A note on the similarity solutions for free convection on a vertical plate

Summary The similarity solutions for free convection on a vertical plate when the (non-dimensional) plate temperature is x and when the (non-dimensional) surface heat flux is –x are considered. Solutions valid for 1 and 1 are obtained. Further, for the first problem it is shown that there is a value ₀, dependent on the Prandtl number, such that solutions of the similarity equations are possible only for >₀, and for the second problem that solutions are possible only for >–1 (for all Prandtl numbers). In both cases the solutions becomes singular as ₀ and as –1, and the natures of these singularities are discussed.     

Microstructure and mechanical properties of rapidly quenched L20 and L20+L12 alloys in Ni-Al-Fe and Ni-Al-Co systems

Ductile L2₀-type wires and+L1₂-type duplex wires with high strengths and large elongation in the Ni-Al-Fe and Ni-Al-Co ternary systems have been manufactured directly from the liquid state by an in-rotating-water spinning method. The wire diameter was in the range 80 to 180m and the average grain size was 2 to 4m for the wires and 0.2 to 1.0m for the+ wires. _y, _f and _p of the wires were found to be about 360 to 760 MPa, 560 to 960 MPa, and 0.2 to 5.5%, respectively, for the Ni-Al-Fe system, those of the+ wires were about 395 to 660 MPa, 670 to 1285 MPa, and 3.5 to 17%, respectively, for the Ni-Al-Fe system, and about 260 to 365 MPa, 600 to 870 MPa, and 4.0 to 7.0%, respectively, for the Ni-Al-Co system. Cold-drawing caused a significant increase in _y and _f and the values attained were about 1850 and 2500 MPa, respectively, for Ni-20Al-30Fe and Ni-25Al-30Co wires drawn to about 90% reduction in area. The high strengths, large elongation and good cold-workability of the melt-quenched and+ compound wires have been inferred to be due to the structural change into a low-degree ordered state containing a high density of phase boundaries, suppression of grain-boundary segregation and refinement of grain size.     

Synthesis of aluminum infiltrated boron suboxide drag cutters and drill bits

Synthesis of boron suboxide (B₆O) was made by reactive sintering of crystalline boron and zinc oxide powders at 1450 °C, in argon, for 12 h. After sintering, Vickers microhardness testing was performed on the material synthesized and an average hardness value of 34 GPa was obtained. Sintered suboxide (in crushed and ground powder form) was then analyzed through optical and scanning electron microscopies and X-ray diffraction. Following the completion of the analyses, consolidation of the powder was performed. Two different routes were carried out: (1) explosive consolidation which was performed in double tube (with a density value of 2.22 g/cm³) and single tube (with a density value of 2.12 g/cm³) canister design arrangements and (2) hot pressing which was performed in a graphite die assembly, at 1600 °C, in vacuum, for 2 and 4 h (with density values of 2.15 and 2.18 g/cm³ respectively). Consolidated samples of both routes showed different levels of mechanical attachment, agglomeration, porosity, fracture toughness and fracture strength values, whereas microhardness values and X-ray diffraction plots (as shown in Table I and Figs 6 and 8 respectively) were determined to be similar. Following characterizations, compacts of both routes were then given a high temperature sintering treatment (pressureless sintering) at 1800 °C, in vacuum, for full densification. Both in the as consolidated and densification sintered stages test results revealed the most desirable and well-established properties for the explosively consolidated double tube design compacts (with densification sintered density, microhardness and fracture toughness values of 2.46 g/cm³, 38 GPa and 7.05 MPa m^1/2 respectively). Consolidation and desification sintering steps were then followed by a pressureless infiltration step. Aluminum was infiltrated into densification sintered double tube design consolidated and 4 h of pressed samples (better-compacted and better-sintered compacts) in the temperature range 1100–1250 °C, in argon, for 10 h. During infiltrations, the optimum temperature of the infiltration process was determined to be 1200 °C. Characterization results revealed the most uniform and well established properties once more for the double tube design explosively consolidated compact (with aluminum infiltrated density, microhardness and fracture toughness values of 2.55 g/cm³, 41 GPa and 8.70 MPa m^1/2 respectively).     

