Vortex-Loops and Solid Nucleation in Superfluid 4He and 3He

We propose a new model for the nature of the nucleation of solid from the superfluid phases of ⁴He and ³He. Unique to the superfluid phases the solid nucleation involves an extremely fast solidification front. We depart from the usual quasi-static treatment of solid nucleation by proposing that the nucleation of a solid seed is helped by the simultaneous nucleation of vortex-loops in the superfluid around it. It is the composite entity which is nucleated out of the over-pressurized liquid. This occurs when the local release of pressure creates a velocity field in the superfluid which in turn facilitates the nucleation of vortex-loops. The kinetic energy gain of this process balances the surface tension, as the solid surface is quickly covered by many vortex-loops (hairy snow-ball). We show that this scenario gives good agreement with many experiments on heterogeneous nucleation, where the energy barrier is found to differ with the classical theory of homogeneous nucleation by 8 orders of magnitude. We propose several experiments that could show the involvement of vortices with solid nucleation.     

Nucleation of Solid Helium from Liquid Under High Pressure

We consider the homogenous nucleation of solid helium from the liquid phase at pressures above the normal freezing pressure. We find that if the liquid-solid surface energy is assumed to be independent of pressure, then at 1 K nucleation should occur at a liquid pressure in the range 60 to 70 bars. Allowance for the variation of with pressure is found to result in a very large reduction in the nucleation rate.     

Mechanisms of the Allotropic Transition of Sn

The mechanisms of -Sn nucleation on foreign seeds, including metastable ones, are considered. Based on earlier and new experimental data for induction times of -Sn nucleation from 10² to 10¹¹ s, it is suggested that spontaneous -Sn nucleation is impossible because of kinetic hindrances in the solid phase.     

Comments on Heterogeneous Nucleation in Helium

We first recall some basic ideas on homogeneous and heterogeneous nucleation. We then reconsider the heterogeneous nucleation of solid helium from liquid helium in the presence of walls. Recent experiments by Ruutu et al. demonstrate that the presence of walls drastically reduces the energy barrier for such heterogeneous nucleation events, although walls are usually more favorable to the liquid phase. In order to explain this reduction, we propose a simple model based on the unpinning of an already existing interface. In the light of such results, we then reconsider the nucleation of the B-phase of superfluid helium 3 from its A-phase. We propose a model where the B-phase nucleation is thermally activated on walls, without need of cosmic rays.     

On the nucleation ofθ′ and T1 on Al3Zr precipitates in Al-Li-Cu-Zr alloys

Two quaternary Al-Li-Cu-Zr alloys have been investigated using electron microscopy. Ageing at 190° C resulted in the nucleation of precipitates on the Al₃Zr/matrix interface in addition to heterogeneous nucleation on matrix dislocations. In the majority of cases, the broad, coherent face of the plans ms in contact with the Al₃Zr precipitates. Similar evidence showed that nucleation of T₁ precipitates occurred on the Al₃Zr, but to a lesser extent than. Solid-solid nucleation theory has been used to account for the Al₃Zr acting as a nucleation substrate.     

The nucleation of polyethylene dendrites from solution

This paper is a study of nucleation mechanisms in the formation of polyethylene dendrites from dilute solutions. Polyethylene dendrites may be either of regular morphology or of irregular morphology (hedgehog dendrites). By varying the temperatures of dissolution and crystallisation, as well as the general impurity level of the system, it was possible to alter systematically the relative ratio of regular to hedgehog dendrites. It was found that regular dendrites could be nucleated through a self-seeded process, as well as through homogeneous nucleation. The irregular hedgehog dendrites were observed to be nucleated heterogeneously. The degree of super-cooling necessary for dilute solution homogeneous nucleation was established (30° C).     

Liquid helium at negative pressures: Nucleation of bubbles and anomalous phonon dispersion

We calculate the rate at which bubbles nucleate in⁴He when the liquid is at negative pressure. Previous calculations have predicted that at low temperatures (T0.3 K) the nucleation rate remains low until a pressure of roughly –15 bar is reached. We show that this result is incorrect, and that at a critical pressure P_c (–9 bar) the liquid becomes macroscopically unstable. We have made a calculation of the nucleation rate allowing for this effect. It is shown that the effect of quantum nucleation is small and probably hard to observe experimentally. Finally, we demonstrate that one can understand the pressure dependence of the phonon dispersion relation by a simple model. This model uses a parameter which also enters into the nucleation calculation.     

