Growth Kinetics Of Precipitates Research Articles

Transmission electron microscopy characterization of Al 2Cu precipitate growth kinetics by in situ heat treatment

Growth kinetics of the Al 2Cu (θ) precipitate in an Al–1.5Cu alloy thin film were characterized in situ using transmission electron microscopy (TEM). The sizes of θ precipitates during isothermal growth in TEM were measured during aging at 250, 275 and 300 °C. The results of precipitate growth were analyzed based on the model of the “collector plate mechanism” for bulk alloys. The lengthening of the θ precipitate in thin film varies as t 0.29 for short annealing times (up to ∼10–20 min) at temperatures between 250 and 300 °C. This is in good agreement with the analysis in bulk alloys. For longer annealing time, however, the t 0.29 time law does not fit as the distances of Cu volume diffusion exceed one half of the film thickness.

Effects of light pre-deformation on pitting corrosion resistance of copper-bearing ferrite antibacterial stainless steel

Ferrite antibacterial stainless steel has found wide potential applications in many fields, such as kitchen appliances, medical and public equipments. Good corrosion resistance is one of required properties for these applications. This study aims to improve the pitting corrosion resistance of ferrite antibacterial stainless steel, without a notable loss in the antibacterial property. Light pre-deformation with a reduction of 10–20% was performed on the steel and the pitting corrosion resistance in 3.5% NaCl solution was measured by potentiodynamic polarization and electrochemical impedance spectroscopy (EIS). It is found that pre-deformation improves the pitting corrosion resistance to an extent, without notably sacrificing the antibacterial property. Refined epsilon copper precipitates and suppressed copper surface segregation might explain the improvement of pitting corrosion resistance. The refinement mechanism is revealed that pre-deformation brings about a modification both in precipitation mechanism and growth kinetics of epsilon copper. Copper surface segregation is suppressed by the drag force exerted on the copper atoms by high-density dislocations which are induced by pre-deformation. Light pre-deformation is expected to increase the affordability of ferrite antibacterial stainless steel.

X-ray diffraction investigation into the specific features of the growth kinetics of oxygen-containing precipitates in Czochralski-grown silicon crystals

The formation and growth of defects (precipitates and dislocation loops) during isothermal decomposition of a supersaturated oxygen-containing solid solution in Czochralski-grown silicon crystals are investigated using triple-crystal x-ray diffractometry. It is established that oxygen-containing precipitates grow through diffusion and that the formation of dislocation loops is associated with both the coagulation of embedded silicon atoms and the generation of dislocation loops by stresses induced in the vicinity of the oxygen-containing precipitates.

Thermodynamic description and growth kinetics of stoichiometric precipitates in the phase-field approach

In theoretical analyses and computational simulations chemical free energies of stoichiometric compounds and solid solution phases are often approximated by parabolic functions. In the present work, we focus on examining the effect of different approximations of chemical free energies on predicted precipitate growth kinetics with phase-field modelling. As an example, we studied the precipitation of plate-like θ ′ ( Al 2 Cu ) in Al–4 wt%Cu Alloys. Using six sets of chemical free energies for θ ′ and Al–Cu solid solution, growth kinetics of θ ′ precipitates were simulated by assuming either constant diffusivity or constant atomic mobility. It is demonstrated that the parabolic function provides a good description for the chemical free energy of a stoichiometric compound while the growth kinetics is sensitive to the approximation of chemical free energy for the solution phase.

Shape factors in modeling of precipitation

Recently, a model for the growth and dissolution kinetics of precipitates in multi-component multi-phase environments has been developed. In the original treatment, the evolution equations for the size and chemical composition of the precipitates have been derived for spherical precipitates. In this paper, shape factors are introduced, which provide extensions of the existing formalism to needle-shaped and disc-shaped precipitate geometries. The mathematical formalism can be seamlessly incorporated into the existing model. The growth kinetics of precipitates with different shapes are discussed and compared to the spherical case.

Influence of diffusional stress relaxation on growth of stoichiometric precipitates in binary systems

Precipitation is usually connected with a significant misfit strain which may drastically influence the precipitation kinetics. Very recently it was demonstrated by Svoboda et al. [Svoboda J, Gamsjäger E, Fischer FD. Philos Mag Lett 2005;85:473] that the stress fields due to misfit strains can be effectively relaxed by the diffusive transport of vacancies in the matrix and their annihilation or generation at the precipitate/matrix interface. This idea has provided motivation to develop a new model for the simultaneous precipitate growth and misfit stress relaxation in binary systems. The actual state of the precipitate is described by its effective radius and by the thickness of the layer of the matrix atoms deposited at the precipitate/matrix interface. For these parameters the evolution equations are derived by application of the thermodynamic extremal principle. The model is applied to the Fe–C system by considering the growth of a cementite precipitate in the ferritic matrix. The influence of the stress relaxation on the precipitate growth kinetics is demonstrated.

