On the spurious increase in particle volume fraction during coarsening simulations

The problem of spurious increase in volume fraction of second-phase particles during computer simulations of coarsening is examined. The origin of this problem is traced to the use of too long a time step (used for numerical integration of growth rates with respect to time) which leads to small particles with large negative growth rates shrinking to negative radii at the end of the time step. Such a shrinkage to negative sizes has the effect of pumping solute into the system. It is therefore suggested that the length of the time step be chosen in accordance with the size of the smallest particle present in the system. It is shown that spurious increase in particle Volume has a significant effect on the particle size distributions in the scaling regime (making them broader and more skewed in the Lifshitz-Slyozov-Wagner model). Its effect on coarsening kinetics, however, is found to be small.

On variant distribution and coarsening behavior of the a phase in a metastable beta titanium alloy

The stereology, variant distribution and coarsening behavior of semicoherent alpha(hcp) precipitates in a beta(bcc) matrix of a Ti5553 alloy has been analyzed, and a dominant 3-variant cluster has been observed in which the variants are related to each other by an axis-angle pair <<11(2)over bar> 0 >/60 degrees. Shape and spatial distribution independent elastic self and interaction energies for all pairwise and triplet combinations of a have been calculated and it is found that the 3-cluster combination that is experimentally observed most frequently has the lowest energy for the semicoherent state. The coarsening behavior of the delta distribution follows LSW kinetics after an initial transient, and has been modeled by phase field methods. (C) 2016 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Part I. Kinetics of coarsening of the gamma-prime precipitate in nickel-silicon alloys. Part II. Rate of crystallization of an amorphous Fe-P-C alloy

The coarsening kinetics of Ni₃ Si(γ') precipitate in a binary Ni-Si alloy containing 6.5 wt. % silicon was studied by magnetic techniques and transmission electronmicroscopy. A calibration curve was established to determine the concentration of silicon in the matrix. The variation of the Si content of the Ni-rich matrix as a function of time follows Lifshitz and Wagner theory for diffusion controlled coarsening phenomena. The estimated values of equilibrium solubility of silicon in the matrix represent the true coherent equilibrium solubilities.

The experimental particle-size distributions and average particle size were determined from dark field electron micrographs. The average particle size varies linearly with t^-1/3 as suggested by Lifshitz and Wagner. The experimental distributions of particle sizes differ slightly from the theoretical curve at the early stages of aging, but the agreement is satisfactory at the later stages. The values of diffusion coefficient of silicon, interfacial free energy and activation energy were calculated from the results of coarsening kinetics. The experimental value of effective diffusion coefficient is in satisfactory agreement with the value predicted by the application of irreversible the rmodynamics to the process of volume constrained growth of coherent precipitate during coarsening. The coherent γ' particles in Ni-Sialloy unlike those in Ni-Al and Ni-Ti seem to lose coherency at high temperature. A mechanism for the formation of semi-coherent precipitate is suggested.

Anomalous coarsening of self-assembled InAs quantum dots on vicinal GaAs (100) substrates

The formation process of InAs quantum dots (QDs) on vicinal GaAs (1 0 0) substrates is studied by atomic force microscopy (AFM). It is found that after 1.2 MLs of InAs deposition, while the QDs with diameters less than the width of the multi-atomic steps are shrinking, the larger QDs are growing. Photoluminescence measurements of the uncapped QDs correspond well to the AFM structure observations of the QDs. We propose that the QDs undergo an anomalous coarsening process with modified growth kinetics resulting from the restrictions of the finite terrace sizes. A comparison between the QDs on the vicinal GaAs (1 0 0) substrates and the QDs on the exact GaAs (1 0 0) further verifies the effect of the multi-atomic steps on the formation of QDs.

Photoluminescence study on coarsening of self-assembled InAlAs quantum dots on GaAs (001)

Red-emission at similar to 640 nm from self-assembled In0.55Al0.45As/Al0.5Ga0.5As quantum dots grown on GaAs substrate by molecular beam epitaxy (MBE) has been demonstrated. We obtained a double-peak structure of photoluminescence (PL) spectra from quantum dots. An atomic force micrograph (AFM) image for uncapped sample also shows a bimodal distribution of dot sizes. From the temperature and excitation intensity dependence of PL spectra, we found that the double-peak structure of PL spectra from quantum dots was strongly correlated to the two predominant quantum dot families. Taking into account quantum-size effect on the peak energy, we propose that the high (low) energy peak results from a smaller (larger) dot family, and this result is identical with the statistical distribution of dot lateral size from the AFM image.

Photoluminescence study on coarsening of self-assembled InAlAs quantum dots on GaAs (001)

Red-emission at similar to 640 nm from self-assembled In0.55Al0.45As/Al0.5Ga0.5As quantum dots grown on GaAs substrate by molecular beam epitaxy (MBE) has been demonstrated. We obtained a double-peak structure of photoluminescence (PL) spectra from quantum dots. An atomic force micrograph (AFM) image for uncapped sample also shows a bimodal distribution of dot sizes. From the temperature and excitation intensity dependence of PL spectra, we found that the double-peak structure of PL spectra from quantum dots was strongly correlated to the two predominant quantum dot families. Taking into account quantum-size effect on the peak energy, we propose that the high (low) energy peak results from a smaller (larger) dot family, and this result is identical with the statistical distribution of dot lateral size from the AFM image.

