Precipitate Size Distribution Research Articles

Kinetics of Overlapping Precipitation and Particle Size Distribution of Ni3Al Phase

The precipitation kinetics of overlapping process from nucleation and growth to coarsening of the γ′(Ni3Al) phase in Ni–Al alloys are investigated quantitatively by using the interface diffusion-controlled phase field model. It is found that the time exponent of average particles radius of the γ′ phase is about 1/3 at the growth and coarsening stage, while the exponent is smaller than 1/3 at the later steady-state coarsening stage. The decrease rate of the number density of the γ′ phase is larger at the steady-state coarsening than that of the growth and coarsening stage. The particle size distribution (PSD) is widened at the nucleation and growth stage, then is narrowed at the growth and coarsening stage, and becomes wide again at the steady-state coarsening stage; the width of PSDs obtained by the quantitative calculation is greater than 0.215 proposed by the LSW theory. Moreover, the position of the PSDs peak moves from 1.0 of the normalized radius at the nucleation and growth stage to less than 1.0 of the growth and coarsening stage, and then moves back to 1.0 at steady-state coarsening stage. The non-monotonically variation of kinetics of the γ′ phase during the precipitation process are reasonable and theoretically significant for the kinetics evolution.

Analytical Solutions for Precipitation Size Distributions at Steady State

Abstract Analytical solutions are derived for the steady-state size distributions of precipitating rain and snow particles assuming growth via collection of suspended cloud particles. Application of the Liouville equation to the transfer of precipitating mass through size bins in a “cascade” yields a characteristic gamma distribution with a Marshall–Palmer exponential tail with respect to particle diameter. For rain, the principle parameters controlling size distribution shape are cloud droplet liquid water path and cloud updraft speed. Stronger updrafts lead to greater concentrations of large precipitating drops and a peak in the size distribution. The solutions provide a means for relating size distributions measured in the air or on the ground to cloud bulk microphysical and dynamic properties.

Microstructural investigation of twin-roll cast magnesium AZ31B subjected to a single monotonic compressive stress

In this research paper the microstructure of the magnesium AZ31B alloy is investigated after the application of a single monotonic compressive strain of −0.4%. A band of twinned grains is observed to form in the test bar approximately 10 mm wide, corresponding to the zone of highest plastic strain. The microstructure of this region is studied using electron backscatter diffraction and transmission electron microscopy (TEM). Twinning mode and fraction are reported along with a detailed analysis of precipitate phase and size distribution. Evidence is given for twin-precipitate interaction during the twin formation process. High resolution TEM and energy dispersive X-ray spectroscopy are used in conjunction with structural simulation software to identify the Al-Mn phase. A zinc shell is observed forming around precipitates, and this is related to zinc exclusion by the precipitating Al-Mn phase.

Magnetic characterisation of grain size and precipitate distribution by major and minor BH loop measurements

Grain size and precipitates have a significant effect on the mechanical properties of steels and it is desirable to be able to characterise these in a non-destructive manner. Grain and precipitate sizes and their spatial distributions in both an extra-low-carbon steel and a laboratory model steel have been individually varied and compared with a variety of characteristic magnetic parameters measured from major and minor magnetisation loops. These magnetic parameters are shown to be very sensitive to grain size distribution when there are no precipitates within the grains. However, the magnetic parameters exhibit complex behaviours with precipitate size distribution, which is linked to a critical precipitate size for effective pinning and another critical precipitate size for strongest pinning to domain walls. The interaction between grain size and precipitate distribution effects on the minor loop properties in the studied steels are discussed.

Seasonal Variations of Observed Raindrop Size Distribution in East China

Seasonal variations of rainfall microphysics in East China are investigated using data from the observations of a two-dimensional video disdrometer and a vertically pointing micro rain radar. The precipitation and rain drop size distribution (DSD) characteristics are revealed for different rain types and seasons. Summer rainfall is dominated by convective rain, while during the other seasons the contribution of stratiform rain to rainfall amount is equal to or even larger than that of convective rain. The mean mass-weighted diameter versus the generalized intercept parameter pairs of convective rain are plotted roughly around the “maritime” cluster, indicating a maritime nature of convective precipitation throughout the year in East China. The localized rainfall estimators, i.e., rainfall kinetic energy–rain rate, shape–slope, and radar reflectivity–rain rate relations are further derived. DSD variability is believed to be a major source of diversity of the aforementioned derived estimators. These newly derived relations would certainly improve the accuracy of rainfall kinetic energy estimation, DSD retrieval, and quantitative precipitation estimation in this specific region.

