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Extra info for Ancient Blacksmith, the Iron Age, Damascuc Steel, and Modern Metallurgy
In this method, the fractal dimension D is obtained from the log–log plot of R and N(R) . From the log–log plot of the perimeter P and the projection area A of each particle, the average fractal dimension of many particle perimeters 103 Number of lines N(r) (−) nanoparticle. Quantification of particle shape is classified roughly into the shape index which is the ratio of two kinds of different definition particle diameter and the other expression such as fractal dimension or Fourier analysis of particle perimeter.
2 Density measurement of individual particles (1) Effective density of individual particles When particles are not in a powder state, but are dispersed in a gas or a liquid, the density of individual particles is often of concern. For particles dispersed in a gas, there are three major methods of measuring the density of individual particles: (A) the combined measurement of mobility and mass, (B) the combined measurement of mass and volume, and (C) the combined measurement of mobility and aerodynamic diameter.
In order to rebuild the original outline completely, the infinite number of Fourier coefficients would be required. diameters obtained by different kinds of method such as a particle size by dynamic-light-scattering method and the specific surface diameter by the gas adsorption is used. These particle sizes include the influence of particle shape and, so the ratio of these diameters can be used for a simple particle shape expression. References  M. Suzuki, K. Kawabata, K. Iimura and M. Hitota: J.
Ancient Blacksmith, the Iron Age, Damascuc Steel, and Modern Metallurgy