Algorithms for Coloring Quadtrees

We describe simple linear time algorithms for coloring the squares of balanced and unbalanced quadtrees so that no two adjacent squares are given the same color. If squares sharing sides are defined as adjacent, we color balanced quadtrees with three colors, and unbalanced quadtrees with four colors; these results are both tight, as some quadtrees require this many colors. If squares sharing corners are defined as adjacent, we color balanced or unbalanced quadtrees with six colors; for some quadtrees, at least five colors are required.     

Effect of thermal residual stresses on fatigue crack opening and propagation behavior in an Al/SiC p metal matrix composite

The effects of a thermal residual stress field on fatigue crack growth in a silicon carbide particle-reinforced aluminum alloy have been measured. Stress fields were introduced into plates of material by means of a quench from a solution heat-treatment temperature. Measurements using neutron diffraction have shown that this introduces an approximately parabolic stress field into the plates, varying from compressive at the surfaces to tensile in the center. Long fatigue cracks were grown in specimens cut from as-quenched plates and in specimens which were given a stress-relieving overaging heat treatment prior to testing. Crack closure levels for these cracks were determined as a function of the position of the crack tip in the residual stress field, and these are shown to differ between as-quenched and stress-relieved samples. By monitoring the compliance of the specimens during fatigue cycling, the degree to which the residual stresses close the crack has been evaluated. formerly Research Student, Department of Materials Science and Metallurgy, University of Cambridge formerly Lecturer, Department of Materials Science and Metallurgy, University of Cambridge This article is based on a presentation made in the symposium entitled “Creep and Fatigue in Metal Matrix Composites” at the 1994 TMS/ASM Spring meeting, held February 28–March 3, 1994, in San Francisco, California, under the auspices of the Joint TMS-SMD/ASM-MSD Composite Materials Committee.     

Comparison of supports for the direct synthesis of hydrogen peroxide from H2 and O2 using Au–Pd catalysts

The direct synthesis of hydrogen peroxide from H₂ and O₂ using a range of supported Au–Pd alloy catalysts is compared for different supports using conditions previously identified as being optimal for hydrogen peroxide synthesis, i.e. low temperature (2 °C) using a water–methanol solvent mixture and short reaction time. Five supports are compared and contrasted, namely Al₂O₃, -Fe₂O₃, TiO₂, SiO₂ and carbon. For all catalysts the addition of Pd to the Au only catalyst increases the rate of hydrogen peroxide synthesis as well as the concentration of hydrogen peroxide formed. Of the materials evaluated, the carbon-supported Au–Pd alloy catalysts give the highest reactivity. The results show that the support can have an important influence on the synthesis of hydrogen peroxide from the direct reaction. The effect of the methanol–water solvent is studied in detail for the 2.5 wt% Au–2.5 wt% Pd/TiO₂ catalyst and the ratio of methanol to water is found to have a major effect on the rate of hydrogen peroxide synthesis. The optimum mixture for this solvent system is 80 vol.% methanol with 20 vol.% water. However, the use of water alone is still effective albeit at a decreased rate. The effect of catalyst mass was therefore also investigated for the water and water–methanol solvents and the observed effect on the hydrogen peroxide productivity using water as a solvent is not considered to be due to mass transfer limitations. These results are of importance with respect to the industrial application of these Au–Pd catalysts.     

Propane conversion over zeolite catalysts: Comments on the role of Ga

The activation of propane using zeolite H-Y and Ga³⁺ exchanged zeolite Y indicates that in the presence of Ga³⁺ the mechanism of propane activation is changed from a cracking pathway to a dehydrogenation pathway. The presence of both Ga³⁺ and H⁺ are required to achieve this effect.     

Erosion of unfilled elastomers by solid particle impact

The response has been studied of eight unfilled elastomers (four natural rubber compounds, epoxidized natural rubber ENR50, butyl rubber, polybutadiene and polyurethane) to erosion by 150 m silica sand at an impact velocity of 48 m sec^–1. All were tested at an impact angle of 30°, close to the impact conditions occurring in pipe bends, while two were also tested at 90°. Wide variations in erosion rate were observed between different rubbers. These differences did not correlate systematically with the nature of the base elastomer, glass transition temperature or mechanical properties such as hardness, tensile strength or ultimate tensile elongation, nor with resistance to abrasive wear. Good correlation was, however, found with rebound resilience. A high resilience tended to imply high erosion resistance, The erosion rate was found empirically to be proportional to the quantity (1 - fractional resilience) raised to the power 1.4. Different surface morphologies were found in specimens of high and low resilience after erosion at 30°. Finely spaced transverse ridges formed on high-resilience rubbers, whereas surface features on low-resilience rubbers showed no directionality. Preliminary conclusions are drawn about possible mechanisms of material removal.     