Transport results from untwinned YBCO: Washboard frequency of the vortex lattice,and the quasiparticle mean free path

The washboard frequency of the moving vortex lattice in untwinned YBa₂ Cu₃ O_6.93 may be observed through mode-locking to an externally applied ac current of frequency _ext. The interference between and _ext results in jumps in the dc current-voltage characteristics when and _ext are harmonically related¹. The interference effect disappears in the vortex liquid state. The Hall conductivity _xy below T_c in YBCO contains contributions² from a positive quasiparticle (qp) term (H) and a negative vortex term (1/H). The qp term is surprisingly large well below T_c and implies a large gap anisotropy and a long qp mean free path (mfp). The thermal Hall effect³ _xy is closely related to the qp _xy; _xy is produced by asymmetric scattering of qp by pinned vortices. The qp mfp at H = 0, extracted from _xy and extended to low T by _xy, increases remarkably from 90 Å at T_c to more than 0.5m at 22 K.     

γ ? α2 Phase transformation in fractured high temperature stress rupture Ti-48Al-2Nb(at.%)

The ₂ phase transformation in fractured high temperature stress rupture Ti-48Al-2Nb(at.%) alloy has been studied by analytical electron microscopy. ₂ and phases were found at grain boundaries. ₂ layers that suspended in layers and interfacial ledge higher than 2d ₍₁₁₁₎ at /₂ interfaces were observed in the lamellar grains. These facts indicated that ₂ phase transformation and dynamic recrystallization have occurred during high temperature stress rupture deformation. It can be concluded that deformation induced ₂ phase transformation and dynamic recrystallization resulted in the presence of particles at grain boundaries. A structural and compositional transition area between deformation-induced ₂(or ) and its adjacently original (or ₂) phases was found by HREM and EDS and is suggested as a way to transform between and ₂ phase during high temperature stress rupture deformation. The transition area was formed by slide of partial dislocations on close-packed planes and diffusion of atoms.     

Mechanical properties and microstructure of β-SiAION-β-SiC composites by pressureless sintering

-SiAION--SiC composites containing up to 12 wt% -SiC were prepared by pressureless sintering. The strength of composites at room temperature remained relatively unchanged, whereas strength at 1200 °C increased for composites. The fracture toughness (K _IC) for composites was higher than that for -SiAION ceramics. The maximum value was 5.4 MPa m^1/2 for 6 wt% -SiC, and this was an improvement of 15% in comparison with -SiAION ceramics. From SEM observations, an improvement inK _IC values was attributed to crack deflections and branching-off of cracks. Intra-granular fractures were frequently observed in -SiAION. From TEM observations, -SiAION crystals were nanocomposites, within which existed the fine crystals in -SiAION crystal. For composite, -SiAION and -SiC crystals were directly in contact. The mismatching zone was observed in -SiC.     

The microstructure of sintered Si-Al-O-N ceramics

Fine-grained ceramics, based on the substituted -Si₃N₄ crystal structure, have been prepared with near theoretical densities by pressureless sintering of compacts containing a large Y₂O₃ additive concentration. The microstructure contains two phases, and an Y/Al rich silicate glassy matrix, in the as-sintered condition. The matrix may be crystallized on heat treatment to a Si-substituted yttrium-aluminium garnet phase. The phase compositions and transformation mechanisms have been analysed by X-ray microanalysis, electron diffraction and imaging of thin sections.A preliminary survey of mechanical properties of these sintered ceramics shows that they are comparable with commercial hot-pressed silicon nitrides, particularly at high temperatures. The possibility of development of a range of ceramic alloys, dependent on their chemical environment and temperature of application, is discussed.     

Investigation of the excitonic insulator phase in bismuth-antimony alloys

Pressure-induced metal-semiconductor transitions in bismuth-antimony alloys in a strong magnetic field (up to 70 kOe) at helium temperatures have been investigated. It is found that for values of the overlap-gap |G|1 meV the alloy forms an excitonic insulator (EI) in magnetic fields above a certain threshold (30–40 kOe). It is inferred that the EI energy gap increases with the magnetic field. The maximum gap observed in fields of 70 kOe turns out to be ₀₀7.5 K. An analysis of the results shows that transitions to the EI phase are observed from both the semimetal and the semiconducting states. The critical transition temperatureT _c is related to the EI gap by the expressionT _c0.7. Arguments are advanced in support of the fact that the formation of the EI phase involves the pairing of electrons at theL point with holes at theT point.     

