Continuous-cooling α-to-γ transformation behaviour of Ti–45.5 at.% Al–0.05 at.% B alloy

The continuous-cooling transformation behaviour of Ti–45.5?at.%?Al–0.05?at.%?B alloy was quantitatively measured using a real-time resistivity–temperature–time measurement apparatus operating under a high vacuum. The addition of a small amount of B does not significantly alter the α–γ-phase equilibria but significantly raises the α–γ lamellar start temperature of Ti–45.5?at.%?Al alloy at most cooling rates. Furthermore, it markedly increases the critical cooling rate for the ordering reaction. The effect of B addition, which greatly stabilizes the lamellar structure up to a fast cooling rate, is to accelerate the lamellar formation kinetics; the lamellar spacing was nevertheless distinctively larger in a B-doped alloy. This is because lamellae in B-doped alloy nucleate heterogeneously on titanium borides at the grain boundary; the borides are effective nucleation sites particularly since local Ti depletion can occur near the interface of the growing titanium borides during cooling. In the absence of B addition, the lamellar structure starts to form only at temperatures below T ₀, suggesting that a large undercooling is required for the nucleation of lamellae even at the grain boundaries. On the other hand, the B addition greatly retards the kinetics of the α-to-α₂ ordering reaction by markedly increasing its critical cooling rate without a large change in the ordering temperature. This is believed to be due to its tendency to segregate strongly to the antiphase boundaries.     

Initiation of discontinuous precipitation at interphase boundaries in a two-phase Zn–6.3 at.% Ag alloy

Discontinuous precipitation (DP) was found to initiate at both η′–ε interphase and η′–η′ grain boundaries in a two-phase Zn–6.3?at.%?Ag alloy consisting of ε and supersaturated η′ phases. The η′–ε interphase boundaries at which DP has initiated illustrated a sinusoidal interface during ageing, which implies that the morphological instability is a prerequisite for the DP initiation at an η′–ε interphase boundary. The application of the morphological instability model for solid–solid interfaces has indicated that the interface protuberances grow into the supersaturated η′ and the interphase boundary becomes unstable since the observed wavelength of serrated η′–ε interphase boundaries was larger than the critical value predicted by the model. A solute-depleted region is therefore established in front of the η′–ε interphase boundary, which provides an appropriate site leading to a DP reaction. Based on this, a nucleation mechanism of DP at the interphase boundaries is proposed accordingly: the allotriomorphs of DP can be directly developed from ε protuberances of a serrated interphase boundary.     

Defect-dependent nitride surface layer development upon nitriding of Fe–1 at.% Mo alloy

Upon nitriding of binary Fe–1 at.% Mo alloy in a NH₃/H₂ gas mixture under conditions (thermodynamically) allowing γ′-Fe₄N_{1– x} compound layer growth (nitriding potential: 0.7?atm^?1/2 at 753?K (480?°C) – 823?K (550?°C)), a strong dependency of the morphology of the formed compound layer on the defect density of the specimen was observed. Nitriding of cold-rolled Fe–1 at.% Mo specimens leads to the formation of a closed compound layer of approximately constant thickness, comparable to nitriding of pure iron. Within the compound layer, that is, in the near-surface region, Mo nitrides are present. The growth of the compound layer could be described by a modified parabolic growth law leading to an activation energy comparable to literature data for the activation energy of growth of a γ′-Fe₄N_{1? x} layer on pure iron. Upon low temperature nitriding (i.e. ?793?K (520?°C)) of recrystallized Fe–1 at.% Mo specimens, an irregular, ‘needle-like’ morphology of γ′-Fe₄N_{1? x} nucleated at the surface occurs. This γ′ iron nitride has an orientation relationship (OR) with the matrix close to the Nishiyama–Wassermann OR. The different morphologies of the formed compound layer can be interpreted as consequences of the ease or difficulty of precipitation of Mo as nitride as function of the defect density.     

