Classical Nucleation Model Research Articles

Homogeneous Nucleation of Misfit Dislocations in Strained Layers

The mechanism of strain relaxation by homogeneous nucleation of misfit dislocations from the interface in strained layers has been investigated. Transmission electron microscopy examination in a coherently strained GaInAsP/GaInP heterostructure demonstrated that the critical thickness of the strained layer for the nucleation of 90° 1/6<112> partial dislocations from a tensile interface is much shallower than that of 60° 1/2<110> perfect dislocations from a compressive interface. A critical thickness model for the interface nucleation of these dislocations is developed as a modification of the classical surface nucleation model.

Atomic-scale characterisation of precipitation in copper-cobalt alloys

Cu-1.0at%Co, Cu-2.0at%Co and Cu-2.6at%Co alloys, aged at 723 K for various times up to 120 h, have been examined using FIM-AP and PoSAP. The alloys were chosen such that the free-energy barrier to decomposition was small (less than ≈ 10 kT). Three-dimensional atomic reconstructions of the alloys are presented, and the resulting fine-scale (sub-nanometre) microstructures are analysed in terms of: degree of phase separation; cluster sizes and densities; matrix and cluster compositions; and cluster morphology. The experimental results from the PoSAP are compared with three-dimensional Monte Carlo simulations, the sub-regular solution model and the classical nucleation model. There is a good qualitative match between the Monte Carlo simulations and the experimental data: the simulations exhibit nucleation and growth, coarsening and Ostwald ripening behaviour. In addition, a quantitative comparison between experiment and simulation has been undertaken and there is good agreement for quantities such as cluster densities and matrix compositions, as a function of ageing time.

Formation of Cu-rich particles on the surface of YBa2Cu3O7−x thin film grown by in situ off-axis sputtering

Experiments on the formation of Cu-rich particles on the surface of high quality YBa2Cu3O7−x thin films have been carried out systematically. The films on (001) LaAlO3 were grown using in situ off-axis sputtering. The particle formation observed in our experiment can be described using a classical thin film nucleation and growth model based on the concept of capture zones. In the temperature range from 670 to 750 °C, the nuclei density saturates at the early stage of deposition, and the formation of the Cu-rich particle belongs to the case of initial complete condensation. The saturation nuclei density of the particles N decreases as the temperature increases. It has been also found that N is deposition rate dependent and substrate dependent. Based on the experiments, the activation energy for surface diffusion of the Cu atoms that form the particles is estimated to be 1.5 eV in this temperature range.

A Statistical Mechanical Model of Heterogeneous Nucleation Including the Effects of Line Tension and Surface Diffusion

A statistical mechanical model for the heterogeneous nucleation process has been constructed in order to give a more solid foundation to the classical model based on continuum thermodynamics. A size correction of the surface tension has been included in the present model, which leads to the evaluation of a microscopic contact angle. The heterogeneous nucleation of water on different substrates has been examined. With the introduction of the concepts of negative line tension and surface diffusion into the statistical mechanical model, a smaller value for the critical supersaturation for heterogeneous nucleation is expected, in agreement with the experimental results, as compared with the predictions of the classical theory. Moreover, our model gives higher nucleation rates for small aerosol particles as compared with the predictions of the classical model of heterogeneous nucleation.

Formation of scattering centres in fluoride glass preforms and fibres

The fluorozirconate family of glasses has been identified as suitable candidate material for trivalent rare-earth ion doped fibre laser amplifier devices. Their unsuitability however for passive application in the telecommunication network has been recognised due to the formation of scattering centres in the vitreous phase. These are predominantly crystals that form as a result of the tendency for glass devitrification. In the present work, the origin of these scattering centres, particularly crystals, has been identified by considering the thermodynamic aspects of the melting behaviour of crystals. The classical nucleation and crystal growth models have been taken into consideration to explain the origin of crystals as scattering centres in glass preforms and in fibres.

Size effects in the epitaxial realignment of polycrystalline silicon films onto Si substrates

The epitaxial realignment of As-doped polycrystalline silicon layers has been investigated by varying the dimensions of the contact area with the crystalline silicon substrate. Rectangular strips of width in the 0.2–100 μm range and length in the mm range were used. In the 1–100 μm strips the realignment proceeds by the two-dimensional growth of epitaxial columns, while in the 0.2–0.3 μm strips by the one-dimensional growth. The experimental realigned fractions quantitatively follow the trend predicted by the classical model of nucleation and growth in two and one dimension, respectively. The growth kinetics is slowed down in the small width geometry and the thermal budget to realign the films increases.

