The quantitative analysis of thin specimens: a review of progress from the Cliff-Lorimer to the new ζ-factor methods

A new quantitative thin‐film X‐ray analysis procedure termed the ζ‐factor method is proposed. This new ζ‐factor method overcomes the two major limitations of the conventional Cliff‐Lorimer method for quantification: (1) use of pure‐element rather than multielement, thin‐specimen standards and (2) built‐in X‐ray absorption correction with simultaneous thickness determination. Combined with a universal, standard, thin specimen, a series of ζ‐factors covering a significant fraction of the periodic table can be estimated. This ζ‐factor estimation can also provide information about both the detector efficiency and the microscope–detector interface system. Light‐element analysis can also be performed more easily because of the built‐in absorption correction. Additionally, the new ζ‐factor method has several advantages over the Cliff‐Lorimer ratio method because information on the specimen thickness at the individual analysis points is produced simultaneously with compositions, thus permitting concurrent determination of the spatial resolution and the analytical sensitivity. In this work, details of the ζ‐factor method and how it improves on the Cliff‐Lorimer approach are demonstrated, along with several applications.     

Comparison between simulated moving bed and reverse flow chromatographic reactors for equilibrium limited reactions

A staged linear model, containing five parameters, is developed to compare equivalent simulated moving bed chromatographic reactors (SMBCR) and reverse flow chromatographic reactors (RFCR). A first order reversible reaction and linear adsorption equilibrium, with preferential adsorption of the reactant is assumed. The analysis uses simple, easily computable analytical solutions that rigorously represents the transients in the cyclic steady state for both the RFCR and the SMBR. A comparison between the two types of reactors is carried out to determine the maximum conversion attainable and the range of operation where these systems have advantages over conventional steady state reactors. It is found that the maximum conversion of both reactors is similar. The range of operation in terms of amount of catalyst and range of switching times favors the RFCR, while the conversion at low separation factors favors the SMBCR.     

Molecular design of supported niobium oxide catalysts

The current investigation demonstrates that it is possible to molecularly design supported niobium oxide catalysts with the assistance of molecular characterization methods such as Raman spectroscopy. The formation and location of the surface niobium oxide species are controlled by the surface hydroxyl chemistry, and the surface niobium oxide species are located in the outermost layer of the catalysts as an overlayer. The catalyst composition is a critical parameter since it affects the presence of different niobium oxide species (several different surface species and crystalline phases), and the reactivity also varies somewhat with surface niobium oxide coverage. The preparation method is not a critical parameter since it does not appear to influence the structure or reactivity of the surface niobium oxide species. However, for silica supported niobium oxide catalysts the preparation method does affect the amount of niobium oxide that can be dispersed as a two-dimensional overlayer. Calcination temperature is an important parameter that controls the activation and deactivation of the supported niobium oxide catalysts, but calcination temperature is not critical if moderate temperatures, 400–500°C, are used. The specific oxide support is a critical parameter since it dramatically affects the reactivity of the surface niobium oxide species and determines if the surface niobium oxide site is active for redox or acid catalysis. Thus, the critical parameters that affect the catalytic properties of the supported niobium oxide catalysts are the specific oxide support and catalyst composition.     

A yang-mills type minimal coupling theory for materials with dislocations and disclinations

Noting that the group $\text{S0(3) ? T(3)}$ may be viewed as a 6-parameter gauge group that leaves the Lagrangian of elasticity theory invariant, the Yang-Mills universal gauge theory construction is used to erect a complete continuum theory of material bodies with dislocation and disclination fields. Breaking of the homogeneity of the action of $\text{S0(3)}$ is shown to give rise to disclinations and rotational dislocations while homogeneity breaking of $\text{T(3)}$ gives rise to translational dislocations. A rigorous justification for replacing displacement gradients by the components of the distortion tensor and Newtonian kinematic velocity by distortional velocity is obtained. Exact determinations are made of the elastic excess forces, the forces on dislocations and the forces on disclinations, and these forces are shown to be totally equilibrating in all instances. Implications of the theory are given and an analysis is made of the field equations and associated dispersion relations that obtain in a disclination free material in the linear elasticity approximation.     

