
| Prototype | NV$_{2}$ |
| AFLOW prototype label | AB2_hP9_162_ad_k-001 |
| Strukturbericht designation | $L'3_{2}$ |
| ICSD | 8236 |
| Pearson symbol | hP9 |
| Space group number | 162 |
| Space group symbol | $P\overline{3}1m$ |
| AFLOW prototype command |
aflow --proto=AB2_hP9_162_ad_k-001
--params=$a, \allowbreak c/a, \allowbreak x_{3}, \allowbreak z_{3}$ |
Other compounds with this structure
$\epsilon$-Fe$_{2}$N, Cr$_{2}$N, $\beta$-Nb$_{2}$N, $\beta$-Ta$_{2}$N
- (Parthé, 1993) is the only reference we have seen with a $L'3_{2}$ Strukturbericht designation.
- (Christensen, 1979) states that $\epsilon$–Fe$_{2}$N is the prototype for this structure. We will instead follow (Villars, 1991), which uses $\beta$–V$_{2}$N as the prototype.
- The ternary version of this structure is rosiaite, PbSb$_{2}$O$_{6}$.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (1a) | N I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2d) | N II |
| $\mathbf{B_{3}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2d) | N II |
| $\mathbf{B_{4}}$ | = | $x_{3} \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{3} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (6k) | V I |
| $\mathbf{B_{5}}$ | = | $x_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{3} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (6k) | V I |
| $\mathbf{B_{6}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+c z_{3} \,\mathbf{\hat{z}}$ | (6k) | V I |
| $\mathbf{B_{7}}$ | = | $- x_{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{3} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (6k) | V I |
| $\mathbf{B_{8}}$ | = | $- x_{3} \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{3} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (6k) | V I |
| $\mathbf{B_{9}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}- c z_{3} \,\mathbf{\hat{z}}$ | (6k) | V I |
References
- P. Villars and L. Calvert, Pearson's Handbook of Crystallographic Data for Intermetallic Phases (ASM International, Materials Park, OH, 1991), 2nd edn.
Found in
- P. Villars and L. Calvert, Pearson's Handbook of Crystallographic Data for Intermetallic Phases (ASM International, Materials Park, OH, 1991), 2nd edn.
Prototype Generator
aflow --proto=AB2_hP9_162_ad_k --params=$a,c/a,x_{3},z_{3}$