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Information about the metal phase in a supported-metal catalyst can be obtained using anomalous small-angle X-ray scattering (ASAXS). The difference between the scattering profiles for SAXS at two different wavelengths near the metal's absorption edge is essentially the scattering of the metal alone. Novelin situASAXS measurements are made on mordenite impregnated with platinum metal while the temperature and composition of gas in the sample cell are changed. Measurements are made 62 times during treatment of the catalyst. The metal particles are assumed to be randomly distributed spheres withN(R)dR= number of spheres with radii betweenRandR+ dR. It is found thatN(R) is always a monotonically decreasing function ofR, and that the average value ofR, obtained fromN(R), decreases by a factor of two over the time (approximately 6 h) for which the system is observed.

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 toin situASAXS 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 withN(R)dRbeing the number of spheres with radii betweenRandR+ dR. FromN(R) one can obtain the average value ofR.

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 0 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.

Solid, multicomponent, multiphase catalysts, for example platinum supported on SiO2, play an important technological and economic role. The correlations between catalytic activity and the physical and chemical properties of these materials have been the subject of many investigations (see, for instance, Treacy, Thomas &. White, 1988). From the point of view of small-angle scattering (SAS), these catalysts are favorable objects of study: contrasts are high, and the important morphological features are of a size appropriate for SAS measurements.

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.

Small-angle X-ray scattering measurements have been performed on TiO2 supports and PtTiO2 catalysts reduced at low and high temperatures, the latter exhibiting a strong metal-support interaction. For the supports the small-angle scattering yielded specific surface areas in good agreement with those from gas adsorption measurements, although with smaller error. To extract surface areas for the multiphase (support, metal, void) catalysts requires additional theory, developed here. In addition to scattering intensities for the catalyst, one uses the scattering intensities of a support which has undergone similar treatment (acidification, reduction, etc.). Metal surface areas considerably smaller than those deduced from electron micrographs of model catalysts are then calculated from the small-angle X-ray scattering. The free metal surface decreases by about 14 in going from “normal” to SMSI catalyst, and this agrees well with electron microscopic observations. Temperature-programmed reduction, undertaken to gain information on the state of the metal, suggested the possible existence of PtO and PtO2. If electron densities appropriate to these bulk phases are assumed in interpreting the X-ray scattering results, we find a much larger difference between “normal” and SMSI catalyst surfaces, however, than is suggested by electron micrographs.

The Porod law states that i(h), the intensity of X-radiation scattered by an ideal multiphase noncrystalline system, for `large' momentum transfer values (≡ h) approaches lh−4 and that l 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 [h4i(h) = constant]. The momentum transfer range where 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.

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.

For amorphous multiphase systems, a model based on the division of space into cells, each of which is filled with one phase or another on a random basis, has been shown useful. We here propose an improvement, which allows for correlations between the contents of neighboring cells, and apply it to samples of SiO 2 , Al 2 O 3 , and catalysts using SiO 2 and Al 2 O 3 as supports. Compared to the uncorrelated-cell model, the predicted scattering intensities fit the measured intensities significantly better. The value determined for the additional correlation parameter indicates an enhanced tendency for neighboring cells to contain the same phase. Interphase surface areas are derived and compared with other measurements. The additional parameter does not suffice to define all the surfaces for a system of more than two phases; an additional assumption is required.

A method for obtaining the surface areas `void-support' (S21), `metal-support' (S31) and `metal-void' (S32) from small-angle X-ray determinations of the initial slopes of the correlation functions of metal-free porous support and supported metal catalyst is given. The postulated model requires no special assumptions about the numerical value of S31, and appears applicable to certain experimentally observed systems.

Das Ziel der vorliegenden Untersuchung ist vor allem die Ermittlung des kristallinen und amorphen Anteils der untersuchten Proben aus dem mittleren Schwankungsquadrat der Elektronendichte, die aus der Absolutintensitat der Rontgenkleinwinkelstreuung hergeleitet werden kann. Es sollen ferner die mittleren Dimensionen der kristallinen Anteile aus der Intensitat des Auslaufes der Streukurven berechnet werden.

Die Naherungsmethode, die Losungsmittelstreuung von der Streuung der Losung abzuziehen, um so die Streuung der gelosten Partikel zu erhalten, wird fur mehrere Modelle im Detail gepruft. Es stellt sich heraus, das von der Losungsmittelstruktur herruhrende winkelabhangige Terme in der Intensitatsdifferenz aufscheinen, wenn das Losungsmittel raumlich korrelierte Dichtefluktuationen zeigt. Diese Terme werden auf ihr Verhalten hin untersucht.

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 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 S21, S23 and S31, provided the volume fractions of the phases are known.

Experimental small-angle X-ray scattering intensities, generated from a primary beam of known intensity profile, are often `desmeared' to obtain point-collimated intensities. A much simpler way is shown of using the known beam intensity profile to derive, from the experimental scattering intensity, the quantities required for calculation of surface areas.

Small-angle X-ray scattering of the liquid sodium-37 w/o lithium system in the range 1.034 × 10 -4 ⪕ (T−T c )/T c ⩽ 1.503 × 10 -2 yields the critical exponents v = 0.655 ± 0.030 and λ = 1.296 ± 0.061 for the temperature dependence of the correlation length η and of the coefficient (∂ c /∂μ) T, P respectively.