Precipitation and grain growth modelling in Ti-Nb microalloyed steels

Mechanical properties of microalloyed steels are enhanced by fine precipitates, that ensure grain growth control during subsequent heat treatment. This study aims at predicting austenite grain growth kinetics coupling a precipitation model and a grain growth model. These models were applied to a titanium and niobium microalloyed steel. The precipitate size distributions were first characterized by TEM and SEM and prior austenite grain boundaries were revealed by thermal etching after various isothermal treatments. From CALPHAD database, a solubility product was determined for (Ti,Nb)C precipitates. A numerical model based on the classical nucleation and growth theories was used to predict the time evolution of (Ti,Nb)C size distributions during various isothermal heat treatments. The precipitation model was validated from TEM/SEM analysis. The resulting precipitate size distributions served as entry parameters to a simple grain growth model based on Zener pinning. The pinning pressure was calculated using the whole size distribution. The resulting austenite grain growth kinetics were in good agreement with the experimental data obtained for all investigated heat treatments.

Surface-Kinetics-Limited Ostwald Ripening of Spherical Precipitates at Grain Boundaries

Ostwald ripening of sufficiently large (usually macroscopic) precipitates is the late stage of the diffusion decomposition of a supersaturated solid solution, occurring through the formation of fluctuations and subsequent growth of centers (nuclei) of a new phase. The paper describes a theoretical study of the Ostwald ripening of spherical precipitates of a newly formed phase at the grain boundary of finite thickness with the diffusion of impurity atoms from the grain interior to the grain boundary considered. The precipitate growth is assumed to be limited by the kinetics of impurity atom imbedding into the precipitate rather than by the impurity atom diffusion inside the grain boundary. The speed of diffusion growth of spherical precipitate located on the grain boundary is found. A system of equations which describes surface-kinetics-limited growth of Oswald ripening of spherical precipitates on the grain boundary is formulated. This system consists of the equation of growth rate of the precipitate, the kinetic equation for the precipitates size distribution function which is normalized by the precipitates density, and the equation of the balance of matter in the system (the law of conservation of matter). The law of conservation of matter takes into account the atoms of impurities which are in solid solutions of the grain boundary and the body of the grain as well as in the precipitates which is the specifics of our problem. The asymptotic time dependences are found for the average and critical precipitate radius, supersaturation of solid solution of impurity atoms in the grain boundary, precipitate size distribution function, precipitate density, and for the factor of grain boundary filling with precipitates (the area covered by the precipitates per unit area of the grain boundary) and the total number of impurity atoms in precipitates. The factor of grain boundary filling with precipitates is a characteristic of the two-dimensional Ostwald ripening problem. A discussion of the limits of validity of obtained results is given.

Microstructural Comparison of an Al-8.0Zn-1.8Mg-2.0Cu Alloy with Typical T6 and T76 Tempers

In order to analyze aging behavior of an Al-8.0Zn-1.8Mg-2.0Cu alloy, the microstructure of the alloy subjected to T6 and T76 states are investigated by transmission electron microscopy (TEM) and high-resolution electron microscopy (HREM). Based on the precipitate observations, precipitate size distributions and average precipitate size are extracted from bright-field TEM images projected along 〈110〉Al orientation with the aid of an imaging analysis. The results indicate that the main precipitates are GPI zone, GPII zone and η' phase in the T6 alloy while η' phase and η phase in the T76 alloy. The bright-field TEM observations reveal that the matrix precipitates for the T6 alloy have small size and dispersive distribution while that for the T76 alloy has big size and sparse distribution. Both have discontinuously distributed grain boundary precipitates. Quantitative structural information including precipitate size distribution and average precipitate size has been calculated by an image analysis based on the bright-field TEM images projected along 〈110〉Al orientation. The results show that the T6 alloy has a narrower precipitate size range than the T76 alloy and thus the T6 alloy possesses a smaller average precipitate size than the T76 alloy.

Precipitation kinetic model and its applications to Mg alloys

Precipitation calculations for Mg alloys have been performed using an in-house precipitation model. The size distribution, number density and volume fraction of precipitates are complex functions of thermodynamics, nucleation, and diffusion kinetics dependent on solute composition and heat treatment parameters. The mathematical description and the numerical approach for the precipitation model are given in details. The precipitation model is dynamically linked to the FTlite light alloy database of the FactSage system for accurate input of thermodynamic data. The simulation results are compared with the available experimental data for Mg alloys such as Mg-Al, Mg-Zn and Mg-Al-Zn alloys to ascertain the predictive ability of the precipitate model. The precipitation model is also applied to deduce the precipitation kinetics in AZ91 + Ca alloy in comparison to conventional AZ91 alloy.

