Al$_{3}$Ti ($D0_{22}$) Structure: A3B_tI8_139_ad_b-001
Other compounds with this structure
Al$_{3}$Hf, Al$_{3-x}$Fe$_{x}$Mo, Al$_{3}$Nb, Al$_{3}$Sc, Al$_{3}$Ta, Al$_{3}$V, Ga$_{3}$Hf, Ga$_{3}$Nb, Ga$_{3}$Ti, α-NbPd$_{3}$, Ni$_{3}$V, Pd$_{3}$Nb, Pd$_{3}$Ta, Pd$_{3}$V, Pt$_{3}$V
- When $c=2a$ the atoms are on the sites of a face-centered cubic lattice. When $c/a=1/\sqrt{2}$, this becomes the cubic $D0_{3}$ structure.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | Al I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2b) | Ti I |
| $\mathbf{B_{3}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4d) | Al II |
| $\mathbf{B_{4}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4d) | Al II |
References
- P. Norby and N. Christensen, Preparation and Structure of Al$_3$Ti, Acta Chem. Scand. pp. 157–159 (1986), doi:10.3891/acta.chem.scand.40a-0157.
- J. Nic, S. Zhang, and D. Mikkola, Observations on the systematic alloying of Al3Ti with fourth period elements to yield cubic phases, Scripta Metallurgica et Materialia 24, 1099–1104 (1990), doi:10.1016/0956-716X(90)90306-2.
Found in
- W. B. Pearson, A Handbook of Lattice Spacings and Structures of Metals and Alloys, Volume 2, International Series of Monographs on Metal Physics and Physical Metallurgy, vol. 8 (Pergamon Press, Oxford, London, Edinburgh, New York, Toronto, Sydney, Paris, Braunschweig, 1967).
First cited in
- M. J. Mehl, D. Hicks, C. Toher, O. Levy, R. M. Hanson, G. L. W. Hart, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 1, Comp. Mat. Sci. 136, S1-S828 (2017). (doi=10.1016/j.commatsci.2017.01.017)
Geometry files
Prototype Generator
aflow --proto=A3B_tI8_139_ad_b --params=$a,c/a$