Critical fields in inhomogeneous superconductors

The nucleation fields in a type II superconducting alloy with periodically modulated concentration are calculated. The transition curve for the bulk nucleation has positive curvature near T _c when the applied field is parallel to the equiconcentration planes, similar to the case of layered superconductors. In both cases the enhancement of the critical field is due to the matching of vortices with the periodic structure of the material. The surface nucleation field can be enhanced, diminished, or even suppressed, depending on the inhomogeneity distribution near the surface. The effects of modulation are less in perpendicular field than in the parallel one.     

Vortex-Loops and Phase Nucleation in Superfluid 4He and 3He

We propose a new model for the nature of the nucleation of solid from the superfluid phases of ⁴ He and ³ He. A fast solidification event in the superfluid results in a local release of pressure and a velocity field in the superfluid. This in turn facilitates the nucleation of vortex-loops. The kinetic energy gain of this process balances the surface tension, as the solid surface is quickly covered by many vortex-loops (hairy snow-ball). We show that this scenario gives good agreement with experiments on heterogeneous nucleation.     

Flux nucleation in the current-induced resistive state of a constricted type I superconductor

The current-induced resistive state in a constricted type I superconductor is characterized by a train of flux tubes traversing the sample perpendicular to the direction of the applied current following its nucleation at the sample edge. The temporal structure of the nucleation process can be investigated by attempting to synchronize this process with small periodic current pulses superimposed on the direct bias current. The resistive dc voltage is then to be measured as a function of the pulse parameters such as frequency and width. We have performed such experiments at 4.2 K on constricted Pb films of 6–8 m thickness and 100 m width. Simultaneously with the electrical measurements the dynamic behavior of the flux tubes was directly observed using a stroboscopic magnetooptical method for magnetic flux detection. Our electrical measurements clearly show how the size of the nucleated flux tubes varies with the direct bias current and the nucleation frequency. The positive wall energy in the Pb films results in a lower limit for this size as expected. The influence of the preceding flux tubes still existing within the constriction upon the flux nucleation process is revealed in detail. All observations can be understood from a consideration of the energy balance during the flux nucleation process.Supported by a grant of the Deutsche Forschungsgemeinschaft.     

The formation of α-Al2O3 from θ-Al2O3: The relevance of a “critical size” and: Diffusional nucleation or “synchro-shear”?

The coarsening of -Al₂O₃ crystals to a 'critical size' is often interpreted as the first step in the shear nucleation of -Al₂O₃. The existence of this so-called critical size has also been used to explain the observation that -Al₂O₃ nuclei are generally twice as large as the crystals in the -Al₂O₃ matrix. This paper discusses the important issues in the nucleation of -Al₂O₃ from -Al₂O₃. A few key experiments are also presented to clarify the nucleation process. It is concluded that a critical -Al₂O₃ crystal size is not a prerequisite for -Al₂O₃ nucleation, but is primarily a result of the incubation time required to produce -Al₂O₃ nuclei by diffusional nucleation. It is proposed that the large observed -Al₂O₃ crystal size also does not result from a shear nucleation event in a 'critical size' -Al₂O₃ crystal, but is due to the intrinsically low -Al₂O₃ nucleation density, together with rapid growth of -Al₂O₃ after nucleation.w     

Mechanism of primary nucleation and origin of hysteresis in the rotator phase transition of an Odd n-alkane

The rotator phase transition in n-alkane single crystal was investigated mainly by means of in situ optical microscopy. It was found that wrinkles appeared on heating at a temperature slightly below the transition point, and that the rotator phase grew from the wrinkle. It is proposed that the appearance of the winkle is a precursor of the transition. The nucleus of the rotator phase was considered to be formed in the wrinkle. The nucleation rate of the primary nucleus of the rotator phase was also measured. The primary nucleation rate was found to be proportional to exp(–C/T²), which means that the primary nucleus is three-dimensional one. It was concluded from the results of the morphological observation and the consideration of the observed C value that the primary nucleus is heterogeneously formed in the precursor winkle and that the rotator phase transition is controlled by the nucleation and growth. On cooling, on the other hand, no precursor was observed prior to the transition, and significant large supercooling was observed. This type of hysteresis is commonly observed in the first-order phase transitions in materials. It was shown that the origin of the hysteresis has close relation to the mechanism of the primary nucleation. A universal model of the origin of the hysteresis was proposed, and the tangible evidence of it was shown in the case of n-alkane.     

