Stochastic statistical theory of nucleation and evolution of nano-sized precipitates in alloys with application to precipitation of copper in iron

A consistent and computationally efficient stochastic statistical approach (SSA) is developed to study the kinetics of nucleation and evolution of nano-sized precipitates in alloys. To increase the accuracy of the method, many refinements of the previous simplified versions of this approach have been made. We consider a realistic vacancy-mediated exchange kinetics rather than the simplified direct-atomic-exchange model; use quantitative, cluster statistical methods rather than simple mean-field-type approximations; allow strong concentration and temperature dependences of generalized mobilities in the resulting kinetic equations; consider realistic alloy models based on first-principle calculations, and so on. We also introduce the “maximum thermodynamic gain” principle to determine the key kinetic parameter of the SSA, the characteristic length of local equilibrium in the course of the nucleation process. For several realistic models of iron-copper alloys studied, the results of the SSA-based simulations of precipitation kinetics made in this work agree well with the kinetic Monte Carlo simulation results for all main characteristics of the microstructure. The approach developed is also used to study the kinetics of nucleation and changes in microstructural evolution under variations of temperature or concentration.     

Effects of liquid structure transition on solidification by the Newton thermal analysis method

This paper is to explore the effects of the liquid structure transition (LST) on the solidification kinetics of Sn-30 wt% Sb alloy by the Newton thermal analysis (NTA) method and the solidified microstructure analysis. Influence of the cooling rate on solidification behavior and microstructure was also concerned. With a self-designed sand mold, the cooling curves of five points were collected automatically in the process of solidification by a HYDRA. In the case of the liquid structure transition and a faster cooling rate, the modification melt treatment will lead to a higher undercooling of nucleation and an increased solidification latent heat in central part of solidifying castings, then the eventual grain size was evidently refined.     

Phase transitions in condensed media at a finite rate of formation of a metastable state

The influence of the finite rate of formation of a metastable state on the kinetics of the first-order phase transition is analyzed. The conditions determined by the thermodynamic parameters and the cooling rate of the system under consideration are derived. Under these conditions, the formation of the metastable state can be treated either as an instantaneous process, when nucleation occurs at the end of the cooling stage, or as a slow process, when intensive nucleation of a new phase proceeds within the cooling stage. An equation describing the time and temperature that correspond to intensive nucleation of new-phase particles is obtained. The nucleation stage of the new phase takes place in the immediate vicinity of the temperature determined from this equation. All the other parameters, which determine the kinetics of the initial and transient stages of the phase transition, are calculated with respect to this temperature. As an example, all the relationships for a weak solid solution are presented.     

Spatial stability of a homogeneous system of voids under cascade damage

We consider the microstructural evolution of a system consisting of voids and sessile interstitial clusters continuously produced by irradiation. The stability of the evolution is rigorously analyzed, assuming spatial homogeneity as represented by a mean-field formulation. It is found that, in fully annealed pure metals with a sufficiently low void growth rate, the development of a spatially homogeneous microstructure is unstable. In fact, heterogeneous development already takes place during the void nucleation stage. The characteristic scale of the developing heterogeneity and its temperature dependence are obtained from the analysis, and are found to be consistent with experimental observations. Received: 21 March 2001 / Accepted: 30 May 2001 / Published online: 30 August 2001     

Following individual grains during solid-state phase transformations with 3DXRD microscopy

The mechanical properties of metals strongly depend on the microstructure, which is formed during their production and processing. Understanding the underlying mechanisms of the nucleation and growth kinetics during solid-state phase transformations in steel is of vital importance to control its microstructure. The kinetics of individual grains in the bulk of steel can be measured in situ with the three-dimensional X-ray diffraction microscopy (3DXRD) at the European synchrotron radiation facility (ESRF). Simultaneously the fraction transformed, the nucleation rate, and the growth rate of individual grains can be measured. Unique in situ measurements of nucleation and growth rates of individual austenite and ferrite grains are presented.     