Precipitation of Nanostructured Copper Oxalate: Substructure and Growth Mechanism

The possibility of controlling materials properties by tailoring their substructure at the nanometer scale is a current topic of great interest. To do so, a fundamental understanding of the growth mechanism is of key importance and an analytical challenge as nanostructured materials are often produced by precipitation methods at high supersaturations where formation kinetics are fast. The current study focuses on the precipitation of copper oxalate, which has been previously shown to produce self-assembled ordered nanostructured particles with the promise of being able to tailor this nanometer substructure. In the current study we investigate in detail the growth mechanism and kinetics of precipitation by using in-situ particle size measurement or by stopping the reaction at various stages and using ex-situ methods. Combining the ex-situ methods of high-resolution scanning electron microscopy, transmission electron microscopy, and X-ray powder diffraction along with the in-situ methods, we were able to follow the growth process from 2 min to 2 weeks. The results in the 2-30 min period lead to the proposal of a core-shell growth model with a poorly ordered core and a well-structured shell of nanosized crystallites (50-70 nm), adding support to the brick-by-brick model previously proposed for this phase of particle growth. Particle evolution over long periods up to 2 weeks show a ripening which produces lens-shaped particles that eliminate the "high" surface energy faces observed in the earlier stages of growth. A more complete growth mechanism for copper oxalate precipitation at moderate supersaturations is proposed similar to recent findings for other self-assembled nanostructured particles.

A serial sectioning technique for evaluating grain and twin boundary precipitate growth kinetics in bulk specimens

A new measurement technique for the growth kinetics of both grain boundary and twin boundary bainite precipitates in bulk specimens is demonstrated. The key advance is the use of coarse-scale serial sectioning to determine the angle made by the grain or twin boundary to the plane of polish, so an explicit stereological correction to the precipitate thickness can be made. This technique is applied to the thickening of bainite at the bay temperature of Fe–0.24C–4Mo, where grain boundary bainite growth kinetics had been measured previously in much thinner specimens using the “bamboo-specimen” method developed by Bradley et al. Several key assumptions implicit in the “bamboo-specimen” method are critically examined using the data obtained from this new technique. Twin boundary bainite growth thickening kinetics, which cannot be obtained using the bamboo method, are also obtained for the first time, and are measured in the same steel.

Modelling of Precipitation Kinetics with Simultanous Stress Relaxation

AbstractMisfit strain connected with the formation of large internal stresses may drastically influence the precipitation kinetics. A new model for the simultaneous precipitate growth and misfit stress relaxation in binary systems has been developed based on the idea that the internal stresses are relaxed by generation or annihilation of vacancies at the matrix/precipitate interface. The model is applied to the Fe-C system by considering the growth of the cementite precipitate in the ferritic matrix. The influence of the stress relaxation on the precipitate growth kinetics is demonstrated.

Variation of cadmium sulfide nanoparticle size and photoluminescence intensity with altered aqueous synthesis conditions

Water-soluble cadmium sulfide (CdS) nanocrystal quantum dots were synthesized by aqueous-phase arrested precipitation in the presence of thiolate capping ligands. The relationship between the synthesis conditions and spectroscopic properties was studied. Several factors affect the absorbance and photoluminescence (PL) spectra, including reactant concentration, Cd:S mole ratios, reactant to ligand mole ratios, ligand length, pH, and ligand R group. Particle size increased with higher pH or sulfur concentration, yet particles approximately 2 nm in diameter exhibited maximum PL quantum yield regardless of synthesis conditions. The data support the idea that specific Cd–thiolate ligand complex formation modulates nanocrystal growth. These results illustrate the importance of intermediate metal-ligand complex formation to nanocrystal arrested precipitation growth kinetics, particle stabilization, and ultimately, their optical properties.

