The cubic autocatalator: The influence of the quadratic autocatalytic and the uncatalysed reactions

The proptotype chemical reaction scheme, the cubic autocatalator, A + 2B 3B; B C is taken in a closed system, with A formed from the precursor P by the simple step P A. The pooled chemical approximation is invoked whereby the concentration of P can be assumed to remain constant throughout. The effects of allowing the quadratic autocatalytic reaction A + B 2B and the uncatalysed reaction A B in the scheme are considered in detail. The full scheme is described by the non-dimensional parameters µ (measuring the reaction rate of the initiation step) ands andr (measuring the reaction rates of the quadratic autocatalytic and the uncatalysed steps respectively). It is shown, provided only thatr ors (or both) are non-zero, no matter how small, the solution remains bounded for all (positive) values of µ, whereas withr =s = 0 the solution is bounded only for µ > µ₀ (µ₀ = 0.900 32). It is shown that withr = 0 ands 0 the governing equations have a Hopf bifurcation at µ = 1 –s producing a stable limit cycle which exists for all µ in 0 < µ <1 –s. The behaviour of these limit cycles as µ 0 is also discussed.     

The longitudinal electrical conductivity of metal matrix composites at cryogenic temperature in the presence of a longitudinal magnetic field

In this paper we use the results of Part I to derive two integral expressions for the electrical conductivity of metal matrix composite materials when a magnetic field, B, is added to a small electric field also parallel to fibres. One expression applies to strong magnetic fields meaningR ₀/a < 1, whereR ₀ =m ^* v _F/eB when the Fermi velocity is perpendicular to the magnetic field. WhenB , the integral expression reduces to the well known conductivity value = ₀(1 -V _f), where ₀ is the bulk matrix conductivity andV _f is the fibre volume fraction. For weak magnetic fields,R ₀/a > 1, then the electrical conductivity is expressed by the sum of two integrals. When B 0, the electrical conductivity reduces to the integral expression obtained in our earlier results when there is only a longitudinal electric field. In this paper we correct an incorrect derivation of the composite conductivity in the absence of a magnetic field published earlier [J. Mater. Sci.21 (1986) 2409].     

Influence of Stefan Flow and Convection on the Kinetics of Chemical Reactions and Heat and Mass Exchange of Carbon Particles with Gases

The problem of the heat and mass transfer and the kinetics of chemical transformation of a carbon particle (C + O₂ CO₂ (I), 2C + O₂ 2CO (II), C + CO₂ 2CO (III)) is solved within the framework of the model of a reduced film with account for the Stefan flow and natural and forced convection. Analytical expressions are obtained for the velocity of the Stefan flow, the rates of chemical reactions, the concentrations of gaseous components, the densities of the heat and mass fluxes, and the density of chemical heat release on the surface of the carbon particle.     

Characterization of crystallization in Metglas 2826 MB alloy

The crystallization behaviour of the Metglas 2826 MB alloy (Fe₄₀Ni₃₈Mo₄B₁₈) has been studied using resistance measurements and X-ray diffraction techniques. Three annealing sequences were used to follow the process. Samples were annealed isothermally (a) at 780° C in a vacuum of 2×10^–5 torr for times in the range 1 sec to 4 h, (b) for 2 h in an argon atmosphere at temperatures where the resistance curve indicated phase changes to occur, and (c) for 300 h in 100 torr of helium at 400, 600, 700 and 850° C. From these annealing sequences it was found that the alloy did not crystallize below 410° C and followed a crystallization process of: amorphous Fe₄₀Ni₃₈Mo₄B₁₈ Fe _x Ni_23–x B₆ (cubic)+glassy matrix Fe _x Ni_23–x B₆+(Fe, Ni) (FCC) (Fe, Ni)₃B(bct). This series of transformations was followed for Sequences (a) and (c) above, but was slightly different for Sequence (b). An orthorhombic (Fe, Ni)₃ B phase was found in the samples annealed in a vacuum of 2×10^–5 torr.Trademark of Allied Chemical Co.     

A novel method of introducing PbO dopant and (the study of) its influence on the electrical properties of semiconducting Cd2−x Pb x SnO4 thick films

The sheet resistance of Cd₂SnO₄ thick films was reduced from 15580 to 0.09 k with respect to dopant concentration and peak firing temperature (600 to 900° C). Distinct colour changes were observed in these films. The inorganic binder introduced an impurity which greatly induce changes in its electrical properties. The Arrhenius relation (logR–10³/T) generally indicated slopes of 2 to 3 for all the compositions of Cd_2–x Pb _x SnO₄ (x=0.002, 0.01, 0.02, 0.04 and 0.1). The donor ionization energies (E _d) varied from 0.01 to 0.76 eV. Resistance measurements during heating-cooling cycles indicated the possible presence of structural defects such as oxygen vacancies and cadmium interstitials. The oxidation of dopant (Pb²⁺Pb⁴⁺+2e) contributed in a major way to the overall conductivity. Scanning electron micrographs showed a progressive network formation due to sintering, thus contributing to the carrier mobility.     

