Heterogeneous nucleation in entrained Sn droplets

Differential thermal analysis has been used in conjunction with entrained droplet specimens to measure the nucleation rates of uncontaminated Sn-rich liquids in contact with solid Bi, Zn and Al. The Bi(Sn) system gave a linear nucleation rate plot and an analysis of the data in terms of the classical theory of heterogeneous nucleation at variable composition, yielded a pre-exponential frequency factor, J^s₀, that was in good agreement with the predicted value for pure Sn. On the other hand, the nucleation rates plots for Zn(Sn) and Al(Sn) were irregular and could only be analysed to give approximate estimates of J^s₀ for these two systems. The origin of the irregularity was discussed in terms of the surface structure of entrained droplets. In the case of Bi(Sn), the nucleation rate data yielded a catalyst surface energy difference of − 50 ± 26 mJm⁻² which agreed with a theoretical estimate for pure Sn nucleating in contact with pure Bi.     

基于均匀形核的金属液滴凝固过程

研究了均匀形核的金属液滴凝固过程,应用渐近分析法求得金属液滴内晶核生长数学模型的渐近解,分析了表面张力、界面动力学参数、初始晶核尺寸和过冷度对晶核界面生长速度、晶核半径以及液滴凝固时间的影响.在一定的过冷条件下,表面张力和界面动力学参数显著减缓了晶核界面生长速度.在凝固开始的很短时间内晶核界面生长速度迅速上升,当速度上升到最大值后,随着晶核半径的增大,界面生长速度逐渐减慢,表面张力和界面动力学参数对晶核生长速度的作用也逐渐减小.过冷度越大,液滴凝固时间越短.经过在开始的瞬变凝固阶段之后,温度场从设定的初始分布迅速地调整为由过冷度、表面张力、界面动力学参数等所确定的特定温度分布.     

Computation of continuous cooling transformation diagrams for the heterogeneous nucleation in Sn-5 mass pct Pb droplets

A method was developed to compute continuous-cooling-transformation (CCT) diagrams for the heterogeneous nucleation of alloy droplets from a few experimental data. The developed model addresses both oxidation-catalyzed surface nucleation and internal nucleation caused by another catalyst. Droplet surface oxidation is regarded as a first-order reaction in order to account for the effects of the gradual increase in surface oxidation on the kinetics of surface nucleation. CCT curves were computed for Sn-5 mass pct Pb droplets cooling in atmospheres with various oxidation potentials using data determined with monosize droplets produced by capillary jet breakup. The developed model may be used to predict droplet nucleation kinetics in industrial thermal spraying processes.     

Bubble nucleation

The theory of bubble nucleation in cavitation, degassification, and boiling is reconsidered. As background material, the theory of droplet nucleation from the vapor phase is reviewed briefly. In both cases, prior treatments contain serious errors in describing the free energy of formation of the critical nucleus. The one exception known to us for the bubble case, is the work of Landau and Lifshitz, which is correct, but which contains a minor ambiguity in the definition of the pertinent thermodynamic potential. The previous formulations of nucleation rate expressions are corrected. Implications of the results are discussed.     

Application of heterogeneous nucleation theory to precipitate nucleation at GP zones

The accelerated nucleation of precipitates at GP zones is explained using heterogeneous nucleation theory. Nucleation at zone : matrix boundaries is encouraged by several factors: 1) the chemical interfacial energy of zone : matrix boundaries can significantly decrease the interfacial energy barrier to nucleation; 2) destruction of quenched-in excess vacancies at incoherent portions of the nucleus surface may make the change in the volume free energy significantly more negative; 3) the crystal structures of the zone and matrix are identical and parallel which permits the nucleus to be faceted in both phases. Some additional assistance to nucleation at GP zones is provided by: 4) the accelerated diffusivity resulting from the presence of excess vacancies and 5) the large area of zone : matrix boundary per unit volume of matrix. These factors can more than compensate for the decreased solute supersaturation due to the formation of GP zones and provide an explanation for the enhanced nucleation of precipitates in the presence of GP zones.     

Application of heterogeneous nucleation theory to precipitate nucleation at GP zones

The accelerated nucleation of precipitates at GP zones is explained using heterogeneous nucleation theory. Nucleation at zone : matrix boundaries is encouraged by several factors: 1) the chemical interfacial energy of zone : matrix boundaries can significantly decrease the interfacial energy barrier to nucleation; 2) destruction of quenched-in excess vacancies at incoherent portions of the nucleus surface may make the change in the volume free energy significantly more negative; 3) the crystal structures of the zone and matrix are identical and parallel which permits the nucleus to be faceted in both phases. Some additional assistance to nucleation at GP zones is provided by: 4) the accelerated diffusivity resulting from the presence of excess vacancies and 5) the large area of zone : matrix boundary per unit volume of matrix. These factors can more than compensate for the decreased solute supersaturation due to the formation of GP zones and provide an explanation for the enhanced nucleation of precipitates in the presence of GP zones.     

