Diffusion-controlled Coarsening Research Articles

Precipitation evolution of Al-Zn-Mg-Cu-(Ag) alloys with a low Zn/Mg ratio

The influence of minor Ag on the precipitation evolution of the Al-4.2Zn-2.8Mg-1.0Cu (wt.%) alloy from early stages to over-aged stages at 150 °C was investigated. Surprisingly, co-precipitation of strengthening phases T′ and η′ are found in both Ag-free and Ag-added alloys. With Ag addition, precipitation of both T′ and η′ is refined and increased, such that the age-hardening capabilities and peak-aged tensile strength are improved. In addition, the quantitative proportion of η′ precipitates increases with the increase of Ag content due to the increase in the (Zn+Cu)/Mg ratio of nucleating particles. The narrowed precipitate-free zones (PFZs) are considered responsible for the undiminished fracture elongation in Ag-added alloys. Essentially, these effects of Ag are closely related to the strong Ag-vacancy and Ag-solute interactions. In over-aged stages, the Ag-added alloys still possess higher hardness values compared to the Ag-free alloy, which is related to precipitate coarsening mechanisms. The Ag-free alloy follows classical coarsening behavior by solid solution mediated diffusion, while the Ag-added alloy follows two possible coarsening mechanisms, coalescence of aggregates and diffusion of atoms. The smaller average size and higher residual number density of precipitates benefited from the slow diffusion-controlled coarsening behavior depending on the precipitate composition characteristics of the two-stage differentiation and the precipitate distribution characteristics of high-density dispersion in early-aged stages could explain why the hardness of Ag-added alloy keeps at a higher level than that of Ag-free alloy even after 1000 h ageing. Meanwhile, the transformation of metastable phases to stable phases is inhibited due to the addition of Ag, such that GP zones, T′, η′, η and T phases coexist even after 14 d of ageing. In terms of phase composition, the addition of Ag decreases the ratio of Mg/(Al+Zn) in T-type phase. For the Ag-added alloy, the sum concentration of Zn+Mg in η′ phase is about 10 at.% higher compared to T′ phase, and η phase continues to have a high sum concentration of Zn+Mg, besides, the Zn/Mg ratio and Cu concentration exhibit obvious differences from T phase.

Anisotropic growth of nano‐precipitates governed by preferred orientation and residual stress in an Al‐Zn‐Mg‐Cu alloy

Through an understanding of diffusion, precise control of the size distribution of nano-precipitates can be essential to developing superior properties in precipitation-strengthened alloys. Although a significant influence of crystallographic orientation on the diffusion process is known to exist in low-symmetry hexagonal close-packed alloys, such anisotropic diffusion is still unidentified in high-symmetry cubic alloys. In this work, we reveal the diffusion-controlled coarsening induced anisotropic growth process of nano-precipitates in an Al-Zn-Mg-Cu alloy. Our experimental and theoretical studies demonstrate that with an increase in the residual stress, the diffusion-controlled coarsening rate is slow along the 〈112〉 fiber texture in the alloy matrix with smaller grain sizes. As such, we find that the diffusion activation energy will be increased along the preferred orientation with largest residual stress, which leads to a reduced diffusion-controlled coarsening rate. Specifically, we demonstrate that the increase in the volume fraction of nano-precipitates originates from the rapid grain-boundary controlled coarsening of the grain-boundary precipitates. Based on these results, an underlying microstructural design strategy is proposed, involving the crystallographic orientation, the residual stress and the grain boundaries to manipulate the precipitate size distribution in this class of alloys.