Solidification behaviour of Pb droplets embedded in a Cu matrix

A hypomonotectic alloy of Cu-5wt%Pb has been manufactured by melt spinning and the resulting microstructure examined by transmission electron microscopy. As-melt spun hypomonotectic Cu-5wt%Pb consists of a homogeneous distribution of faceted 20–100 nm diameter Pb particles embedded in a matrix of Cu, formed during the monotectic solidification reaction. The Pb particles show a cube-cube orientation relationship with the surrounding Cu matrix and a truncated octahedral shape bounded by {111} and {100} facets. The kinetics of Pb particle solidification have been examined by heating and cooling experiments in a differential scanning calorimeter over a range of heating and cooling rates. Pb particle solidification is nucleated catalytically by the surrounding Cu matrix, with an undercooling of 0.5 K and a contact angle of 4°. Analysis of the nucleation kinetics of Pb particle solidification seems to indicate a breakdown of the classical spherical cap model of heterogeneous nucleation.

Homogeneous heteromolecular nucleation of sulphuric acid and water vapours in stratospheric conditions: a theoretical study of the effect of hydrate interaction

The formation of new H 2SO 4 particles in stratospheric conditions has been investigated using classical nucleation theories. The classical hydrate interaction model and a recently derived equation for the saturation vapour pressure of sulphuric acid have been used in the numerical simulations. The present study is compared with earlier ones that ignore the effect of hydrate interaction. The nucleation rates given by the hydrate interaction model are some orders of magnitude smaller than those given by the classical condensation model. The amount of hydrates in the stratosphere is found to be considerable in some situations. Also, the limitations of classical nucleation models are discussed.

Crystallization in Ni-Si-B glass: the influence of dispersoid additions

Crystallization processes in an Ni-Si-B metallic glass have been examined both for the glass alone and for the glass containing a distribution of fine crystalline particles. In the absence of dispersoids, nucleation of crystals occurs uniformly throughout the glass volume on heating following an initial slow, transient period. Nucleation occurs preferentially at the glass-dispersoid interface for the particle-containing glasses. The rate of nucleation at the dispersoid-particle interface depends on the nature of the particle and can best be correlated with the degree of misfit between the substrate and nucleating crystal for the planes and orientation relationships considered. The rate of nucleation at the dispersoid surface is shown to be completely explained on the basis of the classical heterogeneous nucleation model. Nucleation in the bulk occurs many orders of magnitude faster than predicted by classical homogeneous nucleation: the implication of this on the interpretation of nucleation is discussed.

Kinetics of liquid–liquid phase separation in a binary mixture with miscibility gap: Study of noncritical mixtures of 2,6-dimethyl pyridine/water near the lower critical point

Temperature jump experiments with a characteristic heating time of 0.5 ms are used to study the kinetics of liquid/liquid phase separation in noncritical mixtures of 2,6-dimethyl pyridine and water (‖x-xc‖&amp;gt;0.02; x, mole fraction of 2,6-dimethyl pyridine; xc, critical composition) as functions of composition and supersaturation. The response of the system to a temperature jump is monitored by measuring the intensity of light scattered by the sample at different scattering angles Θ (30°&amp;lt;Θ&amp;lt;90°) as a function of time (up to several seconds). Starting from a level of constant intensity reached with a time constant in the range of milliseconds after a temperature jump the scattered intensity increases with time. For small supersaturations consecutive maxima and minima of scattered intensity develop. They reflect diffusion limited growth of droplets of the emerging second liquid phase (linear relationship between the square of the radius of growing droplets and time). The growth rate increases with increasing supersaturation. Practically no nucleation barrier is found for the onset of growth of droplets for small supersaturations and compositions (‖x−xc‖&amp;gt;0.03). The number density N of growing droplets is obtained from simultaneous measurements of scattered intensity and turbidity. For small supersaturations N is independent of time but changes with supersaturation in a characteristic way (classical nucleation model). There exists an upper limit of overheating δT* above which the number density N increases drastically. The ratio (δT*/ΔTc,p) is independent of the reduced temperature ε̃ of phase separation (ε̃=ΔTc,p/Tc; ΔTc,p=Tc−Tp; Tc, critical temperature, Tp, temperature of phase separation). This is expected for mixtures of noncritical composition. The theory proposed by Langer and Schwartz to treat nucleation and growth of droplets in metastable near critical fluids does not describe the phenomena observed in this study. The composition of the samples used (‖x−xc‖&amp;gt;0.02) appears to be too far away from the critical.