Preferentially orientated precipitation in MnTiO3 single crystals

Preferentially orientated precipitation of -TiO₂ (rutile) needles in single crystals of MnTiO₃ grown by a floating-zone method under a controlled atmosphere of oxygen fugacity was studied. Optical microscopy and X-ray analysis revealed that the orientation relation between the -TiO₂ precipitates and the MnTiO₂ matrix is: {000 1}MnTiO₃// {111}-TiO₂ and 11¯20MnTiO₃// 110-TiO₂. The precipitation phenomenon was explained by introducing a nucleation and growth mechanism which was experimentally supported by heat treating experiments.     

A linear differential equation with a time-periodic damping coefficient: stability diagram and an application

In this paper the second-order differential equation with time-dependent damping coefficientx + cos (2t) x + x = 0,will be studied. In particular the coexistence of periodic solutions corresponding with the vanishing of domains of instability is investigated. The coexistence of -periodic solutions occurs for 4n ² where n is integer. This implies that the instability area which is emanating from =4n ² in the – stability diagram disappears. In applications, this equation can be considered as a model equation for the study of rain-wind-induced vibrations of a special oscillator.on leave as a PhD reseacher at Delft University of Technology, The Netherlands     

Carbothermal production of β′-sialon from alumina,silica and carbon mixture

Mixtures of pure nanometer-sized amorphous silica and -alumina with the atomic ratio SiAl=1 were reduced by a stoichiometric amount of carbon between 1100 and 1450 °C in flowing nitrogen in order to produce -sialon powder. Using aqueous suspensions of starting materials, compacts with different microstructures were prepared for reaction. Silica reduction to SiO occurred at a temperature as low as 1300 °C and part of it was removed with flowing nitrogen. Carbothermal reaction involving nitrogen stated at 1350 °C and Si₂N₂O was found as an intermediate together with SiC, resulting in -sialon formation. Loss of silica from the system led to AlN formation. Decomposition of -sialon into sialon polytypoids (15R, 12H) was observed as a result of sialon and AlN reaction at 1450 °C. The reaction rate of sialon formation was slowed down compared to the carbothermal reduction of kaolin because of the lack of impurities. The microstructure of the reacted pellets influenced the reaction products, and the narrow pore size distribution as well as good homogeneity enhanced -sialon formation.On leave, from Silesian Technical University, Krasiskiego 8, 40-019 Katowice, Poland.     

Sintering mechanisms and microstructural development of coprecipitated mullite

Coprecipitated mullite precursor powders of the bulk compositions 78 wt% Al₂O₃+22 wt% SiO₂ (high-Al₂O₃ material) and 72 wt% Al₂O₃+28 wt% SiO₂ (low-Al₂O₃ material) have been used as starting materials. The precursor powders were calcined at 600, 950, 1000, 1250, and 1650 C, and test sintering runs were performed at 1550, 1600, 1650, 1700, and 1750 C. Homogeneous and dense ceramics were obtained from cold isostatically pressed (CIPed) powders sintered in air at 1700 C. Therefore, all further sintering experiments were carried out at 1700 C. After pressureless sintering, sample specimens were hot isostatically pressed (HIPed) at 1600 C and 200 bar argon gas pressure. Sintering densifications of low Al₂O₃ materials ranged between 94% and 95.5%. There was no clear dependency between densification and calcination temperature of the starting powders. High-Al₂O₃ compositions displayed sintering densities which increased from 97% at 600 C calcination temperature to 99% at 950 C calcination temperature. Higher calcination temperatures first caused slight lowering of the sintering density to 95.5% (calcination temperature 1250 C) but later the density strongly decreased to a value of 85% (calcination temperature 1650 C). HIPing of pressureless sintered specimens prepared from powders calcined between 600 and 1100 C yielded 100% density. At the given sintering temperature of 1700 C, the microstructure of sample specimens was influenced by Al₂O₃/SiO₂ ratios and by calcination temperatures of the starting powders. Homogeneous and dense microstructures consisting of equiaxed mullite plus some minor amount of -Al₂O₃ were produced from high-Al₂O₃ powders calcined between 600 and 1100 C. Low-Al₂O₃ sample specimens sintered from precursor powders calcined between 600 and 1100 C were less dense than high-Al₂O₃ materials. Their microstructure consisted of relatively large and elongated mullite crystals which were embedded in a fine-grained matrix of mullite plus a coexisting glass phase. The different microstructural developments of high- and low-Al₂O₃ compositions may be explained by solid-state and liquid-phase sintering, respectively. The microstructure of HIPed samples was very similar to that of pressureless sintered materials, but without any pores occurring at grain boundaries.     

