The mechanism of morphogenesis in a phase-separating concentrated multicomponent alloy

Neural network kinetics for exploring diffusion multiplicity and chemical ordering in compositionally complex materials

Diffusion involving atom transport from one location to another governs many important processes and behaviors such as precipitation and phase nucleation. The inherent chemical complexity in compositionally complex materials poses challenges for modeling atomic diffusion and the resulting formation of chemically ordered structures. Here, we introduce a neural network kinetics (NNK) scheme that predicts and simulates diffusion-induced chemical and structural evolution in complex concentrated chemical environments. The framework is grounded on efficient on-lattice structure and chemistry representation combined with artificial neural networks, enabling precise prediction of all path-dependent migration barriers and individual atom jumps. To demonstrate the method, we study the temperature-dependent local chemical ordering in a refractory NbMoTa alloy and reveal a critical temperature at which the B2 order reaches a maximum. The atomic jump randomness map exhibits the highest diffusion heterogeneity (multiplicity) in the vicinity of this characteristic temperature, which is closely related to chemical ordering and B2 structure formation. The scalable NNK framework provides a promising new avenue to exploring diffusion-related properties in the vast compositional space within which extraordinary properties are hidden.

Rafting and redissolution of γ' phase in Ni-Al alloy under external stress

The volume fraction and rafting degree of the γ'-Ni3Al phase under stress and high temperature are the key characteristics of mechanical properties in Ni-based superalloys, the rafting and redissolution of γ' phase caused by the creep at high temperature damage the morphology and properties of Ni-based superalloys. The phase-field simulation is performed to study the rafting accompany with the redissolution of γ' phase under high temperature and loading stress in Ni-Al alloy, the driving force and kinetics evolution of the γ' rafting were revealed. During the rafting under continuous heating, the elastic energy in the vertical γ channel is different to that of the horizontal γ channel, this difference in elastic energy drives the elements diffusion directionally to form the γ' rafts morphology. With the increased tensile stress, the decrease of specific surface of the γ' phase slows down the redissolution, a higher volume fraction is reserved for the rafted γ' phase. With temperature increases, the interface of γ/γ' phase becomes more diffusional and wider under stress. The results give an insight on the rafting mechanism of γ' phase and the kinetics evolution in Ni-based superalloys under excess temperature.

Vacancy assisted diffusion on single-atom surface alloys

Bimetallic surfaces can exhibit an improved catalytic activity through tailoring the concentration and/or the arrangement of the two metallic components. However, in order to be catalytically active, the active bimetallic surface structure has to be stable under operating conditions. Typically, structural changes in metals occur via vacancy diffusion. Based on the first-principles determination of formation energies and diffusion barriers we have performed kinetic Monte-Carlo (kMC) simulations to analyse the (meta-)stability of PtRu/Ru(0001), AgPd/Pd(111), PtAu/Au(111) and InCu/Cu(100) surface alloys. In a first step, here we consider single-atom alloys together with one vacancy per simulation cell. We will present results of the time evolution of these structures and analyse them in terms of the interaction between the constituents of the bimetallic surface.

Revealing Solute Clusters in Coalescence by Atom Probe Tomography Analysis

Experimentally revealing dynamic evolution and growth behavior of small solute clusters in alloys remains a technical challenge. To date, the coalescence of the solute clusters has seldom been experimentally addressed. To address the challenge, we used atom probe tomography (APT) to access boundary information of solute clusters and identify those in close contact. By systematically investigating the population and size evolution of the clusters in close contact with aging time, we unveiled important information regarding the clusters in coalescence with the exsitu experimental technique. In this work, the maximum separation method was employed to identify clusters in APT datasets of naturally aged Al–Zn–Mg alloy. Coalescence was found to significantly contribute to the growth of small clusters and remained predominant for the formation and growth of large Guinier–Preston II ${\rm \lpar G}{\rm P}_{{\eta }^{\prime}}\rpar$ zones after 3 months aging.

Aging of γ′ Precipitates at 750 °C in the Nickel-Based Superalloy AD730TM: A Thermally or Thermo-Mechanically Controlled Process?

The microstructural stability during aging at 750 °C of the γ/γ′ nickel-based superalloy AD730TM is investigated in this work. Strain-free aging and aging during fatigue tests are conducted, with a focus on the influence of the strain ratio, the maximum applied strain, and the cycle waveform (with or without dwell). Two classical mechanisms of γ′ precipitates aging are identified at 750 °C: the coarsening of small spherical γ′ precipitates via the thermally-activated Ostwald ripening process and the coalescence of at least two precipitates into one. These mechanisms appeared to be concomitant during aging. It has been demonstrated that the coarsening kinetics of γ′ precipitates can be described by a classical Lifshitz-Slyozow-Wagner (LSW) equation. The introduction of a cyclic strain during aging at 750 °C increases the coarsening kinetics by means of changes in the volume diffusion of γ′-forming elements and of constraint misfit effects. More precisely, it is shown that the higher the maximum applied strain and/or the strain rate, the higher the coarsening rates. Finally, dwell-fatigue promotes the activation of the γ′ coalescence at 750 °C.

