Precipitate Shape Research Articles

Modelling of precipitate hardening in ferroelectric materials

AbstractThis investigation presents a mechanical model to determine energetically favourable particle shapes, motivated by precipitation hardening in ferroelectric materials. We examine Li-doped $$\text {NaNbO}_3$$ NaNbO 3 and propose a system of equations to derive the correct material constants for this material system. To model the elongated precipitate shape we introduce two approaches: An elliptic shape and a shape based on cubic B-spline-curves. We subject both definitions to an optimisation routine that yields equilibrium shapes. We further use the spline approach to derive configurational forces on the interface.

A molecular dynamics investigation of nano-twins and nano-precipitates effects in CoCrFeNi-based high-entropy alloys

Abstract This study systematically investigates the effects of twin boundaries and precipitates on the performance of CoCrFeNi HEAs matrix using molecular dynamics simulation methods. By constructing corresponding HEAs models and conducting simulations of their structural evolution and mechanical behavior at the nanoscale, the influence mechanisms of nanotwins (NTs) and nano-precipitates (NPs) on the mechanical properties of the material were explored through in-depth analysis of simulation results. The findings suggest that twin boundaries effectively impede the movement and slip of dislocations and stacking faults in the material. As a result, this enhances its mechanical properties and inhibits plastic deformation, ultimately improving its ductility. Meanwhile, precipitates also impact the material's performance, and the shape of precipitates may exert different effects on the material, while the phase interface between precipitates and the matrix can hinder the expansion of defects. The presence of twin boundaries can enhance the strengthening effect of precipitates, further improving the material's performance. This study provides a new perspective for understanding the relationship between the microstructure and mechanical properties of HEAs materials, offering important references for the design and optimization of HEAs materials.

Influence of microstructural and loading direction on the ductility and anisotropy of Ni-based superalloys

The influences of phase coarsening and loading direction on the ductility of Ni-based superalloys with phase coarsening are investigated, and the relationship between their microstructural and macroscopic mechanical properties is also explored in detail. It is found that the precipitation phase and the corresponding phase coarsening significantly influence the ductility of alloys. Furthermore, anisotropic features in ductility are observed after phase coarsening. Generally, as the volume fraction of precipitation particles or the degree of phase coarsening increases, the ductility of alloys gradually decreases; and it initially increases and then decreases gradually with the increase of loading angle, presenting an inverted ‘V’ shape. Comparatively, for the alloys with lower volume fraction of precipitation particles and higher degree of phase coarsening, the ductility shows different variation trends with the degree of phase coarsening and loading angle compared with that in materials with other microstructure features, taking the minimum value at the loading angle of 45°. The variations of ductility are closely connected to the characteristics of precipitate shape, size and distribution. The microstructure evolution and the loading direction significantly affect the initiation and movement of dislocations within the material, and result in various macroscopic ductility characteristics in the Ni-based superalloys.

Topology optimization for precipitation hardening in ferroelectric material

AbstractRecent studies have shown that precipitation hardening effectively enhances the mechanical quality factor of ferroelectric material. In this work, Li‐doped , a material system with elliptical precipitates is investigated. We present a mechanical model to determine energetically stable precipitate shapes by minimizing the total energy, consisting of elastic and interface energy. Furthermore, we investigate the influence of external loads on the precipitate topology. Correct elastic constants as well as lattice misfits for the simulation are provided. The shapes determined from finite element simulations agree well with observed results.

