A new parameter for describing the structure bifurcation in two-phase alloys containing coherent particles

The so-called bifurcation diagrams for precipitate particles in nickel-based alloys were obtained by calculating the energy state for a pair of particles on the basis of the bifurcation theory. Based on the bifurcation diagrams, we have proposed a new parameter for describing the two-phase structure containing coherent particles. The parameter is defined as the mean particle radius at the intersection of the energy ridge and the line ofR=–0.5 orR=0.5 in the bifurcation diagram (R(r –r )/(r +r ), wherer andr are the radii of and ), and is symbolized by¯r ^* _±0.5. Because the energy state of the paired and is maximum at¯r ^* _±0.5 whenR=±0.5,¯r ^* _±0.5 is just like the watershed and hence we have termed it structureshed. This parameter successfully describes the effects of elastic energy as well as surface energy on the microstructural changes during coarsening of precipitate particles.     

Phase equilibria in the Ti-rich corner of the Ti-Si-Sn-Al system Part I Section 9Si-1Sn (at.%)

Phase equilibria in Ti-rich corner of the Ti-Si-Sn-Al system were studied using differential thermal analysis, X-ray diffraction, microscopy, and electron microprobe analysis. Projections of solidus and liquidus surfaces, an isothermal section at 1300°C and an isopleth at 9Si-1Sn (at.%) were constructed. It was shown that in the concentration interval studied at the solidus and 1300°C temperatures two two-phase Ti₅(Si,Sn,Al)₃ + <-Ti< and Ti₅(Si,Sn,Al)₃ + <-Ti< regions are present. The liquidus surface is characterised by the regions of and Z primary crystallisation, resulting in bivariant L + Ti₅(Si,Sn,Al)₃ eutectic. The character of horizontal and vertical sections is similar to that for the Ti-Si-Al system.     

Influence of rhenium on the microstructures and mechanical properties of a mechanically alloyed oxide dispersion-strengthened nickel-base superalloy

The influence of a 3 wt% Re addition on the creep strength and microstructure of a mechanically alloyed and oxide dispersion-strengthened nickel-base superalloy was investigated. Two alloys, Ni–8Cr–6.5Al–6W–3Ta–1.5Mo–6Co–1Ti–3Re–0.15Zr–0.05C–0.01B–0.9Y₂O₃ (3Re alloy) and a non-rhenium containing (0Re) alloy were prepared for this study.The 3Re alloy showed two-fold improvement in creep life compared with that of 0Re alloy, presumably due to a change in the mode of the precipitate-dislocation interaction. For the 3Re alloy, finer, more cuboidal and aligned precipitates are formed, which force the mobile dislocations at the – interfaces to cut precipitates in order to proceed. Shearing of precipitates is evinced by the existence of stacking faults and results in an increase of creep strength. In constrast, lower creep strength was observed for 0Re alloy because a dislocation looping mode is dominant with coarser and more irregularly shaped precipitates present in this alloy. Another possible explanation for an improved creep strength of 3Re alloy is related to the tangled dislocation structure formed by the interaction between glide dislocation and interfacial dislocation, which also acts as an effective barrier for further glide dislocation motion. A 3 wt% Re addition significantly retards coarsening kinetics. Rhenium acts as a rate-controlling species upon the volume diffusion-controlled coarsening process because it is a heavy elemenet and also it almost solely partitions to the matrix. X-ray diffraction experiments showed that the magnitude of the lattice mismatch between and increased with the 3 wt% Re addition from 0% to –0.26% at room temperature. Increased lattice mismatch for 3Re alloy causes the formation of more aligned and cuboidal precipitates rather than random and odd-shaped precipitates for 0Re alloy, and it also accelerates the coalescence between cuboidal precipitates.     

Phase transformation and densification during pressureless sintering of Si3N4 with MgO and Y3Al5O12 additives

The - transformation of Si₃N₄ during liquid-phase sintering appears to be controlled by the growth of the -Si₃N₄ grains in the direction perpendicular to thec-axis in the case of MgO additive. The diffusion through the liquid is the rate-controlling step in the case of the Y₄Al₅O₁₂ additive. The density of the sintered body at the solid skeleton stage was influenced by the change in the - transformation rate and/or by a change of the transformation mechanism. The indirect proportionality between the -phase content in the starting powder and the density at the solid skeleton stage was found. The microstructure of the sintered body is influenced by both the -phase content in the starting powder and the chemical composition of the additive. Fine, uniform microstructure with a high aspect ratio of -grains is obtained, when the -phase content in the starting powder is as small as possible and when the - transformation is controlled by grain growth.     