Influence of the α/β-SiC phase transformation on microstructural development and mechanical properties of liquid phase sintered silicon carbide

The transformation kinetics and microstructural development of liquid phase sintered silicon carbide ceramics (LPS-SiC) are investigated. Complete densification is achieved by pressureless and gas pressure sintering in argon and nitrogen atmospheres with Y2O3 and AlN as sintering additives. Studies of the phase transformation from to -SiC reveals a dependency on the initial -content and the sintering atmosphere. The transformation rate decreases with an increasing -content in the starting powder and in presence of nitrogen. The transformation is completely supressed for pure -SiC starting powders when the additive system consists of 10.34 wt% Y2O3 and 2.95 wt% AlN. Materials without phase transformation showed a homogeneous microstructure with equiaxed grains, whereas microstructures with elongated grains were developed from SiC powders with a high initial /-ratio (>1:9) when phase transformation occurs. Since liquid phase sintered silicon carbide reveals predominantly an intergranular fracture mode, the grain size and shape has a significant influence on the mechanical properties. The toughness of materials with platelet-like grains is about twice as high as for materials with equiaxed grains. Materials exhibiting elongated microstructures show also a higher bending strength after post-HIPing.     

Effects of aluminium on the electrical and mechanical properties of PTCR BaTiO3 ceramics as a function of the sintering temperature

The effect of AI additions on the electrical behaviour of positive temperature coefficient of resistance (PTCR) BaTiO₃ ceramic sintered in air at temperatures ranging between 1220 and 1400° C have been investigated. Two batches of material, both showing a PTCR effect, were prepared identically except that additions of AI₂O₃ (0.55 mol %) were made to one of them. It has been confirmed that the presence of aluminium results in an increase in the temperature at which the maximum resistivity, _max, occurs as well as reducing the sintering temperature, in the presence of silicon, to 1240° C. Additionally, direct comparisons between the two materials have demonstrated that such additions result in an increase of 100% in the minimum resistivity, _min, at sintering temperatures beyond 1280° C. A similar increase in _max for sintering temperatures below 1360° C and a five-fold reduction in the ratio of _max/_min in samples sintered above 1320° C have also been attributed to the presence of aluminium. It was further found that aluminium increases the average grain size by 30% and promotes the formation of a liquid phase.     

Theory of RF SQUIDs Operating in the Presence of Large Thermal Fluctuations

A comprehensive analytical theory is presented for non-hysteretic RF SQUIDs operating in the adiabatic mode in the presence of large thermal fluctuations. When 1 ( = 2LI_c/₀ is the hysteresis parameter, L is the SQUID inductance, I_c is the critical current of the Josephson junction, and ₀ is the flux quantum) the theory is applicable also for RF SQUIDs operating in the non-adiabatic mode. In contrast to previous theories in which the noise is treated perturbatively and which therefore are applicable only if the product 1 ( = 2k_BT/ ₀ I_c is the noise parameter, k_B is the Boltzmann constant, and T is the absolute temperature)—the case of small thermal fluctuations—the present theory is valid for around unity or higher. In the limit 0 the theory reproduces the results of small thermal fluctuations theories. It has been found that in the presence of large thermal fluctuations the screening current in the SQUID inductance is suppressed by a factor that increases with increasing . Taking into account this new basic fact, all SQUID characteristics (output signal, transfer function, noise spectral density and energy sensitivity) have been recalculated and a good agreement with experimental data has been obtained. It has been also found that RF SQUIDs can be operated with substantially higher values of the inductance and of the noise parameter than DC SQUIDs. These two aspects, which are of particular importance at liquid nitrogen temperature, make high T_c RF SQUIDs very attractive.     