Effects of heat treatment and geometry on mechanical properties and precipitate development in martensitic additively manufactured 17-4 PH

Reliable mechanical properties of precipitation strengthened alloys like 17-4 PH stainless steel are conventionally obtained through tightly controlled thermomechanical processing to optimize the size and distribution of strengthening precipitates. In additive manufacturing, however, the thermal history (e.g. heating and cooling rates) can vary significantly across a part or individual layer causing the precipitate distribution and resulting mechanical properties to be non-uniform. This is especially true for precipitation strengthened alloys like 17-4 PH which require a specific thermal history to achieve the expected phases and properties. To explore this material and the effect that standard heat treatments have on the processing-structure-properties relationship for AM 17-4 PH, a series of thin-wall (0.8 mm) and ASTM E8 size dogbones were printed via SLM and tensile tested in the as-built, solution annealed, and H900 condition. A Vic-2D DIC system was used during tensile testing to obtain full-field strain data. SEM BSE imaging and TEM EDS were used to characterize the larger (60–120 nm) precipitate phases (SiO and NbC) along with the overall microstructure. GISAXS and TEM EDS were used to quantify the size (5–15 nm), shape, distribution, and composition of nanoscale copper-rich precipitates. Overall, the mechanical properties between the E8 and thin-wall samples were similar with yield strengths of 677 and 734 MPa and ultimate strengths of 1049 and 941 MPa in the H900 condition, respectively. The other sample conditions follow similar trends with the only significant difference being a drop in average ductility (0.27 vs 0.17) for the thin-wall geometry. These similarities were hypothesized to stem from several factors which work to lessen the cooling rate dependence of 17-4 PH.

A crystal plasticity-based micromechanical model for precipitate shearing: Application to cyclic softening of polycrystalline Ni-based superalloys

Cyclic deformation of polycrystalline Ni-based superalloys leads to cyclic hardening followed by softening, in terms of the mechanical response. A micromechanical constitutive model is proposed and implemented in a dislocation density-based, crystal plasticity framework to simulate the shearing of γ′ precipitates, which leads to the observed cyclic softening. The framework accounts for physically based deformation mechanisms. A slip-system level backstress model has been implemented to account for the kinematic hardening. Further, a micromechanical model for microstructure evolution due to precipitate shearing is developed that accounts for the dislocation-precipitate interactions and the resultant change in precipitate strengthening. The model is used to simulate cyclic deformation in two polycrystalline Ni-based superalloys, with different microstructures (in terms of the shape, size and volume fraction of precipitates), referred as Alloy 1 and Alloy 2. Room temperature cyclic deformation tests, followed by microstructure characterization were performed at different strain amplitudes for Alloy 1 to validate our predictions. For Alloy 2, the experimental stress–strain response was used from the literature to fit and validate our predictions. It is shown that the model can predict cyclic softening due to precipitate shearing for different initial microstructures and a range of loading conditions in polycrystalline Ni-based superalloys.

Interannual fluctuations in precipitation shape the trajectory of ecosystem respiration along a grazing exclusion chronosequence in a typical steppe in Inner Mongolia

Grazing exclusion (GE), as an effective strategy for revitalizing degraded grasslands, possesses the potential to increase ecosystem respiration (Re) and significantly influence the capacity of grassland soils to sequester carbon. However, our current grasp of Re dynamics in response to varying durations of GE, particularly in the context of precipitation fluctuations, remains incomplete. To fill this knowledge gap, we conducted a monitoring of Re over a 40-year GE chronosequence within Inner Mongolia temperate typical steppe across two distinct hydrologically years. Overall, Re exhibited a gradual saturation curve and an increasing trend with the duration of GE in the wet year of 2021 and the normal precipitation year of 2022, respectively. The variance primarily stemmed from relatively higher microbial biomass carbon observed in the short-term GE during 2022 in contrast to 2021. Moreover, the impacts of GE on the sensitivities of Re to moisture and temperature were intricately tied to precipitation patterns. increasing significantly with prolonged GE duration in 2022 but not in 2021. Our study highlights the intricate interplay between GE duration, precipitation variability, and Re dynamics. This deeper understanding enhances our ability to predict and manage carbon cycling within typical steppe in Inner Mongolia, offering invaluable insights for effective restoration strategies and climate change mitigation.