The surface areas of a homologous series of silica-alumina catalysts carefully prepared by co-precipitation methods have been determined by small-angle X-ray scattering (SAXS) and BET. A model assuming a single homogeneous solid phase at the average electron density corresponding to the sample composition has been used to analyze the scattering data. The results demonstrate the validity of the simple model, BET and SAXS areas are in good agreement for the mixed oxides of intermediate composition. The largest differences occur for those samples where alumina aggregation is expected during preparation.

Geil1 and Keith and Padden2 prepared small spherulites and hedrites of poly-L-alanine. We have now studied the morphology and structure of such spherulites of larger size and much greater perfection which were formed in essentially 100 per cent yield by casting poly-L-alanine (40 mg) from solution (4 ml.) of trifluoroacetic acid and trifluoroethanol (1:1 v/v). The solvent was allowed to evaporate very slowly (1 ml./12 h) at room temperature from a large watch glass.

The slit-smeared intensity of X-radiation scattered from carbon-supported metal catalysts behaves as clh−1 + c2h−3 for higher h-values in the small-angle region (h+4πλ−1 sinθ, λ + X-ray wavelength,θ + half of scattering angle, c1, c2 are constants). For three-phase systems with sharp phase boundaries, uniform electron-densities in the metal and void phases, and lamellar electrondensity fluctuations in the carbon phase, the small-angle X-ray scattering (SAXS) can be described in terms of inter- and intraphase electron-density correlation functions, and can be shown to yield the observed behavior. Further assumptions are required to separate these contributions and calculate interfacial specific surfaces. SAXS measurements on Pt, Ru, Pd, and Rh/C are presented.

The homogeneous gas phase reaction between diborane and phosphine at 0°C, yielding a solid product of composition BH_3PH_3, has been observed to give a linear relation between the initial rate of reaction and the pressure of either reactant, provided a certain pressure of each reactant, determined by the equilibrium constant and the pressure of the other gas, is exceeded. The reaction rate is independent of the amount of surface of the solid product or of the wall. When either reagent is in appreciable excess, the rate‐time data obey a pseudo first‐order equation. These facts are consistent with a rate‐controlling reaction of diborane with phosphine to give BH_3PH_3 and BH_3, the borine reacting further with phosphine, and the BH_3PH_3 condensing rapidly to a solid. This mechanism leads to a rate equation which is in good agreement with the experimental evidence. The activation energy of the rate‐controlling step is 11.4±2.0 kcal mole^(-1).

The radius of gyration and “persistence length” of poly-L-alanine, calculated from small-angle x-ray scattering data, have values of 56 A and 44 A, respectively, in dichloroacetic acid, and 78 A and ∼30 A in a 1:1 v/v mixture of trifluoroacetic acid and trifluoroethanol. This can be interpreted to mean that poly-L-alanine exists in a relatively rigid, predominantly α-helical conformation in dichloroacetic acid and in an extended, more flexible form in the mixed solvent system.

It is shown that the correlation function and X-ray scattering of a random two-phase system are different from that of a scatterer formed from a random three-phase system by replacement of one of the phases with material of equal electron density to one of the other two (for example, pores filled with liquid of equal density to that of the support in a supported-metal catalyst).

Design of a high‐temperature furnace and sample cell for measuring the small‐angle x‐ray scattering of liquids or solids with the Kratky camera is reported. The cell may be used to 750°C with constancy of ±0.05 C°; a crucible for charging liquid metal mixtures into the cell in situ under inert atmospheres is also described.

The small-angle X-ray slit-correction computer programs of Heine & Roppert, Schmidt and Hossfeld have been compared. The scattering function for monodisperse spheres was used as the test case. With the exception of relatively minor differences in machine time and ease of application, all three programs appear adequate in meeting the usual demands of the experimenter.

WE have recently examined various effects of high-speed electron radiation on the properties of polyethylene. Among other effects, we observed that the intensity of fluorescence (excited by mercury-lamp illumination of a polyethylene sample previously electron-beam irradiated) increased linearly with radiation dosage in the range from 0 to 40 Mrads. The fluorescence is persistent, reproducible and easily measured, and thus may be useful for dosimetry applications.

Thyroglobulin is a protein involved in the synthesis, storage and secretion of thyroid hormones, reported here are some small-angle X-ray measurements primarily concerned with determination of its shape parameters in solution.

A thin single crystal difl'racting in the Laue position astigmatically images the source at a distance from the crystal eq ual to that of the ~ourcc from the crystal. 2 The focusing is not dependent on the spectral purity of the source to a first approximation. If the source is made small (i.e., a microfocus tube) and the optical path length made large, conditions obtain which are of interest for small-angle scattering; the scatterer is placed close to the crystal between it and the detector and a beam stop employed at the focus. Since crudely monochromatized radiation suffices in most small-angle scattering work, the lack of wavelength discrimination in the above arrangemen t may be exploited to gain intensity. Realization of such a scattering camera is, of course, crucially dependent on the perfection of the crystal. The problems of preparing a suitably thin (Mtl< 1) crystal and subsequently mounting it in some strain-free fashion appear somewhat formidable. The requirement that the crystal be thin may be avoided by employing a crystal of sufficiently high perfection that it exhibits a strong Bonmann efl'ect. Such crystals have recently become readily available and have been used in the device described below. The intensity loss in the crystal used (Mzt "",40) is, however, quite appreciable compared to the thin crystal case so that, when intensity requirements are severe, efforts toward realization of the thin crystal case should be considered.