Multirange fractal approach to analyze the microstructure of Sn melt

Based on results of X-ray diffraction experiment, multirange fractal approach has been used to discuss the discontinuous microstructure changes of Sn melt. Partially-overlapping multirange fractal structure is observed, and as temperature decreases from 900°C to 240°C, low fractal dimension reveals discontinuous changes from 2.8682 to 2.4192, which can divide the cooling process into three regions. Nevertheless, high fractal dimension is still 3.000 without alteration. Multirange fractal characteristics of Sn melt were correlated with the evolution of microstructure. The discussion was made in detail. Multirange fractal model was proposed to calculate transition curves of multirange fractals by utilizing relevant low dimensional fractals and high dimensional fractals of Sn melt at different temperatures. The results show that values of simulation show good agreement with experimental values, the maximum error ranges from 0.09% to 0.89%. From the analysis, the range of the transition region between two fractal regions is speculated to be related with the properties of metal melts. In addition, ultrafine particle and its aggregation mechanism were used to analyze the fractal morphologies.