Ultrastrong and ductile FeNi-based alloys through Pd-containing multicomponent L12-type precipitates

Precipitation strengthening stands as a paramount strategy for enhancing the mechanical properties of FeNi-based alloys. Conventional precipitates used for strengthening typically contain only two major constituent elements selected from Ni, Al, and Ti. However, knowledge about the intrinsic properties and strengthening mechanisms of multicomponent precipitates remains limited. Here, we propose introducing novel multicomponent L12-type precipitates containing palladium (Pd) to strengthen FeNi-based alloys. The strengthened FeNi alloy achieves an eightfold increase in strength compared to the FeNi matrix while maintaining good ductility. Using meticulous micro-characterization and energy-dispersive X-ray spectroscopy (EDS) techniques, in conjunction with first-principles calculations, this study investigated the effects of Pd addition on the thermodynamic stability, morphology, coherency, and strengthening mechanisms of the precipitates. Results indicate that the addition of Pd induces the nucleation of L12-type precipitates, increases their ductility, and eliminates anisotropy in the shear modulus of the precipitates. Excessive Pd content can alter the shape of precipitates from spherical to acicular due to increased interfacial mismatch between the precipitates and the FeNi matrix. These insights shed light on the impact of Pd addition on the intrinsic properties of L12-type precipitates, offering a promising pathway for the design of advanced FeNi-based alloys with optimized mechanical performance.

Molecular dynamics simulation of intergranular fracture in austenitic steel containing precipitation

Molecular dynamics simulation is applied to study the crack propagation in austenitic steel containing precipitation. Based on the experimental results, models containing precipitation with two shapes and three volume fractions are constructed. The interactions of the crack with precipitation, dislocation, twin and stacking faults are investigated. It demonstrates that the crack propagation process is strongly related to the temperature and the characteristic parameter of the precipitation. However, the microstructure evolution and dislocation emission are more affected by the temperature. At the same temperature, the initial emission position of the dislocation is changed due to the variation of the precipitation shape. It also indicates that the peak dislocation density is weakly correlated with the single characteristic parameter of the precipitation. Combined with the variation of the crack propagation rate and the peak dislocation density with temperature, it illustrates a negative relationship between these two results.

Continuous precipitation behavior of Mg17Al12 phase during multiple steps of twinning-aging procedure in Mg-Al alloys

Twinning was regarded as an effective way to modify the precipitation in Mg alloys. Two procedures were designed to illustrate twinning-aging consequence on Mg17Al12 phase evolution. The effect of multiple steps of twinning-precipitation on the morphology and density of the continuous precipitates inside the twins and the matrix were comprehensively analyzed through phase-orientation related observation. The results show the shape of precipitates in twins was similar to that in the matrix as the CPs mostly lay on the basal planes with an asymmetric-lozenges shape. The CPs were remarkably refined and its density became much higher inside twins. Moreover, the aspect ratio of the CP plates in twins was around 45% of that in the matrix, which means the CPs inside twins became more globular. The precipitation behavior of Mg17Al12 phase inside double extension twins was different from the primary twin or the matrix. The Mg17Al12 phases lay on both basal and prismatic planes can be observed in double twins of two-step precipitation. The growth behavior of pre-precipitates in twins is different from those in the matrix. The growth rate along its thickness became higher than that in the matrix, which is probably related to dislocation-assisted diffusion at the basal plane.

Simultaneously Improving Strength and Plasticity of Al–Cu Alloy by Introducing Spherical Precipitates

The trade‐off relation between strength and plasticity is the bottleneck that limits the development of high‐strength and high‐plasticity Al–Cu alloys. Inspired from the influence of precipitate shape on the work‐hardening behavior of Al–Cu alloys, an Al–Cu–Zr–Sc alloy containing a mixed microstructure of spherical‐shaped Al3(Zr, Sc) phases and disk‐shaped θ′ phases is successfully designed and fabricated. Surprisingly, it is found that the strength and plasticity of the Al–Cu–Zr–Sc alloy are synchronously improved compared to the Al–Cu alloy with only disk‐shaped θ′ phases. The introduction of spherical‐shaped Al3(Zr, Sc) phases can increase the yield strength without sacrificing the work‐hardening ability of the Al–Cu–Zr–Sc alloy, which is mainly attributed to the extremely small strain‐hardening exponent of the Al alloy with spherical‐shaped precipitates. Besides, the predicted strength–elongation relation of the Al–Cu alloy is established based on the exponential strain‐hardening model.

