The effect of rare earth elements on the kinetics of the isothermal coarsening of the globular solid phase in semisolid AZ91 alloy produced via SIMA process

In the present study, the effects of rare earth (RE) elements on the microstructure and coarsening kinetics of the solid globular particle in the semisolid slurry of AZ91 magnesium alloy have been studied at 570 °C and 580 °C. The results showed that the coarsening kinetics of the solid globular particles in semisolid slurry of AZ91 alloy satisfies the Ostwald ripening theory. It was shown that the coarsening rate of the solid particles decreases by adding RE elements into AZ91 alloy, specially at 580 °C, which results in the smaller particles size. It was attributed to the solid–liquid interfacial energy reduction due to the addition of RE elements.     

Analytical description of phase coarsening at high volume fractions

An analytical theory of volume fraction effects in diffusion-controlled phase coarsening is developed. It is based on the application of the Lifshitz–Slyozov–Wagner procedure of Ostwald ripening theory to a self-similar particle volume evolution equation which is approximated by a quadratic polynomial of the scaled particle size. A family of analytical particle size distributions with the scaled maximum particle size as a parameter is derived, which contains the size distribution of normal grain growth as a genuine limit distribution at ultra-high volume fraction without changing the t^1/3-Ostwald ripening kinetics. This reflects an important characteristic feature of particle coarsening at nearly space filling, which was first noted by Ardell and which is in principle in agreement with recent observations. The obtained analytical expressions for the maximum particle size, the particle size distribution and the coarsening rate constant are easy to use for evaluating coarsening data. The results compare well with a number of experimental and simulation results at intermediate and high volume fractions of the second phase.     

A theoretical model for digestive ripening

Recently, gram quantities of monodisperse gold or silver nanoparticles were reported to be produced through a digestive ripening process, in which colloidal particles of size from 2 to 40 nm are transformed to nearly monodisperse particles of 4–5 nm diameter. Digestive ripening, an example for inverse Ostwald ripening, is a puzzling phenomenon since it appears to avoid the usual capillary consequence, i.e., reduction of interfacial free energy. This paper presents a theoretical model which accounts for the self-assembled monodisperse state of such nanoparticles by considering the effect of charges, and therefore electrostatic energy, in the coarsening behavior of the particles. An appropriate Gibbs–Thomson equation is first derived, and then particle growth rates are calculated. The results show that success of a monodisperse state depends on, among other things, the initial particle distribution, and the size distribution at equilibrium follows some of the thermodynamic principles observed in binary phase diagrams of alloy systems.     

Phase-field simulation of coarsening of γ precipitates in an ordered γ′ matrix

The evolution of the microstructure and coarsening kinetics of disordered γ precipitates in an ordered monovariant γ′ matrix was studied using a diffuse-interface phase-field model in two dimensions. Specifically, we studied the morphological evolution, average precipitate size and size distribution as a function of time for a given temperature and for different concentrations. It was found that the coarsening kinetics for the average particle size are described by a t^1/3 power law with a rate constant that increases with the volume fraction of the γ phase. The particle size distribution scaled by the average particle size is time invariant. We find that the particle shapes are perturbed by elastic interaction and local distributions of γ particles. Comparison of the phase-field simulation results with experiments shows good qualitative agreements.     

Large-scale three-dimensional simulation of Ostwald ripening

Large-scale three-dimensional simulations of Ostwald ripening were carried out using a multiphase-field model for accurate and efficient computation of multiparticle diffusional interaction in order to clarify coarsening kinetics in systems with finite particle fractions. The simulations were performed on 400³ grid systems in a particle fraction range of 0.25–0.86, where the initial microstructures with 20,000–100,000 solid particles in a liquid matrix evolve into structures with 1500–3000 particles. The simulation results were carefully analyzed and compared with those from the previous simulations and experiments, which have data range relevant to the present simulation range. The present results are in excellent agreement with the simulations by Akaiwa and Voorhees at low particle volume fractions, with the recent results from the 3-D reconstruction of serial sections at high fractions and with the grain size distribution of ideal grain growth at very high fractions.     