Solvent-free oxidation of benzyl alcohol with oxygen using zeolite-supported Au and Au–Pd catalysts

The oxidation of benzyl alcohol to benzaldehyde has been investigated in the absence of solvent using zeolite-supported Au and Au–Pd catalysts. Three zeolites were investigated, ZSM-5, zeolite β and zeolite Y, and these were contrasted with the titanoslicalite TS-1 and TiO₂ as supports. For the Au catalysts the best results are obtained with zeolite β as the support and the conversions were comparable or better than those observed with TiO₂ in terms of turn over frequencies. However, the selectivities observed with the acidic zeolites were lower than the non-acidic TS-1 and TiO₂. This is due to the subsequent reaction of benzaldehyde via acid catalysed reactions to give benzyl benzoate and its dibenzyl acetal, and, in some cases dibenzylether. Initial catalysts were evaluated with a gold loading of 2 wt% and increasing this to 4 wt% showed the expected increase in activity, indicating that there is scope to improve the performance of these catalysts. The most active catalysts were prepared by impregnation and catalysts prepared by deposition precipitation were considerably less active. Introduction of Pd into the catalyst improved the activity without significantly affecting the selectivity.     

Au/ZnO and Au/Fe2O3 catalysts for CO oxidation at ambient temperature: comments on the effect of synthesis conditions on the preparation of high activity catalysts prepared by coprecipitation

The preparation of Au/ZnO and Au/Fe₂O₃ catalysts using two coprecipitation methods is investigated to determine the important factors that control the synthesis of high activity catalysts for the oxidation of carbon monoxide at ambient temperature. In particular, the factors involved in the preparation of catalysts that are active without the need for a calcination step are evaluated. The two preparation methods differ in the manner in which the pH is controlled during the precipitation, either constant pH throughout or variable pH in which the pH is raised from an initial low value to a defined end point. Non-calcined Au/ZnO catalysts prepared using both methods are very sensitive to pH and ageing time, and catalysts prepared at a maximum pH = 5 with a short ageing time (ca. 0–3 h) exhibit high activity. Catalysts prepared at higher pH give lower activity. However, all catalysts require a short operation period during which the oxidation activity increases. In contrast, the calcined catalysts are not particularly sensitive to the preparation conditions. Non-calcined Au/Fe₂O₃ catalysts exhibit high activity when prepared at pH ≥ 5. Calcined Au/Fe₂O₃ prepared using the controlled pH method retain high activity, whereas calcined catalysts prepared using the variable pH method are inactive. The study shows the immense sensitivity of the catalyst performance to the preparation methods. It is therefore not surprising that marked differences in the performance of supported Au catalysts for CO oxidation that are apparent in the extensive literature on this subject, particularly the effect of calcination, can be expected if the preparation parameters are not carefully controlled and reported.     

Premodification of Pt/γAl2O3 with Cinchonidine for the Enantioselective Hydrogenation of Ethyl Pyruvate: Effect of Premodification Conditions on Reaction Rate and Enantioselection

The premodification of a 5 wt% Pt/-Al₂O₃ catalyst with cinchonidine (0.01 and 0.2 g g^-1 _catalyst) is described and discussed. Premodification is carried out by treating the catalyst with a solution of cinchonidine followed by solvent removal. Catalysts premodified in this way give the same ee and initial rate of reaction for the enantioselective hydrogenation of ethyl pyruvate as those using the standard in situ modification procedure. Investigations of different solvents for premodification and reaction (dichloromethane, ethanol) show that it is the solvent used for the reaction that controls the observed enantioselection. Premodified catalysts also display the initial transient behavior typically observed with in situ modified catalysts in which the ee increases with conversion in the early part of the reaction. Premodified catalysts show an enhanced rate of reaction when ethanol is used as the reaction solvent compared with in situ modified catalysts under the same conditions. Premodification using aerobic conditions gives the best results and premodified catalysts can be stored prior to use for up to a week without loss of catalytic performance.     

Oxidation of Butane to Maleic Anhydride using Vanadium Phosphate Catalysts: Comparison of Operation in Aerobic and Anaerobic Conditions using a Gas-gas Periodic Flow Reactor

The use of a periodic flow reactor is described for the oxidation of butane to maleic anhydride to compare the catalytic performance of vanadium phosphate catalysts operating under aerobic and anaerobic conditions. It is found that for the catalyst prepared via a standard VPO method, operation in the absence of oxygen leads to a very small enhancement in selectivity when butane concentrations in the range 0.9–2.9% are used. Operation in the absence of oxygen leads to very small differences in conversion such that the overall yield is enhanced and this effect is maximised for reactor feeds containing 1.5% butane. However, the enhancement is negligible when the catalyst is operated at high conversion required for commercial operation, indicating that reactors operating with continuous flow with aerobic conditions are preferred. Similar experiments are conducted for a catalyst prepared by the VPD method and, in contrast, this catalyst gives lower butane conversion and maleic anhydride selectivity when operated in the absence of oxygen.