Surface precipitate analysis of gas atomized Ni-Base superalloy powders

Powders surface precipitate has strong relations with the microstructure and properties of powder metallurgy components. Morphology, element distribution and crystal structure of the precipitate at gas atomized Ni-base superalloy powders surface were investigated. Results show that the precipitate is lamelliform and prefers to form at grain boundaries and interdendrite regions than dendrite arms. With powders size decreasing, the precipitate shape observed from surface varies from strip to rectangular and to nearly round, and the precipitate density increases, measured 17.75 μm−2, 21.42 μm−2, 26.50 μm−2 at nearly 45μm, 30μm and 10μm powders surface respectively, but the precipitate average size changes conversely, that is 228nm, 193nm, 77nm respectively. The precipitate enriches in high melting point elements Ti, Nb, Mo, W, Zr and poor in low melting point elements Ni, Cr, Co, Al. Crystal structure analysis reveals that the precipitate is MC, M23C6 or M6C carbide.

Degradation and anisotropy characteristics of fracture toughness in Ni-based superalloys after phase coarsening

The effect of phase coarsening on the crack propagation characteristics and the corresponding fracture toughness in Ni-based superalloys is investigated by integrating with the finite element method simulations and related mechanism analysis, and the relationship between the macroscopic mechanical properties of alloys and the evolution in their microstructures are discussed in detail. Related analysis shows that the fracture toughness of alloys degraded considerably with phase coarsening. Moreover, the fracture toughness also demonstrates an anisotropic characteristic. Specifically, when the volume fraction of precipitate is low or the degree of phase coarsening is relatively low, the fracture toughness of alloys increases first and then decreases gradually along with increasing the loading angle, showing an inverted "V" shape. In comparison, in the case of a higher volume fraction of precipitate or higher degree of phase coarsening, the fracture toughness displays an opposite variation trend, and reaches the minimum value at the loading direction of 45°. The corresponding variation characteristics of fracture toughness are correlated with the evolutions of precipitate shape, size, and distribution within the alloys. The change in the microstructure or that in the loading direction affects remarkably the initiation and growth of micro-voids within the alloys, and it further affects the crack propagation characteristics, resulting in the degradation and anisotropy characteristics of macroscopic fracture toughness in the alloys. Related work is of great significance for the structure design of Ni-based superalloys components, the mechanical property evaluation and the life prediction during their service process.

Effect of precipitate shape and distribution on mechanical behavior of shape memory metallic glass composites by molecular dynamics method

The deformation behaviors of metallic glass composites enhanced with brick and cylindrical shape B2-CuZr precipitates were investigated by molecular dynamics method. Both specimens experience a two-stage phase transformation and triple-yielding phenomenon. The brick-shaped precipitate enhanced bulk metallic glass composite (BMGC) exhibits significantly improved strength and mildly enhanced plasticity compared to cylindrical shape inclusion reinforced BMGC. The larger aspect ratio of brick-shaped precipitate enhanced BMGC strengthens the composite by improving elastic lattice deformation along loading direction, while the enhanced plasticity is ascribed to smaller free path for mature shear bands formation. The deformation mechanism for brick-shaped BMGCs is shear band cutting through precipitates, while that for cylindrical shape precipitate reinforced BMGCs is shear band wrapping around crystalline particles. Both specimens display high strain at crystalline/amorphous interface (CAI) region and might experience interfacial stability issue.