Correlations among micro- and macromechanical properties of composite materials based on the interphase concept

In this paper an attempt was made to define microstructural properties of carbon fiber/PP composites, with respect to fiber surface chemistry and morphology. In order to define the effects of the fiber surface sizings and morphology on the polymer microstructure, the interphase and mechanical properties of the composites, carbon fibers with similar, but not identical surface chemistry (CH and CT) were used. Characterization was performed by several techniques: SEM, POM, reflection microscopy, DSC, FTIR, XPS, contact angle measurements. For microstructural analysis, the geometrical method, method of intercept and DIF method were used. It was found that both carbon fibers have a strong influence on the nucleation mechanism and crystallization as well as on the microstructural parameters in the model and macro composites. Nucleation efficiency of the fibers has been confirmed by the nucleation parameter Q, measured by Muchova–Lednicky method and by the interfacial energy parameters. Microstructural analysis based on the photographs obtained by POM, SEM and reflection microscopy has shown that in the CH/PP model and macrocomposites the sieve-grain network was formed, which indicates better mechanical properties. The results obtained for the macromechanical properties of PP composites reinforced with CH and CT have confirmed the prediction based on micostructural analysis.     

Influence of the mode of deformation on recrystallisation kinetics in Nickel through experiments,theory and phase field model

Abstract

In this paper, we report the influence of the mode of deformation on recrystallisation kinetics through experiments, theory and a phase field model. Ni samples of 99.6% purity are subjected to torsion and rolling at two equivalent plastic strains and the recrystallisation kinetics and microstructure are compared experimentally. Due to significant differences in the distributions of the nuclei and stored energy for the same equivalent strain, large differences are observed in the recrystallisation kinetics of rolled and torsion-tested samples. Next, a multi-phase field model is developed in order to understand and predict the kinetics and microstructural evolution. The coarse-grained free energy parameters of the phase field model are taken to be a function of the stored energy. In order to account for the observed differences in recrystallisation kinetics, the phase field mobility parameter is a required constitutive input. The mobility is calculated by developing a mean field model of the recrystallisation process assuming that the strain free nuclei grow in a uniform stored energy field. The activation energy calculated from the mobilities obtained from the mean field calculation compares very well with the activation energy obtained from the kinetics of recrystallisation. The recrystallisation kinetics and microstructure as characterised by grain size distribution obtained from the phase field simulations match the experimental results to good accord. The novel combination of experiments, phase field simulations and mean field model facilitates a quantitative prediction of the microstructural evolution and kinetics.     

非晶一次晶化过程微观组织演化和生长动力学的相场法研究

在晶化物理模型中添加扩散系数对晶化过程的影响, 采用相场方法研究初始形核率和初始形核半径对一次晶化过程中微观组织和生长动力学的影响。结果表明: 随着初始形核率的增加, 相同时间内非晶一次晶化的晶粒数量逐渐增加, 晶粒尺寸逐渐减小。晶化分数随着演化时间和初始形核率的增加逐渐增大, 初始形核率越大, 相同演化时间内的晶化分数越高。不同初始形核半径情况下, 非晶一次晶化过程中的晶粒数量和尺寸随着演化时间的增加基本保持不变。晶化分数随着演化时间的增加而增大。不同初始形核率和初始形核半径情况下所对应的生长指数均小于1, 表明初始形核率和初始形核半径对晶化方式无影响, 均为一次晶化。改变初始形核率和初始形核半径可调控一次晶化微观组织结构, 而晶粒尺寸及晶化分数直接关系到合金性能。     

微重力条件下Ni-Cu合金的快速枝晶生长研究

采用落管方法实现了Ni-50%Cu过冷熔体在微重力和无容器条件下的快速枝晶生长.对微重力条件下的晶体形核和快速生长进行了研究，发现随着过冷度的增大，晶体生长形态由粗大枝晶向规划均匀的等轴晶转变.实验中最大冷却速率达到8×103K/s，获得了218K(014TL)的最大过冷度.理论分析表明，过冷熔体中优先发生异质形核，形核率可达1012m-3s-1以上；Ni-50%Cu过冷熔体中的枝晶生长随过冷度的增大发生由溶质扩散控制向热扩散控制的生长动力学机理转变.在68K过冷度条件下，生长界面前沿的偏析程序最大. 关键词： 落管 微重力 深过冷 枝晶 熔体     

Supercube grains leading to a strong cube texture and a broad grain size distribution after recrystallization

This work revisits the classical subject of recrystallization of cold-rolled copper. Two characterization techniques are combined: three-dimensional X-ray diffraction using synchrotron X-rays, which is used to measure the growth kinetics of individual grains in situ, and electron backscatter diffraction, which is used for statistical analysis of the microstructural evolution. As the most striking result, the strong cube texture after recrystallization is found to be related to a few super large cube grains, which were named supercube grains. These few supercube grains become large due to higher growth rates. However, most other cube grains do not grow preferentially. Because of the few supercube grains, the grain size distribution after recrystallization is broad. Reasons for the higher growth rates of supercube grains are discussed, and are related to the local deformed microstructure.     

