Application of fracton theory to nanocrystalline iron

The dimensionality of harmonic modes in nanocrystalline iron is determined by a nonlinear method, and the result is analysed in terms of the Debye model and a fracton model. The negative of the exponent of the recoiless fraction, F, is calculated as a function of temperature from data in the literature. It is found that the temperature variation of F cannot be reproduced by the Debye model for two- or three-dimensional lattices, but can be reasonably well fit by a fracton model. Using the fracton model, it is found that the density of states scales with modal frequency and has a scaling exponent of 1.22 +/- 0.13. This suggests that the modes have a dimensionality,<(d)double over bar> , of 2.22 +/- 0.13. It is concluded that the value of <(d)double over bar> may indicate the presence of fractons and a fractal atomic structure in nanocrystalline iron.