Analysis of the α to β phase transformation in Y-Si-Al-O-N ceramics

The silicon nitride- sialon phase transformation in the Y-Si-Al-O-N system was investigated by transmission and scanning electron microscopy and X-ray diffractometry using samples which contained up to 40% liquid-forming components at temperatures between 1500 and 1600 °C. Completely dense samples suitable for TEM analysis, in which the to transformation could be examined, were prepared using hold times as short as 5 min under a nominal uniaxial pressure followed by rapid cooling. Spheroidal, partially dissolved, silicon nitride grains, together with acicular grains of sialon, were observed in a glass phase containing a very low nitrogen content (undetectable by electron microprobe analysis). This absence of nitrogen build-up in the liquid phase between the dissolution and precipitation sites during the to transformation indicates that the diffusion of nitrogen through the liquid phase is extremely rapid. Nucleation of the sialon was almost entirely homogeneous and the unconstrained nature of the liquid environment resulted in growth of defect-free sialon grains with curved growth fronts perpendicular to the c-axis. The technique described allows direct observation of the effect of various additives on the to phase transformation.     

Die Herleitung von Schalengleichungen über ein erweitertes Variationsprinzip bei Berücksichtigung der Querschubverzerrungen

Ohne ZusammenfassungBezeichnungen L Bezugsgrößen für dimensionslose Koordinaten - L charakteristische Schalenabmessung - t Schalendicke - Schalenparameter - körperfeste, krummlinige, dimensionslose Koordinaten der Schalenmittelfläche - Dimensionslose Koordinate in Richtung der Schalennormalen - i, j,...=1,2,3 Indizierung des dreidimensionalen Euklidischen Raumes - ,,...=1,2 Indizierung des zweidimensionalen Riemannschen Raumes - (...), Partielle Differentiation nach der Koordinate - (...), Kovariante Differentiation für Tensorkomponenten des zweidimensionalen Raumes nach der Koordinate - (...)| Kovariante Differentiation für Tensorkomponenten des dreidimensionalen Raumes nach der Koordinate - Variationssymbol - a ,a ₃ Basisvektoren der Schalenmittelfläche - V Verschiebungsvektor - U ,U ₃ Verschiebungskomponenten des Schalenraumes - v ,w,w ,W Verschiebungskomponenten der Schalenmittelfläche - Verhältnis der Metriktensoren des Schalenraumes und der Schalenmittelfläche - _ik Verzerrungstensor des Raumes - _{(, )}, Symmetrische Verzerrungstensoren der Schalenmittelfläche - _{[, ]} Antimetrischer Term des Verzerrungsmaßes - ^, Spannungstensor - n ,m ,q Tensorkomponenten der Schnittgrößenvektoren - p ,p,c Tensorielle Lastkomponenten     

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.     

Self-reinforcement in li-α-sialon ceramics

Self-reinforcement of Li--sialon ceramics by in situ growth of elongated and -sialon grains has been explored and analysed. Properties of Li--sialon ceramics are mainly determined by the overall starting composition and the crystalline modification of the starting Si₃N₄ powder which in turn determine the final microstructure of the materials. Both the morphology and crystalline phase of the elongated sialon grains have strong effects on the toughening mechanism. The results indicate that -sialons reinforced by elongated -sialon grains have advantages over similar materials reinforced by elongated -sialon grains because of the type of crack deflection toughening mechanism involved.     

Grain-boundary sliding and intergranular cavitation during superplastic deformation of α/β brass

Intergranular and interphase cavitation in binary alpha/beta brass has been investigated in tension at 600° C under conditions of superplastic deformation. The sites for nucleation of cavities has been studied by quantitative metallography and the cavities are observed to nucleate preferentially at- interfaces. The process of cavitation is associated with grain boundary sliding and cavity nucleation occurs at points of stress concentrations in the sliding interfaces. Measurements of grain and phase boundary sliding at various interfaces demonstrate that sliding occurred on- boundaries more readily than on- and-gb interfaces. The predominance of- interface cavitation is believed to be as a result of greater sliding at the- boundary and of an unbalanced accommodation of sliding adjacent to this type of boundary.     

