Nucleation Rate Function Research Articles

The Martensitic Transformation in Ti-6Al-4V

The effect of heat treatment on the phase transformation of Ti-6Al-4V alloy was investigated. This heat treatment consisted of solution treatment at 850°C,900°C,950°Cfor 1h and subsequent water quenching. The phase transformation data was obtained by X-ray diffraction and differential scanning calorimetry (DSC).The differences were observed in the changes of lattice parameters of martensite phase among the different solution temperature. The volume of single cells for a' phase increases from 34.84 Å3 to 35.09 Å3 and then decreases to 34.63 Å3 with the solution temperature increased. These changes are believed to be due to partitioning of vanadium in b phase and its strong effect on the lattice parameter of a' martensite phase. The nucleation rate function has been obtained by thermodynamic theory. Based on these equations, it could be proved that the nucleation rate of martensite should be increased with the increase of the content of vanadium and the decrease of aluminum in b phase.

Numerical modeling of soot formation in a turbulent C2H4/air diffusion flame

Soot formation in a lifted C 2 H 4 -Air turbulent diffusion flame is studied using two different paths for soot nucleation and oxidation; by a 2D axisymmetric RANS simulation using ANSYS FLUENT 15.0. The turbulence-chemistry interactions are modeled using two different approaches: steady laminar flamelet approach and flamelet-generated manifold. Chemical mechanism is represented by POLIMI to study the effect of species concentration on soot formation. P1 approximation is employed to approximate the radiative transfer equation into truncated series expansion in spherical harmonics while the weighted sum of gray gases is invoked to model the absorption coefficient while the soot model accounts for nucleation, coagulation, surface growth, and oxidation. The first route for nucleation considers acetylene concentration as a linear function of soot nucleation rate, whereas the second route considers two and three ring aromatic species as function of nucleation rate. Equilibrium-based and instantaneous approach has been used to estimate the OH concentration for soot oxidation. Lee and Fenimore-Jones soot oxidation models are studied to shed light on the effect of OH on soot oxidation. Moreover, the soot-radiation interactions are also included in terms of absorption coefficient of soot. Furthermore, the soot-turbulence interactions have been invoked using a temperature/mixture fraction-based single variable PDF. Both the turbulence-chemistry interaction models are able to accurately predict the flame liftoff height, and for accurate prediction of flame length, radiative heat loss should be accounted in an accurate way. The soot-turbulence interactions are found sensitive to the PDF used in present study.

Analytical Approximation Schemes for Mean Nucleation Rate in Turbulent Flows

Nucleation rate is a very sensitive function of the temperature and vapor mole fraction. Analytical approximation schemes for the mean nucleation rate in turbulent flows are derived using Laplace’s approximation method. The schemes only require the derivative of the nucleation rate function and the probability density function (pdf) of the vapor mole fraction and/or temperature at the point of maximum nucleation rate. Based on the relation between the mole fraction and temperature, i.e., linearly correlated or not, different approximation schemes are developed. Numerical examples are constructed to investigate the accuracy of these approximation. In the examples, the pdfs of mole fraction and/or temperature in various turbulent flows are assumed to come from the beta distribution with five distinct forms. The mean nucleation rate of dibutyl phthalate (DBP) aerosol in these turbulent flows are calculated from the approximation schemes, and compared with exact numerical integration. The relative errors are less than 1% for cases when nucleation rate diminishes at the bounds of temperature fluctuations, and no more than 50% for all studied examples. Furthermore, the approximation schemes are not sensitive to the precise form of the pdfs. Hence, these developed approximation schemes can be used to estimate the mean nucleation rate in a broad range of turbulent flows conveniently. Copyright 2014 American Association for Aerosol Research

Effects of grain size on the dynamic tensile damage of ductile polycrystalline metall

In the paper, we propose a new nucleation rate function, which combines grain size, and models for nucleation and growth of voids in a ductile polycrystalline metal. The proposed model is used to analyse the effects of grain size on the dynamic tensile damage of high purity Cu samples with different grain sizes. Numerical results show that pull-back minima and void number decrease with grain size increasing, slope after pull-back and average void diameter increase with grain size increasing. The computed results are in qualitative agreement with experimental results.

A quantitative model for describing crystal nucleation in pressurized solidification during squeeze casting

A model describing the thermal and mechanical effects on heterogeneous nucleation during squeeze casting of metal alloys has been developed based on classical nucleation theory. Squeeze casting experiments were carried out using an aluminum alloy, where the temperature change inside the casting during pressurized solidification was measured and the grain density at the locations where the temperature was measured was determined. By correlating the grain density and local thermal history, a quantitative function of nucleation rate with pressure and temperature was obtained.

A constitutive theory of particulate-reinforced viscoelastic materials with partially debonded microvoids

In particulate-reinforced viscoelastic materials, the interfacial debonding between particles and matrix is usually a significant damage mechanism. In this paper, a new theoretical model of constitutive relation for particulate-reinforced viscoelastic materials is proposed. In the new constitutive model, both the reinforced effect of particles and weak effect due to microdamage evolution are taken into account. First, the deformation of a nucleated microvoid due to partially interfacial debonding between a particle and infinite viscoelastic matrix is analyzed in terms of Eshelby’s equivalent inclusion method. Secondly, the porosity of nucleated microvoids is calculated based on the computation of density function of nucleation rate, in which, the size distribution of particles is assumed to be a logarithmic normal function, and the debonding probability of interface between particles and matrix is assumed to obey Weibull’s distribution. Thirdly, a new definition of average stress and average strain for nucleated microvoids is proposed with considering the effect of nucleation time. Based on definition, a new constitutive model is suggested. This new model is consistent with experimental results. Finally, the effects of loading rate, interfacial adhesive energy, geometrical parameters of particles, and relaxation time on the constitutive relation are examined numerically. The simulation results indicate that the increase of loading rate, volume fraction of particles, and relaxation time of matrix not only reinforces the stiffness of composites, but also speeds up the evolution of microdamage. Such a competition mechanism should be taken into account when designing particulate-reinforced composites.