Influence of chemical composition on coarsening kinetics of coherent L12 precipitates in FCC complex concentrated alloys

In this study, we report the experimental coarsening kinetics at 850, 900 and 950 °C of four complex concentrated alloys in the Al–Ti–Cr–Fe–Co–Ni senary system with different chemical compositions but a similar γ’ (L12) volume fraction (∼35 % at 950 °C) in a face-centered cubic (γ, FCC) matrix. The selected alloys were specifically designed to investigate the influence of Fe additions and Ni–Co substitutions on Ostwald ripening kinetics. Atom Probe tomography (APT) was used to determine the compositions of the FCC and L12 phases, which agree very well with Calphad calculations at thermodynamic equilibrium. Thermo-kinetic modeling of L12 precipitation was carried out using the Prisma module developed by Thermo-Calc and compared with experimental results. Apparent activation energies were determined and discussed in light of diffusion-controlled coarsening models to identify the key parameters affecting Ostwald ripening. We suggest that the abnormally high apparent activation energies results from composition-dependent parameters. When the latter are accounted for, the corrected activation energies for coarsening are in better agreement with available diffusion data.

On the phase stability of MARM247LC alloy during long term thermal exposure

The microstructures stability of directional-solidified (DS) MarM247LC alloy were investigated during thermal exposure at 800–950 °C up to 5000 h. In the dendrite core (DC), the particle size distribution (PSD) of γ′ phase shows that the coarsening mechanism is consistent with the trans-interface diffusion-controlled coarsening (TIDC) theory. While at the second dendrite arms (SDA), the γ′ phase gradually undergoes directional coarsening, with the coarsening direction perpendicular to the SDA growth direction. Besides, when the temperature increases to 900 °C, the effective diffusion coefficient and the lattice misfit of γ/γ′ lead to a significant increase in the coarsening rate of the γ′ phase. At the same time, the M6C carbides precipitated a lot in the DC enriching with W element and its distribution gradually changed to a cross-like distribution due to the formation of misfit dislocations of γ matrix. And the{200} plane is the coherent interface of M6C and γ matrix.

Microstructural evolution of Si(HfxTa1−x)(C)N polymer-derived ceramics upon high-temperature anneal

Ultra-high temperature ceramic nanocomposites (UHTC-NC) within the Si(HfxTa1−x)(C)N system were synthesized via the polymer-derived ceramics (PDC) synthesis route. The microstructure evolution of the materials was investigated upon pyrolysis and subsequent heat treatment. The crystallization behavior and phase composition were studied utilizing X-ray diffraction, scanning- and transmission electron microscopy. Single-source-precursors were converted into amorphous single-phase ceramics, with the exception of surface crystallization effects, at 1000 °C in NH3. Annealing in N2 at 1600 °C resulted in fully crystalline UHTCs. The powder samples revealed microstructures consisting of two characteristic regions, bulk and surface; displaying intrinsic microstructure and phase composition differences. Instead of the expected nitrides, transition metal carbides (TMC) were detected upon high-temperature anneal. The residual carbon available in the system triggered a decomposition reaction, resulting in the formation of TMCs plus gaseous nitrogen and SiC. Experimental data underline that N-containing PDCs are prone to phase separation accompanied by thermal decomposition and diffusion-controlled coarsening.

Phase Transformations of 5Cr-0.5Mo-0.1C Steel after Heat Treatment and Isothermal Exposure

This study consists of the experimental and numerical analysis of the phase transformations of 5Cr-0.5Mo.0.1C steel after heat treatment. The microstructure of the as-received steel comprised ferrite and bainite, which is in agreement with the microconstituents predicted by the Calphad-calculated TTT diagram. Calphad-based precipitation calculations show that the cooling stage of normalizing treatment did not cause carbide formation. In contrast, tempering at 700 °C for 15 min promotes the intergranular precipitation of Fe3C, M7C3 and M23C6 carbides, which is consistent with experimental results. Aging at 600 °C for short periods caused the precipitation of both M7C3 and M23C6 carbides; however, M23C6 is the dominant phase after prolonged aging. This is in agreement with experimental results. A rapid decrease in the steel hardness was observed after short aging, which is attributable to bainite transformation. Further reduction in hardness is associated with the diffusion-controlled coarsening of M23C6 carbide.