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.     

Flux-line cutting in type II superconductors

Experimental evidence for flux-line cutting in superconductors (intersection and cross-joining of singly quantized vortices) is briefly reviewed. The interaction energy between two straight vortices tilted at an angle ( 0)is then shown to be finite in the London model, i.e., in the limit of vanishing core radius. Next, the activation energy and maximum interaction force are calculated for the vortices in an analytic approximation to the Ginzburg-Landau theory. Here two competing interactions determine the behavior. Electromagnetic repulsion (0 < < /2) varies as cos and decays over distances scaled by the penetration depth , while core attraction is independent of and varies over distances scaled by the coherence length . The force is always repulsive at large flux-line separation (0 < < /2) and its maximum decreases rapidly as decreases, so that flux-line cutting isexpected to be more probable in low- materials. The calculations provide a basis for explaining longitudinal flux-flow resistance as well as some intriguing magnetization behavior in the same configuration.This work was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Materials Sciences Division, and by the Deutsche Forschungsgemeinschaft.On leave from Max-Planck-Institut für Metallforschung, Institut für Physik, Stuttgart, West Germany.On leave from New University of Ulster, Coleraine, Northern Ireland.     

Critical properties of4He in aerogel near the λ-line

We measured the superfluid fraction _s/ and the isobaric thermal expansion coefficient _P of⁴He confined in an aerogel. Data were obtained near the -line along several isobars. Powerlaw fits to the results for _s/ as a function of tT/T_c–1 (T_c is the transition temperature) give a pressure—independent exponent =0.755 when a confluent singular term is included. Fits to the _P data of power laws yield the specific-heat exponents –0.6 and –1.0 above and below T_c respectively. When an analytic background term a×t is included in the fit, the pressure-independent value =–0.59 is permitted, but the amplitude ratio A/A is found to be near zero and the coefficient of the analytic term is large. The measured values for and or are inconsistent with hyperscaling in three dimensions.     

A high-resolution-electron-microscopy study of a γ/γ′-α directionally solidified eutectic alloy

The microstructure of a /- directionally solidified (DS) eutectic alloy with a nominal composition of Ni-30.26Mo-6.08Al-1.43V (wt%) was investigated by means of high-resolution electron microscopy (HREM) and analytical electron microscopy. The -fibres exhibited a typical morphology with a rectangular cross-section and they displayed the Bain orientation relationship (OR) with the / matrix; that is, [001][001] and (110)(010). Misfit dislocations and lattice strain fields existed at the / interface for different habit planes; that is, (110)(010) and (100)(110) were analysed. EDAX (Energy dispersive X-ray) analysis showed that the composition of the -phase was approximately Ni₄(Mo, Al, V); it contained 90° rotational domains of Ni₃(Mo, Al, V) with a DO₂₂ structure and Ni₂(Mo, Al, V) with a Pt₂Mo structure.     

Growth of Gray Tin Crystals

A method is proposed for growing large -Sn single crystals without their disintegration as a result of the phase transition. -Sn crystals are prepared by freezing the closed system water–Sn–seed in such a way that the pressure exerted by the expanding ice minimizes the amount of -Sn nuclei and reduces the growth rate.     

A mixed finite element formulation for shells through a reduced Reissner's principle in elastodynamics

Summary The use of Mixed models based in Reissner's principle in statics has been found to lead to some desirable simplifications in Finite Element formulations, in particular in plates and shells. Reduced formulations of Reissner's principle such as the one used by Prato have proved to be even more successful. In this paper, a reduction similar to that of Prato is attempted on a mixed elastodynamic variational principle by Karnopp.

---

Eine gemischte finite Elemente-Formulierung für Schalen durch ein reduziertes Reissnersches Prinzip der Elastodynamik

Zusammenfassung Die Verwendung von gemischten Modellen basiert auf Reissners Prinzip der Statik führt zu erwünschten Vereinfachungen bei der Formulierung von finiten Elementen im speziellen bei Untersuchungen von Platten und Schalen. Reduzierungen des Reissnerschen Prinzips, wie sie von Prato angewendet worden sind, haben sich sogar als noch erfolgreicher erwiesen. In dieser Untersuchung wird eine Reduktion, ähnlich der von Prato, für ein gemischtes elastodynamisches Variationsprinzip nach Karnopp, vorgenommen.