Impact of long-term relaxation on the phase composition of Pd–5.3 at % In–0.5 at % Ru alloy after hydrogenation

The structural state of a hydrogenated foil of Pd 5.3 at %–In 0.5 at % Ru alloy with a long relaxation time (55000 h) is studied via X-ray diffraction. Changes in the phase composition of the alloy during relaxation after hydrogen escapes from it are established. The quasi-stability of the distribution of the widths of areas of coherent scattering (ACS) is revealed by the concentration of indium atoms in directions ?100? and ?111?.     

Directional solidification of Ti–49 at.%Al alloy

Ti–49Al (at.%) alloy was directionally solidified in Bridgman-type directional solidification furnace. The specimens were directionally solidified under an argon atmosphere with the different growth rate (V=5–30 μm/s) at a constant temperature gradient (G=12.1 K/mm), and with the different temperature gradient (G=2.8–12.1 K/mm) at a constant growth rate (V=10 μm/s). The dendritic spacings (λ ₁) were measured from both transverse and longitudinal sections of the specimens. The dependence of λ ₁ on the growth rate (V) and temperature gradient (G) were determined by using linear regression analysis. According to the experimental results, the value of λ ₁ decreases with the increase of values of V and G. The experimental results were compared with the current theoretical and numerical models, and similar previous experimental results.     

Unusual nucleation and growth of γ′ iron nitride upon nitriding Fe–4.75 at.% Al alloy

The influence of substitutionally dissolved Al in ferritic Fe–4.75 at.% Al alloy on the nucleation and growth of γ′ iron nitride (Fe₄N_{1? x} ) was investigated upon nitriding in NH₃/H₂ gas mixtures. The nitrided specimens were characterised employing optical microscopy, scanning electron microscopy, transmission electron microscopy, electron probe microanalysis and X-ray diffraction. As compared to the nitriding of pure ferrite (α-Fe), where a layer of γ′ develops at the surface, upon nitriding ferritic Fe–4.75 at.% Al an unusual morphology of γ′ plates develops at the surface, which plates deeply penetrate the substrate. In the diffusion zone, nano-sized precipitates of γ′ and of metastable, cubic (NaCl-type) AlN occur, having, with the ferrite matrix, a Nishiyama–Wassermann orientation relationship and a Bain orientation relationship, respectively. The γ′ plates contain a high density of stacking faults and fine ε iron nitride (Fe₂N_{1? z} ) precipitates, although the formation of ε iron nitride is not expected for the employed nitriding parameters. On the basis of dedicated nitriding experiments it is shown that the unusual microstructural development is a consequence of the negligible solubility of Al in γ′ and the obstructed precipitation of the thermodynamically stable, hexagonal (wurtzite-type) AlN in ferrite.     

Solute-diffusion-controlled dislocation creep in pure aluminium containing 0.026 at.% Fe

Pure aluminium containing about 200?at.ppm Fe in solution is shown to creep about 10⁶ times slower at 200°C than the same aluminium containing a negligible amount of iron in solution. The high creep resistance of the Al–200?at.ppm?Fe alloy is attributed to the presence of subgrain boundaries containing iron solute atoms. It is proposed that the opposing stress fields from subgrain boundaries and from the piled-up dislocations during creep are cyclically relaxed, by iron solute diffusion, to allow climb of the lead dislocation in the pile-up. The mechanism is a form of mechanical ratcheting. The model is applied to Al–Fe alloys and correctly predicts that the creep rate is controlled by the rate of iron solute diffusion and by a temperature dependence equal to the activation energy for iron diffusion, namely Q _c?=?221?kJ?mol^?1. Basic creep studies on solid-solution alloying with solute atoms that diffuse slowly in the lattice of aluminium (e.g. manganese, chromium, titanium and vanadium) appear worthy of study as a way of enhancing creep strength and of understanding creep mechanisms involving solute-atom-containing subgrain boundaries.     

