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Optical Determination of the Lattice Constants of
1984 Langmuir 2003, 19, 1984 1986
Optical Determination of the Lattice Constants of
Colloidal Crystals without Use of the Refractive Index
Toshimitsu Kanai, Tsutomu Sawada,* and Kenji Kitamura
National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan
Received November 22, 2002. In Final Form: January 8, 2003
Angle-dependent reflectance spectra were measured for charge-stabilized colloidal crystals of polystyrene
particles dispersed in water. We found that diffraction peaks due to the two-dimensional surface lattice
of the colloidal crystal were observable in the spectra, in addition to normal three-dimensional Bragg
peaks. On the basis of the nature of the two-dimensional diffraction, we show that the lattice constant can
be determined without the knowledge of the refractive index of the crystal, unlike the case of using three-
dimensional Bragg diffraction. The lattice constant depends only on the diffraction angle and the wavelength
of light and therefore can be determined with high precision. The accurate determination of the lattice
constant would provide a basis for quantitative evaluation and design of colloidal crystals for applications
in the optical regime, such as photonic crystals.
Introduction the lattice constants of colloidal crystals from the 3D Bragg
diffraction has not been accurate or reliable.
Monodisperse, charged colloidal particles form a three-
dimensional (3D) periodic structure in dispersions. Such In this paper, we report a
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