---

Symbol Table A Domain of integration of the Functional. Also area of the triangle - b Second fundamental form of the shell middle surface - C ^ijkl Elastic Constants - E ₁,E ₁ ^* Strain Energy and Co-Energy density - e _ij Elastic strain tensor - f _i Body force density tensor - I _ks Karnopp's functional, specialized to shells - I _ksc Contracted Karnopp's functional, specialized to shells - i, j, k Index 1, 2, 3 - K ₁,K ₁ ^* Kinetic Energy and Co-Energy density - K ^* Kinetic co-energy density for shell - m Moment tensor defined at the mid-surface - n In-plane stress tensor defined at the middle surface - n Qualifier for the boundary normal - p ,p ³ Boundary forces - Prescribed boundary forces - p Shear force tensor defined at the mid-surface - R Position vector of a point in the volume of the shell - r Position vector of a point on the mid-surface - r _i Net impulse density tensor - S _u Portion of the boundary where displacements are preseribed - S Portion of the boundary where forces are prescribed - s Qualifier for the direction tangent to the boundary - t Time variable - t ^ij Stress tensor - u ,u ₃ Mid-surface displacements - Mid-surface velocities - V Volume - v _i Displacement tensor - , Indices. Range 1, 2 - Shear strain tensor for the middle surface - Variation operator - Mid-surface strain tensor - Mid-surface curvature strain tensor - Direction cosine tensor for boundary normal - Mid-surface rotation tensor - Mid-surface angular velocity tensor - _M Strain energy density - _M * Strain co-energy density - _B * Bending strain co-energy density - _TS ^* Transverse shear strain co-energy density - | Covariant differentiation with respect tox , etc - Partial differentiation with respect tox , etc - .(dot) Time differentiation - -(bar) Prescribed quantities     

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.     

Ageing characteristics of dendritic and non-dendritic (stir-cast) Zn-Al alloy (ZA-27)

The dimensional changes of dendritic and non-dendritic (stir-cast) Zn-Al alloy (ZA-27) were investigated during ageing at temperatures in the range 20–245 °C. The linear expansion of both dendritic and non-dendritic samples increased rapidly with ageing time after about 24 h at 95 °C. An initial normalization treatment led to a large initial growth of the alloy which increased further after prolonged ageing times ( 10⁴h). Accelerated ageing tests in the range 75–250 °C showed that increasing the ageing temperature decreased the long term linear expansion of the alloy. In comparing the behaviour of the two materials, the stir-cast material grew less than the dendritic alloy. Extensive SEM and TEM done on as-stir-cast and aged samples showed that the main changes during ageing occurred in the (FCC) lamellae of the +(Zn) eutectoid, the phase at the primary _particles/_eutectoid interface and in the interparticle areas. In the lamellae and at the interface, zinc precipitated whilst the phase precipitated in the interparticle areas. It is considered that the occurrence of this latter phase, rich in copper, is responsible for the growth of stir-cast material during ageing.     

Boundary layer similarity flow driven by power-law shear

Summary Similarity solution of the Prandtl boundary layer equations describing wallbounded flows and symmetric free-shear flows driven by rotational velocitiesU(y)=y are determined for a range of exponents and amplitudes . Asymptotic analysis of the equations shows that for <–1 no similarity solutions with proper algebraic decay exist. For wall-bounded flow, exact solutions found at =–1/2 and =1 correspond to an Airy function wall jet and uniform planar Couette flow. Numerical integration of the governing similarity equation reveals singular behaviour for wall-bounded flows as ₀ = –2/3, and no solutions are found in the range –1<–2/3. For >–2/3 the shear stressf(0) parameter is determined as a function of and . Symmetric free-shear flow solutions become singular as ₀ = –1/2 and no solutions are found in the range –1<–1/2. For >–1/2 the centerline velocityf(0) is determined as a function of and . An asymptotic analysis of the singular behavior of these two problems as ₀, given in a separate Appendix, shows excellent comparison with the numerical results. Similarity solutions at the critical values ₀ have exponential decay in the far field and correspond to the Glauert wall jet for wall-bounded flow and to the Schlichting/Bickley planar jet for symmetric free-shear flow.     