Studies on coarsening of microdomains in binary polymer mixtures by Lattice Boltzmann methods

An improved free energy approach Lattice Boltzmann model(LBM) is proposed by introducing a forcing term instead of the pressure tensor. This model can reach the proper thermodynamic equilibrium after enough simulation time. On the basis of this model, the phase separation in binary polymer mixtures is studied by applying a Flory-Huggins-type free energy. The numerical results show good agreement with the analytic coexistence curve. This model can also be used to study the coarsening of microdomains in binary polymer mixtures at the early and intermediate stages.

STUDY OF COARSENING OF MICRODOMAINS IN BLOCK COPOLYMERS BY LATTICE BOLTZMANN METHODS

In order to understand the coarsening of microdomains in symmetric diblock copolymers at the late stage, a model for block copolymers is proposed. By incorporating the self consistent field theory with the free energy approach Lattice Boltzmann model, hydrodynamic interactions can be considered. Compared with models based on Ginzburg-Landau free energy, this model does not employ phenomenological free energies to describe systems. The model is verified by comparing the simulation results obtained using this method with those of a dynamical version of the self consistent mean field theory. After that,the growth exponents of the characteristic domain size for symmetric block copolymers at late stage are studied. It is found that the viscosity of the system affects the growth exponents greatly, although the growth exponents are all less than 1/3 Furthermore, the relations between the growth exponent, the interaction parameter and the chain length are studied.

The role of recrystallization and coarsening in the formation of ultrafine grained steels through thermomechanical processing.

There is now considerable interest in the development of ultrafine grained steels with an average grain size of the order of 1µm. One of the methods with currently the greatest industrial interest is by dynamic strain induced transformation from austenite to ferrite. This involves deformation below the
equilibrium transformation temperature so that transformation occurs during the deformation. However, large strains are required to completely transform the microstructure during deformation. It is potentially possible to activate transformation during deformation then continue transformation
during subsequent cooling. It is shown that there are two critical strains: the first is where dynamic transformation commences and the second is the minimum strain for a fully ultrafine final microstructure after cooling to room temperature. The deformation and potential role of dynamic
recrystallization of the dynamically formed ferrite is also considered. Overall it is clear that for full industrial exploitation there is a need to understand and exploit the competing issues of nucleation, growth and recrystallization of the ferrite by both dynamic and static processes.

Dynamical scaling properties of nanoporous undoped and Sb-doped SnO2 supported thin films during tri- and bidimensional structure coarsening

The coarsening of the nanoporous structure developed in undoped and 3% Sb-doped SnO2 sol-gel dip-coated films deposited on a mica substrate was studied by time-resolved small-angle x-ray scattering (SAXS) during in situ isothermal treatments at 450 and 650 degrees C. The time dependence of the structure function derived from the experimental SAXS data is in reasonable agreement with the predictions of the statistical theory of dynamical scaling, thus suggesting that the coarsening process in the studied nanoporous structures exhibits dynamical self-similar properties. The kinetic exponents of the power time dependence of the characteristic scaling length of undoped SnO2 and 3% Sb-doped SnO2 films are similar (alpha approximate to 0.09), this value being invariant with respect to the firing temperature. In the case of undoped SnO2 films, another kinetic exponent, alpha('), corresponding to the maximum of the structure function was determined to be approximately equal to three times the value of the exponent alpha, as expected for the random tridimensional coarsening process in the dynamical scaling regime. Instead, for 3% Sb-doped SnO2 films fired at 650 degrees C, we have determined that alpha(')approximate to 2 alpha, thus suggesting a bidimensional coarsening of the porous structure. The analyses of the dynamical scaling functions and their asymptotic behavior at high q (q being the modulus of the scattering vector) provided additional evidence for the two-dimensional features of the pore structure of 3% Sb-doped SnO2 films. The presented experimental results support the hypotheses of the validity of the dynamic scaling concept to describe the coarsening process in anisotropic nanoporous systems.

Densification and coarsening of SnO2-based materials containing manganese oxide

The present work presents results on natural sintering of tin dioxide ceramics, prepared by a chemical route or by conventional mixing and containing manganese (X-Mn = Mn/(Mn + Sn)(atomic) with 0 less than or equal to X(Mn)less than or equal to 0.15). This cation, which is practically insoluble in SnO2 network, stays at the grain surface. During thermal treatment (500 degrees C less than or equal to T-s less than or equal to 1400 degrees C), as long as the manganese surface concentration is lower than a critical value, equal to 5.10(-6) mol m(-2), no densification takes place. As soon as this value is reached, densification and grain growth occur simultaneously. The shrinkage kinetics is fast and high rho/rho(t) values can be obtained (for example. rho/rho(t)=0.95 for T-s=1300 degrees C and X-Mn=0.004). The dependence between manganese content, manganese distribution, grain size and sintering behaviour is also discussed. (C) 1998 Published by Elsevier B.V. Limited.