VC-Precipitation Kinetics Studied by Small-Angle Neutron Scattering in Nano-Steels

Nanosteels are used in automotive applications to accomplish resource-efficiency while providing high-tech properties. Quantitative data and further understanding on the precipitation kinetics in Nanosteels can contribute to fulfil this goal. Small-Angle Neutron Scattering measurements are performed on a Fe-C-Mn-V steel, previously heat-treated in a dilatometer at 650°C for several holding times from seconds to 10 hours. The evolution of the precipitate volume fraction, size distribution and number density is calculated by fitting the experimental Small-Angle Neutron Scattering curves. The effect of phase transformation on precipitation kinetics is also discussed. Complementary Transmission Electron Microscopy, Scanning Electron Microscopy and Inductively Coupled Plasma Optical Emission Spectroscopy measurements are performed to support the Small-Angle Neutron Scattering data analysis.

Precipitation and strengthening modeling for disk-shaped particles in aluminum alloys: Size distribution considered

For an ICME (Integrated Computational Material Engineering) modeling framework used for the age-hardening aluminum alloy design and heat treatment parameters optimization, it is critical to take into account the geometric shape of precipitates, as it is tightly related to the precipitation kinetics and particles' hardening effect. The aim of this paper is to present such an ICME modeling approach to describe the precipitation of disk-shaped hardening particles during aging treatment and predict the final yield strength. The classical Kampmann–Wagner Numerical (KWN) model is extended to consider the influence of disk-shaped particle morphology on growth kinetics. The extension consists of two correction factors to the growth rate equation and to the Gibbs-Thomson effect. The extended model, coupled with a metastable thermodynamic database, is applied to simulate precipitation kinetics of Al-Cu and Al-Mg-Zn alloys during aging treatment. The predicted microstructural features are in reasonable agreement with the reported experimental observations. Furthermore, a strengthening model for disk-shaped particles, which considers the size distributions of precipitates, is developed. The predicted yield strengths are compared with reported tensile test results and with predictions from other strength models. Unlike other models, the proposed strength model can reveal the strength contribution from disk-shaped precipitates without an additional tuning parameter for accounting for the impact of the mean particle spacing in the slip plane.

Controlling the grain boundary morphology and secondary γ′ precipitate size distribution in Ni-base superalloys

The size, morphology and fraction of each of the γ′ precipitate populations in polycrystalline γ- γ′ nickel-base superalloys are highly sensitive to the cooling rate from the solution temperature. As a result, thermal processing parameters are carefully selected to control precipitate populations in an effort to modify specific microstructural features that can impact resulting properties. The present investigation reports on how a stepped cooling rate was able to modify the microstructure of two experimental Ni-base superalloys. Cooling rates of 0.1 °C/s and 0.01 °C/s were maintained through the γ′ solvus temperature to a transition temperature ∼10 °C to 15 °C below the solvus. Following the transition temperature, a controlled cooling rate of 1 °C/s was applied to control the size and distribution of the secondary γ′ precipitates. For both experimental alloys, slow cooling rates through the γ′ solvus temperature resulted in the formation of coarse grain boundary precipitates while secondary γ′ precipitates formed upon the subsequent faster cooling rate of 1 °C/s. Coarse grain boundary γ′ precipitates resulted in higher amplitudes and wavelengths of serration along the boundary. In addition to cooling rate, the grain boundary misorientation was also found to influence the precipitation of grain boundary γ′ with larger precipitate populations found along high angle grain boundaries. Results from this study appear to support the concept that meso-scale engineering of grain boundary structures may potentially be used to enhance and optimize the high temperature properties of Ni-base superalloys.

On the Dependence of γ' Precipitate Size in a Nickel-Based Superalloy on the Cooling Rate from Super-Solvus Temperature Heat Treatment.

The ability to predict the sizes of secondary and tertiary γ′ precipitate is of particular importance for the development and use of polycrystalline nickel-based superalloys in demanding applications, since the size of the precipitate exerts a strong effect on the mechanical properties. Many studies have been devoted to the development and application of sophisticated numerical models that incorporate the influence of chemical composition, concentration gradients, and interfacial properties on precipitate size and morphology. In the present study, we choose a different approach, concentrating on identifying a correlation between the mean secondary and tertiary γ′ size and the cooling rate from solution treatment temperature. The data are collected using the precipitate size distribution analysis from high-resolution scanning electron microscopy. This correlation is expressed in the form of a power law, established using experimental measurement data and rationalized using a re-derivation of McLean’s theory for precipitate growth, based on well-established thermodynamic principles. Specifically, McLean’s model is recast to consider the effect of cooling rate. The derived model captures the correlation correctly despite its simplicity, and is able to predict the mean secondary and tertiary γ′ precipitate size in a nickel superalloy, without complex modeling.

