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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
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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.% Auannealed ~0 at.% Au
FCC–Au(Fe)as-cast 33 at.% Feannealed 23 at.% Fe
Fe70Au30 and Fe50Au50
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 – 300000x
Fe70Au30 as-castEDS results (1 μm scale)
14 at.% Au in dark regions and 45 at.% Au in bright regions
Fe50Au50 as-castEDS results (1 μm scale)
49 - 56 at.% Au
Fe70Au30 annealedEDS results (1 μm scale)
14 at.% Au in dark regions and 45 at.% Au in bright regions
Fe50Au50 annealedEDS 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 fractalSierpiński carpet and triangle, Mandelbrot set, Julia set, Barnsley’s fern (atractor)
2) natural fractalmountain landscape, window frost, cauliflower surface, blood vessels,
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2
1
2
4
1
21
12 )2( )2( 4
N
n
M
m iL
inm xxMNR
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
rR loglog
lo
g R
log r
d = 1.903(4)
d = 1.8928
Test
diffusion limited aggregation (DLA) fractal d = 1.71
Results
500 μm 500 nm
Conclusions
– self-similarity
– fractal dimension similar to (hydrodynamic) DLA fractal
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