Parametrization of ternary nucleation rates for H2SO4‐NH3‐H2O vapors

A parametrization of nucleation rates for H2O‐H2SO4‐NH3 vapors in atmospheric conditions is developed. The parametrization is based on nucleation rates obtained from a self‐consistent model of ternary nucleation, including state‐of‐art thermodynamics, H2O‐H2SO4 hydration model, and rigorous treatment of nucleation kinetics. The parametrized nucleation rates are shown to be within one order of magnitude from those given by the full model with enhanced accuracy at higher nucleation rates. Parametrizations for particle numbers and radius of the critical nucleus are given as a function of nucleation rate and temperature. The parametrizations are valid for temperatures 240–300 K, relative humidities 5–95%, sulfuric acid concentrations 104–109 molecules cm−3, ammonia mixing ratios 0.1–100 ppt, and nucleation rates 10−5–106 cm−3 s−1.

Molecular-scale surface processes during the growth of calcite in the presence of manganese

This paper deals with the growth behaviour of the Mn-Ca-CO 3-H 2O solid solution-aqueous solution system on calcite {104} surfaces. This system represents a model example, which allows us to study the effect of a number of controlling factors on the crystallisation: (1) the supersaturation function, β(x), and nucleation rate function, J(x), for the Mn-Ca-CO 3-H 2O system, (2) the relationship of such functions to the molecular scale growth mechanisms operating on growing surfaces, and (3) the surface structure of the calcite {104} faces. In situ atomic force microscopy (AFM) growth experiments revealed a wide variety of surface phenomena, such as the transition between growth mechanisms, anisotropic changes in the step rates, and the influence of the Mn-bearing newly formed surface on subsequent growth (step stoppage followed by the formation of two-dimensional nuclei and the reproduction of the original calcite {104} surface microtopography). These phenomena result from the interplay between the controlling parameters and are explained in those terms.

Experimental verification of the formal nucleation and growth rate equations – initial UH 3 development on uranium surface

A Hot Stage Microscopy (HSM) technique was utilized for continuous observations of UH 3 nucleation and growth on hydrogen exposed uranium (U–0.1 wt% Cr) surface. Such observations enabled the quantitative evaluation of both, nucleation rate function, N ⋅ (t) , and the average lateral growth velocity, u, of the individually growing nuclei. Knowing these kinetic parameters, the validity of the different assumptions made in the derivation of the formal nucleation and growth rate equations (i.e. the Avrami-Erofeev or Johnson-Mehl equations) can be checked. It was found that the basic assumption underlying the Avrami's approach, namely, the relation between the extended and the experimental reacted fractions, is very accurate over a wide range of surface coverages. However, the time dependence of the nucleation rate function was not monotonous, as commonly applied in the conventional treatments. Instead, the nucleation rate first accelerated, passed through a maximum and finally decayed again. At about 7–10% of the reaction, the nucleation rate decayed to zero, and saturation in the number of growing nuclei was attained. This nucleation behavior leads to overall kinetics which do not fit the simplified power law time dependence that is usually applied in the kinetic analysis of nucleation and growth processes.

Interpretation of the nonisothermal crystallization kinetics of polypropylene using a power law nucleation rate function

A nucleation rate function is proposed for use in analyzing the overall crystallization kinetics of polymers. This function allows for the possibility that the nucleation rate varies substantially during the crystallization. This feature is particularly useful in analyzing nonisothermal crystallization, but it can be used to analyze isothermal crystallization as well. The nucleation rate function was used in the derivation of a modified transformation kinetics equation of the Avrami type. The modified Avrami equation was found to be suitable for kinetics analysis for the data obtained from nonisothermal crystallization at rapid cooling rates. Kinetics parameters used to describe nonisothermal crystallization under rapid cooling rates are presented and discussed. These include crystallization induction time, plateau (crystallization) temperature, crystallization half-time, crystallization rate constant, Avrami index, and newly defined quantities called nucleation index, geometric index, and nucleation rate constant. The procedure used to obtain the nucleation rate constant and nucleation index for the nucleation rate function is described and illustrated by application to the analysis of the crystallization kinetics of polypropylene. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1077–1093, 1997

Stability and occurrence of polymorphic modifications of the stearic acid in polar and nonpolar solutions

The crystallization of A, B and C polymorphs of stearic acid was examined in polar (methanol) and nonpolar (decane and benzene) solutions. First, the stability of the three modifications was determined by comparing the relative degree of solubility of each polymorph; B and C are the most stable forms below and above about 30°C respectively, whereas the A form is unstable at any temperature. Thereafter, the occurrence of the three forms was investigated by controlling the effects of temperature, supersaturation and solvent independently. The general trend is that: in nonpolar solvents, the A and C forms prevail at higher supersaturation, while the B form preferably occurs at lower supersaturation; in polar solvents, the occurrence domain of B is more extended towards the higher supersaturation range. In all cases, particularly in nonpolar solvents, the relative importance increases for A and C but decreases for B with increasing temperature. This trend was semi-quantitatively interpreted on the basis of a homogeneous nucleation rate function. Further, it was shown that a variety of previous studies, which have been so far rather contradictory to each other, could consistently be explained by the present study taking the thermodynamic and kinetic parameters in the crystallization process into account.