Activated slip systems during yielding of α-β brass two-phase bicrystals

- brass two-phase bicrystals, consisting of fcc () single crystals and bee () single crystals, which were made by the solid state diffusion couple technique, were tensile-tested at room temperature in order to clarify the role of phase-interface on the deformation. The two-phase bicrystals had small concentration gradients in the- and-phases and satisfied the Kurjumov-Sach's orientation relationships i.e. {1 1 1} {1 1 0} and [1 1 0] [1 1 1] at the interface. The slip traces observed in bicrystals deformed to about 3% plastic strain showed a striking contrast between the- and-phases; the slip traces in the-phase were clear and straight, while those in the-phase were fine and wavy. The slip systems in the bicrystals were attributed to those observed in and single crystals, and were explained by a plastic strain incompatibility mechanism. The slip systems, originating at the interface or propagating from another phase, were observed on matching planes.On leave from Mechanical Engineering Department, Faculty of Engineering, Al-Azhar University, Cairo, Egypt.     

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.     

Vibrational properties of wood along the grain

The dynamic Young's modulus (E_L) and loss tangent (tan _L ) along the grain, dynamic shear modulus (G_L) and loss tangent (tan _S) in the vertical section, and density () of a hundred spruce wood specimens used for the soundboards of musical instruments were determined. The relative acoustic conversion efficiency ( ) and a ratio reflecting the anisotropy of wood (, (E_L/G_L)(tan _S/tan _L)) were defined in order to evaluate the acoustic quality of wood along the grain. There was a positive correlation between and , and the variation in was larger than that in . It seemed logical to evaluate the acoustic quality of spruce wood by a measure of . By using a cell wall model, those acoustic factors were expressed with the physical properties of the cell wall constituents. This model predicted that the essential requirement for an excellent soundboard is smaller fibril angle of the cell wall, which yields higher and higher . On the other hand, the effects of chemical treatments on the and of wood were clarified experimentally and analyzed theoretically. It was suggested that the and of wood cannot be improved at the same time by chemical treatment.     

Eutectoid decomposition mechanisms in hypoeutectoid Ti-X alloys

A TEM study has been made of the bainite reaction in five hypoeutectoid Ti-X alloys, where X was successively cobalt, chromium, copper, iron and nickel. Rational orientation relationships were demonstrated amongst eutectoid , eutectoid intermetallic compound and the matrix in Ti-Ni, Ti-Co and Ti-Cr. Formation of Ti₂Co at : boundaries was observed. Eutectoid in bainite was found to be slightly misoriented with respect to proeutectoid , indicating that it is separately nucleated, perhaps sympathetically, rather than the result of the continued growth of proeutectoid . Eutectoid Ti₂Co and Ti₂Cu crystals in bainite were approximately equiaxed whereas Ti-Cr₂ crystals were elongated, a result ascribed to a ledge height-to-spacing ratio / at intermetallic compound crystal: boundaries approaching that of eutectoid (: boundaries in Ti-Cr but not in the other two systems. In the Ti-Fe alloy, eutectoid and eutectoid TiFe were directly observed to have ledged interphase boundaries with their matrix, but with different inter-ledge spacings and growth directions. Observation of pearlite lamellae growing normal to the broad faces of proeutectoid plates in the Ti-Ni alloy indicates that this mode of eutectoid decomposition, like that of bainite, can develop from partially coherent interphase boundaries. The suggestion was offered that pearlite forms when approachesh at the nucleating proeutectoid : interface and that bainite develops when h at this interface.     

