Fractal behavior of the BCC / FCC phase separation in iron-gold alloys

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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, - PowerPoint PPT Presentation

Text of Fractal behavior of the BCC / FCC phase separation in iron-gold alloys

  • Fractal behavior of the BCC/FCC phase separation in iron-gold alloys

    Artur Bachowski 1, Krzysztof Ruebenbauer 1, Anna Rakowska 2,3

    1 Mssbauer Spectroscopy Division,Institute of Physics, Pedagogical University, Krakw, Poland

    2 Faculty of Materials Science and Ceramics, AGH University of Science and Technology, Krakw, Poland

    3 Institute of Metallurgy and Materials Science, Polish Academy of Science, Krakw, Poland

  • Fe-Au Phase Diagram

    BCCFe(Au)as-cast 3 at.% Auannealed ~0 at.% Au

    FCCAu(Fe)as-cast 33 at.% Feannealed 23 at.% FeFe70Au30 and Fe50Au50

    as-cast and annealed 250C/24h + 500C/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 300000x

  • Fe70Au30as-castEDS results (1 m scale)14 at.% Au in dark regions and 45 at.% Au in bright regions

  • Fe50Au50as-castEDS results (1 m scale)49 - 56 at.% Au

  • Fe70Au30annealedEDS results (1 m scale)14 at.% Au in dark regions and 45 at.% Au in bright regions

  • Fe50Au50annealedEDS results (1 m scale)19 at.% Au in dark regions and 75 at.% Au in bright regions

  • What is fractal? self-similarity fractal dimension1) mathematical fractalSierpiski carpet and triangle, Mandelbrot set, Julia set, Barnsleys fern (atractor)

    2) natural fractalmountain 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 = 1.8928 Test

  • diffusion limited aggregation (DLA) fractal d = 1.71Results

  • 500 m 500 nmConclusions

    self-similarity fractal dimension similar to (hydrodynamic) DLA fractal