The athermal α → ω transformation in Zr-2 at% Nb alloy

The athermal transformation in Zr-2 at.% Nb alloy has been investigated by transmission electron microscopy. Analysis of the selected-area diffraction pattern has shown that the orientation relationships between the omega and the parent-phase in quenched Zr-2 at.% Nb alloy are the same as have been previously observed for the reaction in pure zirconium. Thus it was deduced that the direct transition has taken place in the alloy during cooling. The-originated -particles were visualized using the dark-field technique. The formation of the athermal omega in the-region of-stabilized Zr-Nb alloy is discussed in terms of the relative positions of the free energy equilibrium curvesT ₀ ,T ₀ ,T ₀ and the correspondingM _s ,M _s andT _s start curves. It is concluded that the omega phase can occur over a much wider range of alloy compositions than is usually recognized on the basis of transformation data.     

A new metastable phase near 60 at% Zr from amorphous Ni-Zr

Metallic glass alloys of Ni-Zr were prepared by vapour and liquid quenching. For glass compositions at and near 60 at% Zr, crystallization proceeded by the sequence: amorphous metastable crystalline phase NiZr₂ + NiZr. The metastable Ni₄₀Zr₆₀ phase exhibited a very distinctive X-ray diffraction pattern and was present in both liquid- and vapour-quenched samples. Long-term anneals of samples with the metastable structure produced the equilibrium phases NiZr₂ and NiZr. The crystallization of the amorphous structure directly to a single metastable phase shows a correspondence between the compositions of the amorphous and crystalline phases. These results thus suggest a connection between the short-range structure of the glassy phase and the crystalline phases to which they transform. An observation of peaks and valleys in a plot of the X-ray scattering vector,Q _p, against glass composition is noted.     

Investigation of the gapless state in bismuth-antimony alloys

The results are presented from an experimental study of the gapless state produced in semiconducting alloysBi _1–x Sb _x by pressure-induced band inversion. The magnetoresistance properties of the alloys have been investigated both in weak magnetic fields (H « 1) and in strong fields (H75 kOe) at liquidhelium temperatures in the Sb concentration interval 0.06x0.15 and pressure interval 1 bar p<20 kbar. At pressuresp close to the pressurep _k at which the gapless state is realized a semiconductor-semimetal-semiconductor transition is detected inBi _1–x Sb _x alloys withx=0.070 and 0.071. The rates of change of the gap _gL before and after inversion are determined: –(2.5±0.5)×10^–6 eV/bar and (1.5±0.5)×10^–6 eV/bar, respectively. A reduction in the carrier effective mass as _gL 0 is observed down to values of 10^–4 m ₀. It is shown that as _gL 0 the carrier mobilities in the alloys increase abruptly, the effect being a maximum in the purest alloys, where forT=4.2 K the mobility along the binary axis attains the record-high value of 3×10⁸ cm²/V · sec.     

Oxygen Stoichiometry and Phase Transitions of SrCo1– xFexO3 – δ

The oxygen stoichiometry of SrCo_{1 – x} Fe _x O_{3 –} (0.1 x 0.9) solid solutions was determined by solid-electrolyte coulometry as a function of temperature (20–1000°C) and oxygen partial pressure (1–100 Pa). The results, together with X-ray diffraction studies between 400 and 900°C, indicated a sequence of phase transitions: perovskite brownmillerite high-temperature perovskite. The composition stability region of the parent perovskite structure was shown to be 0.2 <x 1.0. The Co-rich samples (x 0.2) consisted of perovskite and hexagonal phases.     

The relationship between the mean dopant-ion radii and conductivity of co-doped ZnO systems, Zn1−x−y M x M′ y O (M, M′ = Al, In, Ga, Y)

The conductivities of the Zn_1–x–y M _x M _y O (M, M = Al, In, Ga, Y) and Zn_1–x M _x O (M = Al, In, Ga) systems were measured from room temperature to 1173 K in order to elucidate a dominant parameter of the conducting mechanism. The conductivity at 873 K first increased with the dopant content. However, it showed a maximum value at a given dopant content, and then gradually decreased. For the samples with the same dopant content, their conductivity at 873 K was strongly dependent on the mean dopant-ion radii, and reached a maximum value at around 0.51 Å of the mean dopant-ion radii. The results suggested that the conductivity of the system would be influenced not only by the dopant content, but also by the mean dopant-ion radii. It was found that the co-doped ZnO system of Zn_0.995Al_0.003In_0.003O had a conductivity higher than that of the other usual mono-doped system.     

