A numerical method for the solution of multi-point problems for ordinary differential equations with integral constraints

We propose a method for the solution of a system of nonlinear ordinary differential equations with integral constraints, by transforming to multi-point boundary value problems. Examples are given.     

Chemical reactions of N 2+ ion beams with group IV elements and their oxides

Ion beam studies of the reactions between nitrogen and surfaces of Group IV elements and their oxides resulting in nitride formation are reported. XPS and UPS are used to examine the products induced by 500 eV N ₂⁺ beams on diamond, graphite and elemental Si, Ge, Sn, Pb and their oxides. Nitrogen adds to the graphite in two positions: at the carbon rings and intersitually between the layers of rings. Reaction with Si, Ge and Sn produces nitrides which are similar to those of the type M ₃N ₄. Reaction with oxides forms nitrides with no evidence of nitrate or nitrite formation. The chemical nature of the reaction is supported by identification of the products through energy level shifts and by the agreement with thermodynamic predictions.     

Far infrared laser magnetic resonance spectra of the ClSO and FSO radicals in the gas phase

The detection of the free radicals ClSO and FSO by the technique of far infrared laser magnetic resonance is reported. Observations of the former have been made with several laser lines; the spectra are complicated and have not been assigned but are attributed to ClSO on the basis of several chemical tests. The FSO radical was generated by the reaction of carbon disulphide with the products of a discharge through CF₄ + O₂. Spectra have been observed with laser lines at 394, 419 and 513 μm. Using the results of a subsequent microwave study of FSO, the rotational transitions involved in these spectra have been identified. The spectrum at 513 μm has been studied in detail and is shown to arise through level anticrossings between the levels 14_5,Kc (the lower levels involved in the transition) and 15_4,Kc+2. All aspects of this spectrum are reproduced quantitatively by the parameters determined from the microwave spectrum. It is thought that the other two FSO spectra arise in a similar manner. Such anticrossing signals are likely to be widespread in LMR experiments, causing intense narrow lines to occur at high magnetic fields even for molecules with weakly coupled electron spin.     

Global perspectives for secondary reference materials for analysis of food and related biological samples

Primary, secondary and tertiary reference materials (RM) play an important role in quality controls of analytical measurements. Logistics of preparation and proper use of primary and secondary RMs are presented. Tertiary (i.e. in-house) control materials are useful as substitutes in the absence of recognized primary or secondary RMs. The lack of interdisciplinary interaction during development of RMs (e.g. in specific areas such as foods), has an important impact on limiting the usefulness of certain types of RMs. The abundance of RMs in some countries and regions appears to have little effect on the existing paucity in RMs in other regions, and the underlying causes are outlined. The ability of a laboratory to produce good quality in-house RMs traceable to recognized primary or secondary RMs is a direct measure of its quest for reliable analytical data. Therefore many laboratories should be encouraged to engage in secondary and tertiary RM activities designed to answer specific measurement problems. In this context, assistance (e.g. practical training opportunities) in identifying simple methods of analyses for their efficacy in determining specific analytes is a source of help that can be extended to countries experiencing limitations in laboratory instrumentation.     

Low-temperature relaxations in styrene-crosslinked polyester networks. III. Influence of water concentration and chemical structure on the γ relaxation

The intensity of the water-induced γ relaxation (see ref. 1) in crosslinked polyester networks in creases rapidly at low water concentrations (0 to 0.5% by weight). At higher water concentrations (0.5 to 3.0%) the intensity of the γ relaxation approaches a constant value. The shift of the relaxation peak to lower temperatures shows a similar pattern of behavior. These results have been related to the fraction of water involved in the relaxation and the changing nature of the relaxation sites with the increase in water concentration. The important role that fumarate units play in the γ relaxation has also been confirmed; however, the chemical nature of the relaxing unit appears to be more complex than was originally considered. Two models are proposed for this behavior.     

Methoxylation of magnesium studied by direct recoil spectroscopy,SIMS and XPS: Calibration of relative surface hydrogen concentration

Chemisorption of methanol on polycrystalline magnesium is studied by time-of-flight analysis of directly recoiled (DR) surface atoms, angular resolved X-ray photoelectron spectroscopy (XPS), and secondary ion mass spectrometry (SIMS). The combined measurements show that decomposition occurs to form ～ 0.14 monolayers of surface hydroxide at methanol exposures < 4 L. High exposures result in molecular chemisorption to form a single methoxide overlayer. The DR results reveal that the C and H of the methyl group are the outermost atoms on the saturated surface. Analysis of DR intensities allows calibration of the relative signals and comparison with calculated recoil cross sections. The methoxide/Mg system provides a standard for surface hydrogen concentrations by the direct recoil technique.     

High-frequency measurements of blast wave propagation

Blast wave propagation measurements were conducted to investigate nonlinear propagation effects on blast waveform evolution with distance. Measurements were made with a wide-bandwidth capacitor microphone for comparison with conventional 3.175-mm (1/8-in.) microphones with and without baffles. It was found that the 3.175-mm microphone did not have sufficient high-frequency response to capture the actual rise times in some regions. For a source of 0.57 kg (1.25 lb) of C-4 plastic explosive, the trend observed is that nonlinear effects steepened the waveform, thereby decreasing the shock rise time, up to a range of 50 m. At 100 m, the rise times had increased slightly.