Cylindrical and spherical shells with cracks

The symmetric problem for the cylindrical and spherical shells containing a meridional crack is considered. The problem is solved for a uniform membrane load and a uniform bending moment applied to the surface of the crack. The extensional and bending components of the stress intensity factor ratio are obtained as functions of shell parameter and are tabulated. The results are also plotted in order to compare them with the existing asymptotic solutions.

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Zusammenfassung Das symmetrische Problem für zylindrische and sphärische Schalen, die einen meridionalen Riß haben, wurde behandeft. Das Problem wurde für eine einheitliche Membranlast and ein einheitliches Biegungsmoment auf der Oberfläche des Risses angewandt, gelöst.Die ausdehnenden und biegenden Komponente des Druckstärkefaktorenradius wurden als Funktionen des Schalenparameters erhalten and tabuliert. Die Ergebnisse wurden auch aufgezeichnet, um sie mit den bestehenden asymmetrischen Lösungen zu vergleichen.

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Résumé On considère le problème symétrique d'enveloppes cylindriques et sphériques comportant une fissure qui se développe suivant un méridien. La solution est apportée dans le cas d'une contrainte de membrane uniforme et d'un moment de flexion uniformément appliqué aux lèvres de la fissure.Ces composantes de traction et de flexion qui agissent sur le facteur d'intensité des contraintes sont determinées en fonction des paramètres de l'enveloppe, et présentées sous forme de tableaux. Les résultats ont 6t6 également portés en diagrammes, de manière à les comparer aux solutions asymptotiques existantes.

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This work was supported by the National Aeronautics and Space Administration under the Grant NGR 39-007-011.     

Failure prediction of the thermal fatigue resistance of a glass

The thermal fatigue behaviour of circular rods of soda-lime-silica glass subjected to a water quench was predicted from data for the rate of slow crack growth as a function of stress intensity factor, the pertinent physical properties, the initial crack depth as well as the heat transfer environment. A numerical integration technique was developed in order to calculate the total extent of slow crack growth for each cycle over the total duration of the transient thermal stress and temperature, as well as the total number of cycles required for catastrophic failure to occur. Good agreement between the predicted and experimental data was found.     

Fatigue crack propagation in polymeric materials

In order to gain a better understanding of matrix-controlled fatigue failure processes in non-metallic materials a series of fatigue tests were performed on several different polymer materials representing different classes of mechanical response. Fatigue crack propagation rates between 5×10^–6 in. cycle^–1 (127 nm cycle^–1) and 4×10^–4 in. cycle^–1 (10 300 nm cycle^–1) were measured in nylon, polycarbonate, ABS resin, low-density polyethylene and polymethyl methacrylate. A strong correlation was found between the fatigue crack propagation rate and the stress intensity factor range prevailing at the advancing crack tip. Whereas metals exhibit comparable fatigue growth rates for a given stress intensity range when normalised with respect to their static elastic modulus, the polymer materials exhibited a 1300-fold difference in crack growth rate for a given normalised stress intensity range. This observation dramatically illustrates the importance of understanding molecular motion and energy dissipation processes in polymer materials as related to their chemistry and architecture. The relative behaviour of the different polymer materials could be generally correlated with their reported damping characteristics.     

The effect of alkali halides and silver nitrate on the crystallization of silica powders

The effect of alkali halides on the crystallization of amorphous silica powders has been investigated. Normally crystallization does not occur below 1000°C, but in the presence of about 20% by weight of lithium chloride, -quartz forms within 2 h at 700°C. In the presence of sodium and potassium salts, -cristobalite forms at about 800 to 850°C. It appears that quartz is formed in the presence of the lithium salt because Li⁺ can enter the quartz lattice, whereas Na⁺ and K⁺ can penetrate the more expanded polymorphic form, cristobalite. It is possible that the cations are accompanied by oxide ions in all cases to maintain electrical neutrality. Limited penetration of the amorphous particles is sufficient to nucleate the new phase. Other properties of silica products treated with salts are reviewed.