Nuclear susceptibility of liquid He3—II

Pulsed NMR measurements of the nuclear susceptibility of liquid He³ at various molar volumes are presented over the temperature range between 0.035 and 1°K. The scatter in the data is about 0.2%, while the absolute accuracy is estimated to be about ±1%. At temperaturesT such that ₀ T/C0.35 the susceptibility data can empirically be represented by the expression =₀[1–(x₀ T/C)²]. Here ₀ is the extrapolated molar susceptibility atT=0 for a given volume, assuming the expression to be valid below 35 m°K.C is the molar Curie constant and is a factor that appears to be somewhat dependent on molar volume and whose average value is found experimentally to be about 0.53. This result compares with the theoretical prediction by Béal-Monadet al. who used the paramagnon model for liquid He³ and obtained the expression given above with a value of =0.58. However, the observed apparentT ²dependence of the susceptibility is over a greater temperature range than the theory would lead one to expect, and this point is discussed. The experimental results are also compared with a molecular-field approach by Goldstein, who proposed a representation of the susceptibility by a universal curve T/C=f(₀ T/C), wheref is the function for the ideal gas. In spite of some systematic discrepancies, a scaled presentation of the data is in good overall agreement with the calculated curve. The data disagree with the Stoner model of a Fermi gas with interactions. Finally, the values of ₀ are compared with those of previous work.Research supported by grants from the National Science Foundation and from the Army Research Office (Durham).     

Characterization of α ? β PbF2 phase transition by several techniques

X-ray Diffraction (XRD), Dynamic-Mechanical Analysis (DMA), Impedance Spectroscopy (IS), and Scanning Electron Microscopy (SEM) have been used to the study of phase transition in PbF₂ pellets pressed uniaxially in the 37 MPa–480 MPa range. A mixture of and phases is detected and the -phase content at room temperature is found to be dependent on the applied load. The dilation results on DMA, the phase identification by XRD, the ionic conductivity results by IS analysis and the SEM micrographs of -PbF₂ pellets show evidences for the increase in -phase content at the expense of the -phase. SEM analysis provided further evidence for specimen sintering under heating at approximately 498 K.     

Constitution of the Ni3Cr-Ni3Al-Ni3W system

Isothermal sections of the Ni-Cr-Al-W system have been investigated at 75 at % Ni and temperatures of 1523 and 1273 K, by means of phase compositional analysis, X-ray diffraction and microscopical examination. The alloys studied lay in the range 2.5 to 10 at % Cr, 12.5 to 20 at% Al, 2.5 to 6.25 at % W, The phases formed were, and the bcc solid solution based on tungsten (designated ₂). The maximum extent of the region was found to be 3 at % each of chromium and tungsten. Preferential partitioning of tungsten to occurred. Study of an Ni-10Cr-12.5Al-2.5W alloy aged at 1273 and 1073 K, after quenching from 1573 K, showed that changes in and compositions and lattice parameters occur as a function of ageing time.     

Thermodynamics of the quasiequilibrial growth of crazes

By comparing the morphology and physical properties (averaged over the scale of 1 to 10m) of a crazed and uncrazed polymer, it can be concluded that crazing is a new phase development in the initially homogeneous material. The present study is based on recent work on the general thermodynamic explanation of the development of a damaged layer of material. The treatment generalizes the model of a crack-cut in mechanics. The complete system of equations for the quasiequilibrial craze growth follows from the conditions of local and global phase equilibrium, mechanical equilibrium and a kinematic condition. Constitutive equations of craze growth-equations are proposed that are between the geometric characteristics of a craze and generalized forces. It is shown that these forces, conjugated with the geometric characteristics of a craze, can be expressed through the known path independent integrals (J, L, M,). The criterion of craze growth is developed from the condition of global phase equilibrium. F Helmholtz's free energy - G Gibb's free energy (thermodynamic potential) - f density ofF - g density ofG - T absolute temperature - S density of entropy - strain tensor - components of - stress tensor - components of - _y stress along the boundary of an active zone (yield stress) - _b stress along the boundary of an inert zone - applied stress - value of at the moment of craze initiation - K stress intensity factor - C tensor of elastic moduli - C ^–1 tensor of compliance - internal tensorial product - V volume occupied by sample - V ₁ volume occupied by original material - V ₂ volume occupied by crazed material - V boundary ofV - (V) vector-function localized on V - (x) characteristic function of an area - (x) variation of(x) - (x) a finite function - tensor of alternation - components of the boundary displacement vector - l components of the vector of translation - n components of the normal to a boundary - _k components of the vector of rotation - e symmetric tensor of deviatoric deformation of an active zone - expansion of an active zone - J ⁽ⁱ⁾ ,L _k ⁽ⁱ⁾ ,M ⁽ⁱ⁾,N ⁽ⁱ⁾ partial derivatives ofG ⁽ⁱ⁾ with respect tol , _k, ande , respectively - [ ] jump of the parameter inside the brackets - thickness of a craze - 2l length of a craze - 2b length of an active zone - l _c distance between the geometrical centres of the active zone and the craze - ^* craze thickness on the boundary of an active and the inert zone - l ^* craze parameter (length dimension) - A craze parameter (dimensionless) - ^* extension of craze material     

