Fractal behavior of the BCC/FCC phase separation in iron-gold alloys Artur Błachowski 1, Krzysztof Ruebenbauer 1, Anna Rakowska 2,3 1 Mössbauer Spectroscopy.

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Fractal behavior of the BCC/FCC phase separation in iron-gold alloys Artur Błachowski 1, Krzysztof Ruebenbauer 1, Anna Rakowska 2,3 1 Mössbauer Spectroscopy Division, Institute of Physics, Pedagogical University, Kraków, Poland 2 Faculty of Materials Science and Ceramics, AGH University of Science and Technology, Kraków, Poland 3 Institute of Metallurgy and Materials Science, Polish Academy of Science, Kraków, Poland

Fe-Au Phase Diagram BCC–Fe(Au) as-cast 3 at.% Au annealed ~0 at.% Au FCC–Au(Fe) as-cast 33 at.% Fe annealed 23 at.% Fe Fe 70 Au 30 and Fe 50 Au 50 as-cast and annealed 250ºC/24h + 500ºC/48h Nanoparticles of FCC-Au(Fe) and BCC-Fe(Au) phases with diameter about 50 nm !!! Ultra high-resolution scanning electron microscope SEM-FEG + EDS (Nova 200 NanoSEM) 200x – x

Fe 70 Au 30 as-cast EDS results (1 μm scale) 14 at.% Au in dark regions and 45 at.% Au in bright regions

Fe 50 Au 50 as-cast EDS results (1 μm scale) at.% Au

Fe 70 Au 30 annealed EDS results (1 μm scale) 14 at.% Au in dark regions and 45 at.% Au in bright regions

Fe 50 Au 50 annealed EDS results (1 μm scale) 19 at.% Au in dark regions and 75 at.% Au in bright regions

What is fractal? – self-similarity – fractal dimension 1) mathematical fractal Sierpiński carpet and triangle, Mandelbrot set, Julia set, Barnsleys fern (atractor) 2) natural fractal mountain landscape, window frost, cauliflower surface, blood vessels, exchange quotations

Roughness method Image were pixelized into square pixels with L = 8 bits per pixel representing linear gray scale with the highest value ( 255 ) representing white. N = 2048 pixels vertical and M = 2375 pixels horizontal. fractal dimension r - pixel edge size log R log r

d = 1.903(4) d = Test

diffusion limited aggregation (DLA) fractal d = 1.71 Results

500 μ m 500 nm Conclusions – self-similarity – fractal dimension similar to (hydrodynamic) DLA fractal