Statistics of martensitic nucleation

Nucleation statistics, incorporating the particle size effects and the temperature effects, of martensitic transformations in ZrO₂-containing ceramics and in Fe-Ni alloys was analyzed. A phenomenological potency distribution of nucleating defects, of the form of (excess driving force)², was found. Using a simple model of long range nucleating defects, of the type of a dislocation wall, a theoretical potency distribution was predicted. The model was in good agreement with the experimental data and with the phenomenological form, over a broad range of excess driving force. A universal potency distribution for intrinsic, pre-existing defects thus became apparent Experimental evidence was found, in literature and in new data reported here, that both the size effects and the universal potency distribution will be violated when nucleation is extrinsically induced, especially in very small particles or in strain-induced transformations. An essential distinction in the origin of nucleation, as reflected in nucleation statistics, can thus be drawn for classification of martensitic nucleation.     

Microstructures of undercooled Germanium droplets

Small liquid Ge droplets (0.3–0.5 mm diameter) have been undercooled 150–415 ± 20°C below T_m in B₂O₃ flux before solidifying to the diamond cubic phase. A correlation was found between initial undercooling and final grain size. Droplets undercooled <300°C exhibited a coarse grain structure. At greater undercoolings, the grain size became progressively finer. This correlation may be subsidiary to the dependence of grain size on interfacial undercooling. Ge droplets lightly doped with Sn solidified dendritically for undercoolings greater than 250°C. Twinned dendrites have been observed at small undercoolings (~ 10°C) in other experiments. It appears that larger interfacial undercoolings are necessary to grow the twin-free dendrites which we have observed. The correlation between grain size and the presence of dendrites suggests that the grain refinement observed in Ge samples undercooled > 300°C stems from dendritic break-up during solidification.     

Levitation of liquid sodium droplets

Droplets of liquid sodium ranging from 1.2 to 2.1 g, immersed in mineral oil, were levitated in an electromagnetic field. The experimental setup was designed and constructed to levitate small metal droplets at audio frequencies. The levitated droplet was found to be very stable inside the inductor, and the equilibrium shape attained by the droplet in the electromagnetic field was measured during the experiment. A surface coupled mathematical model was used to calculate the self-consistent equilibrium droplet shape of liquid sodium under the influence of an electromagnetic field. The predicted shapes of the metal droplet and the position of the droplet inside the inductor compare well with the experimental data. S.S. ROY, formerly Graduate Student, Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh B. LALLY, formerly Post Doctoral Fellow with the Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh     

The scaling of nucleation rates

The homogeneous nucleation rate,J, forT → T _c can be cast into a “corresponding states” form by exploiting scaled expressions for the vapor pressure and for the surface tension, δ. In the vapor-to-liquid case with δ= δ₀[T _c -T], the classical cluster energy of formation /kT = [16π/3] ? ?³ [T _c -1]³/(lnS)² = [x₀/x]², where ? ≡ δ₀/[k ñ^2/3] and ñ is liquid number density. [1] The ?≈ 2 for normal liquids. (A similar approach can be applied to homogeneous liquid to solid nucleation and to heterogeneous nucleation formalisms using appropriate modifications ofσ and ?.^[2]) The above [x₀/x]² is sufficiently tenable that in some cases, one can use it to extract approximate critical temperatures from experimental data.^[3,4] In this work, we point out that expansion cloud chamber data (for nonane, toluene, and water) are in excellent agreement with lnJ ≈ const. -[x₀/x]² [centimeter-gram-second (cgs) units], and that the constant term is well approximated by ln (Γ_c), whereT _c is the inverse thermal wavelength cubed per second atT =T _c . The ln (Γ_c) is ≈ 60 in cgs units (74 in SI units) for most materials. A physical basis for the latter form, which includes the behavior at smalln, the discrete integer behavior ofn, and a configurational entropy term, τ ln (n), is presented.     

Simulation of protein crystal nucleation

To attempt to understand the physical principles underlying protein crystallization, an algorithm is described for simulating the crystal nucleation event computationally. The validity of the approach is supported by its ability to reproduce closely the wellknown preference of proteins for particular space group symmetries. The success of the algorithm supports a recent argument that protein crystallization is limited primarily by the entropic effects of geometric restrictions imposed during nucleation, rather than particular energetic factors. These simulations provide a new tool for attacking the problem of protein crystallization by allowing quantitative evaluation of new ideas such as the use of racemic protein mixtures.     

Kinetics of strain-induced martensitic nucleation

Intersections of shear bands in metastable austenites have been shown to be effective sites for strain-induced martensitic nucleation. The shear bands may be in the form of ε’ (hcp) martensite, mechanical twins, or dense bundles of stacking faults. Assuming that shear-band intersection is the dominant mechanism of strain-induced nucleation, an expression for the volume fraction of martensite vs plastic strain is derived by considering the course of shear-band formation, the probability of shear-band intersections, and the probability of an intersection generating a martensitic embryo. The resulting transformation curve has a sigmoidal shape and, in general, approaches saturation below 100 pct. The saturation value and rate of approach to saturation are determined by two temperature-dependent parameters related to the fee-bee chemical driving force and austenite stacking-fault energy. Fitting the expression to available data on 304 stainless steels gives good agreement for the shape of individual transformation curves as well as the temperature dependence of the derived parameters. It is concluded that the temperature dependence of the transformation kinetics (an important problem in the development of TRIP steels) may be minimized by decreasing the fee, bec, and hep entropy differences through proper compositional control.