Coarsening kinetics of Cu particles in an Fe-1.5% Cu alloy

Abstract The Ostwald ripening of spherical and rod-shaped Cu precipitate particles in an Fe-1.5 mass% Cu alloy aged between 873 and 1023 K has been examined by measuring both the particle size by electron microscopy and the Cu concentration in the α-Fe matrix by electrical resistivity. The average radius of spherical and rod-shaped particles increases with ageing time t as t 1/3, in agreement with the growth by diffusion-controlled coarsening. The kinetics of the depletion of supersaturation with t obey the predicted t – 1/3 time law. The Cu/α-Fe interfacial energy and the diffusivity of Cu in α-Fe have been independently derived from the data on coarsening. The interfacial energies are measured as 0.57 and 1.1 Jm–2 for the spherical and rod-shaped particles respectively. The pre-exponential factor and the activation energy for bulk diffusion are found to be 4.54α10 –5 m2s– 1 and 241 kJmol – 1.

Atomic-scale investigation of coarsening kinetics by the phase-field crystal model

Coarsening is a common physical process that occurs in polydisperse two-phase mixture systems, which had been widely studied for decades. However, accurate prediction of the volume fraction dependence of the diffusion-controlled coarsening kinetic process is still very difficult. In this work, by using the atomic-scale phase-field crystal model, we investigated the coarsening kinetics of crystalline nanoparticles in the semi-solid region. The results showed that the details of the atomic-scale nature of particles do not affect the kinetics of coarsening for low solid volume fractions and the coarsening process of the nanoparticles is in agreement with the classical coarsening theory. While, for high solid volume fractions, our simulation results show that the coarsening rates of crystalline particles decrease with the solid volume fraction, which runs counter to the theoretical models based on mean-field theories. By checking the competitive growth process of all the particles, we found the appearance of grain rotation and volume diffusion mechanisms leads to the failure of the classical coarsening models.

Mechanisms of Ti[formula omitted]Al precipitation in hcp [formula omitted]-Ti

Nucleation and growth of Ti3Al α2 ordered domains in α-Ti–Al–X alloys were characterised using a combination of transmission electron microscopy, atom probe tomography and small angle X-ray scattering. Model alloys based on Ti–7Al (wt.%) and containing O, V and Mo were aged at 550∘C for times up to 120d and the resulting precipitate dispersions were observed at intermediate points. Precipitates grew to around 30nm in size, with a volume fraction of 6–10% depending on tertiary solutes. Interstitial O was found to increase the equilibrium volume fraction of α2, while V and Mo showed relatively little influence. Addition of any of the solutes in this study, but most prominently Mo, was found to increase nucleation density and decrease precipitate size and possibly coarsening rate. Coarsening can be described by the Lifshitz-Slyozov-Wagner model, suggesting a matrix diffusion-controlled coarsening mechanism (rather than control by interfacial coherency). Solutionising temperature was found to affect nucleation number density with an activation energy of Ef=1.5±0.4 eV, supporting the hypothesis that vacancy concentration affects α2 nucleation. The observation that all solutes increase nucleation number density is also consistent with a vacancy-controlled nucleation mechanism.

A Fast-Acting Method for Simulating Precipitation During Heat Treatment of Superalloy 718

A fast-acting, mean-field method for simulating precipitation of the γ′′ and γ′ phases during aging of superalloy 718 following super-delta-solvus solution treatment was formulated and validated using observations in the literature. The approach assumed classical (homogeneous) nucleation and diffusion-controlled growth (N&G) of disk/ellipsoidal-shaped-γ′′ and spherical-γ′ particles. For the γ′′ precipitates in particular, the evolution equations for both nucleation and growth incorporated corrections for the non-spherical shape, assuming a fixed aspect ratio. In addition, special attention was paid to the choice of input material properties for simulations. These parameters included the bulk free energies of transformation, particle-matrix (misfit) elastic strain energy (for γ′′), effective diffusivities, and the γ′′–γ and γ′–γ interface energies. The applicability of the diffusivities and interface energies chosen for the N&G simulations was established by their consistency in replicating previously measured rate constants for the diffusion-controlled coarsening of both γ′′ and γ′. The N&G formulation was discretized to obtain numerical (spreadsheet) solutions via the Kampmann–Wagner approach. Simulation results for the temporal evolution of volume fraction and average size of the precipitates showed good agreement with experimental measurements. The sensitivity of model predictions to various input parameters was also quantified.