Simulation of convection and ripening in a binary alloy mush using the phase-field method

Two-dimensional Ostwald ripening of an Al–4% Cu alloy solid/liquid mush in the presence of melt convection, and the influence of ripening on the flow, is studied numerically using a recent extension of the phase-field method that accounts for flow in the liquid phase. Through a parametric study, the ripening kinetics are investigated and compared for cases with and without melt convection. The cases without convection show good agreement with available coarsening theories for a finite fraction of solid. In the cases with flow the mean radius of the solid particles increases at a faster rate than without convection. The ripening exponent changes from 1/3 to 1/2, while the rate constant depends on the fraction of solid. Comparisons are made with the convective ripening theory of Ratke and Thieringer. Although the present analysis of coarsening is hampered by the limited number of particles in the domain, some qualitative results are presented for the effect of convection on the particle radius distribution. Finally, the present simulations allow for a determination of the permeability of the mush as a function of the fraction of solid, and the dependence of the permeability on the ripening kinetics is shown to be scalable using the specific surface area or the mean radius.     

Two- and three-dimensional equilibrium morphology of a misfitting particle and the Gibbs–Thomson effect

The equilibrium shapes of misfitting precipitates in elastically anisotropic systems are obtained in both two and three dimensions, and the corresponding Gibbs–Thomson equation is derived as a function of the characteristic ratio between elastic and interfacial energies, L′. The effect of elastic inhomogeneity is investigated systematically. For soft or moderately hard particles, the stable equilibrium shape bifurcates from a fourfold symmetric shape to a twofold symmetric one in 2D and from a cubic symmetric shape to a plate-like one in 3D. For a very hard particle, the shape bifurcation is not observed in 2D for the range of L′ investigated, but both plate-like and rod-like shapes are found in 3D. The computed Gibbs–Thomson equation is well approximated by a piecewise linear function of L′. Predictions are made for coarsening of many-particle systems based on an established mean-field theory. The results predict that the elastic stress has no effect on coarsening kinetics where most particles are highly symmetric (fourfold in 2D and cubic in 3D), and the exponent remains 1/3 but the rate constant increases if stress is sufficient to induce symmetry-breaking bifurcation on most particles.     

The development of spatial correlations during Ostwald ripening: a test of theory

The coarsening of solid-Sn particles in a Pb–Sn liquid was studied under microgravity conditions. Spatial correlation functions were measured on plane sections in a low-volume fraction system undergoing Ostwald ripening. The correlation functions changed with time in a way that indicated that the microstructure initially consisted of clusters of particles and evolved into one which was more dispersed. The model by Akaiwa and Voorhees (AV) was used to study the effect of spatial correlations on the ripening process. We found that the initially highly correlated structure had no observable effect on the evolution of particle size distributions, but did have an effect on the coarsening rate of the system. Specifically, we determined that a structure consisting of clusters of particles coarsened faster than a system with a random, spatial arrangement of non-overlapping particles. We also found that the approach of the microstructure towards the steady-state regime could be monitored more sensitively using spatial correlations rather than using particle size distributions. The spacial correlations and the particle size distributions measured from the experiment agreed well with those calculated from the AV simulations using the initial experimental correlations and size distribution.     

Liquid formation and microstructural evolution during re-heating and partial melting of an extruded A356 aluminium alloy

Thixoforming processes require feedstock having a non-dendritic, equiaxed microstructure, which in some cases can be obtained by a deformation–recrystallisation technique followed by partial melting. From the study of an extruded, re-heated and partially re-melted A356 alloy, a number of phenomena were observed and analysed: grain and particle growth, texture and low angle grain boundary formation, primary phase coarsening during isothermal holding in the semi-solid state and uneven distribution of Si particles and liquid phase. Both grain growth (solid state) and particle growth (semi-solid state) obey a R³ against time relationship. It was also found that microstructural coarsening follows an Ostwald ripening type of growth and that coalescence was also present, although exerting a minor role. Finally, phenomena such as the evolution with time of the proportion of low angle grain boundaries, and the relationship between recrystallisation, the onset of liquid formation and the coarse Si particle precipitation and dissolution are presented and discussed.     