Assessing the predictive capabilities of precipitation strengthening models for deformation twinning in Mg alloys using phase-field simulations

Precipitation strengthening is a key strategy for improving the overall mechanical properties of Mg alloys. In Mg-Al alloys, basal precipitates are known to strengthen against twinning, resulting in an increase in the critical resolved shear stress (CRSS) necessary for continued deformation. Although several models have been proposed to quantify the influence of precipitate shape, size, and distribution on the CRSS, the accuracy, scope, and applicability of these models has not been fully assessed. Accordingly, the objectives of this study are: (i) to analyze the accuracy of analytical models proposed in the literature for precipitation strengthening against twin thickening and propagation (in Mg-Al alloys) using phase-field (PF) simulations, (ii) to propose modifications to these model forms to better capture the observed trends in the PF data, and (iii) to subsequently test the predictiveness of the extended models in extrapolating to experimental strengthening data. First, using an atomistically-informed phase-field method, the interactions between migrating twin boundaries (during the propagation and thickening stages) and basal plates are simulated for different precipitate sizes and arrangements. In general, comparison of the increase in CRSS determined from the PF simulations and the predictions from four precipitation strengthening models reveals that modifications are necessary to the model forms to extend their applicability to precipitation strengthening against both twin thickening and propagation. A subsequent comparison between predictions from the extended models and experimental strengthening data for peak age-hardened samples reveals that the (extended) single dislocation and dislocation wall models provide reasonably accurate values of the increase in CRSS. Ultimately, the results presented here help elucidate the fidelity and applicability of the various hardening models in predicting precipitation strenghtening effects in technologically important alloys.

Nonclassical Crystallization Causes Dendritic and Band‐Like Microscale Patterns in Inorganic Precipitates

AbstractThe self‐organization of complex solids can create patterns extending hierarchically from the atomic to the macroscopic scale. A frequently studied model is the chemical garden system which consists of life‐like precipitate shapes. In this study, we examine the thin walls of chemical gardens using microfluidic devices that yield linear Ni(OH)2 precipitate membranes. We observe distinct light‐scattering patterns within the compositionally pure membranes, including disorganized spots, dendrites, and parallel bands. The bands are tilted with respect to the membrane axis and their spacing (20–100 μm) increases with increasing flow rates. Scanning electron microscopy reveals that the bands consist of submicron particles embedded in a denser material and these particles are also found in the reactant stream. We propose that dendrites and bands arise from the attachment of solution‐borne nanoparticles. The bands are generated by particle‐aggregation zones moving upstream along the slowly advancing membrane surface. The speed of the aggregation zones is proportional to the band distance and defines the system's dispersion relation. This speed‐wavelength dependence and the flow‐opposing motion of the aggregation zones are likely caused by low particle concentrations in the wake of the zones that only slowly recover due to Brownian motion and particle nucleation.

Nonclassical Crystallization Causes Dendritic and Band-Like Microscale Patterns in Inorganic Precipitates.

The self-organization of complex solids can create patterns extending hierarchically from the atomic to the macroscopic scale. A frequently studied model is the chemical garden system which consists of life-like precipitate shapes. In this study, we examine the thin walls of chemical gardens using microfluidic devices that yield linear Ni(OH)2 precipitate membranes. We observe distinct light-scattering patterns within the compositionally pure membranes, including disorganized spots, dendrites, and parallel bands. The bands are tilted with respect to the membrane axis and their spacing (20-100 μm) increases with increasing flow rates. Scanning electron microscopy reveals that the bands consist of submicron particles embedded in a denser material and these particles are also found in the reactant stream. We propose that dendrites and bands arise from the attachment of solution-borne nanoparticles. The bands are generated by particle-aggregation zones moving upstream along the slowly advancing membrane surface. The speed of the aggregation zones is proportional to the band distance and defines the system's dispersion relation. This speed-wavelength dependence and the flow-opposing motion of the aggregation zones are likely caused by low particle concentrations in the wake of the zones that only slowly recover due to Brownian motion and particle nucleation.

Heterogeneous Catalyst as a Functional Substrate Governing the Shape of Electrochemical Precipitates in Oxygen-Fueled Rechargeable Batteries.