Magnetic and microstructural investigations of melt-spun Fe(NdPr)B

The magnetic behavior of rapidly solidified FePrB was investigated in the composition range Fe_77+χPr₁₅B_8−χ (0 ≤ χ ≤ 4). Furthermore, the magnetic and microstructural properties of Fe(NdPr)B were analyzed in the range Fe₇₈(Nd_χPr_1−χ)₁₅B₇ (0 ≤ χ ≤ 1). The temperature dependence of the critical field was analyzed with a modified form of Brown's expression for the nucleation field. From this analysis the values for the microstructural parameters, _K and N_eff, were determined which describe the deteriorating effects of the non-ideal microstructure on the coercivity.     

INTERNAL STRUCTURE OF CO-INJECTION MOLDED PP/PP SPECIMEN

An overview of the microstructural characteristics of co-injection molded isotactic polypropylene products is given. Polarized light optical microscopy is used for comparison of traditional injection molded and co-injection molded products' microstructure. It is shown that a transcrystalline layer occurs on the boundary of the skin and the core components when a nucleation agent was added to either of the components; this proves that this surface layer is not shear induced cylindritic structure. Also shown is a method for preparing β-phase transcrystalline structure capitalizing on the advantages of the co-injection molding technology.     

Effect of heat input on microstructure and properties of hybrid fiber laser-arc weld joints of the 800 MPa hot-rolled Nb-Ti-Mo microalloyed steels

Hybrid fiber laser-arc welding (HLAW) process was applied to a novel hot-rolled Nb-Ti-Mo microalloyed steels of 8 mm thickness. The steel is primarily used to manufacture automotive and construction machinery components, etc. To elucidate the effect of heat input on geometry, microstructure and mechanical properties, different heat inputs (3.90, 5.20 and 7.75 kJ/cm) were used by changing the welding speeds. With increased heat input, the depth/width of penetration was decreased, and the geometry of fusion zone (FZ) changed to “wine cup-like” shape. In regard to the microstructural constituents, the martensite content was decreased, but granular bainite (GB) content was increased. The main microstructural difference was in the FZ cross-section at 7.75 kJ/cm because of the effect of thermal source on the top and bottom. The microstructure of the top part consisted of GB, grain boundary ferrite, and acicular ferrite, while the bottom part was primarily lath martensite. The hardness distribution was similar for different heat inputs. Hardness in FZ, coarse-grained HAZ and mixed-grained HAZ was higher than the base metal (BM), but for the fine-grained HAZ was similar or marginally less than the base metal (BM). Tensile strain was concentrated in the BM such that the fracture occurred in this region. In summary, the geometry, microstructure, and mechanical properties of weld joints were superior at heat input of 5.20 kJ/cm.     

Autocatalytic nature of the bainitic transformation in steels: a new hypothesis

To ensure improvements in predicting the kinetics of bainite formation, it is important to understand the autocatalytic nature of the transformation so that this accelerating effect can be rigorously incorporated in kinetic models. In the present paper, it is assumed that the broad faces of bainitic plates in particular provide new potential nucleation sites for autocatalytic nucleation. The dislocations in the austenite near a bainitic plate are thought to stimulate autocatalysis because carbon is assumed to pile up at these regions and thereby other austenite–bainite interface regions may contain less carbon which promotes nucleation. Based on these assumptions, it is derived that the autocatalytic contribution is proportional to the volume fraction of as-formed bainite, which is consistent with the dependence proposed by Entwisle [V. Raghavan and A.R. Entwisle, Special Report No. 93, The Iron and Steel Institute, London, 1965, p.30] on the basis of empirical knowledge. In addition, it is assumed that autocatalytic nucleation can also depend on the morphology of bainite due to the associated difference in cementite precipitation. This new hypothesis for autocatalysis offers a viable explanation for the irregular variation in kinetics associated with the transition from upper to lower bainite measured for an alloy with eutectoid composition. Furthermore, comparison with experimental data of a Si-rich steel demonstrates that the isothermal kinetics of bainite formation can only be satisfactorily described when the autocatalytic factor is inversely proportional to the thickness of bainitic plates, which is consistent with the model proposed.     