High-Energy Low-Temperature Physics: Production of Phase Transitions and Topological Defects by Energetic Particles in Superfluid 3He

I review three sets of experiments conducted in the last decade, in which superfluid ³ He was irradiated with high-energy particles and the nucleation either of vorticity or of the A–B phase transition reported. I consider how far the known atomic physics constrains possible scenarios for such nucleation, and comment on two such scenarios which have appeared in the literature, namely the baked-Alaska and cosmological (Kibble–Zurek–Volovik) models. I point out that there is a fundamental difference between the problems of nucleation of vorticity on the one hand and the B phase on the other: and that as a result, it is by no means necessary that the same scenario should describe both phenomena. In an appendix I discuss possible sinks of energy in the calorimetric (Grenoble–Lancaster) experiment, with the conclusion that it is entirely consistent with the data to assume that no vorticity at all was produced in this experiment.     

Intrinsic critical velocities in superfluid4He flow through 12-μm diameter orifices near Tλ: Experiments on the effect of geometry

We report super fluid⁴He flow measurements at temperatures from 1.2 K up to T — 3 mK in three orifices of different mesoscopic geometry. Under conditions of our experiments, the flow usually reaches a temperature-dependent intrinsic critical velocity, where dissipation is believed to occur by thermal (or quantum) nucleation of individual quantized vortex rings or loops. The nucleation rate should be sensitive to the wall geometry of the flow channel and to any local velocity enhancement at the most favorable nucleation site. According to the Iordanskii-Langer-Fisher (ILF) theory, the radius of the critical vortex ring, the threshold size which can grow freely by extracting energy from the flow, increases inversely as the superfluid density on approach to the superfluid onset temperature, T. Thus sufficiently near T the critical ring should be large enough that the geometry relevant to the nucleation process and local velocity enhancement can be studied by scanning electron microscope (SEM). We examined our three orifices by SEM. One, a standard optical pinhole, has a relatively smooth taper on one side and a sharp lip on the other. The second is similar, but contains a 1-m flake perpendicular to the flow, which should provide additional velocity enhancement at its edge. In the third, the sharp lip is beveled to reduce the velocity enhancement at that site. Contrary to expectation, the intrinsic critical velocities are the same, within a relative calibration error of 10%, in all three cases. Thus, local sites of enhanced velocity do not appear to be active in nucleating vortices. This raises a question whether the classical two-fluid model which underlies the ILF calculation is adequate to describe the superfluid hydro-dynamics near walls, as it affects the vortex nucleation process.     

Microcrack nucleation and growth in elastic lamellar solids

The nucleation and growth of microcracks in elastic lamellar microstructures is studied numerically. The analyses are carried out within a framework where the continuum is characterized by two constitutive relations: one relating the stress and strain in the bulk material and the other relating the traction and separation across a specified set of cohesive surfaces. In such a framework, fracture initiation and crack growth, including micro-crack nucleation ahead of the main crack, arise naturally as a consequence of the imposed loading, without any additional assumptions concerning criteria for crack growth, crack path selection or micro-crack nucleation. Full transient analyses are carried out and plane strain conditions are assumed. The specific problem analyzed is a compact tension specimen with two regions of differing lamellar orientation separated by a fracture resistant layer of finite width d, which is small compared to the physical dimensions of the specimen. An initial crack, normal to the applied loading, is assumed to exist in the first region whose lamellar orientation is fixed. The lamellar orientation of the second region, , is varied, as is the thickness of the fracture resistant layer. It is found that microcrack nucleation in the second region is highly sensitive to the lamellar orientation in that region for small values of d. However, microcrack nucleation becomes rather insensitive to with increasing d. It is also shown that a linear elastic fracture mechanics model with one adjustable parameter gives good agreement with the numerical results for fracture initiation.     