Lithium-oxygen batteries have the potential to become the most eminent solution for future energy storage with their theoretical energy density exceeding all existing batteries. However, the insulating and insoluble discharge product (lithium peroxide; Li2O2) impairs practical application. Conventional catalyst designs based on the electronic structure and interfacial charge transfer descriptors have not been able to overcome these limitations due to Li2O2. Herein, we revisit the role of heterogeneous catalysts as substrates to regulate Li2O2 growth and the formation of solid/solid reaction interfaces. We demonstrate that controlled solid/solid interfacial structure design is a critical performance parameter beyond the inherent electronic structure. In particular, the Cu2O substrate in this study induces a homogeneous deposition of Pd atoms, which leads to well-controlled growth of Li2O2 resolving mass and charge transport limits (i.e., the bottleneck of oxygen reduction/evolution reactions), thus improving reversibility, capacity, and durability of the cells by dissipating electrochemical and mechanical stress. We thus verified the essential role of solid/solid interfaces to regulate the nucleation and growth process of Li2O2 in lithium-oxygen batteries.

Development of morphology and lattice misfit in modified Ni-base superalloy with Al, Co and Ni additions

Abstract This research work studied the effect of aluminium, cobalt and nickel additions in superalloys grade GTD-111 and IN-738 on morphology of gamma prime particles and their lattice misfits after subjected to heat treatment and long-term cyclic exposure by using SEM and XRD. It was found that the particles became more cuboidal in shape after heat treatment in modified GTD-111 and IN-738 alloys. When adding 1 wt% aluminium and 6 wt% nickel, larger negative values of lattice misfit were found at −0.57 % and −0.28 %, respectively. However, 6 wt% cobalt addition reduced the negative value of the lattice misfit to −0.20 % in modified GTD-111 and small positive lattice misfit (+0.08 %) was found in modified IN-738. Also, modified GTD-111 alloy shows more spherical shape of the gamma prime precipitates than those in modified IN-738. After long-term cyclic exposure at 1173 K for 1440 ks, it was found that the particles become more spherical shape comparing to those of heat treated ones. The shape of particles in both modified alloys with 1 wt% aluminium and 6 wt% nickel additions maintained more cuboidal compared to others. Furthermore, the effect of 6 wt% cobalt addition is more pronounced for modified IN-738 than that of modified GTD-111.

A combined simulation and experimental study of the equilibrium shapes of η′ and α precipitates in Mn-containing 7xxx Al-alloys

The addition of Mn to 7xxx series Al-alloys helps improve tensile properties owed to the presence of α precipitates (Al(Mn,Fe)Si, simple cubic, 50–200 nm, non-shearable) in addition to the η′ precipitates (Mg2Zn5−xAl2+x, hexagonal, 4–6 nm, shearable) commonly observed in the 7xxx series Al-alloys. The coexistence of multiple α and η′ variants, 24 for α and 4 for η′, coupled with their small size-scale, makes the experimental determination by x-ray diffraction (XRD) and scanning transmission electron microscopy (STEM) challenging. This work formulates a phase-field model to predict precipitate shapes in three-dimension (3D) using experimental characterization as inputs to create virtual precipitate cross-sections for use in morphological comparison with experimental 2D (S)TEM images. Based on the atomic structures and orientation relationships observed in the experiments, the lattice site correspondences between the matrix and the two precipitate phases are derived, which are required for the prediction of shapes of coherent precipitates. Systematic phase-field simulations are then carried out to document the 3D shapes for all possible variants, as well as the corresponding 2D cross-sectional shapes when observed parallel to low-index matrix planes. These 2D cross-sectional shapes are compared with high-angle annular dark-field STEM (HAADF-STEM) images, which demonstrates that the identification of Mn precipitate type is possible by such comparisons. This helps unravel some of the complications encountered when characterizing precipitate microstructures in Mn containing Al-alloys by STEM. Finally, the equilibrium shapes as a function of precipitate size and the effect of interfacial energy anisotropy are investigated.