Using small-angle x-ray scattering, we show that porous silica aerogel has a fractal backbone structure. The observed structure is traced to the underlying chemical (polymerization) and physical (colloid aggregation) growth processes. Comparison of scattering curves for aerogel with silica aggregates confirms this interpretation.In spite of the importance of random porous media in nature and in technology, the structure of these materials has eluded characterization.In this paper we show that certain classes of porous materials can be characterized through fractal geometry and that the appropriate geometry can be determined by small-anglex-ray scattering. We report the structure of a silica aerogel prepared by critical-point drying of an alcoholic (sic) silica gel. This material is chosen because of its exceedingly low density (0.09 g/cm3) and concomitant high porosity. We show that the porosity in this material is due to a random colloid aggregation process in the solution precursor. To our knowledge, this is the first time that the structure of a porous material has been explained in terms of random growth. Classical models of porosity-dependent properties are based on highly simplified geometrical structures like packed spheres or bottlenecked bubbles. ' Recently, fractal2 structures (percolation networks, fractal surfaces) have also been postulated to explain fluorescence3 and adsorption4 5 data for porous media. Although there have been many attempts to characterize the microstructure of porous materials, modeldependent geometric assumptions, like those above, have doomed all indirect methods.A primary goal of our work is to establish the existence of a fractally porous solid. To this end, we first outline the expected scattering patterns for simple fractal structures. The key to our interpretation is based on a qualitative distinction between surface and volume fractals. We find that the low-density aerogel has purely mass-fractal character and find no evidence for fractally rough surfaces.Scattering Pom Pactals. -To interpret scattering curves it is useful to distinguish between bulk and surface scattering. In systems without distinct surfaces, such as polymers in solutions, the scattered intensity,
The liquidus relations in the system YO1.5–BaO–CuOx in air in the compositional region near the superconducting oxide YBa2Cu3Ox were studied by differential thermal analysis, x-ray diffraction, electron microprobe analysis, and visual observation. The temperatures of 11 invariant points and the corresponding reactions were determined. YBa2Cu3Ox was found to melt incogruently at 1015 °C to Y2BaCuO5, which in turn melts incongruently to Y2O3 at 1270 °C. These reactions mean that preparing the superconducting phase by melting and rapid cooling will result in the presence of these two phases as well. The peritectic reaction YBa2Cu3Ox + CuO⇉Y2BaCuO5 + liquid at 940 °C accounts for the observation of partial melting, improved synthesis purity, and grain growth at temperatures of 950 °C. The determination of these invariant temperatures and reactions provide insight into optimal processing conditions.
Aluminum ions may exist in one of several different types of polynuclear species depending upon the degree to which it is hydrolyzed. The hydrolysis of aluminum can be explained by a metastable equilibrium among A1(H2O)6+, Al(OH)(H2O)s+, Al13O4(OH)24(H2O)i2f, and an oligomer. We have made small angle x-ray scattering and 27Al NMR measurements on 0.3 M aluminum chloride solutions over a range of OH/A1 ratios. 27A1 NMR shows two sharp peaks corresponding to the monomer A1(H2O)6+ and the tetrahedrally coordinated aluminum in Ali3O4(OH)24(H2O)i2f, and a broad peak due to the octahedrally coordinated aluminum in the oligomer. The observed radius of gyration (Rg) of the species in solution increases from 3.0 to 3.6 A, and the intensity at zero angle (which is proportional to the weight average molecular weight of the species) also increases as the 0H/A1 ratio increases from 1.0 to 2.2. The oligomer has an Rg of approximately 3.3 A, a hydrolysis ratio close to 2.0, and may be a six-membered ring with a structure similar to that of a gibbsite layer.
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