Similarity solutions in axisymmetric mixed-convection boundary-layer flow

The similarity equations for mixed-convection axisymmetric boundary-layer flow are considered. The equations involve a buoyancy parameter and a curvature parameter . The equations are solved numerically and it is found that for large , and of O(1), an asymptotic solution is approached, the nature of which is discussed. When is also large, of O(^1/4), the problem, at leading order, becomes independent of the mainstream and the free-convection limit is obtained. This problem is also discussed, including the behaviour for large values of ₀, the free-convection curvature parameter. For < 0 we find that the solution can be continued past the point where the wall heat transfer becomes zero (where previous mixed-convection similarity solutions in plane geometry were terminated) with the solution ending as 0^–. The nature of this limit is also discussed. For < 0 it is also found that there are solutions only in _b = < 0 with two branches of solution bifurcating out of = _b , and values of _b are computed for a range of . The behaviour of the solution for large values of the curvature parameter , and of O(1), is discussed where it is shown that the solution proceeds in inverse powers of log .     

Supercarrier Effective Mass Isotope Effect by Interband Scattering

Supercarrier effective mass isotope effect (exponent ) is investigated using a two-band model with interband pair scattering. The corresponding repulsive interaction incorporates besides the dominating electronic (Coulomb) part an electron-phonon contribution inversely proportional to the ionic mass factor. Calculations illustrating the behaviour of T _c , its isotope exponent , and with doping in La _2–x Sr _x CuO ₄ type underdoped system reflect the observed tendencies. ² Both and diminish with doping, the sign of is opposite to . A typical estimation gives || 0.2.     

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.     

Phase decomposition of liquid-quenched β-type Ti-Cr alloys

Phase decomposition behaviour of liquid-quenched (bcc) type Ti-Cr alloys was investigated by means of transmission electron microscopy and hardness measurements. It was found that decomposition of to ₁ (Ti-rich, bcc) + ₂ (Ti-lean, bcc) takes place in the intermediate composition range of the Ti-Cr system. This experimental result proves the theoretical prediction made by Menon and Aaronson, but the observed ₁ + ₂ two-phase field expands towards higher temperatures than the predicted binodal line. The coherent ₁ + ₂ two-phase state exhibits the so-called 100 modulated structure and it was concluded that the formation of such a structure is a result of spinodal decomposition of the -phase. We obtained time-temperature-transformation (TTT) diagrams of -type Ti-30, 40 and 50 at % Cr alloys. A typical sequence of structural change is coherent ₁ + ₂ incoherent ₁ + ₂ incoherent ₁ + ₂ + grain boundary precipitates stable state of + TiCr₂ or + TiCr₂. Not all the states in the above sequence appear, depending on alloy composition, liquid-quenching rate and ageing temperature.     

The relative stability ofβ andβ″-phases in Na2O-Al2O3 beta alumina

To reveal the relative stability of and -phases in beta alumina, effects of Na₂0 content and calcination and annealing history on the relative content of and -phases have been studied for compositions ranging from Na₂O-5Al₂O₃ to Na₂O-9.5Al₂O₃. The relative stability appears to be dependent on the calcination or annealing history, except holding time such as annealing or re-annealing time, but independent of the Na₂O content and the holding time. From these results it can be demonstrated that the relative stability of and -phases is sensitive to the heat treatment path, except the holding time. The two stage model on the /. polytypic transition in silicon carbide has been quoted to explain the heat treatment pathdependent characteristics.     

Structure of martensite formed in Cu-Al-Fe single crystals duringin situ HVEM pseudoelastic tensile experiment

Single crystals of the CuAlFe alloy, containing 14.5 wt% Al and 2.2 wt% Fe were subjected toin situ tensile experiment using straining attachment in a 1 MV electron microscope. Loadelongation curves were obtained for three foil plane/tensile direction orientations: (001) [0 1 0], (0 0 1) [1 1 0] and (1 1 0) [¯1 1 2]. Each crystal was subjected to two cycles of pseudoelastic deformation up to maximum 2% strain, showing almost complete shape recovery. Structure observations and electron diffraction pattern indicated that during deformation of samples of (0 0 1) [1 1 0] and (1 1 0) [1 1 2] orientations, formation of ₁ martensite was observed and only at later stages narrow needles of ₁ nucleate in front of ₁. During pseudoelastic deformation in the (0 0 1) [1 0 0] direction, martensite forms as a mixture of narrow plates possessing either 2H or 18R structures. The following crystallographic relationship between the parent phase and both types of martensite was observed: [1 00] ₁ [101] ₁ and (0 0 1) ₁ (0 1 0)₁;(0 0 1) ₁ (0 1 0) ₁ and [1 1 0] ₁ [0 0 1] ₁. From the character of sidebands reflections presence of 1 0 1 1 0¯1 static displacement waves was inferred.     