Coarsening kinetics of γ′ precipitates in a Re-containing Ni-based single crystal superalloy during long-term aging

The morphological evolution and coarsening kinetics of γ′ precipitates in a Re-containing Ni-based single crystal superalloy were investigated during isothermal aging at 900, 950 and 1000 °C. After heat treatment, well-defined cuboidal γ′ precipitates with low misfit was obtained within the experimental alloy. Then coarsening rate constants and particle size distribution (PSD) of γ′ phases were calculated and specified based on the measured precipitate sizes for varying periods of aging times from 100 to 2000 h. After aging for 2000 h, γ′ precipitates maintained cubical shape at 900 °C, while exhibited sphere at 950 and 1000 °C. Coarsening models based on diffusion-controlled process with a functional relationship of r3 vs. t (classic Lifshitz-Slyozov-Wagner coarsening model) and interface-controlled model with a function of r2 vs. t (trans-interface diffusion-controlled coarsening model) were investigated to fit between the experimental results and theoretical analysis. It was found that Re as the slowest diffusing solute in the alloy constituted the rate-limited step for coarsening based on LSW model, while the process limiting coarsening as governed by an interface diffusion process could possibly be related to the Al diffusion through the γ/γ′ interface. The PSDs and coarsening exponent were discussed by comparing the experimental data with predictions of LSW and TIDC models. Finally, coarsening mechanism could be divided into four regimes: (i) coarsening by diffusion-controlled; (ii) coarsening by diffusion and interface co-controlled; (iii) coarsening by interface-controlled; (iv) coarsening by interface-controlled accompanied with γ′ coalescence.

Three-dimensional phase-field simulation of microstructural evolution in three-phase materials with different interfacial energies and different diffusivities

The coarsening behavior of three-phase materials, such as eutectic alloys, is of high technological interest. In this study, 3D ternary three-phase polycrystalline materials were modeled to study the effect of bulk diffusion and phase arrangement on the coarsening kinetics. The diffusion mobilities were defined to be different in the three phases. By varying the phase boundary and grain boundary energies, microstructures with different phase arrangements were obtained, in which the different types of grains had a tendency to alternate or cluster. In all cases, a regime was reached where the average grain size follows a power growth law with growth exponent $$n=3$$ , indicating bulk diffusion-controlled coarsening. The overall growth rate and that of the individual phases were clearly affected by the phase arrangement, the magnitude of the phase boundary energy and the diffusion mobilities of the different phases. In all cases, the phase with the lowest diffusion mobility showed the highest growth rate and on average a larger number of grain faces. While the average number of grain faces became constant in time in systems with constant grain boundary energy, the average number of grain faces continued to increase during the whole simulation time when the grain boundary energy was misorientation dependent.

Ostwald Ripening Process of Coherentβ′ Precipitates during Aging in Fe0.75Ni0.10Al0.15and Fe0.74Ni0.10Al0.15Cr0.01Alloys

The Ostwald ripening process was studied in Fe0.75Ni0.10Al0.15and Fe0.74Ni0.10Al0.15Cr0.01alloys after aging at 750, 850, and 950°C for different times. The microstructural evolution shows a rounded cube morphology (Fe, Ni)Alβ′ precipitates aligned in the ferrite matrix, which changes to elongated plates after prolonged aging. The variation of the equivalent radii of precipitates with time follows the modified Lifshitz-Slyozov-Wagner theory for diffusion-controlled coarsening. Thermo-Calc analysis shows that the chromium content is richer in the matrix than in the precipitates which causes higher hardness and coarsening resistance in the aged Fe0.74Ni0.10Al0.15Cr0.01alloy.