Numerical simulation of grain boundary carbides evolution in 316H stainless steel

In the present work, a numerical model based on the coupling of Kampmann and Wagner Numerical (KWN) framework and thermodynamic software ThermoCalc has been developed to predict grain boundary precipitate evolution in 316H stainless steel during thermal aging. The model is calibrated and validated against precipitate size distributions obtained by accelerated isothermal heat treatment and analysed using scanning electron microscopy (SEM). Elemental distribution was also investigated using electron microprobe analysis (EPMA). The predicted average particle size, particle size distribution and precipitate number density predicted by the model were found to be in good agreement with the experimental results. The model was then applied to predict the particle size distribution after several years exposure at service temperature. It is demonstrated that these predictions are consistent with measurements from a service-exposed part. The sensitivity of the precipitate size distribution to temperature is emphasised, and it is demonstrated that the model has potential as a useful tool for predicting evolution of the precipitate size distribution during service, providing reliable thermal data are available for the whole service life.

A quantifiable and automated volume fraction characterization technique for secondary and tertiary γ′ precipitates in Ni-based superalloys

Ni-based superalloys are extensively used in high temperature, high stress applications. The presence of coherent γ′-Ni3Al precipitates provides the requisite elevated temperature strength and creep resistance in these alloys. Therefore, quantification of the precipitate size distribution and volume fraction is essential for accurate model predictions and future alloy design. Current γ′ volume fraction characterization techniques suffer from a lack of precision and repeatability. Without a reproducible procedure, unacceptable variations and errors have plagued the past 6 decades of superalloys research and have inhibited the implementation of accurate precipitation models for these alloys. Through the use of high resolution, low kV, scanning electron microscopy and state-of-the-art image post-processing, a new, accurate γ′ characterization technique is presented. Using the new technique, secondary γ′ volume fractions in superalloy ME3 were calculated, and confirmed through phase extraction, thus opening the possibility for validation of presently used superalloy precipitation databases.

Single-stage aging behaviour and precipitate evolution in a high Zn-containing Al–9.78Zn–2.02Mg–1.76Cu alloy

ABSTRACTProperty evolution in a high Zn-containing Al–9.78Zn–2.02Mg–1.76Cu alloy treated at 120°C, with the microstructure subjected to under-aging (UA), peak-aging (PA) and over-aging (OA), is investigated. Precipitate size distributions and distances between neighbouring precipitates are determined. Results indicate that a certain time is required to reach peak hardness and yield strength, and that peak values can be sustained for a relatively long time. As the aging time increases, the conductivities increase persistently. As the alloy temper varies from UA to PA to OA, the main matrix precipitates change from ‘GPI zone and GPII zone and η′ phase’ to ‘GPII zone and η′ phase’ and then to η′ phase. Meanwhile, the precipitate size distribution becomes broader, and the average precipitate size increases.

Stratiform Precipitation Processes in Cyclones Passing over a Coastal Mountain Range

Abstract The Olympic Mountains Experiment (OLYMPEX) documented precipitation and drop size distributions (DSDs) in landfalling midlatitude cyclones with gauges and disdrometers located at various distances from the coast and at different elevations on the windward side of the mountain range. Statistics of the drop size and gauge data for the season and case study analysis of a high-rainfall-producing storm of the atmospheric river type show that DSDs during stratiform raining periods exhibit considerable variability in regions of complex terrain. Seasonal statistics show that different relative proportions of drop sizes are present, depending on synoptic and mesoscale conditions, which vary within a single storm. The most frequent DSD regime contains modest concentrations of both small and large drops with synoptic factors near their climatological norms and moderate precipitation enhancement on the lower windward slopes. The heaviest rains are the most strongly enhanced on the lower slope and have DSDs marked by large concentrations of small to medium drops and varying concentrations of large drops. During the heavy-rain period of the case examined here, the low-level flow was onshore and entirely up terrain, the melting level was ~2.5 km, and stability moist neutral so that large amounts of small raindrops were produced. At the same time, melting ice particles produced at upper levels contributed varying amounts of large drops to the DSD, depending on the subsynoptic variability of the storm structure. When the low-level flow is directed downslope and offshore, small-drop production at low altitudes is reduced or eliminated.