Microstructure,creep, and tensile behaviour of a Ti–15Al–33Nb (at.%) beta+orthorhombic alloy

The microstructural evolution, creep and tensile deformation behaviour of a Ti–15Al–33Nb (at.%) alloy was studied. Monolithic sheet material was produced through conventional thermomechanical processing techniques comprising non-isothermal forging and pack rolling. Electron microscopy studies showed that depending on the heat-treatment schedule, this alloy may contain three constituent phases including:?β?(disordered body-centred cubic), α₂ (ordered hexagonal close-packed based on Ti₃Al) and O (ordered orthorhombic based on Ti₂AlNb). Heat treatments at all temperatures above 990°C, followed by water quenching, resulted in fully-β microstructures. Below 990°C, Widmanstätten O-phase or α₂-phase precipitated within the?β?grains. The fine-grained as-processed microstructure, which exhibited 90?vol.% β-phase, exhibited excellent strength (UTS?=?916?MPa) and ductility (?_f>12%). After heat treatment, greater volume fractions of the orthorhombic phase precipitated and resulted in lower ? _f values with UTS values ranging between 836–920?MPa. However, RT elongations of more than 2% were recorded for microstructures containing up to 63?vol.% O-phase. Specimens subjected to 650°C tensile experiments tended to exhibit lower strength values while maintaining higher elongation-to-failure. Tensile creep tests were conducted in the temperature range 650–710°C and stress range 49–275?MPa. The measured creep exponents and activation energies suggested that grain boundary sliding operates at intermediate stress levels and dislocation climb is active at high stresses. Microstructural effects on the tensile properties and creep behaviour are discussed in comparison to a Ti–12Al–38Nb O?+?β alloy.     

Bohmian mechanics at space–time singularities: II. Spacelike singularities

We develop an extension of Bohmian mechanics by defining Bohm-like trajectories for quantum particles in a curved background space–time containing a spacelike singularity. As an example of such a metric we use the Schwarzschild metric, which contains two spacelike singularities, one in the past and one in the future. Since the particle world lines are everywhere timelike or lightlike, particles can be annihilated but not created at a future spacelike singularity, and created but not annihilated at a past spacelike singularity. It is argued that in the presence of future (past) spacelike singularities, there is a unique natural Bohm-like evolution law directed to the future (past). This law differs from the one in non-singular space–times mainly in two ways: it involves Fock space since the particle number is not conserved, and the wave function is replaced by a density matrix. In particular, we determine the evolution equation for the density matrix, a pure-to-mixed evolution equation of a quasi-Lindblad form. We have to leave open whether a curvature cut-off needs to be introduced for this equation to be well defined.     

Magnetic properties of nano-sized 5 at.%Fe–Al systems

High energy ball milling is a promising materials processing technique that is widely used to produce nanocrystalline structures. However, when stainless steel or hardened steel containers and balls are used for milling, contamination from the milling medium can influence the material properties of the final nanostructured products due to intercalation of iron (Fe) as an impurity. This study reports the effect of iron contamination on nanocrystalline aluminum (Al) powder. ⁵⁷Fe Mössbauer spectroscopy and bulk magnetization studies using a vibrating sample magnetometer show that pure Al powder milled in hard steel media is strongly ferromagnetic at room temperature due to Fe contamination of about 5 at.% from the milling medium. TEM studies indicate that the system consists mainly of nano-sized Fe interspersed in Al with average crystallite sizes of ~2 and ~5 nm for Fe and Al, respectively. A comparative study of this system made with a mechanically alloyed Fe–Al system with the same percentage of Fe mixed with pure Al and mechanically alloyed using tungsten carbide vials and balls shows that the saturation magnetization, coercivity, Curie temperature, and low temperature behavior (field cooled–zero field cooled) are very different in the two cases. The different magnetic properties of the two systems can be attributed to the presence of magnetic and non-magnetic phases present.     

Comparison of the deformation behaviour of commercially pure titanium and Ti–5Al–2.5Sn(wt.%) at 296 and 728 K