Quantitative predictions of the trans-interface diffusion-controlled theory of particle coarsening

Data on the coarsening of γ′ (Ni 3Al) precipitates in binary Ni–Al alloys are re-examined quantitatively in light of the theory of trans-interface diffusion-controlled (TIDC) coarsening, which predicts time-dependent behavior of the type 〈 r〉 n ≈ k Tt for the growth of precipitates of average radius 〈 r〉 and X ≈ κ Tt –1/ n for the depletion of solute concentration in the matrix, X. The exponent n is intimately related to the width of the precipitate–matrix interface, δ, which depends on r as δ ∝ r m ( m = n − 2). The scaled distribution of particle sizes (PSD) also depends on n, while the rate constants k T and κ T depend on the thermophysical constants of the alloy system. In Ni–Al alloys n = 2.4, determined from analyzing three different sets of PSDs. Quantitative analysis yields interfacial free energies and chemical diffusion coefficients that agree exceptionally well with extant data. The TIDC theory is the only theory that is consistent, both qualitatively and quantitatively, with the entirety of the data.

Hardening Behavior in Aged Al-4%Cu-0.3%Mg Alloys with 0.5 and 2%Ag Additions

The precipitation characterization of Al-4 mass% Cu-0.3 mass% Mg alloy with additions of 0.5 and 2 mass% Ag during aging treatments was carried out by transmission electron microscopy (TEM) and microhardness measurements. TEM observation of aged samples showed that thephase is the dominant phase and it is in coexistence with the � 0 phase. Additionally, thephase has the morphology of polygonal prism (almost hexagonal) with flat interfaces and a thin thickness. The variation of the cube of mean radius of precipitates, r 3 , followed a linear relationship, as predicted by the Lifshitz, Slyosov and Wagner (LSW) theory for diffusion-controlled coarsening in both alloys. The coarsening process of thephase was slower in the aged Al-4 mass% Cu-0.3 mass% Mg-2 mass% Ag alloy. The decrease in hardness seems to be related to the coarsening of thephase and the loss of coherency. (doi:10.2320/matertrans.M2009233)

Scattering Modeling of Nucleation Gels

On the basis of elastic scattering theory, we propose a methodological framework to exactly reconstruct the entire course during the structural formation of the nucleation gel. The focus of the present work is on command of the interaction relations between scattering factors and on understanding of how and to what extent these interactions obtain information on aspects of a complex event in gelation. The scattering modeling provides a much more detailed and direct examination on the quantitative structure−evolution relationship and differentiates the gelation process into—nucleation and growth, aggregation, diffusion-controlled coarsening (fast process), and Ostwald ripening (slow process)—four stages in which the kinetic evolutions are predicted by either the growth or the coarsening theory. We demonstrate that the scattering modeling can be practically implemented, can provide valuable results, and would serve as the basis for a study of temporal and spatial complexity of soft matter on a mesoscopic le...

Cinética de engrosamiento de precipitados coherentes en la aleación Fe-10 % Ni-15 % Al

The coarsening kinetics and the morphology evolution of the coherent β’ (Fe, Ni)Al precipitates embedded in a ferritic matrix were studied in the aged Fe-10 % Ni-15 % Al alloy. Samples were solution treated at 1,100°C for 24 h and subsequently aged at 750, 850 and 920 °C for different times. XRD, SEM and TEM results showed the following decomposition reaction after aging treatment, α sss → α + β. Intragranular particles distribution changes from a random to an aligned on the elastically soft crystallographic directions of the matrix. Additionally, the morphological evolution of the precipitates was as follows: spheres → cuboids → parallelepipeds → plates. The variation of the cube of mean radius of particles, r 3 , and the particle density as a function of time followed a linear relationship, as predicted by the Lifshitz, Slyosov and Wagner (LSW) theory for diffusion-controlled coarsening. The rate constant (K) increased with the aging temperature. The activation energy for coarsening process was determined to be about of 220 kJ/mol.