Sintering and crystallization of mullite powder prepared by sol-gel processing

Mullite powder with the stoichiometric composition (3Al₂O₃.2SiO₂) was synthesized by a sol-gel process, followed by hypercritical drying with CO₂. Within the limits of detection by X-ray diffraction, the powder was amorphous. Crystallization of the powder commenced at 1200 °C and was completed after 1 h at 1350 °C. In situ X-ray analysis showed no intermediate crystalline phases prior to the onset of mullite crystallization and the pattern of the fully crystallized powder was almost identical to that of stoichiometric mullite. The synthesized powder was compacted and sintered to nearly theoretical density below 1250 °C. The microstructure of the sintered sample consisted of nearly equiaxial grains with an average size of 0.2 m. The effect of heating rate (1–15 °C min^–1) on the sintering of the compacted powder was investigated. The sintering rate increased with increasing heating rate, and the maximum in the sintering curve shifted to higher temperatures. The sintering kinetics below 1150 °C can be described by available models for viscous sintering.     

Catalytic decomposition of hydrazine in weakly alkaline solutions on platinum nanoparticles

The kinetics and stoichiometry of catalytic decomposition of hydrazine in 0.01 M NaOH solutions in the presence of unstabilized (gray colloid) and stabilized with sodium polyacrylate (brown colloid) platinum nanoparticles were studied. The main decomposition products are ammonia and N₂ with H₂ impurity (up to 1.5%), i.e., hydrazine decomposition predominantly follows the stoichiometric equation 3N₂H₄ = 4NH₃ + N₂. The catalytic activity was studied as influenced by nanoparticle size distribution. Despite higher nanoparticle dispersion, the catalytic activity of the stabilized brown colloid is lower than that of the gray colloid. The reaction mechanism is discussed.Translated from Radiokhimiya, Vol. 46, No. 6, 2004, pp. 531–535.Original Russian Text Copyright © 2004 by Ananev, Boltoeva, Sukhov, Bykov, Ershov.     

Equal-channel angular pressing of an Al-6061 metal matrix composite

An Al-6061 metal matrix composite, reinforced with 10 vol % Al₂O₃ particulates, was subjected to equal-channel angular (ECA) pressing at room temperature to a total strain of 5. It is shown that the intense plastic straining introduced by ECA pressing reduces the grain size from 35 m to 1 m and this leads to an increase in the microhardness measured at room temperature. Inspection revealed some limit cracking of the larger Al₂O₃ particulates as a consequence of the ECA pressing. Tensile testing after ECA pressing gave a maximum ductility of 235% at a temperature of 853 K when testing at strain rates from 10^–4 to 10^–3 s^–1. It is suggested that high strain rate superplasticity is not achieved in this material after ECA pressing due to the presence of relatively large Al₂O₃ particulates.     

Size-strength effects in sapphire and silicon nitride whiskers at 20° C

Tensile tests at 20° C have been carried out on seventy-three sapphire whiskers and on seventeen silicon nitride whiskers. The sapphire whiskers were of 0001, 1¯120, 10¯10, and 10¯11 orientations, while the silicon nitride whiskers were 0001, 11¯20, and 10¯13. Tensile strengths were in the range 45 to 1500 kg/mm², and deformation was found to be purely elastic. The tensile strength data have been analysed and fitted to empirical equations describing the effect of size on strength for different orientations. These empirical equations have been used to deduce possible fracture nucleation mechanisms. It is concluded that, in the case of 0001 sapphire whiskers, fracture nucleation may be due to dislocation pile-ups or interactions, while in the other cases a Griffith flaw mechanism is probably applicable.     

Microdeformation of a polydomain, smectic liquid crystalline thermoset

The microdeformation and fracture mechanisms of a densely crosslinked, polydomain, smectic liquid crystalline thermoset (LCT) were investigated in order to gain some insight into its interesting mechanical properties (e.g. improved fracture toughness). A difunctional LC epoxy monomer, diglycidyl ether of 4,4-dihydroxy--methylstilbene (DGDHMS), was crosslinked with the tetrafunctional, aromatic crosslinker, 4,4-methylene dianiline (MDA) to produce the LCT. Thermoset films (30 m in thickness) were bonded to copper grids, strained in tension, and observed under the polarizing optical microscope. A new type of microdeformation and fracture mechanism was observed for the smectic LCT. At small strains, numerous microcracks formed which were oriented at various angles to the straining direction. Many smaller isolated and interconnected defects (of the order of a single LC domain, 1 m in size) surrounded and emanated from the crack tips. At larger strains, the microcracks propagated slowly and stably until reaching a critical size of 250 m, at which time they began to widen and change direction, indicative of plastic deformation which extended over many LC domains. Film failure occurred through microcrack interconnection. A fracture mechanism for the LCT is proposed based on microscopic voiding near the crack tip through the failure of individual LC domains.