The irradiation of tungsten with metallic diatomic molecular ions: atomic resolution observations of depleted zones

Direct evidence, on an atomic scale, is presented for the enhancement of damage production per projectile ion in diatomic metallic molecular ion (dimer) irradiations of tungsten as compared to monatomic metallic ion (monomer) irradations. Irradiations were performed in situ at ⩽10 K, in a field-ion microscope, employing 20 keV ag + or W + monomer ions and the results are compared with 40 keV W 2 + or Ag 2 + dimer ion bombardments; the average energy per ion was 20 keV. Firstly, in the near-surface region the depleted zones produced by the W 2 + dimer ions give rise to void-like contrast effects. The W + monomer ions do not produce this void-like damage. The existence of voids was explained employing a classical nucleation and diffusion-limited growth model which suggests that the growth can occur on a time scale of <10 −10 s, if the effective diffusivity of an atom in the fully-developed collision cascade is > 30 × 10 −4 cm 2 s −. Secondly, by counting the number of vacancies in individual depleted zones, produced by the different ions, it was demonstrated that the number of vacancies produced per incoming ion of the dimer is 1.55 time the number of vacancies produced per monomer ion. This constitutes direct evidence for non linear (or spike) effects during the creation of collision cascades by the metallic dimer ions. Further information is presented concerning the dimensions of the depleted zones and the values of the average concentration of vacancies in depleted zones.

A correction to classical homogeneous nucleation theory for polar molecules exhibiting an electric double layer at the liquid surface

An oriented dipole surface layer is added to the classical liquid drop model of nucleation to account for the surface behavior of substances having polar nonsymmetrical molecules. The preliminary treatment of the change in free energy as given by Abraham is modified to include Fletcher's exponential decay of the degree of orientation. An additional correction for the excess binding energy due to the presence of a foreign molecule in the prenucleation cluster is included to account for the inflections observed in the experimental results of Allen and Kassner. The resulting free energy of formation is combined with the kinetic treatment of Frenkel to obtain a nucleation rate law. The theoretical results are compared to the experimental results of Allen and Kassner as a function of both supersaturation and temperature. The agreement is good once the heterogeneous component is taken into account.

Condensation of zinc vapor in a supersonic carrier gas

A study of the condensation of a metal vapor in an inert carrier gas is made. Superheated zinc vapor is generated in a hot shot wind tunnel in a helium carrier gas and expanded in a converging-diverging nozzle. Static pressure measurements along the length of the nozzle are made to determine the location of the onset of condensation. A conical nominal Mach 5 (helium) nozzle is employed. The amount of supercooling before the onset of condensation is found to be approximately 430 K, measured along the isentrope over a range of initial zinc mass fractions of .35 to .70 for saturation partial pressures of zinc between 10 psia and 70 psia. The measurements are compared with results of an analysis based on the classical liquid drop model of nucleation. The computed results agree reasonably well with the measurements.

Nonadiabatic Compressible Flow Of Humid AirAround Airfoils

The heat addition by the phase transition of water vapor in humid air, which changes the properties of compressible flows around airfoils, is investigated by numerical simulations. The computations are based on a recent small-disturbance approach by Rusak and Lee [11]. This approach describes the heat release by the nonequilibrium and homogeneous condensation process using the classical nucleation and droplet growth models. The nonlinear interaction between the heat transfer by the condensation, the kinetic energy of the compressible flow, and the thermal properties of the flow is explored and the similarity parameters which govern the problem are presented. The results of the calculations show good agreement with available simulations using the Euler equations. The similarity rules are used to suggest various flow cases which have a sufficiently close behavior of both the flow dynamics and the condensation properties. It is shown that nonadiabatic compressible flows of humid air may be applied to augment the aerodynamic performances of airfoils used in fluid machinery.