Chemical approach to the conduction mechanism in copper tellurite glasses containing lutetium oxide

Measurements of d.c. electrical conductivity were made on 65TeO₂-(35 -x)CuO-xLu₂O₃ (mol%) glasses with x=0, 1, 2, 3, 4. The experimental results show that whenx is changed from 1 to 2 mol%, the conductivity increases due to the additional electrons obtained by the oxidation of TeO₂ as well as due to the Cu⁺ Cu²⁺ transition under the effect of interelectronic repulsion in the 4f shell of the lutetium present in the glass. Whenx is increased to greater than 2 mol%, the conductivity decreases because hopping is inhibited due to the formation of oxygen bridge associates or because of the strong ligand repulsive field of lutetium indicating its non-reactivity in the glassy network. The conductivity has a distinct maximum atx=2.     

Ionic conductivity and crystal structure relationships in Ti/Cu substituted Bi4V2O11

Crystal structure and oxide ion conductivity of a series of Ti and Ti-Cu double substituted Bi₄V₂O₁₁ compounds, Bi₂V_(1–x)Ti _x O_(11–x)/2 (0.085 x 0.15), and Bi₂V_0.9Cu_(0.1–x)TixO_5.35+x (0 x 0.1), were investigated using X-ray powder diffraction and ac impedance spectroscopy in the temperature and frequency range of 100–700°C and 10^–2–10⁷ Hz, respectively.Structural phase transitions, and , occur as a function of composition in Ti substituted compounds for which the is evidenced to be stable at room temperature when x exceeds 0.125. For all Ti-Cu double substituted compounds studied, the room temperature phase was identified to be phase.The required amount of Ti for phase stabilization at room temperature was significantly reduced and the conductivity improved when Cu substituted a part of Ti. Therefore, for the Bi₂V_0.9Cu_(0.1–x)Ti _x O_5.35+x (0 x 0.075) compounds the ionic conductivity increased and activation energy decreased with decreasing x. At low temperature, the highest ion conductivity was obtained for Bi₂V_0.9Cu_0.1O_5.35. At high temperature (T>500°C), a different behavior was observed. The total conductivity increased at first with decreasing x values down to x = 0.05 and then decreased. The maximum conductivity was obtained for Bi₂V_0.9Cu_0.05Ti_0.05O_5.4, and the activation energy decreased with decreasing x values, such as what happened at low temperature.     

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.     

The effect of a Cr2O3-addition on the phase transformation and catalytic properties of γ-Al2O3 in treatment of lean-burn exhausts

The solid-state thermal behaviour of -Al₂O₃ doped with 10 mol% Cr (oxide) was studied with respect to phase-transition behaviour and the co-ordination of the dopant Cr cations. A series of transformations: -Al₂O₃ -Al₂O₃ -Al₂O₃ -Al₂O₃ was observed for Cr₂O₃-doped alumina samples between 500 °C and 1100 °C. Rapid grain growth occurred at temperatures close to 1100 °C. The electron spin resonance (ESR) spectra for the sample heat-treated at 500 °C corresponded to the resonance of -Cr³⁺ in an amorphous Cr oxide impregnated onto the - and -alumina support. The change of ESR spectrum indicated the existence of Cr³⁺, suggesting the formation of a solid solution with the same structures as -Al₂O₃ and/or -Al₂O₃ at 800–1000 °C. The evaluation of catalytic activities for model exhaust was performed under lean-burn (an excess of oxygen) condition of air/fuel ratio A/F = 18 and space velocity SV = 100 000 h^–1 . The modified Al₂O₃ catalyst heat-treated at 1000 °C in air showed removal conversion of 100% for hydrocarbon (C₃H₆), 92% for CO and 5% for NO at 550 °C. Present results suggest that Cr-modification to Al₂O₃ leads to catalytic improvement with good thermal durability.     