The tension and tensile-creep deformation behaviours of a fully-α phase commercially pure (CP) Ti and a near-α Ti–5Al–2.5Sn(wt.%) alloy deformed in situ inside a scanning electron microscope were compared. Tensile tests were performed at 296 and 728?K, while tensile-creep tests were performed at 728?K. The yield stress of CP Ti decreased dramatically with increasing temperature. In contrast, temperature had much smaller effect on the yield stress of Ti–5Al–2.5Sn(wt.%). Electron backscattered diffraction was performed both before and after the deformation, and slip trace analysis was used to determine the active slip and twinning systems, as well as the associated global stress state Schmid factors. In tension tests of CP Ti, prismatic slip was the most likely slip system to be activated when the Schmid factor exceeded 0.4. Prismatic slip was observed over the largest Schmid factor range, indicating that the local stress tensor varies significantly from the global stress state of uniaxial tension. The basal slip activity in Ti–5Al–2.5Sn(wt.%) was observed in a larger faction of grains than in CP Ti. Pyramidal ?c?+?a? slip was more prevalent in CP Ti. Although twinning was an active deformation mode in tension tests of the CP Ti, it was rare in Ti–5Al–2.5Sn(wt.%). During creep, dislocation slip was the primary apparent deformation mechanism in CP Ti, while evidence for dislocation slip was much less apparent in Ti–5Al–2.5Sn(wt.%), where grain boundary sliding was dominant. A robust statistical analysis was carried out to assess the significance of the comparative activity of the different slip systems under the variety of experimental conditions examined.     

Decomposition of an Fe-Cr 38 wt.% chromium stainless steel at 475 °C

The physical changes occurring at 475 °C in an Nb and Al stabilized stainless steel containing 38 wt.% Cr have been studied by Mössbauer spectroscopy. The specimen started to decompose when held at 475 °C. Decomposition still continues after 500 hours into a paramagnetic Cr-rich -phase and a nearly pure Fe -phase. The magnetic field distribution of the initial sample indicates that considerable decomposition has already taken place into an -phase with an estimated 15 at.% iron, and an iron-rich -phase with an estimated 18 at.% Cr.     

Precipitation structure in an Al-2·0 at. % Zn-1·0 at. % Mg alloy within and close to the grain boundaries and its effects on mechanical properties

During ageing the Al-2·0 at. %Zn-1·0 at. % Mg alloy at elevated temperatures the width of the precipitation free zone (PFZ) at both sides of the grain boundaries (GB) is identical with that free of quenched-in dislocation loops (DL). After sufficiently long ageing a band of precipitates is growing inside the former PFZ and the DLs in the midgrain regions act as sites for the heterogeneous nucleation of the-phase. Two precipitation processes significantly affect the mechanical properties. TEM correlates grain boundary precipitate density and morphology with grain boundary misorientation.     

Active metal brazing of Al2O3 to Kovar® (Fe–29Ni–17Co wt.%) using Copper ABA® (Cu–3.0Si–2.3Ti–2.0Al wt.%)

The application of an active braze alloy (ABA) known as Copper ABA® (Cu–3.0Si–2.3Ti–2.0Al wt.%) to join Al₂O₃ to Kovar® (Fe–29Ni–17Co wt.%) has been investigated. This ABA was selected to increase the operating temperature of the joint beyond the capabilities of typically used ABAs such as Ag–Cu–Ti-based alloys. Silica present as a secondary phase in the Al₂O₃ at a level of ~5 wt.% enabled the ceramic component to bond to the ABA chemically by forming a layer of Si₃Ti₅ at the ABA/Al₂O₃ interface. Appropriate brazing conditions to preserve a near-continuous Si₃Ti₅ layer on the Al₂O₃ and a continuous Fe₃Si layer on the Kovar® were found to be a brazing time of ≤15 min at 1025 °C or ≤2 min at 1050 °C. These conditions produced joints that did not break on handling and could be prepared easily for microscopy. Brazing for longer periods of time, up to 45 min, at these temperatures broke down the Si₃Ti₅ layer on the Al₂O₃, while brazing at ≥1075 °C for 2–45 min broke down the Fe₃Si layer on the Kovar® significantly. Further complications of brazing at ≥1075 °C included leakage of the ABA out of the joint and the formation of a new brittle silicide, Ni₁₆Si₇Ti₆, at the ABA/Al₂O₃ interface. This investigation demonstrates that it is not straightforward to join Al₂O₃ to Kovar® using Copper ABA®, partly because the ranges of suitable values for the brazing temperature and time are quite limited. Other approaches to increase the operating temperature of the joint are discussed.     