Numerical investigation of the microstructure of a clad layer produced via laser cladding with coaxial metal powder injection

The microstructure of a clad layer produced via selective laser cladding with coaxial metal powder injection is studied numerically. The Johnson–Mehl–Avrami–Kolmogorov equation for condensed systems with inhomogeneous rates of nucleation is used to model the phase change kinetics. The impact of the substrate boundary along with interconnected heat transfer and phase change processes on the final microstructure of a built-up layer is demonstrated. The qualitative difference between the behavior of the temperature on the built-up layer’s surface and at the depth of the substrate is established, revealing the inhomogeneous microstructure of the final layer.     

Microstructural evolution during containerless rapid solidification of Co-Si alloys

The Co-12%Si hypoeutectic, Co-12.52%Si eutectic and Co-13%Si hypereutectic alloys are rapidly solidified in a containerless environment in a drop tube. Undercoolings up to 207K (0.14T_E) are obtained, which play a dominant role in dendritic and eutectic growth. The coupled zone around Co-12.52%Si eutectic alloy has been calculated, which covers a composition range from 11.6 to 12.7%Si. A microstructural transition from lamellar eutectic to divorced eutectic occurs to Co-12.52%Si eutectic droplets with increasing undercooling. The lamellar eutectic structure of the Co-12.52%Si alloy consists of εCo and Co_3Si phases at small undercooling. The Co_3Si phase cannot decompose completely into εCo and αCo_2Si phases. As undercooling becomes larger, the Co_3Si phase grows very rapidly from the highly undercooled alloy melt to form a divorced eutectic. The structural morphology of the Co-12%Si alloy droplets transforms from εCo primary phase plus lamellar eutectic to anomalous eutectic, whereas the microstructure of Co-13%Si alloy droplets experiences a `dendritic to equiaxed' structural transition. No matter how large the undercooling is, the εCo solid solution is the primary nucleation phase. In the highly undercooled alloy melts, the growth of εCo and Co_3Si phases is controlled by solutal diffusion.     

Phase transformations of 2,4,6,8,10,12-hexanitrohexaazaisowurtzitane: the role played by water, dislocations, and density

A comparative study of the kinetics and mechanisms of the α → γ and ? → γ polymorphic transitions in polycrystalline haxanitrohexaazaisowurtzitane was performed using electron and optical microscopy, calorimetry, IR spectroscopy, and quantitative X-ray phase analysis. The kinetics of both processes is complex because of the morphology of the crystals, their defect structure, and impurities. As distinct from the ? → γ process, which always occurs as a single crystal-polycrystal transition (through nucleation by the dislocation mechanism with subsequent movement of the phase separation front), the α → γ process can also follow the quasi-homogeneous mechanism and occur as a single crystal-single crystal transition.     

The kinetics of the (5 × 20) → (1 × 1) structural transition for Au(100)

The kinetics of the anion-induced (5 × 20) → (1 × 1) surface structural transition of reconstructed Au(100) electrodes was studied in sulfate-containing solutions by current transients. It is shown that lifting of the reconstruction follows a nucleation-and-growth type behavior which can be described by the Avrami equation. Moreover, for high positive potentials, i.e., high anion coverages, the current-transient analysis reveals instantaneous nucleation, whereas for low transition overpotentials and long transition times a mechanism with constant transition rate prevails. Apparent activation energies, which depend strongly on the electrode potential, are derived from the temperature dependence of the Avrami plots.     

Analysis of an arc-formed gas-plasma jet in the arc method of fullerene production

A two-component fan-shaped gas jet forming in the discharge gap of a chamber for fullerene production is analyzed. Under standard fullerene production conditions, the averaged parameters of the jet can be found with a reasonable accuracy using the well-known solution for an incompressible liquid jet. Based on the analysis performed in this work, a simple model of gap-jet transition, and the fullerene formation kinetics considered earlier, the dependences of the fullerene yield on observable experimental parameters (current, helium pressure, gap width, and electrode radii) are constructed. The calculated and experimental results are in good agreement. The analytical data obtained in this work may be helpful in considering the fullerene production kinetics in a real, finite-dimension chamber of a given geometry.