Fractal structure and fractal dimension determination at nanometer scale

Three-dimensional fractures of different fractal dimensions have been const ructed with successive random addition algorithm, the applicability of vari ous dimension determination methods at nanometer scale has been studied. As to the metallic fractures, owing to the limited number of slit islands in a slit plane or limited datum number at nanometer scale, it is difficult to use the area-perimeter method or power spectrum method to determine the fr actal dimension. Simulation indicates that box-counting method can be used to determine the fractal dimension at nanometer scale. The dimensions of fr actures of valve steel 5Cr21Mn9Ni4N have been determined with STM. Results confirmed that fractal dimension varies with direction at nanometer scale. Our study revealed that, as to theoretical profiles, the dependence of frac tal dimension with direction is simply owing to the limited data set number , i.e, the effect of boundaries. However, the dependence of fractal dimensi on with direction at nanometer scale in real metallic fractures is correlat ed to the intrinsic characteristics of the materials in addition to the eff ect of boundaries. The relationship of fractal dimensions with the mechanic al properties of materials at macrometer scale also exists at nanometer sca le.