Comparison of the ageing behaviour of PM 2124 Al alloy and Al-SiCp metal-matrix composite

The ageing response of 2124 Al-SiC particulate metal-matrix composite (MMC) and unreinforced alloy has been examined using hardness measurements and Arrhenius analysis. The formation of phases during precipitation has been studied using differential scanning calorimetry (DSC). The MMC exhibits accelerated ageing compared to unreinforced alloy, due to enhanced S formation. The activation energy for diffusion is lower in the MMC than in the unreinforced alloy. DSC scans show Guinier-Preston B (GPB) zone nucleation to occur at a lower temperature in the MMC, whilst the total volume of GPB zones formed is smaller than in the unreinforced alloy. A model has been proposed to explain the GPB zone formation behaviour, in which ease of GPB zone nucleation varies within the MMC, as a function of ageing time and of position within the matrix. S formation is enhanced in the MMC because of improved diffusion and a large increase in density of heterogeneous nucleation sites compared to the unreinforced alloy.     

Temperature Independent Nucleation of Solid Helium 4 Below 1K

Nucleation of solid helium in superfluid helium was studied in a temperature range between 50mK and 1K. Pulsed electrostatical compression was employed to initiate nucleation in a slightly overpressurized superfluid helium. The nucleation rate w was estimated from a distribution of the overpressure P _eff required for nucleation. The temperature dependence of P _eff at constant was essentially flat between 50mK and 1K. The ln was almost linear in P _eff within the resolution of our data.     

Interfacial crystallization of isotactic polypropylene molded against the copper surface with various surface roughnesses prepared by an electrochemical process

The influence of surface topography of copper (Cu) sheet on the heterogeneous nucleation of isotactic polypropylene (iPP) at the iPP/Cu interface had been investigated mainly using polarized optical microscope with hot stage. Various textures of Cu surfaces prepared by sandpaper polishing and electrochemical anodizing had been made and they were utilized to induce interfacial nucleation of iPP upon supercooling. This process enables us to change the topological feature of the copper surface without changing their chemical compositions. The pretreated surfaces were quantitatively characterized by a surface texture instrument in terms of RMS roughness (R _a). Copper surface with higher surface roughness induced more nuclei of iPP and led to a thicker transcrystalline layer in the interfacial region upon supercooling over the temperature range 128°C < T _c < 134°C. Based on the theory of heterogeneous nucleation, it was found that the induction time correlates well with the nucleation rate in determining the interfacial free energy difference function of iPP. The ratio of at the interface to that in the bulk matrix (_TCL/_bulk) for the polished surface (R _a = 0.09 m) is 2.89, implying the transcrystallization growth is unfavorable from a thermodynamic point of view. The ratio of _TCL/_bulk becomes smaller as the current density for anodizing increases, indicating the transcrystallization growth is getting favorable. Moreover, induction times and nucleation rates were also measured to characterize quantitatively the nucleating ability of various Cu surfaces.     

High temperature solution growth of yttrium aluminium garnet crystals using accelerated crucible rotation

The value of ACRT stirring has been confirmed in the case of Y₃Al₅O₁₂ crystal growth, its main advantage being to suppress nucleation in the bulk solution and increase the yield of crystals. Restriction of nucleation to 1 to 5 crystals has been achieved, particularly by close control of temperature stability and by the provision of an anchor to prevent crystals from becoming detached due to the stirring action.     

Tensile strength and crack nucleation in boron fibres

Boron fibres of about 100m diameter have been tested to fracture in a micro-tensile testing machine. The fracture surfaces have been investigated using a scanning electron microscope and classified according to the fracture nucleation type. Comparison with the measured fracture stresses proved a significant correlation with the type of crack nucleation. Transverse cracks, nucleated at the edge of radial cracks along the fibre axis direction, are the most critical weakening feature. Also crack nucleation at the external fibre surface implies a low tensile strength, and is discussed in terms of a notch effect of the well-known nodular surface topography.