Coarsening in liquid-phase-sintered α-SiC

Liquid-phase-sintered (LPS) SiC ceramics represent a new class of microstructurally toughened structural materials. In order to understand better the microstructural evolution in these ceramics, the coarsening kinetics in LPS α-SiC, containing a yttrium aluminum garnet (YAG) based liquid phase, was studied. It was confirmed that the coarsening occurs primarily by solution-reprecipitation (Ostwald ripening). Most importantly, the SiC grains were found to be faceted in nature, and the coarsening rate was found to be independent of the vol.% liquid in the system or the average diffusion path length. Based on these observations it is inferred that interface-reaction controls the solution-reprecipitation coarsening in LPS SiC.     

Coarsening behavior of γ′ particles in a nickel-base superalloy

The coarsening behavior of γ′ particles in a nickel-base superalloy FGH95 was investigated by means of experimental observations and growth kinetics calculations. The results show that when aging at 1000, 1080 and 1140°C for different times, the relation of average particle size to time obeys the cube law (ā/2)³ = kt, where k is 15.49 × 10³, 77.5 × 10³ and 230.04 × 10³ nm³/min, respectively. The particle size distributions are better fit to the LSW theoretical distributions when aging at 1000°C within 1440 min. The activation energy for γ′ particles coarsening is determined to be 288.20±1.79 kJ/mol, which correlates well to the diffusion activation energies of Al, Ti, and Nb in the nickel matrix. This indicates that the coarsening of γ′ particles is controlled by the diffusion of Al, Ti, and Nb in the nickel matrix. The coarsening kinetics of γ′ particles in FGH95 is predicted as _t ³ = 1.04×10¹⁶ t exp[−(288200±1790)/RT]     

失稳分解组织演化和粗化动力学的晶体相场法研究(英文)EI北大核心CSCD

以二元对称与非对称合金的调幅分解为研究对象,采用晶体相场模型从沉淀相演化和粗化机制两方面分析合金的失稳分解。研究表明,当合金的成分由对称点向非对称点转变时,沉淀相形貌逐渐由长条形过渡为球形;后期粗化机制由邻近颗粒的合并机制转变为Ostwald熟化机制;只有当二元合金的成分接近于失稳线时,其粗化动力学才较好地与修正的LSW理论符合。     

Modeling and simulation of grain growth in Si3N4-II. The α–β transformation

The anisotropic Ostwald ripening model has been developed for completely faceted crystals. This model has been applied to the simulation of grain growth in β-Si₃N₄ with a highly anisotropic rod-like grain shape developed in the liquid phase. The reduction of aspect ratio after the phase transformation observed by previous studies is proved to be a consequence of the anisotropic Ostwald ripening. This model predicts a growth exponent n=3 for totally interfacial reaction controlled kinetics, and higher values when the diffusion constant approaches the interfacial reaction constants. This would explain the puzzling results reported by previous works that growth exponents n=3 or higher have been observed in the grain growth of faceted crystals. While the length distribution becomes wider with time, the reduced radius distribution approaches the shape that is known as the asymptotic distribution function derived from the LSW theory.     

Three-dimensional model of precipitation of ordered intermetallics

The development of the two-phase (f.c.c.+L1₂) coherent microstructure in the prototype Ni–Al superalloy is studied by using the three-dimensional computer simulation technique. The dynamics and morphology of the microstructure evolution are described by our three-dimensional version of the stochastic time-dependent kinetic equation which explicitly includes the coherency strain, elastic anisotropy and L1₂ ordering of the preciptate phase. The input parameters, the crystal lattice misfit, elastic moduli, interfacial energy and equilibrium compositions of the coexisting phases are taken from the published independent measurements. The simulation results demonstrate that the strain accommodation in the microstructure evolution results in the cuboidal-like precipitates faceted by the {100} planes. The size of the precipitates obtained in the simulation is of the order of 50 nm. The important conclusion is that the precipitates are always single-domain particles with no antiphase boundaries. This effect is associated with the ordered structure of precipitates. It causes the slowing down of the coarsening kinetics since it excludes the agglomeration of the out-of-phase precipitates in one particle. As has been shown previously, the latter is a very important coarsening mode in an absence of ordering.     