Microstructural development and evolution of liquid phase sintered Cr-Cu composites

Features of the microstructure formation of Cr-Cu composites under impregnation followed by liquid phase sintering of reduced and electrolytic chromium powders at 1200?C in a vacuum of (2-4)?10-3Pa have been studied. The refractory component particle size distribution in the microstructure of samples with reduced chromium sintered for 60 min is shown to obey a normal logarithmic law; with distribution parameters being sensitive to the volume fraction of the refractory particles. The calculated values of the dihedral angle are close to the value of one of the modes in the experimental dihedral angle distribution for the microstructure of electrolytic chromium based samples (115?). The interfacial and interparticle surface energies ratio ?sl/?ss>0.5 is shown to correspond to theory for the Crs-Cul system in equilibrium, which indicates the presence of skeleton structure elements in the course of composition formation under liquid phase sintering (including the case of excess liquid phase). Experimentally determined interparticle and interfacial surface areas, solid particle contiguity and continuity are discussed in terms of concurrent diffusion-controlled particle coarsening (in Lifshitz, Slyozov and Wagner theory) and particle coalescence (in German?s model). The kinetics of shrinkage for the composites with 50...55 % solid-phase volume-fractions at heating and isothermal sintering in a vacuum at a temperature of 1200?C in terms of linearly viscous rheological theory are discussed.

Phase Decomposition in Isothermally Aged MA Cu-Ni-Fe and Cu-Ni-Cr Alloys

Supersaturated solid solutions of Cu-44.5at.%Ni-22.5at.%Fe and Cu-37at.%Ni-6at.%Cr alloy were produced by ball milling of a pure chemical elemental mixture for 1080 ks. Two fcc supersaturated solid solutions with a grain size of about 20 and 50 nm, respectively, were obtained after milling. These alloys were subsequently aged at temperatures between 800 and 1003 K for different times. The aging promoted the phase decomposition of the supersaturated solid solution into a mixture of Cu-rich and Ni- phases in both the aged MA alloy powders. The growth kinetics of the modulation wavelength was determined from the X-ray diffraction results and followed the Lifshitz-Slyozov- Wagner theory for a diffusion-controlled coarsening in the mechanically-alloyed Cu-Ni-Fe alloy after aging. However, the sidebands intensity seems to be very low and overlapped with the peaks corresponding to the Cu-rich phase in the aged mechanically-alloyed Cu-Ni-Cr alloy. The growth kinetics of composition modulation wavelength for the aged MA Cu-Ni-Fe alloy was faster at 803 and 898 K than that for the same alloy composition obtained by a conventional processing and then aged at the same temperatures.

Phase Decomposition in a Mechanically Alloyed Cu-44.5 at%Ni-22.5 at%Fe Alloy during Isothermal Aging

A supersaturated solid solution of Cu-44.5 at%Ni-22.5 at%Fe alloy was produced by ball milling of a pure chemical elemental mixture for 1080 ks. An fcc supersaturated solid solution with a grain size of about 20 nm was obtained after milling. This alloy was subsequently aged at 803, 898 and 1003 K for different times. The growth kinetics of the modulation wavelength was determined from the X-ray diffraction results and followed the Lifshitz-Slyozov-Wagner theory for a diffusion-controlled coarsening in the MA alloy after aging. The growth kinetics of composition modulation wavelength for the MA alloy was faster at 803 and 898 K than that for the same alloy composition obtained by a conventional processing and then aged at the same temperatures. The activation energy for the decomposed phase coarsening process in the MA alloy was lower than that corresponding to the conventionally-processed alloy. [doi:10.2320/matertrans.47.1317]