Size-dependent diffusion controls natural aging in aluminium alloys

A key question in materials science is how fast properties evolve, which relates to the kinetics of phase transformations. In metals, kinetics is primarily connected to diffusion, which for substitutional elements is enabled via mobile atomic-lattice vacancies. In fact, non-equilibrium vacancies are often required for structural changes. Rapid quenching of various important alloys, such as Al- or Mg-alloys, results for example in natural aging, i.e. slight movements of solute atoms in the material, which significantly alter the material properties. In this study we demonstrate a size effect of natural aging in an AlMgSi alloy via atom probe tomography with near-atomic image resolution. We show that non-equilibrium vacancy diffusional processes are generally stopped when the sample size reaches the nanometer scale. This precludes clustering and natural aging in samples below a certain size and has implications towards the study of non-equilibrium diffusion and microstructural changes via microscopy techniques.

Aluminium alloys can naturally age and form microstructural clusters that affect their mechanical properties. Here, the authors show that nanosized samples do not under undergo natural aging because diffusion-controlled clustering processes are inhibited.

The Application of the OPTICS Algorithm to Cluster Analysis in Atom Probe Tomography Data

Atom probe tomography (APT) is a powerful technique to characterize buried three-dimensional nanostructures in a variety of materials. Accurate characterization of those nanometer-scale clusters and precipitates is of great scientific significance to understand the structure-property relationships and the microstructural evolution. The current widely used cluster analysis method, a variant of the density-based spatial clustering of applications with noise algorithm, can only accurately extract clusters of the same atomic density, neglecting several experimental realities, such as density variations within and between clusters and the nonuniformity of the atomic density in the APT reconstruction itself (e.g., crystallographic poles and other field evaporation artifacts). This clustering method relies heavily on multiple input parameters, but ideal selection of those parameters is challenging and oftentimes ambiguous. In this study, we utilize a well-known cluster analysis algorithm, called ordering points to identify the clustering structures, and an automatic cluster extraction algorithm to analyze clusters of varying atomic density in APT data. This approach requires only one free parameter, and other inputs can be estimated or bounded based on physical parameters, such as the lattice parameter and solute concentration. The effectiveness of this method is demonstrated by application to several small-scale model datasets and a real APT dataset obtained from an oxide-dispersion strengthened ferritic alloy specimen.

Nanoscale Phase Evolution during Continuum Decomposition of Fe-Cr Alloys

The continuum decomposition of the Fe-Cr alloys from initial phase separation to steady-state coarsening with concentrations varying from 25 at % Cr and 30 at % Cr to 33 at % Cr aged at 750 K was studied by utilizing three-dimensional phase-field simulations. The dynamic stages of separation of nanoscale Cr-enriched α′ phase were distinguished by the evolution of the volume fraction, particle number density and the average particle radius of the α′ phase. The stage of steady-state coarsening was characterized with an equilibrium volume fraction and decreasing particle number density. The coarsening rate constant by linear fitting of the cube of average radius and aging time shows an increase with the increasing Cr concentration. The time exponents decrease from the growth and coarsening stage to the steady-state coarsening stage and show a dependence on the particles number density at different concentrations. The quantitative evolutions of α′ phase via nucleation growth and spinodal decomposition are theoretically helpful for understanding the microstructure evolution with aging time in Fe-Cr alloys.

In-situ STEM imaging of growth and phase change of individual CuAlX precipitates in Al alloy

Age-hardening in Al alloys has been used for over a century to improve its mechanical properties. However, the lack of direct observation limits our understanding of the dynamic nature of the evolution of nanoprecipitates during age-hardening. Using in-situ (scanning) transmission electron microscopy (S/TEM) while heating an Al-Cu alloy, we were able to follow the growth of individual nanoprecipitates at atomic scale. The heat treatments carried out at 140, 160, 180 and 200 °C reveal a temperature dependence on the kinetics of precipitation and three kinds of interactions of nano-precipitates. These are precipitate-matrix, precipitate-dislocation, and precipitate-precipitate interactions. The diffusion of Cu and Al during these interactions, results in diffusion-controlled individual precipitate growth, an accelerated growth when interactions with dislocations occur and a size dependent precipitate-precipitate interaction: growth and shrinkage. Precipitates can grow and shrink at opposite ends at the same time resulting in an effective displacement. Furthermore, the evolution of the crystal structure within an individual nanoprecipiate, specifically the mechanism of formation of the strengthening phase, θ′, during heat-treatment is elucidated by following the same precipitate through its intermediate stages for the first time using in-situ S/TEM studies.