Tracy–Widom at High Temperature

We investigate the marginal distribution of the bottom eigenvalues of the stochastic Airy operator when the inverse temperature \(\beta \) tends to \(0\) . We prove that the minimal eigenvalue, whose fluctuations are governed by the Tracy–Widom \(\beta \) law, converges weakly, when properly centered and scaled, to the Gumbel distribution. More generally we obtain the convergence in law of the marginal distribution of any eigenvalue with given index \(k\) . Those convergences are obtained after a careful analysis of the explosion times process of the Riccati diffusion associated to the stochastic Airy operator. We show that the empirical measure of the explosion times converges weakly to a Poisson point process using estimates proved in Dumaz and Virág (Ann Inst H Poincaré Probab Statist 49(4):915–933, 2013). We further compute the empirical eigenvalue density of the stochastic Airy ensemble on the macroscopic scale when \(\beta \rightarrow 0\) . As an application, we investigate the maximal eigenvalues statistics of \(\beta _N\) -ensembles when the repulsion parameter \(\beta _N\rightarrow 0\) when \(N\rightarrow +\infty \) . We study the double scaling limit \(N\rightarrow +\infty , \beta _N \rightarrow 0\) and argue with heuristic and numerical arguments that the statistics of the marginal distributions can be deduced following the ideas of Edelman and Sutton (J Stat Phys 127(6):1121–1165, 2007) and Ramírez et al. (J Am Math Soc 24:919–944, 2011) from our later study of the stochastic Airy operator.     

A resistometric investigation of the decomposition kinetics of Al-21·8 at.% Zn solid solution at 276 °C

Under the condition of nearly equilibrium concentration of vacancies, time dependence of the amount of isothermal transformation given byy=R/R _f was investigated whereR _f is the total structural change of resistivity on completion of the whole process andR is the measured resistivity change. The investigation was done on the 21·8 at.% (40·3wt.%) Zn alloy under the condition of relatively low supersaturation of a few degrees centigrade below the metastable _R solvus line. The total transformation involves four kinetic stages: the first two stages correspond probably to diffusion-controlled growth of the _R particles from the supersaturated solid solution and to the ripening of these particles till their conversion to the cubic phase takes place. The last two kinetic stages account analogously for the particles growth and ripening. Both _R and phases were identified by the transmission electron microscopy. When separating the individual stages, the approximation byy=1–exp [–(mt) ⁿ] of the amount of transformationy was used. The approximation allowed to get the starting values of both the time and the change of the structural part of the electrical resistance for individual stages and also to derive the parametersm _i, n_i which had to be redetermined for the individual separated stages. These data made it possible to synthetize the experimental curves ofR andy vs. time for the total transformation.It is a pleasure to thank Doc. Dr. V.Syneek CSc. for stimulating the author's interest in this problem and for providing helpful discussions. I also would like to express my thanks to Ing. P.Bartuka CSc. for the transmission electron microscopic study carried out to identify the particular phases. The author is indebted to Ing.V. íma for the preparation of the investigated alloy and to Mrs. A.Mendlová and Mr. P.Vyhlídka for technical assistance.     

Maxwell–Chern–Simons Casimir effect at finite temperature

We will apply the Feynman path integral method to discuss the Casimir force of Maxwell–Chern–Simons gauge field at finite temperature between two parallel ideal conducting wires.     

Ti-45at.% Al合金定向凝固过程中显微组织演化的计算机模拟

采用基于溶质扩散控制模型CA方法对Ti-45at.% Al合金定向凝固过程中显微组织演化过程进行了数值模拟.模拟结果表明,在温度梯度较高时,初生晶核间距无论大小,均可通过分枝或竞争生长而使一次胞晶/枝晶间距得到调整.在抽拉速度一定情况下,随着温度梯度增加,胞晶/枝晶间距减小,在温度梯度一定情况下,随着抽拉速度增大,观察到胞晶/枝晶混合结构,混合结构区随温度梯增大而增大,模拟结果与实验观察相符合. 关键词： Ti-45at.% Al合金 定向凝固 组织演化 数值模拟