Distribution of α-AlFeSi and β-AlFeSi particles in surface layer of AA6063 alloy billets after heat treatment

We developed the EPMA mapping method of small -AlFeSi(Al_8.3Fe₂Si) and -AlFeSi(Al_8.9Fe₂Si₂) particles in the billets of Al-Mg-Si alloys such as AA6063 alloys. To discriminate between -AlFeSi and -AlFeSi particles we used the relative X-ray intensities of Fe/Si ratio, the I _Fe/I _Si ratio, instead of the Fe/Si mass ratio. To obtain the I _Fe/I _Si ratio, we used a Monte Carlo method. In this study, using this method the mapping of -AlFeSi and -AlFeSi particles in the surface layer of AA6063 billets after the heat treatment (for 2 h at 580°C) was done. Namely, the distribution of -AlFeSi and -AlFeSi particles of zones from the billet surface to a depth of 800 m was measured. Results showed the zone from the surface to a depth of 200 m was occupied mainly by -AlFeSi particles and the zone from a depth of 200 m toward the center was occupied mainly by -AlFeSi particles. From these results, it was found that if we remove zones from the surface to a depth of 200 m, we can remove the majority of the -AlFeSi particles, and thus improve the quality of anodizing performance of Al-Mg-Si alloys extrusions.     

The formation of single-phase Si-Al-O-N ceramics

Si-Al-O-N ceramics have been prepared by hot-pressing mixtures of Si₃N₄, AIN and SiO₂ (with an addition of 1% MgO) having varying ratios of AIN/SiO₂. Microstructural analysis by transmission electron microscopy and Auger electron spectroscopy has demonstrated the progressive increase in grain-boundary silicate glass in pressings prepared from compositions with excess SiO₂ to compositions given by the formula Si_6–zAl_zO_zN_8–z. This formula represents the simple substitution of Al for Si atoms and O for N atoms in the hexagonalSi₃N₄ crystal. Microstructures for this balanced composition are essentially single phase, consiting of non-faceted, sub-micron, grains with a grain-boundary segregate layer of glass-forming silicate composition, containing impurity and additive metal ions, which may be detected only by Auger spectroscopy. This microstructure is in contrast with unbalanced compositions which contain faceted grains joined by a glassy silicate phase which is easily detected by electron microscopy. Final microstructural analysis combined with observations of density and phase content with progress of hot-pressing has confirmed the important role of liquid silicate formation and a solution-reprecipitation mechanism for densification. The presence of a 1% MgO additive is shown to accelerate this process, forming a low melting point silicate by reaction with SiO₂, assisting the early solution of AIN and the reprecipitation of substituted crystals.     

Analytical Theory of DC SQUIDS Operating in the Presence of Thermal Fluctuations

A comprehensive analytical theory of symmetric DC SQUIDs is presented taking into account the effects of thermal fluctuations. The SQUID has a reduced inductance < 1/ where = 2LI_c/₀, L is the loop inductance, ₀ is the flux quantum, and I_c is the critical current of the identical Josephson junctions which are assumed to be overdamped. The analysis, based on the two dimensional Fokker–Planck equation, has been successfully performed in first order approximation with considered a small parameter. All important SQUID characteristics (circulating current, current-voltage curves, transfer function, and energy sensitivity) are obtained. In the limit 1( = 2k_BT/I_c0 is the noise parameter, k_B is the Boltzmann constant, and T is the absolute temperature) the theory reproduces the results of numerical simulations performed for the case of small thermal fluctuations. It was found that for < 1 the SQUID energy sensitivity is optimum when is higher than 1/, i.e., outside the range for which the present analysis is valid. However, for 1 the energy sensitivity has a minimum at L = L_F , where L_F = ( ₀ /2) ²/k_B , and therefore, in this case, the optimal reduced DC SQUID inductance is _opt = 1/, i.e., within the range for which the present analysis is valid. In contrast to the case of an RF SQUID, for a DC SQUID the transfer function decreases not only with increasing L/L_F but also with increasing (as 1/). As a consequence, the energy sensitivity of a DC SQUID with < 1/ degrades more rapidly (as ⁴ ) with the increase of than that of an RF SQUID does (as ² ).     