Structural and electrical conductivity studies on (M,V)-TiO2 (M=Al, Cr, Fe) rutile solid solutions at high temperature

In this study, M _x Ti_0.91–1.82x V_0.09+0.82x O₂ (0x0.1; M=Al, Cr, Fe) solid solutions have been synthesized by ceramic method and characterized by X-ray diffraction and electron microscopy. The results indicate that rutile solid solutions stability depends on the trivalent cation (M). Solid solutions are stable at 1000 °C, but only when M=Cr is a single phase with rutile structure obtained at 1400 °C. The electrical behavior of the system studied corresponds to extrinsic p-type semiconduction and electrical conductivity is related to the stability of rutile solid solutions.     

Study of the paramagnetic-antiferromagnetic transition and the γ → ε martensitic transformation in Fe-Mn alloys

The paramagnetic-antiferromagnetic transition and the martensitic transformation of Fe-Mn (Mn 15–32 wt%) alloys have been investigated by resistivity, dilatometry and X-ray diffraction (XRD). The results show that paramagnetic-antiferromagnetic transition increases the resistivity and the volume of alloys, whereas the martensitic transformation reduces the resistivity and volume of alloys. The A _f that was determined by the dilatometric method is not the temperature that martensites in the Fe-Mn alloys have reverse transformed to austenites completely. Mn additions reduce M _s, increase T _N and the lattice parameter of austenite in the Fe-Mn alloys. Both the antiferromagnetic transition and the martensitic transformation lead to an increase in the lattice parameter of austenite. The lattice parameters both above T _N and below T _N decrease linearly with temperature. The lattice parameter below M _s increases first and then decreases. Moreover, the (110) and (002) atomic planes in the Fe-15Mn-0.15C alloy are separated into two peaks: 2 for (002) is 44.16°, 2 for (110) is 44.47°.     

On the flow of a stratified fluid over a barrier

Summary The flow of a stratified fluid over a barrier is considered. The initial-value problem is solved, and it is shown that there is no disturbance far upstream of the barrier whent . The stationary solution which is obtained by lettingt, is given in a simple closed form for a barrier of an arbitrary shape.     

Pressure anomaly near the triple point on the magnetic phase diagram of bcc solid3He

The nuclear magnetic phase diagram of bcc solid ³ He has been determined by pressure measurements. We have observed a pressure jump at the transition from the high field phase to the paramagnetic phase (HP) near the triple point. This jump indicates that HP is first order.     

Overdamped modes and transport in normal 3He

In earlier work it was shown that a sinusoidal density distribution ~cos x at t = 0 decays to a uniform state with the excitation of damped, standing waves of first sound, in the long-wavelength limit, plus overdamped solutions. Since the latter are independent solutions of the Boltzmann equation, we should expect that as 0, the heat flux J and temperature gradient T in such a relaxing mode are related by Fourier's law, and indeed it is shown that explicit calculation of J and T from the longest lived overdamped solution yields a theoretical expression relating the thermal conductivity to the Landau parameters F ₀ ^s, F ₁ ^s, and F ₂ ^s. To evaluate , one needs to calculate the internal energy per particle to second order in the departure from equilibrium of the quasi-particle momentum distribution, and this is effected with the aid of a reciprocity relation linking the pressure and the viscoelastic relaxation equation. In the final expression for , F ₂ ^s is adjusted to make the theoretical thermal conductivity fit the value tabulated by Wheatley, giving F ₂ ^s = –1.68, which agrees in sign and magnitude with previous estimates from longitudinal and transverse zero sound. To establish the physical significance of the relaxing solution, it is shown that its contribution to the f-sum rule, combined with the contribution from the first-sound poles of the dynamic response function, satisfies the sum rule exactly to fourth order in the wave number. Other relaxing modes contribute in higher order.     

X-ray diffraction from faulted zinc sulphide crystals undergoing phase transitions

Stacking faults in close-packed structures are not always distributed randomly. When they occur preferentially at certain layer spacings. In such cases the classical theories of X-ray scattering from randomly faulted close-packed structures break down and a probability distribution of faults has to be assumed to compute the diffraction effects. This probability distribution faults has to be assumed to compute the diffraction effects. This probability distribution depends on the mechanism of the transformation in the material being studied. By recording the diffuse intensity distribution along reciprocal lattice rows perpendicular to the faults obtained from a partially transformed crystal it is possible to determine the nature of the faults involved and derive information about the mechanism of the transformation. The application of this method to investigate the mechanism of 2H 3C and 2H 6H transformations in ZnS, Zn _x ,Cd_1-x S and Zn _x ,Mn_1-x S is discussed. A three parameter model assuming different fault probabilities for deformation faulting at larger separations (a), at three-layer separations () and at two-layer separations () has been developed, to compute theoretically the diffraction effects from the transforming crystals and explain the experimentally observed distribution of diffuse intensity in reciprocal space.