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The coarsening of the nanoporous structure developed in undoped and 3% Sb-doped SnO{sub 2} sol-gel dip-coated films deposited on a mica substrate was studied by time-resolved small-angle x-ray scattering (SAXS) during in situ isothermal treatments at 450 and 650 deg. C. The time dependence of the structure function derived from the experimental SAXS data is in reasonable agreement with the predictions of the statistical theory of dynamical scaling, thus suggesting that the coarsening process in the studied nanoporous structures exhibits dynamical self-similar properties. The kinetic exponents of the power time dependence of the characteristic scaling length of undoped SnO{sub 2} and 3% Sb-doped SnO{sub 2} films are similar ({alpha}{approx_equal}0.09), this value being invariant with respect to the firing temperature. In the case of undoped SnO{sub 2} films, another kinetic exponent, {alpha}{sup '}, corresponding to the maximum of the structure function was determined to be approximately equal to three times the value of the exponent {alpha}, as expected for the random tridimensional coarsening process in the dynamical scaling regime. Instead, for 3% Sb-doped SnO{sub 2} films fired at 650 deg. C, we have determined that {alpha}{sup '}{approx_equal}2{alpha}, thus suggesting a bidimensional coarsening of the porous structure. The analyses of the dynamicalmore » scaling functions and their asymptotic behavior at high q (q being the modulus of the scattering vector) provided additional evidence for the two-dimensional features of the pore structure of 3% Sb-doped SnO{sub 2} films. The presented experimental results support the hypotheses of the validity of the dynamic scaling concept to describe the coarsening process in anisotropic nanoporous systems.« less

physical review b

Dynamical scaling properties of nanoporous undoped and Sb-doped<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="normal">Sn</mml:mi><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math>supported thin films during tri- and bidimensional structure coarsening

Dynamical scaling properties of nanoporous undoped and Sb-dopedSnO2supported thin films during tri- and bidimensional structure coarsening