Effect of Microstructure and Alloy Chemistry on Hydrogen Embrittlement of Precipitation-Hardened Ni-Based Alloys

The sensitivity to hydrogen embrittlement (HE) has been studied in respect of precipitation size distributions in two nickel-based superalloys: Alloy 718 (UNS N07718) and Alloy 945X (UNS N09946). Quantitative microstructure analysis was carried out by the combination of scanning and transmission electron microscopy and energy dispersive x-ray spectroscopy (EDS). While Alloy 718 is mainly strengthened by γ″, and therefore readily forms intergranular δ phase, Alloy 945X has been designed to avoid δ formation by reducing Nb levels providing high strength through a combination of γ′ and γ″. Slow strain rate tensile tests were carried out for different microstructural conditions in air and after cathodic hydrogen (H) charging. HE sensitivity was determined based on loss of elongation due to the H uptake in comparison to elongation to failure in air. Results showed that both alloys exhibited an elevated sensitivity to HE. Fracture surfaces of the H precharged material showed quasi-cleavage and transgranular cracks in the H-affected region, while ductile failure was observed toward the center of the sample. The crack origins observed on the H precharged samples exhibited quasi-cleavage with slip traces at high magnification. The sensitivity is slightly reduced for Alloy 718, by coarsening γ″ and reducing the overall strength of the alloy. However, on further coarsening of γ″, which promotes continuous decoration of grain boundaries with δ phase, the embrittlement index rose again indicating a change of hydrogen embrittlement mechanism from hydrogen-enhanced local plasticity (HELP) to hydrogen-enhanced decohesion embrittlement (HEDE). In contrast, Alloy 945X displayed a strong correlation between strength, based on precipitation size and embrittlement index, due to the absence of any significant formation of δ phase for the investigated microstructures. For the given test parameters, Alloy 945X did not display any reduced sensitivity to HE compared with Alloy 718 when considering high-strength conditions despite the absence of intergranular δ phase.

Over-aging influenced matrix precipitate characteristics improve fatigue crack propagation in a high Zn-containing Al-Zn-Mg-Cu alloy

A high Zn-containing Al-Zn-Mg-Cu alloy was researched due to excellent overall performances. The hardness, electrical conductivity and mechanical properties were investigated and detailed aging parameters subjected to T6, T79, T74 and T73 were proposed. The matrix precipitates of various aging tempers were investigated by transmission electron microscope (TEM) and high-resolution transmission electron microscope (HREM) techniques and quantitative information of matrix precipitates was extracted from the bright-field TEM images projected along 〈110〉Al orientation with the aid of an imaging analysis. The fatigue crack propagation (FCP) behaviors subjected to different aging tempers were investigated, the related fracture morphology of the stable expanding regions was analyzed and corresponding fatigue striations were measured to verify the FCP rates. The results showed that with the deepening of aging degree, the matrix precipitates coarsened with an expanding of precipitate size distribution and an enlargement of average precipitate size while the precipitates evolved from GP zones and η' phase to η' phase and η phase. The FCP resistance was improved with the aging degree deepens and the evolution of related tearing ridge, tearing dimple and fatigue striation also proved it. Due to a smaller cyclic plastic zone of the alloy with various tempers compared with the average grain size, the FCP rate was significantly influenced by matrix precipitate characteristics and a theoretical model which directly correlated FCP rate with matrix precipitate characteristics was proposed. From T6 state to T73 state, the enlargement of cuttable GP zones and η' phase, its evolution to η phase and the nucleation, growth and coarsening of η phase were in favor of enhancing the FCP resistance.

Experimental evaluation of asphaltene dispersants performance using dynamic light scattering

In this study, the asphaltene particle aggregation process is studied and effects of asphaltene concentration, n-heptane to toluene volume ratio, type and concentration of asphaltene aggregation inhibitor are investigated on onset of precipitation and asphaltene particle size distribution (APSD). The measurement of APSD is performed through dynamic light scattering technique. The results show that the concentration of asphaltene doesn't have significant effect on the onset point; however, it leads to form bigger particles. An increase in n-heptane volume ratio leads to increases the asphaltene particles size where 5% of particles are bigger than 6 μm after 40 min. Dodecyl benzene sulfonic acid component displaces the onset point reasonably and causes 7% rise in the amount of required n-heptane. Dodecyl resorcinol has the best performance at concentration of 50 ppm as an asphaltene dispersant and causes required n-heptane volume increment of 2%. It reduces the asphaltene particles size significantly and delays the asphaltene particles agglomeration process of about 30 min.