Coarsening behavior of γ particles in a nickel-base superalloy

The coarsening behavior of γ' particles in a nickel-base superalloy FGH95 was investigated by means of experimental observations and growth kinetics calculations. The results show that when aging at 1000,1080 and 1140°C for different times,the relation of average particle size to time obeys the cube law ( a /2)3= kt,where k is 15.49 × 103,77.5 × 103 and 230.04 × 103 nm3/min,respectively. The particle size distributions are better fit to the LSW theoretical distributions when aging at 1000°C within 1440 min....     

Behavior of (Ti,Nb)(C,N) complex particle during thermomechanical cycling in the weld CGHAZ of a microalloyed steel

This study aims to investigate the effect of deformation (stress and strain) on the coarsening kinetics of a (Ti, Nb)(C, N) complex particle during isothermal and continuous thermomechanical cycles in the weld coarse-grained heat-affected zone (CGHAZ) of a Ti + Nb microalloyed steel. Results in isothermal coarsening tests showed that the coarsening rate was enhanced by deformation under both compressive and tensile stress: it was enhanced mainly owing to the increased diffusivity of solute atoms. Then the compressive stress was found to be more effective than tensile stress. Interestingly, despite the increase in the coarsening rate, the mean particle size in the weld CGHAZ, after continuous thermomechanical cycle, decreased more than it did in the simple thermal cycle. This was because of enhancement of the precipitation of fine particles by increased precipitation kinetics under deformation.     

Coarsening of γ (Ni–Al solid solution) precipitates in a γ′ (Ni3Al) matrix

The coarsening behavior of Ni–Al solid–solution precipitates in an Ni₃Al matrix was investigated in alloys containing 22.0–22.8 at.% Al aged at 650–800 °C for times exceeding 1800 h. The rate constant for coarsening increases with equilibrium volume fraction as predicted by the MLSW theory. The activation energy for coarsening, 314.1 ± 16.6 kJ mol⁻¹, agrees very well with results from conventional diffusion experiments. The particle size distributions are not in very good agreement with the predictions of any theory; possible reasons are discussed. The particles become more spherical with decreasing elastic self-energy. The results are consistent with the premise that a strong volume fraction effect is observed so long as diffusion in the matrix phase, and not through the precipitate–matrix interface, controls the kinetics.     

Globulization mechanism of the primary Al of Al−15Cu alloy during slurry preparation for rheoforming

Semisolid slurries of Al-15Cu alloy were produced for rheoforming by a low temperature pouring technique. To investigate the morphological change of the slurry in terms of the particle mean diameter and the roundness factor, samples were extracted during the continuous cooling and the isothermal holding stage of the slurry by a simple technique of interrupt quenching. Results demonstrated that the fine-grained equiaxed dendritic structure, which formed during low temperature pouring, is changed to a globular structure when held at a semisolid temperature for sufficiently long holding time. With regard to the globulization mechanism of the primary α-phase, local melting is considered to take place at the neck of equiaxed dendrites, leading to the separation of small new particles during continuous cooling. These newly formed particles eventually grow during isothermal holding in the semisolid temperature by obeying theD ³=Kt kinetic law, which suggests coarsening by Ostwald ripening.     

Coarsening of ordered intermetallic precipitates with coherency stress

The morphological evolution and coarsening kinetics of ordered intermetallic precipitates with coherency stress were studied using a diffuse-interface phase-field model in two dimensions (2D). The emphasis is on the effects of precipitate volume fraction. The average aspect ratio of the precipitates in the microstructure is found to increase with time and decrease with volume fraction. Contrary to all the existing coarsening theories but consistent with a number of experimental measurements on the coarsening kinetics of ordered γ′ precipitates in Ni-base superalloys, we found that the coarsening rate constant from the cubic growth law decreases as a function of volume fraction for small volume fractions (≲20%) and is constant for intermediate volume fractions (20–50%). From the simulation results, we infer that the two length scales in a stress-dominated coherent two-phase microstructure, the average precipitate size and average spacing between arrays of aligned precipitates, follow different growth exponents. It is demonstrated that as the volume fraction increases, the precipitate size distributions become broader and their skewness become increasingly positive.