Kinetic interpretation ofα- andβ-Si3N4 formation from oxide-free high-purity silicon powder

A kinetic analysis of the isothermal nitridation of high-purity oxide-free silicon powder is described. The kinetic analysis suggests that the and polymorphs of Si₃N₄ are formed by separate and parallel reaction paths. This analysis provides for the decoupling and quantitative kinetic interpretation of- and-Si₃N₄ formation reactions. Consistent with existing microstructural and thermodynamic evidence, the-forming reaction is shown to obey a first-order rate law, whereas a phase-boundary controlled rate law describes the-forming reaction. A kinetic model employing these rate laws is developed and is used to predict the/ phase ratio as a function of isothermal reaction temperature and extent of reaction. The/ phase ratios so obtained are shown to be in good agreement with experimental observations made under a variety of reaction conditions.     

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 .     

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.     

Methanation of carbon deposited directly from CO2 on rhodium-bearing activated magnetite

Methanation reactivity was studied for the surface carbon deposited from CO₂ on the surface of Rh-bearing activated magnetite. The most active material (Rh=0.83 wt %) for methanation was prepared by the impregnation method at 60°C and showed 98% conversion at 300°C. The surface carbon was composed of elemental carbon (-carbon) and polymerized carbon (-carbon), the proportion being dependent on the density of carbon deposited. In temperature-programmed surface reaction, the extent of conversion of the - and -carbon to CH₄ was 0.34 (-carbon) and 0.53 (-carbon), respectively, and the total conversion was 0.87. This result indicates that not only elemental carbon but polymerized carbon (-carbon) could be converted to CH₄ on the Rh-bearing activated (-carbon) magnetite, whereas -carbon is not hydrogenated on activated magnetite.     

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.     

Variation of aluminium concentration in β′-sialon grains formed during liquid-phase sintering of Si3N4-Al2O3-Nd2O3

The aluminium concentration in -sialon grains of the 74Si₃N₄ ()-6Al₂O₃-20Nd₂O₃ (wt%) specimen has been determined. As the - transformation proceeded, the average aluminium concentration in -sialon grains decreased. For individual grains, the aluminium concentration at the centre was higher than that at the edge. The observed variation of aluminium concentration has been explained in terms of the compositional change of the liquid matrix during sintering.     

Behaviour of amorphous poly(ethylene terephthalate) annealed at T<T g by thermally stimulated currents

Thermally stimulated current (TSC) discharges in open circuit of amorphous poly(ethylene terephthalate) (PET) corona-charged electrets show a heteropolar relaxation at 87 °C, ₁ between and peaks. This relaxation tends to become homopolar when the sample is annealed at temperatures below the glass transition temperature. This is due to the formation of a trapped charge density on the surface of the material that originates, during the TSC discharge, a current that counteracts the one that results in ₁ This trapping effect, which initially is null, increases with annealing due to the rise in resistivity. On the other hand, TSC discharges in short-circuited annealed samples result in a heteropolar peak, ^*, that corresponds to ₁ The area of ^* increases with the annealing time in a bounded way. This peak is related to the formation of thermal nuclei (embryos) in the bulk of the material that act as heterogeneities. This suggests that ₁ is associated with a barrier-type polarization. If the annealed sample is heated to temperatures above the glass transition temperature, the tendency to the inversion of ₁ vanishes and ^* disappears, whereas and are modified. This suggests that relaxation is related to a Maxwell-Wagner-Sillars effect.     

The influence of ageing on the stability of β-γ/γ′ derived microstructures in Ni-Al-Cr-(Co) alloys

Multiphase Ni-Al-(Fe)-(Cr)-(Co)-based intermetallics with (B2)- (A1)/(L1₂), - or - microstructures can exhibit significant room-temperature tensile ductility. In the case of Ni-Al-Cr-based alloys, microstructural development is complicated by the precipitation of -Cr, which can supplant the -phase during ageing of three-phase -/ microstructures. An investigation of the stability, during ageing, of cast Ni-Al-Cr-(Co) alloys with microstructures derived from -/ is reported. In the as-cast condition, the materials investigated consisted of a dendritic matrix containing L1₀ type martensite and interdendritic /. Extensive intra- and interdendritic -Cr precipitation was also observed. The stability during ageing of the interdendritic / microstructure is also considered and transformation of the L1₀ martensite is examined.