Effects of ledge density on the morphology and growth kinetics of precipitates in a Ni–Cr Alloy

Aging a quenched, face-centered cubic, Ni–45wt%Cr alloy at intermediate temperatures produces Cr-rich body-centered cubic precipitates with a lath morphology and two prominent boundary facets. Both the faceted boundaries migrate by a ledge mechanism. The density of ledges in these boundaries were measured as a function of time and related to the precipitate’s shape and growth kinetics. A tendency of ledges to coalesce on one of the facets contributes to differences in the migration behavior of the two boundaries. One boundary has a distinct crystallographic habit, the other does not, and while both boundaries migrate with parabolic kinetics, they have different rate constants. The rate constants are influenced by the formation rate of ledges on the respective boundaries. Growth models are used in conjunction with the experimental measurements to show that the boundaries and ledges move at rates controlled by solute diffusion in the matrix.

Simulation of growth kinetics of octahedral and platelike oxygen precipitates in silicon

A model describing the growth kinetics of the characteristic size of octahedral and platelike oxygen precipitates in silicon is suggested. It is shown that the experimental data of various authors on the growth kinetics of precipitates are adequately described by the assumption that their growth is limited by diffusion, while the geometry of precipitates is characterized by constant eccentricity.

Comparison of Precipitation Kinetics and Strengthening in an Fe-0.8%Cu Alloy and a 0.8% Cu-containing Low-carbon Steel

The precipitation kinetics and associated change in mechanical properties (hardening and strain hardening rate) have been compared in a Fe-Cu alloy and a Cu-containing low-carbon steel of identical copper content (0.8wt%). A combination of experimental techniques ITEM, Small Angle X-ray Scattering, tensile tests) have been used to quantitatively determine the precipitation phenomena during ageing at 500°C, including the influence of the presence of dislocations prior to the ageing treatment. The precipitation phenomena are shown to be qualitatively identical, in terms of nucleation size, influence of dislocations on the precipitation reaction, or influence of precipitation on the strain hardening rate. However, the growth kinetics of precipitates is shown to be much faster in the steel. Similarly, the time to peak hardness is reduced in the steel. Further, the net precipitation hardening capability is reduced in the steel as compared to the Fe-Cu alloy. The results are discussed in terms of the influence of Mn and C on the precipitation and hardening processes.

Morphology and kinetics of discontinuous precipitation and dissolution in an Fe-8.5Al-27Mn-1.0Si-0.92C alloy

The morphology and growth kinetics of discontinuous precipitation (DP) and discontinuous dissolution (DD) in an Fe-8.5Al-27Mn-1.0Si-0.92C alloy are investigated. The results indicate that the solid-solution-treated austenite phase decomposes into lamellar DP after aging at temperatures ranging from 900 to 1050 K. After the specimens of a preaged DP structure go through further aging at temperatures ranging from 1118 to 1173 K, the lamellar DP falls into dissolution because of the DD reaction. The lamellar spacings of the DP structure, as well as the reaction-front migration rates during DP and DD reactions, are measured. Based on Aaronson and Liu’s simplified kinetics model, the grain-boundary diffusivities are estimated. They are found to be slightly lower than the grain-boundary diffusion data of Mn in Fe and Fe in Fe as reported by Aaronson and Liu.

Modeling the Diffusion-Controlled Growth of Needle and Plate-Shaped Precipitates

AbstractVarious theories have been developed to describe the diffusion-controlled growth of precipitates with shapes approximating needles or plates. The most comprehensive one is due to Ivantsov, Horvay and Cahn, and Trivedi (HIT theory), where all the factors that may influence the precipitate growth, i.e. diffusion, interface kinetics and capillarity, are accounted for within one equation. However, HIT theory was developed based on assumptions that transformation strain/stress and interfacial free energy are isotropic, which are not true in most of the real systems. An improved growth theory of precipitates of needle and plate shapes was developed in the present study. A new concept, the compression ratio, was introduced to account for influences from the anisotropy of transformation strain/stress and interfacial free energy on the precipitate morphology. Experimental evidence supports such compression effect. Precipitate growth kinetics were quantified using this concept. The improved HIT theory (IHIT theory) was then applied to study the growth of Widmanstatten austenite in ferrite in Fe-C-Mn steels. The calculated results agree well with the experimental observations.