Liquid-liquid phase separation of freely falling undercooled ternary Fe-Cu-Sn alloy

The active modulation and control of the liquid phase separation for high-temperature metallic systems are still challenging the development of advanced immiscible alloys. Here we present an attempt to manipulate the dynamic process of liquid-liquid phase separation for ternary Fe_47.5Cu_47.5Sn₅ alloy. It was firstly dispersed into numerous droplets with 66 ~ 810 μm diameters and then highly undercooled and rapidly solidified under the containerless microgravity condition inside drop tube. 3-D phase field simulation was performed to explore the kinetic evolution of liquid phase separation. Through regulating the combined effects of undercooling level, phase separation time and Marangoni migration, three types of separation patterns were yielded: monotectic cell, core shell and dispersive structures. The two-layer core-shell morphology proved to be the most stable separation configuration owing to its lowest chemical potential. Whereas the monotectic cell and dispersive microstructures were both thermodynamically metastable transition states because of their highly active energy. The Sn solute partition profiles of Fe-rich core and Cu-rich shell in core-shell structures varied only slightly with cooling rate.

A model Ni-Al-Mo superalloy studied by ultraviolet pulsed-laser-assisted local-electrode atom-probe tomography

This study investigates the effects of the charge-state ratio of evaporated ions on the accuracy of local-electrode atom-probe (LEAP) tomographic compositional and structural analyses, which employs a picosecond ultraviolet pulsed laser. Experimental results demonstrate that the charge-state ratio is a better indicator of the best atom-probe tomography (APT) experimental conditions compared with laser pulse energy. The thermal tails in the mass spectra decrease significantly, and the mass resolving power (m/Δm) increases by 87.5 and 185.7% at full-width half-maximum and full-width tenth-maximum, respectively, as the laser pulse energy is increased from 5 to 30 pJ/pulse. The measured composition of this alloy depends on the charge-state ratio of the evaporated ions, and the most accurate composition is obtained when Ni2+/Ni+ is in the range of 0.3-20. The γ(f.c.c.)/γ'(L12) interface is quantitatively more diffuse when determined from the measured concentration profiles for higher laser pulse energies. Conclusions of the APT compositional and structural analyses utilizing the same suitable charge-state ratio are more comparable than those collected with the same laser pulse energy.

Critical nucleus composition in a multicomponent system

The properties of a critical nucleus are derived using the capillarity theory in the framework of classical nucleation. An analytical solution for the composition of a critical nucleus is given for low supersaturation. The theory is valid for any multicomponent systems. It is found that the deviation in nucleus composition from the equilibrium tie-line is mainly due to the difference in the Hessian of the Gibbs energy of the phases and the magnitude of the deviation in composition from equilibrium is order of the supersaturation. Despite our analysis strictly holds for low supersaturation, this suggests strong deviations near the spinodal line.

A nanoscale co-precipitation approach for property enhancement of Fe-base alloys

Precipitate size and number density are two key factors for tailoring the mechanical behavior of nanoscale precipitate-hardened alloys. However, during thermal aging, the precipitate size and number density change, leading to either poor strength or high strength but significantly reduced ductility. Here we demonstrate, by producing nanoscale co-precipitates in composition-optimized multicomponent precipitation-hardened alloys, a unique approach to improve the stability of the alloy against thermal aging and hence the mechanical properties. Our study provides compelling experimental evidence that these nanoscale co-precipitates consist of a Cu-enriched bcc core partially encased by a B2-ordered Ni(Mn, Al) phase. This co-precipitate provides a more complex obstacle for dislocation movement due to atomic ordering together with interphases, resulting in a high yield strength alloy without sacrificing alloy ductility.