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.     

Suppression of Anomalous Allotropic Transformations at High Pressures

Anomalous allotropic transformations accompanied by a reduction in the density of the substance can be suppressed by applying a high pressure equal to the ratio of the heat of transition to the difference in the volumes of the phases involved. The estimated pressures necessary to suppress the (ZrO₂), (Fe), and (Sn) phase transitions are 4.34, 3.00, and 0.495 GPa, respectively.     

Formation of nanocrystalline phases in the Cu-Zn system during mechanical alloying

The evolution of various nanocrystalline phases in the Cu-Zn system during the course of mechanical alloying of elemental powder blends, manifests a similar sequence of phase formation in all the compositions. Zinc-rich phases were always first to form, which can be attributed to the diversities of diffusivities and diffusion distances in the constituents. The extent of zinc in -phase becomes significant only after turns nanocrystalline. The crystallite size of reached a minimum (18 nm) near the - phase boundary, while the and phases showed quite coarse crystallite size due to their low melting points. Alloying was sluggish during dry milling compared to wet milling, or at lower milling speed, which demonstrates the effects of oxidation during milling and lower milling energy.     

Self-diffusion of Ti,Zr, and Hf in their hcp phases,and diffusion of Nb95 in hcp Zr

Preliminary values for the self-diffusion constants of -(hexagonal cp) Hf and new values for the self-diffusion constants of -(hcp) Zr are given. A new determination of the latter was considered necessary since existing values disagree widely and the experimental methods employed in their determination are not considered to be sound. Values obtained by the authors for the self-diffusion constants of -Ti are reviewed.The activation energies obtained are much smaller than those predicted by relationships based on physical properties of the elements and, within the experimental error, they have similar values to those corresponding to the -(body-centred cubic) phases. Frequency factors are too small to satisfy Zener's theory; when interpreted according to a vacancy model they give negative activation entropies, and the relationship D ₀()/D ₀() is approximately the same for the three elements.It is suggested that the same diffusion mechanism operates in both the - and -phases. If two mechanisms operate in the -phase, the low temperature one is the same as operates in the -phase.     

The implant material, Ti6Al7Nb: surface microstructure, composition and properties

The excellent biocompatibility of titanium and its alloys is intimately related with the properties of the surface in contact with the biological environment, and therefore it is closely connected with the stable, passivating oxide layer that forms on its surface. In the present paper, the oxide layer on the alloy Ti6Al7Nb has been characterized using X-ray photoelectron spectroscopy, scanning Auger microscopy and pH-dependent lateral force microscopy. The alloying elements Al and Nb are incorporated in the oxide layer and detected in their most stable oxidized form, as Al₂O₃ and Nb₂O₅. Their distribution in the oxide reflects the underlying - microstructure, with enrichment of Al in the - and of Nb in the -phase (determined by electron microprobe). Friction measurements (lateral force microscopy) indicate slightly different, pH-dependent, lateral forces above the - and -phase structures that point to small local variations in surface charges. © 1999 Kluwer Academic Publishers     

Specific analysis of EBSD data to study the texture inheritance due to the β → α phase transformation

A specific processing of EBSD data is proposed to study the texture inheritance of titanium or zirconium alloys. A non standard misorientation map is calculated to localise the colonies inherited from the same parent grain. The calculation of the parent orientation from its inherited variants detailed in previous works has been adapted to the data obtained from an automated EBSD analysis. Finally, a method to derive the orientation map of the parent phase from that of the inherited phase is proposed. The resulting and COMs are used to study some aspects of the variant selection occurring in the transformation of a T40 sample.