Experiments on the angular intensity distribution of x-rays scattered by porous materials (hole structures) in the range of small angles are described. It is shown that the scattering can be characterized by an exponential correlation function in the case of a distribution of holes of random shape and size in solid; a theoretical derivation of the exponential function is given for this case. When the correlation function is an exponential, the rule holds that the reciprocal square root of the scattered intensity is a linear function of the square of the scattering angle. The specific surface of the material is determined by the slope of this straight line. Specific surfaces of a number of compositions are calculated from their experimental correlation functions and compared to surfaces based on adsorption measurements.

The Porod law states that i(h), the intensity of Xradiation scattered by an ideal multiphase noncrystalline system, for 'large' momentum transfer values (= h) approaches C~h-4 and that ~ is linearly related to the interphase surface areas. A more general expression is obtained which relates the value of the correlation-function derivative at the origin to the integral of the discontinuity of the electron density fluctuation along the discontinuity surface. Debye's assumption, by which the continuous electron density of the sample is approximated by a discrete-valued one, is critically discussed. The validity of the approximation results in the presence of a Porod plateau [hai(h) =constant]. The momentum transfer rangewhere the plateau is observed is related to the scale of lengths where the sharp-boundary idealization remains essentially unchanged. It is argued that the scattered intensity can show more than one Porod plateau and some examples of correlation functions with this behaviour are reported. The problem of the background subtraction is discussed and the corresponding coefficients are related to the electron densities relevant to the real and to the associated sharp-boundary sample.

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347major difference between them is that one is based on a narrow sublattice d band (V-V) neglecting the cation-anion-cation interactions, and the other implies a wider band due to a large degree of hybridization between the oxygen 2p and vanadium 3d orbitals. Whichever it may be, the doubling in size of the unit cell from the tetragonal to the monoclinic symmetries results in a reduction by one-half of the size of the Brillouin zone and the opening of an energy gap. The energy gap is a function of the monoclinic distortion, and as described in the previous section, this distortion seems larger in the non-stoichiometric VO2.07 than in VOz.00. Although little can be said about the transport mechanism in the low-temperature phase because of the lack of knowledge regarding the details of the nature of the defects involved, the experimental data with specimens of well-characterized chemical composition (see, for instance, Kimizuka et al., 1970) strongly suggest that the degree of monoclinic distortion has an essential bearing on the transport behaviour of vanadium dioxide. Precise measurement of the lattice parameters of the low-temperature phase is needed as well as further investigations of the lattice vibrational spectra throughout the low-and hightemperature phases.References ADLER, D. (1968) J. AppL Cryst. (1971). 4, 347Scattering from a Multiphase System The theory of small-angle X-ray scattering or light scattering from a system of N randomly distributed, internally homogeneous phases is presented. The special case of three components yields a correlation function which is the sum of two exponential terms whose associated 'correlation lengths' are complicated functions of all the interphase surfaces and volume fractions and cannot, therefore, be interpreted in a simple way. From the correlation function, three independent parameters are obtained which in principle may be used to determine the three interphase surfaces $2~, $23 and $31, provided the volume fractions of the phases are known.

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A supported‐metal catalyst can be considered as a mixture of three homogeneous phases: support, void and metal. Information about the metal phase alone can be obtained using anomalous small‐angle X‐ray scattering (ASAXS), which requires measuring the SAXS for two different wavelengths near the metal's absorption edge. Herein, the conditions that must be obtained so that the difference between the two scattering profiles gives the scattering of the metal alone are presented. In a following contribution, the analysis will be applied to in situ ASAXS measurements made on mordenite impregnated with platinum metal while the temperature and composition of gas in the sample cell are changed. The metal particles are assumed to be randomly distributed spheres with N(R)dR being the number of spheres with radii between R and R + dR. From N(R) one can obtain the average value of R.

Small-angle X-ray scattering observations on Pt/NaY catalysts, made in situ during calcination and reduction stages of processing, demonstrate the usefulness of this technique in following morphological changes. Observations show that the same platinum species (Pt ° under the preparation conditions used) is present in the early stages of calcination, carried out at relatively high heating rates, as after reduction, and that the ultimate dispersity of the metal is already reached within 0.5 h of the start of calcination. Increasing aggregation of metal particles occurs at calcination temperatures higher than 573 K, leading to average particle sizes too large to fit the supercages of the zeolite framework. With the assumption that the metal is a Maxwellian distribution of spheres, values of the distribution parameters giving the best fit to the scattering for each catalyst sample are found; from these parameters, average particle radii are calculated.

A structural model, based on Voronoi polyhedral cells partly filled with support and metallic catalyst, is proposed for interpreting the small‐angle X‐ray scattering of heterogeneous catalysts. The model's properties are described, and the model is applied to porous Al2O3 and Pt/porous Al2O3. Surface areas calculated from the X‐ray data by means of the statistical geometry of Voronoi tesselations are found in good agreement with those determined by BET (Brunauer, Emmett & Teller) adsorption methods.