journal menu
research papers
Small-angle X-ray scattering (SAXS) can be used to obtain interphase surface areas of a system, such as a supported-metal catalyst, composed of internally homogeneous phases with sharp interphase boundaries. Measurements of SAXS for samples of porous silica, alumina, platinum on silica, and platinum on alumina are reported. A variety of models and forms for the correlation function, the Fourier transform of which gives the X-ray scattering, are considered, and theoretical and measured intensities are compared. A criterion of fit for comparing models with different numbers of parameters is proposed. For the two-phase (unmetallized) systems the `Debye-random' model must be rejected. Modifications of the Debye (exponential) correlation function are also not particularly good compared to an exponential-plus-Gaussian form, not derivable from a physical model, and forms based on Voronoi cell models. Since intensities can be fit to experimental error with a five-parameter correlation function, it seems incorrect to ascribe significance to the result of fitting a function with six or more parameters. It is shown that values for the single interphase surface area can be obtained independently of a model. However, fitting intensities using a model-based correlation function gives information about the structure of the system. The two-cell-size Voronoi and the correlated Voronoi cell models are useful in this regard. For the systems containing metal, five-parameter correlation functions again suffice to fit intensities. However, for three-phase systems a model or physical assumption is necessary to obtain values for the three surface areas from X-ray scattering intensities. The area of the surface between support and void is quite insensitive to the assumptions employed and the metal-support surface area somewhat less so, but values for the metal-void surface area S23 are consistent only to one significant figure from model to model. If the support in the three-phase catalyst is known to be unchanged from support in the absence of metal, a `support-subtraction' model can be used to obtain reliable values for S23. In the present systems, the assumption does not seem to be borne out.