Review Progress in Ostwald ripening theories and their applications to the γ′-precipitates in nickel-base superalloys Part II Nickel-base superalloys

The Lifshitz-Slyozof-Wagner (LSW) theory, which corresponds to a zero volume fraction approximation, was developed to model kinetics of precipitate growth from supersaturated solid solutions. The subsequent modifications of the LSW theory for the incorporations of various factors including volume fractions of precipitates to fit the experimental data from the coarsening precipitates were made by various workers during last twenty five years. The LSW theory and its modifications have been applied on the diffusion-controlled Ostwald ripening of the γ′ precipitate particles [Ni3(Al,Ti)] in nickel-based superalloys. The important Ostwald ripening theories were reviewed in the part I of this paper, and the coarsening characteristics of the γ′-precipitates in Ni-base high temperature superalloys are presented in detail in relation to these theories in the present part. A model developed by D. McLean can be used to predict the γ′ particle growth over service lifetimes in the case of relatively Al-rich nickel-base superalloys. Additional fundamental data (such as the precipitate-matrix interfacial energy, diffusivity of the component species of the particle, and the equilibrium solubility with a particle in nickel-based superalloys) can be obtained from experimental results for coarsening, if the concentration changes during coarsening can be measured precisely, using the methods developed by A. J. Ardell. Furthermore, the factors affecting the shape changes and splitting of the γ′ precipitate particles during the coarsening were also considered seperately since the classical Ostwald ripening theories can not explain the morphological changes.

Modelling microstructure evolution in engineering materials

In this paper we describe a general thermodynamically consistent variational principle for the rate of evolution of microstructure, which considers the competition between energy dissipation and the rate of change of Gibbs free energy of the system. We describe how numerical and approximate analytical procedures can be developed from the variational principle. Two examples are presented which demonstrate the utility of the approach: the kinetics of precipitate growth in an elastically strained body and the influence of an elastic strain on interdiffusion in a two-component system. Within these examples we pay particular attention to the effect of changes of elastic stored energy on the evolution process. The sensitivity of the morphology of growing phases to the ratio of the driving forces arising from elastic and chemical considerations is explored.

Precipitate morphologies and growth kinetics in the internal carburisation and nitridation of Fe–Ni–Cr alloys

Model Fe–Ni–Cr alloys were carburised in gas of unit carbon activity, nitrided at p N 2 =0.9 atm, sequentially carburised and nitrided, and simultaneously carburised and nitrided at 1000°C. Internal precipitation kinetics were always parabolic. Carburisation rapidly produced numerous small carbides, and nitridation led to the slow growth of large, sparsely distributed and strongly directional precipitates. In both cases, alloy penetration rates were controlled by volume diffusion of oxidant. The low stability of Cr 2N led to variation in precipitate volume fraction with depth, the distribution being controlled by the diffusion path, not nucleation. Carburisation of nitrided alloys converted prior nitrides to carbides whilst retaining the parent precipitate morphology. The process was diffusion controlled and slow, reflecting the high carbon activity at the nitride–carbide interface. Carbonitriding produced large volume fractions of carbide with, in some cases, nitride-like morphologies, but no obvious nitride phase. Rapid rates reflected fast diffusion along the aligned precipitate-matrix interfaces.

Modelling of the influence of thermomechanical processing of Nb-microalloyed steel on the resulting mechanical properties

Abstract Two-stage compression tests were performed at various temperatures and reductions. The influence of finish deformation temperature in the range of 650–820°C and strain on microstructure and final mechanical properties of Nb steel is investigated. Starting from detailed simulation of microstructure development, i.e. recrystallization, precipitation and grain growth kinetics, the material behaviour was modelled. An empirical model of yield strength, developed in previous work, is employed to predict mechanical properties of microalloying steel during hot deformation above and below the γ–α transformation temperature. The comparison of simulated and measured results shows that the real thermomechanical behaviour as well as the microstructure development of Nb-steel has been correctly implemented. The results provided by both finite element analyses and microstructure modelling were compared with earlier similar investigations of C–Mn steel.

Kinetics of Discontinuous Precipitation and Coarsening in Ni-In Alloys

The morphology and growth kinetics of cellular precipitation and discontinuous coarsening of cellular precipitates have been studied in two Ni-In alloys containing 4 and 6 at.% In in the temperature range 740 to 1010 K. The data for 2 and 8 at. % In alloys have been taken from earlier investigations [1, 2]. Growth rate measurements were carried out utilizing optical microscopy. Both optical microscopy and scanning electron microscopy were utilized for interlamellar spacing measurements. All alloys were observed to decompose completely by the cellular precipitation reaction into a lamellar structure consisting of alternate lamellae of the a and Ni 3 In phases at all aging temperatures. The fine lamellar structure of the primary cells decomposed into a coarse lamellar structure consisting of the same two phases. The primary and secondary cell growth data were analysed by using model after Petermann and Hornbogen. From the diffusivity values, it has been concluded that the growth of primary and secondary cells occurs by diffusion of In along the grain boundaries. The rate of migration of the reaction front for both cellular precipitation and discontinuous coarsening is increased markedly with increasing In content.