The ${\text{Hg}}_2\text{CuTi}$ -type structure is found to be preferable energy wise than the ${\text{Cu}}_2\text{MnAl}$ -type structure for full-Heusler ${\text{Cr}}_2\text{MnAl}$ and exhibits half-metallic ferromagnetism based on first principles. The calculations for the mixed compounds with disorder between $B$ and $D$ sublattices reveal that the case of exchanging one atom maintains the half-metallicity while the case of exchanging two atoms loses it. The electronic structures of the atoms at sites $A$ or $C$ are affected mainly by the nearest-neighboring coordination while that of the atoms at site $B$ are determined by the next-nearest-neighboring coordination.

A liquid crystal (LC) lens array with high light control power and a large aperture using a composited alignment layer is proposed. In our design, the alignment layer is not only used for getting a uniform arrangement of LC molecule, but also for getting a lens-like refractive index distribution in the LC layer when a voltage is applied. Through simple technology processes, a tunable focal length LC lens array with a millimeter scale diameter can be achieved. Furthermore, the maximum phase difference of the proposed LC lens array can achieve 105.38π. So, the proposed LC lens array has a high light control power.

We investigated random lasing from a fluid self-assembly sphere-phase liquid crystal, which was composed of three-dimensional twist sphere structures with disclinations among them. The threshold energy of the random lasing from sphere-phase liquid crystal was 32% of that from the chiral nematic phase because of the interference associated with multiple scattering by randomly distributed sphere-phase platelets. Such random lasers composed of self-assembly soft organic materials may be useful for holographic displays, point-of-care biomedical analysis, and optical security coatings.