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Processing of Ceramics


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microscope, and when it is irradiated with a He–Ne laser (from the left side of the image), the light is scattered from the vicinity of the interface between the base material and the residual pores (the portion where the refractive index fluctuation exists). In this state, when the light of the transmission microscope is turned off and the observation is continued while irradiating the He–Ne laser, circular Mie scattering can be clearly confirmed scattered from the interface of residual pores and the base material. This scattering conditions are shown in Figure 1.19e. Ceramic materials have numerous grain boundaries, and even though the He–Ne laser passes through the grain boundaries, the scattered light cannot be detected by a normal tomography or a tomography using an optical microscope. This means that scattering from the grain boundaries is very insignificant or almost nonexistent (not limited to the spinel ceramics). Therefore, it is still necessary to seriously discuss grain boundary scattering phenomenon in ceramics, which has been doubted to be used as an optical material.

Schematic illustration of (a) Optical loss at 1064 nm and laser tomography at 633 nm of polycrystalline and single crystal, (b) residual pore and Mie scattering from pore by He–Ne laser.

      By the way, Rayleigh scattering is expressed as follows.

upper I equals upper I 0 StartFraction 1 plus cosine squared theta Over 2 upper R squared EndFraction left-parenthesis StartFraction 2 pi Over lamda EndFraction right-parenthesis Superscript 4 Baseline left-parenthesis StartFraction n squared minus 1 Over n squared plus 2 EndFraction right-parenthesis squared left-parenthesis StartFraction d Over 2 EndFraction right-parenthesis Superscript 6

      where θ is the scattering angle, I0 is the light intensity before transmission, n is the refractive index; R is the distance between the measurement point and the scattering source, d is the scatterer size, and λ is the measuring wavelength. Basically, light scattering increases in proportion to the power of the scatterer size to the sixth power, the reciprocal of the measurement wavelength to the fourth power. In common sense which is well recognized by almost all material scientists until now, “There are many dislocations at the grain boundaries in the ceramics and their dislocations become scattering sources causing grain boundary scattering, so the transmittance of the ceramics increases as the wavelength becomes shorter.” However, the obtained result is opposite to the conventional common sense that “polycrystalline ceramics having grain boundaries are superior in optical properties to single crystals, and in particular, in the short wavelength region, they show a significant difference in optical properties.”

Schematic illustration of (a) He–Ne laser irradiation test and (b-1) original and (b-2-4) changing of beam pattern via various specimens. Schematic illustration of optical inspection of polycrystalline Spinel Ceramics by sintering method and Spinel crystal by Verneuil and Czochralski (Cz) methods.

      Figure 1.21a‐1–4 show the appearance of polycrystalline spinel ceramics of ϕ20 × t10 mm produced by the sintering method. It is very transparent and has a lower optical loss than the Czochralski single crystal even in the visible region. The transmitted wavefront image by the interferometer showed a straight fringe (<0.1λ/cm [λ = 633 nm]). In the measurement using the polarizer, the optical stress was below the detection limit. Furthermore, there is no inhomogeneous part in the Schlieren observation. Finally, the reason why the absorption edge of polycrystalline ceramics becomes shorter and the band gap shows a larger value than that of a single crystal will be described in the following. As shown in the Figure 1.21b,c, the spinel single crystals have a domain structure with nonuniform refractive index. The chemical formula of the spinel is MgAl2O4, and this material can also be a solid solution