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One of the crucial characteristics of functionalized thin films is their porosity (i.e., the ratio between the pore volume and the volume of the whole film). Due to the very low amount of material per coated area corresponding to thin films, it is a challenge for analytics to measure the film porosity. In this work, we present an Approach to determine the porosity of thin films by means of electron probe microanalysis (EPMA) either by wavelength-dispersive X-ray spectrometry (WDX) or by energy-dispersive X-ray spectrometry (EDX) with a scanning electron microscope (SEM). The procedure is based on the calculation of the film mass deposition from electron-excited X-ray spectra. The
mass deposition is converted into film density by division of measured film thickness.
Finally, the film porosity is calculated from the measured film density and the density of bulk, nonporous film material. The general applicability of the procedure to determine the
porosity is demonstrated on thin templated mesoporous TiO₂
films, dip-coated on silicon
wafer, with controlled porosity in the range of 15 to 50%. The high accuracy of the mass deposition as determined from X-ray spectra was validated with independent methods (ICP-OES and weighing). Furthermore, for the validation of the porosity results, ellipsometry, interference fringes method (IFM), and focused ion beam (FIB) cross sectioning were employed as independent techniques. Hence, the approach proposed
in the present study is proven to be suited as a new analytical tool for accurate and relatively fast determination of the porosity of thin films.
This work provides accurate experimental (p, rho, T) values for three binary mixtures of methane with helium: (0.95 (amount-of-substance fraction) CH₄+ 0.05 He) and (0.90 CH₄+ 0.10 He) at temperatures of (240, 250, and 260) K and (0.50 CH₄+ 0.50 He) from (240 to 400) K. This work is a continuation of a previous one which reported accurate experimental (p, rho, T) values for the (0.95 CH₄+ 0.05 He) and the (0.90 CH₄+ 0.10 He) binary mixtures over the temperature range from (250 to 400) K. All density measurements were performed by using a single-sinker densimeter with magnetic suspension coupling at pressures up to 20 MPa. Experimental values were compared with the corresponding densities calculated from the GERG-2008 and the AGA8-DC92 equations of state, respectively. Deviations from the GERG-2008 are much larger than from the AGA8-DC92 (up to -6.5%). These deviations increase with decreasing temperature, with increasing pressure, and with increasing helium fraction. In contrast, deviations from the AGA8-DC92 are within the 0.5% band. The experimental values were also used to calculate the second and the third virial coefficients, B(T,x) and C(T,x), as well as the second interaction virial coefficient B12(T) for this mixture.