TEM study of metastable β-phase decomposition in rapidly solidified Ti-6Al-4V alloy

A new rationale is presented for various decomposition products obtained from the metastable -phase found in Ti-6A1-4V alloy produced by hot isostatic pressing comminuted melt-spun fibres and cooled to room temperature by furnace cooling. This alloy has an -matrix with about 8 vol% retained -phase, which is supersaturated with -stabilizers to such an extent that the martensitic transformation has been suppressed. The metastable -phase decomposes by different modes during continuous cooling, depending on the actual composition of individual -grains. Less enrichment of vanadium and iron favours the direct formation of the equilibrium -phase from the -matrix, while greater enrichment of vanadium and iron leads to a spinodal decomposition of the metastable -phase, resulting in a + two-phase structure. During further continuous cooling, the -phase which is lean in -stabilizers will transform into isothermal -phase. In addition, an unknown phase has also been observed in the -phase, which is typified by the appearance of 1/2{112} reflections in the SAD patterns.     

Observation of Hall Scaling in MgB2 Thin Films

We have measured the Hall resistivity, _xy , and the longitudinal resistivity, _xx , in superconducting MgB₂ thin films in a mixed-state while changing the magnetic field and the current density. A Hall scaling behavior without the anomalous Hall effect was observed with a exponent of 2.0±0.1 in _xy =A _xx . This exponent is observed to be constant, i.e., independent of magnetic field, temperature, and current density.     

Thermodynamic investigations of liquid Bi-Na and Sn-Na alloys by coulometric titration using β″-alumina

The following double galvanic cell was assembled and the thermodynamic properties of liquid Bi-Na and Sn-Na alloys, and the ion selectivity of -alumina during coulometric titration, were investigated. Mo, Na(I)¦-alumina¦M-Na(I), Mo [I] M-Na(I)¦-alumina¦Au + Au₂Na, Mo [II] (M = Bi or Sn) where M-Na(1) and Au + Au₂Na were used as the common electrode and reference electrode, respectively. Sodium was coulometrically titrated through the -alumina electrolyte of cell I both ways, and the EMFs were measured. It was found that no ion-exchange reaction occurs between the liquid alloys and the -alumina, and only Na was transferred in the -alumina during coulometric titrations. The thermodynamic properties of liquid Sn-Na and Bi-Na alloys were found to be in agreement with the literature.     

The formation ofβ-SiC fibres with SiO2-C-NaF(AlF3) components

The formation of-SiC fibres with SiO₂-C-NaF(AIF₃) components was investigated. It was found that the formation of a longer-SiC fibre was governed by the mole ratio of C/SiO₂ or C/NaF. Using a mole ratio for C/SiO₂ or C/NaF of 3 or more,-SiC fibres of length 3 mm were prepared in a closed system. On the other hand, short-SiC fibres were obtained in an open system.-SiC fibres prepared under the various experimental conditions were stable when heated in a high-concentration acidic solution such as HCl or H₂SO₄, and in an alkaline solution such as NaOH.     

The redistribution of alloying elements by rapid-heating solution treatment of an (α +β) titanium alloy

Thin-foil X-ray energy-dispersive chemical analysis of an (+) titanium alloy has been used to establish the compositional profiles which develop between the and phases as a result of heating into the field at a rate of 100 K sec^–1. The results show that phase transforms to via a diffusional mechanism as it is progressively enriched in-stabilizing solutes. Complete diffusional transformation of to occurs 160 K above the transus but the phase remains chemically inhomogeneous. On subsequent quenching at a rate of 400 K sec^–1, phase containing less than approximately 10wt% Mo equivalent of -stabilizing solutes transforms to martensite. The proposed transformation mechanisms are consistent with the results of resistivity measurements made during the heating and cooling cycles.     

Compressibility measurements of β- and β″ -alumina

The compressibilities of the a- and c-axes for sodium - and -aluminas were determined up to 10 GPa from the pressure dependence of powder X-ray diffraction measured at room temperature using synchrotron radiation as an X-ray source. Powders of sodium - and -aluminas which were prepared from grinding synthesized single crystals were used as the specimens for X-ray diffraction. The compressibilities of - and -aluminas are 1.5 ± 0.2 ×10^–12 and 1.7 ± 0.2 × 10^–12 Pa^–1 for the a-axis and 2.9 ± 0.2x10^–12 and 1.6 ± 0.2 ×10^–12 Pa^–1 for the c-axis, respectively. For the c-axis, the compressibility of -alumina is larger than that of -alumina. This experimental fact is explained by the different stacking of oxygen layers and the different content in sodium ion between - and -aluminas.     

Precipitation of β particles in a fully lamellar Ti-47Al-2Nb-1Mn-0.5W-0.5Mo-0.2Si (at.%) alloy

The precipitation of (B2) particles at intermediate temperatures, between 760°C and 1050°C, is investigated in a fully lamellar TiAl-WMoSi alloy. The particles, having a thin-plate shape, usually precipitate on the ₂ side of ₂/ interfaces at low aging temperatures in an uneven two-dimensional growth mode. While those formed at higher aging temperatures, growing extensively within the ₂ plate and into the adjacent lamellae, have an ellipsoid shape. The growth of particles at low aging temperatures yields an activation energy of about 366 kJ/mol. It is suggested that at low aging temperatures the growth of particles proceeds via an ₂ precipitation process controlled by diffusion of W and Mo along the /₂ and / interfaces.     

