Model showing how the in-plane stress develops in films during gel film (precursor)-to-polycrystalline or glass (product) film conversion. Residual stress is represented by closed circles. The open circle represents the intrinsic stress of the fired film. αfilm and αsub represent the thermal expansion coefficients of the film and substrate, respectively.
In-plane residual stress of the fired films measured at room temperature as a function of heat-treatment temperature. The heat-treatment was conducted at each temperature for 10 min.
In-plane intrinsic stress for the gel film measured in situ during heating at 5 °C/min. In order to assess the standard deviation of ΔR, the sample preparation and the deflection measurement were conducted three times.
Stress measured in situ during heating and cooling for the fired films. The films were fired at (a) 550, (b) 600, (c) 650, (d) 800, and (e) 950 °C before the stress measurement. The closed and open symbols represent the stress measured during heating and cooling, respectively. The heating and cooling rates in the stress measurement were 5 °C/min, but at low temperatures the cooling rate was smaller than 5 °C/min because of the heat capacity of the stress-measurement apparatus.
Film thickness plotted vs heat-treatment temperature. The gel films were heated at different temperatures (solid triangles) or heated successively up to 500 °C at intervals of 50 °C (solid circles). Each heat-treatment was conducted for 10 min.
TGA curve of the gel film obtained at a heating rate of 5 °C/min in air.
XRD patterns of the films fired at various temperatures for 10 min.
Integrated intensity of (111) and (220) peaks plotted vs firing temperature.
Crystallite size plotted vs firing temperature. The crystallite size was determined from the full width at half maximum of the (111) peak.
SEM pictures of the surface of the films fired at (a) 450, (b) 600, and (c) 950 °C for 10 min. All the films were crack-free in SEM scale as well. The film fired at 450 °C, which was amorphous, was composed of particles smaller than 7 nm in size. The crystallized samples fired at 600 and 950 °C had grains approximately 21–23 nm in size.
Stress-temperature curves showing how the residual stress is developed for films fired at temperatures below 500 °C. The intrinsic stress developed during heating (open circles) and the residual stress (solid squares) were taken from Figs. 2 and 3, respectively. All the residual stress values are plotted at room temperature.
Stress-temperature curves showing how the residual stress is developed for films fired at temperatures over 500 °C. The intrinsic stress developed during heating up to 500 °C (open circles) was taken from Fig. 2. The closed symbols represent the stress values measured in situ during heating the fired films, taken from Fig. 4. The intrinsic stress of the films at their firing temperatures (>500 °C) was estimated by extrapolating the closed symbol lines, and represented by double circles. All the residual stress values are plotted at room temperature.
Modified model showing how the stress develops in films during gel film-to-polycrystalline film conversion, illustrated on the basis of the present work. Intrinsic stress and residual stress are represented by open and closed circles, respectively. The model is drawn on the assumption that the fired films have larger thermal expansion coefficients than the substrate.
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