The laser diffraction from periodic structures typically shows isolated and sharp point patterns at zeroth and ±nth orders. Diffraction from 2D graded photonic super-crystals (GPSCs) has demonstrated over 1000 spots due to the fractional diffractions. Here, we report the holographic fabrication of three types of 3D GPSCs through nine beam interferences and their characteristic diffraction patterns. The diffraction spots due to the fractional orders are merged into large-area diffraction zones for these three types of GPSCs. Three distinguishable diffraction patterns have been observed: (a) 3 × 3 Diffraction zones for GPSCs with a weak gradient in unit super-cell, (b) 5 × 5 non-uniform diffraction zones for GPSCs with a strong modulation in long period and a strong gradient in unit super-cell, (c) more than 5 × 5 uniform diffraction zones for GPSCs with a medium gradient in unit super-cell and a medium modulation in long period. The GPSCs with a strong modulation appear as moiré photonic crystals. The diffraction zone pattern not only demonstrates a characterization method for the fabricated 3D GPSCs, but also proves their unique optical properties of the coupling of light from zones with 360° azimuthal angles and broad zenith angles.
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Coarse-grained density and compressibility of nonideal crystals: General theory and an application to cluster crystals
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null (Ed.)Non-luminescent, isostructural crystals of [(C 6 H 11 NC) 2 Au](EF 6 )·C 6 H 6 (E = As, Sb) lose benzene upon standing in air to produce green luminescent (E = As) or blue luminescent (E = Sb) powders. Previous studies have shown that the two-coordinate cation, [(C 6 H 11 NC) 2 Au] + , self-associates to form luminescent crystals that contain linear or nearly linear chains of cations and display unusual polymorphic, vapochromic, and/or thermochromic properties. Here, we report the formation of non-luminescent crystalline salts in which individual [(C 6 H 11 NC) 2 Au] + ions are isolated from one another. In [(C 6 H 11 NC) 2 Au](BArF 24 ) ((BArF 24 ) − is tetrakis[3,5-bis(trifluoromethyl)phenyl]borate) each cation is surrounded by two anions that prohibit any close approach of the gold ions. Crystallization of [(C 6 H 11 NC) 2 Au](EF 6 ) (E = As or Sb, but not P) from benzene solution produces colorless, non-emissive crystals of the solvates [(C 6 H 11 NC) 2 Au](EF 6 )·C 6 H 6 . These two solvates are isostructural and contain columns in which cations and benzene molecules alternate. With the benzene molecules separating the cations, the shortest distances between gold ions are 6.936(2) Å for E = As and 6.9717(19) Å for E = Sb. Upon removal from the mother liquor, these crystals crack due to the loss of benzene from the crystal and form luminescent powders. Crystals of [(C 6 H 11 NC) 2 Au](SbF 6 )·C 6 H 6 that powder out form a pale yellow powder with a blue luminescence with emission spectra and powder X-ray diffraction data that show that the previously characterized [(C 6 H 11 NC) 2 Au](SbF 6 ) is formed. In the process, the distances between the gold( i ) ions decrease to ∼3 Å and half of the cyclohexyl groups move from an axial orientation to an equatorial one. Remarkably, when crystals of [(C 6 H 11 NC) 2 Au](AsF 6 )·C 6 H 6 stand in air, they lose benzene and are converted into the yellow, green-luminescent polymorph of [(C 6 H 11 NC) 2 Au](AsF 6 ) rather than the colorless, blue-luminescent polymorph. Paradoxically, the yellow, green-luminescent powder that forms as well as authentic crystals of the yellow, green-luminescent polymorph of [(C 6 H 11 NC) 2 Au](AsF 6 ) are sensitive to benzene vapor and are converted by exposure to benzene vapor into the colorless, blue-luminescent polymorph.more » « less