Mechanism of β1 formation in conventional dental amalgams

This study reexamined the mechanism of ₁ formation in conventional dental amalgams in the light of a previously unrecognized intergranular structure, the SnHg-₂ phase. Two amalgams, A (45. 5% Hg) and B (65. 0% Hg), were made from a Zn-free alloy of the following composition (wt%): Ag-70, Sn-26, Cu-4. After storage at 37°C for 1 day, both amalgams were heat treated at 70°C for up to 16 days. The structural changes in the two amalgams as a function of their heat treatment were characterized by differential scanning calorimetry and X-ray diffraction techniques. On the basis of the experimental data, we have proposed a new mechanism on ₁ formation. This mechanism involves a series of interrelated reactions. The primary one is a reaction between AgSn- and ₂ that leads to the nucleation of ₁ at boundaries. Simultaneous operation of several secondary and tertiary reactions result in (1) further growth of ₁ and its continuing change in composition, (2) loss of Sn from the ₁ matrix, (3) conversion of CuHg into , and (4) a possible transformation of ₂ into Sn-rich ₁ or ₁.     

Diffraction studies of β″-magnesium sialon

The compositions of high magnesium content -magnesium sialon crystals within the 3M/4X plane of the Mg-Si-Al-O-N system indicate some form of metal atom ordering wihtin the structure. Although it is not possible using X-ray diffraction to detect weak additional reflections arising from the ordering between magnesium, aluminium, and silicon atoms, such weak reflections are revealed on electron diffraction photographs for a phase, resulting in a tripling of the hexagonal latticec-dimension. These show to have a structure very similar to rhombohedral willemite (Zn₂SiO₄), with the (Mg, Al) metal atoms ordered with respect to the silicon atoms in a 21 ratio. However, there are some additional weak diffraction spots with indices not obeying the rhombohedral condition of –h+k+l=3n. It is proposed that the structure of this is identical to that of willemite and the extra spots are a result of some form of twinning, which implies the existence of ordered microdomains.     

Critical review of the thermodynamics of the Na-Al-O system

The free energies of formation of various phases in the Na-Al-O systems are critically reviewed for the composition range between pure alumina and sodium-aluminate. The results clearly indicate that in the temperature range between 600 and 1100 K neither-alumina nor'-alumina (Na₂O.5Al₂O₃) are stable with respect to sodium; the most stable phase in that range being sodium aluminate. Least square fitting and statistical analysis of all the available data on the free energy of formation of-alumina deemed accurate yields G _form ⁰ (from oxides) = –8772+1.53T (J/mole of O) (600 T 1200K) If the composition of-alumina is assumed to be Na₂0.11Al₂O₃ then G _form ⁰ (Na_1/17Al_11/17O, from elements) = –565100+109.6T (J mole of O) (600 T 1200 K) If the composition is assumed to be 19 then: G _form ⁰ (Na_1/14Al_9/14O, from elements) = –564000+109.6T (J/mole of O) (600 T 1200K) Based on the only study to date, the best estimate for the free energy of formation of-alumina is G _form ⁰ (Na_1/8Al_5/8O, from the elements) = –567860+114T (J/mole of O) (600 T 1200 K)The uncertainty (95% confidence band) is estimated to be about ±200 J/mole of O. Based on these results-alumina should be thermodynamically stable at lower temperatures, but become unstable at temperatures >900 K and should, kinetics permitting, dissociate into-alumina and sodium aluminate. Experimental evidence, however exists that conclusively shows that-alumina is thermodynamically stable at much higher temperatures than 900 K which leads to the conclusion that G °_form for-alumina reported to date is too high and should be more negative.     

Structural transformation during sintering and annealing of beta alumina

Changes in the phase content, microstructure and lattice parameter are observed in stabilized/ alumina specimens following extended sintering and annealing treatments. The resulting state is dependent on composition of the starting powder and on temperature and duration of heat treatment; the kinetics of transformation between and alumina are generally slow and certain/ ceramics remain in a metastable state even after a prolonged high temperature anneal. Following post-sinter heat treatment, splitting of X-ray diffraction peaks reveals a segregation of the phase into two components of differing lattice parameter. With sintering schedules of a long duration the splitting may even be present in the as-fired condition as recently reported by Harbach [1]. The splitting is attributed to a structural change resulting from the expulsion of Na₂O from supersaturated grains.