In this review, the fractals in the fractography is described, using brittle fracture surfaces of chromium and molybdenum, and stress corrosion cracking surfaces of SNCM 439 steel. It is emphasized that the quantitative fractography at the atomic region is opened, combining scanning tunneling microscopy with fractal geometry.

Silicon–oxygen and aluminum–oxygen compounds exhibit significant XPS Auger and photoelectron chemical shifts that are accurately measurable. Chemical state plots of KLL Auger kinetic energy versus 2p photoelectron energy permit identification of chemical species from the locations of their points on the plots. The KLL Auger electrons of Al and Si were generated by the bremsstrahlung component of the radiation, with conventional instrumentation. The location of points on the plots can be understood on the basis of polarizability of the environment (on the Auger parameter grid of lines, slope +1) and on the basis of the factors contributing to the energy of the final state ion in the Auger transition (a grid of line, slope −1). Tetrahedral aluminum has a significantly smaller Auger parameter than octahedral aluminum, and this difference is repeated, but with reduced magnitude on the similar plots for silicon and oxygen lines for the same compounds. Otherwise, the Auger parameters for this class of compounds are remarkably uniform. The Auger parameter values for oxygen and sodium in these compounds, using the 1s and KLL lines, are relatively small compared to those of other compounds of oxygen and sodium. For compounds of similar Auger parameter, differences in Auger final state ion energy are interpretable on the basis of electron density on aluminum and silicon atoms in the initial state, due to extent of bonding to oxygen, or to amount of negative formal charge on the silicate structure. Inclusion of tetrahedral aluminum enhances the negative charge and decreases the final state ion energy in high alumina zeolites. The difference between the energies of the O1s and Si2p lines in the inorganic silicon compounds is almost invariant, 429.0 to 429.6 eV. The three silicon polymers examined have a significantly larger line difference, 429.8 to 430.1 eV, making possible a differentiation between silicones and silicates. The oxygen KVV lines, with Auger transition final vacancies in valence levels, have shapes characteristic of chemical structure. The uncharged Si–O–Si structure exhibits a well-defined shoulder; in Al–O–Si the shoulder is so close in energy it merely gives rise to asymmetry in the peak; Al–O–Al and charged Si–O–Si give oxygen KVV lines as single sharp peaks.

Fractal geometry is a non-Euclidean geometry which has been developed to analyze irregular or fractional shapes. In this paper, fracture in ceramic materials is analyzed as a fractal process. This means that fracture is viewed as a selfsimilar process. We have examined the fracture surfaces of six different alumina materials and five glass-ceramics, with different microstructures, to test for fractal behavior. Slit island analysis and Fourier transform methods were used to determine the fractal dimension, D, of successively sectioned fracture surfaces. We found a correlation between increasing the fractional part of the fractal dimension and increasing toughness. In other words, as the toughness increases, the fracture surface increases in roughness. However, more than just a measure of roughness, the applicability of fractal geometry to fracture implies a mechanism for generation of the fracture surface. The results presented here imply that brittle fracture is a fractal process; this means that we should be able to determine processes on the atomic scale by observing the macroscopic scale by finding the generator shape and the scheme for generation inherent in the fractal process. [

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