Al$_{3}$Ni$_{2}$ ($D5_{13}$) Structure: A3B2_hP5_164_ad_d-001
| Prototype | Al$_{3}$Ni$_{2}$ |
| AFLOW prototype label | A3B2_hP5_164_ad_d-001 |
| Strukturbericht designation | $D5_{13}$ |
| ICSD | 107937 |
| Pearson symbol | hP5 |
| Space group number | 164 |
| Space group symbol | $P\overline{3}m1$ |
| AFLOW prototype command |
aflow --proto=A3B2_hP5_164_ad_d-001
--params=$a, \allowbreak c/a, \allowbreak z_{2}, \allowbreak z_{3}$ |
Other compounds with this structure
Al$_{3}$Cu$_{2}$, Al$_{3}$In$_{2}$, Al$_{3}$Pd$_{2}$, Al$_{3}$Pt$_{2}$, Al$_{3}$Tc$_{2}$, Ga$_{3}$Pt$_{2}$, In$_{3}$Al$_{2}$, In$_{3}$Pd$_{2}$, In$_{3}$Pt$_{2}$, Mg$_{3}$Sb$_{2}$, $\beta'$-Ga$_{3}$Ni$_{2}$, $\delta'$-In$_{3}$Ni$_{2}$
- Either the three Al atoms or Al (1a) and the Ni atoms form a trigonal omega ($C6$) structure. Using the choices of internal parameters for Al$_{3}$Ni$_{2}$, this can be viewed as a five-layer close-packed unit cell with stacking ABCBCA.
- Al$_{3}$Ni$_{2}$ is isostructural with La$_{2}$O$_{3}$ ($D5_{2}$) and Ce$_{2}$O$_{2}$S. We use this structure for the binary intermetallics, $D5_{2}$ for the binary oxides and related structures, and Ce$_{2}$O$_{2}$S for the ternary structures.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (1a) | Al I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (2d) | Al II |
| $\mathbf{B_{3}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c z_{2} \,\mathbf{\hat{z}}$ | (2d) | Al II |
| $\mathbf{B_{4}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (2d) | Ni I |
| $\mathbf{B_{5}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (2d) | Ni I |
References
- A. J. Bradley and A. Taylor, The crystal structures of Ni$_2$Al$_3$ and NiAl$_3$, Philosophical Magazine 23, 1049–1067 (1937), doi:10.1080/14786443708561875.
Found in
- \begin{thebibliography}{1}\expandafter\ifx\csname urlstyle\endcsname\relax \providecommand{\doi}[1]{doi:\discretionary{}{}{}#1}\else \providecommand{\doi}{doi:\discretionary{}{}{}\begingroup \urlstyle{rm}\Url}\fi\providecommand{\selectlanguage}[1]{\relax}\providecommand{\bibAnnoteFile}[1]{% \IfFileExists{#1}{\begin{quotation}\noindent\textsc{Key:} #1\ \textsc{Annotation:} \input{#1}\end{quotation}}{}}\providecommand{\bibAnnote}[2]{% \begin{quotation}\noindent\textsc{Key:} #1\ \textsc{Annotation:} #2\end{quotation}}\bibitem{sm_lbs_978-3-540-44752-8_197}P. Villars, K. Cenzual, J. Daams, R. Gladyshevskii, O. Shcherban, V. Dubenskyy, N. Melnichenko-Koblyuk, O. Pavlyuk, I. Savysyuk, S. Stoyko, and L. Sysa, Structure Types. Part 6: Space Groups (166) R-3m - (160) R3m ยท Ni$_{2}$Al$_{3}$} (2008). Landolt-Börnstein - Group III Condensed Matter 43A6 (Springer-Verlag Berlin Heidelberg).\bibAnnoteFile{sm_lbs_978-3-540-44752-8_197
Prototype Generator
aflow --proto=A3B2_hP5_164_ad_d --params=$a,c/a,z_{2},z_{3}$