Rough surfaces are modeled as two-dimensional, isotropic, Gaussian random processes, and analyzed with the techniques of random process theory. Such surface statistics as the distribution of summit heights, the density of summits, the mean surface gradient, and the mean curvature of summits are related to the power spectral density of a profile of the surface. A detailed comparison is made of the statistics of the surface and those of the profile, and serious differences are found in the distributions of heights of maxima and in the mean gradients. Techniques for analyzing profiles of random surfaces to obtain the parameters necessary for the analysis of the surface are discussed. Extensions of the theory to nonisotropic Gaussian surfaces are indicated.

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The polycrystalline sample of complex tungsten-bronze compound Li 2 Pb 2 Sm 2 W 2 Ti 4 Ta 4 O 30 was prepared by a high-temperature solid-state reaction technique. Room temperature X-ray diffraction (XRD) study suggests the formation of a single-phase compound. Microstructure of the pellet sample was studied by scanning electron microscope. The temperature variation of dielectric constant shows dielectric anomaly in the sample. Study of electrical properties (impedance, conductivity, etc.,) of the material exhibits a strong correlation between its micro-structure (i.e., bulk, grain boundary, etc) and electrical parameters. A typical Arrhenius behavior was observed in the temperature dependence of dc conductivity.

In the present work, zirconium (Zr) modified strontium bismuth titanate (SBT) ceramics were prepared by soild state reaction route and its effects on the structural and electrical properties were thoroughly investigated.