Lattice:AlB2

AlB₂ is a hexagonal lattice, with two distinct kinds of particles.

$8\,\mathrm {corners} :{\frac {1}{12}}+{\frac {1}{6}}+{\frac {1}{12}}+{\frac {1}{6}}+{\frac {1}{12}}+{\frac {1}{6}}+{\frac {1}{12}}+{\frac {1}{6}}=1$ $8\,\mathrm {corners} :{\frac {1}{12}}+{\frac {1}{6}}+{\frac {1}{12}}+{\frac {1}{6}}+{\frac {1}{12}}+{\frac {1}{6}}+{\frac {1}{12}}+{\frac {1}{6}}=1$
- $\left(0,0,0\right),\,(0,0,1),\,(0,1,0),\,(1,0,0),\,(0,1,1),\,(1,0,1),\,(1,1,0),\,(1,1,1)$

These are the two inner particles.

$2\,\mathrm {inner} \,\times \,1=2$ $2\,\mathrm {inner} \,\times \,1=2$
- $\left({\frac {1}{3}},{\frac {1}{3}},{\frac {1}{2}}\right),\,\left({\frac {2}{3}},{\frac {2}{3}},{\frac {1}{2}}\right),$

$\left(0,0,0\right),\,(0,0,c),\,\left({\frac {b}{2}},{\frac {{\sqrt {3}}b}{2}},0\right),\,(a,0,0),\,\left({\frac {b}{2}},{\frac {{\sqrt {3}}b}{2}},c\right),\,(a,0,c),\,\left(a+{\frac {b}{2}},{\frac {{\sqrt {3}}b}{2}},0\right),\,\left(a+{\frac {b}{2}},{\frac {{\sqrt {3}}b}{2}},c\right)$

$\left({\frac {a}{3}}+{\frac {b}{6}},{\frac {{\sqrt {3}}b}{6}},{\frac {c}{2}}\right),\,\left({\frac {2a}{3}}+{\frac {b}{3}},{\frac {{\sqrt {3}}b}{3}},{\frac {c}{2}}\right),$

4.3 nm and 2.3 nm Fe_xPt_1−x nanoparticles
- Sra, A.K.; Ewers, T.D.; Xu, Q.; Zandbergen, H.; Schaak, R.E. One-pot synthesis of bi-disperse FePt nanoparticles and size-selective self-assembly into AB2, AB5, and AB13 superlattices Chem. Commun. 2006, 750-752 doi: 10.1039/B515673D
15 nm Fe₃O₄ and 6 nm FePt nanoparticles assembled at liquid interface
- Dong, A., Chen, J., Vora, P. M., Kikkawa, J. M. & Murray, C. B. Binary nanocrystal superlattice membranes self-assembled at the liquid–air interface Nature 2010 466, 474–477 doi: 10.1038/nature09188
- Korgel, B.A. Nanocrystal superlattices: Assembly at liquid interfaces, Nature Materials 2010, 9, 701-703 doi: 10.1038/nmat2846

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