Voltage-pulsed and laser-pulsed atom probe tomography of a multiphase high-strength low-carbon steel

The differences in artifacts associated with voltage-pulsed and laser-pulsed (wavelength = 532 or 355 nm) atom-probe tomographic (APT) analyses of nanoscale precipitation in a high-strength low-carbon steel are assessed using a local-electrode atom-probe tomograph. It is found that the interfacial width of nanoscale Cu precipitates increases with increasing specimen apex temperatures induced by higher laser pulse energies (0.6-2 nJ pulse(-1) at a wavelength of 532 nm). This effect is probably due to surface diffusion of Cu atoms. Increasing the specimen apex temperature by using pulse energies up to 2 nJ pulse(-1) at a wavelength of 532 nm is also found to increase the severity of the local magnification effect for nanoscale M2C metal carbide precipitates, which is indicated by a decrease of the local atomic density inside the carbides from 68 ± 6 nm(-3) (voltage pulsing) to as small as 3.5 ± 0.8 nm(-3). Methods are proposed to solve these problems based on comparisons with the results obtained from voltage-pulsed APT experiments. Essentially, application of the Cu precipitate compositions and local atomic density of M2C metal carbide precipitates measured by voltage-pulsed APT to 532 or 355 nm wavelength laser-pulsed data permits correct quantification of precipitation.

Highly monodisperse core-shell particles created by solid-state reactions

The size distribution of particles, which is essential for many properties of nanomaterials, is equally important for the mechanical behaviour of the class of alloys whose strength derives from a dispersion of nanoscale precipitates. However, particle size distributions formed by solid-state precipitation are generally not well controlled. Here we demonstrate, through the example of core-shell precipitates in Al-Sc-Li alloys, an approach to forming highly monodisperse particle size distributions by simple solid-state reactions. The approach involves the use of a two-step heat treatment, whereby the core formed at high temperature provides a template for growth of the shell at lower temperature. If the core is allowed to grow to a sufficient size, the shell develops in a 'size focusing' regime, where smaller particles grow faster than larger ones. These results suggest strategies for manipulating precipitate size distributions in similar systems through simple variations in thermal treatments.

Radiation-induced melting in coherent X-ray diffractive imaging at the nanoscale

Coherent X-ray diffraction techniques play an increasingly significant role in the imaging of nanoscale structures, ranging from metallic and semiconductor to biological objects. In material science, X-rays are usually considered to be of a low-destructive nature, but under certain conditions they can cause significant radiation damage and heat loading on the samples. The qualitative literature data concerning the tolerance of nanostructured samples to synchrotron radiation in coherent diffraction imaging experiments are scarce. In this work the experimental evidence of a complete destruction of polymer and gold nanosamples by the synchrotron beam is reported in the case of imaging at 1-10 nm spatial resolution. Numerical simulations based on a heat-transfer model demonstrate the high sensitivity of temperature distribution in samples to macroscopic experimental parameters such as the conduction properties of materials, radiation heat transfer and convection. However, for realistic experimental conditions the calculated rates of temperature rise alone cannot explain the melting transitions observed in the nanosamples. Comparison of these results with the literature data allows a specific scenario of the sample destruction in each particular case to be presented, and a strategy for damage reduction to be proposed.

Inherent structures of phase-separating binary mixtures: nucleation, spinodal decomposition, and pattern formation

An energy landscape view of phase separation and nonideality in binary mixtures is developed by exploring their potential energy landscape (PEL) as functions of temperature and composition. We employ molecular dynamics simulations to study a model that promotes structure breaking in the solute-solvent parent binary liquid, at low temperatures. The PEL of the system captures the potential energy distribution of the inherent structures (IS) of the system and is obtained by removing the kinetic energy (including that of intermolecular vibrations). The broader distribution of the inherent structure energy for structure breaking liquid than that of the structure making liquid demonstrates the larger role of entropy in stabilizing the parent liquid of the structure breaking type of binary mixtures. At high temperature, although the parent structure of the structure breaking binary mixture is homogenous, the corresponding inherent structure is found to be always phase separated, with a density pattern that exhibits marked correlation with the energy of its inherent structure. Over a broad range of intermediate inherent structure energy, bicontinuous phase separation prevails with interpenetrating stripes as signatures of spinodal decomposition. At low inherent structure energy, the structure is largely phase separated with one interface where as at high inherent structure energy we find nucleation type growth. Interestingly, at low temperature, the average inherent structure energy (<E{IS}>) exhibits a drop with temperature which signals the onset of crystallization in one of the phases while the other remains in the liquid state. The nonideal composition dependence of viscosity is anticorrelated with average inherent structure energy.

Spatial resolution in atom probe tomography

This article addresses gaps in definitions and a lack of standard measurement techniques to assess the spatial resolution in atom probe tomography. This resolution is known to be anisotropic, being better in-depth than laterally. Generally the presence of atomic planes in the tomographic reconstruction is considered as being a sufficient proof of the quality of the spatial resolution of the instrument. Based on advanced spatial distribution maps, an analysis methodology that interrogates the local neighborhood of the atoms within the tomographic reconstruction, it is shown how both the in-depth and the lateral resolution can be quantified. The influences of the crystallography and the temperature are investigated, and models are proposed to explain the observed results. We demonstrate that the absolute value of resolution is specimen specific.