Phase Separation In Alloys Research Articles

Asymptotic Behavior and Numerical Simulations of a Conservative Phase-Field Model with Two Temperatures

One of the types of problem that has attracted the attention of mathematicians in recent years is the phase field system. The field of application includes materials science, where phenomena such as phase separation in alloys, crystal formation and thermal welding are legion. Among these phase transition systems, the family of conservative systems is very popular with industry. Indeed, minimising losses in production systems is a major issue for their profitability. In this paper, we study the well-posedness of the formulation and the asymptotic behaviour of the solutions, by proving the existence of a finite-dimensional global attractor for a conservative variant of the two-temperature phase field system with homogeneous Neumann boundary conditions. The inclusion of two temperatures in the definition of the enthalpy of the system is a necessity in the case of a non-simple material. In a simple material, once the phase-change temperature has been reached, the temperature of the system remains constant until the material has completely changed state. This is not true in the case of a non-simple material, where an increase in the temperature of the system is observed even after the phase-change temperature has been reached. To conclude the work, we present a method for numerically approximating the solution and carry out some numerical tests.

Modeling phase separation and composition patterning in FeCrAl alloys at neutron irradiation

Possible scenarios of the microstructural evolution of FeCrAl alloys under neutron irradiation are studied by using the phase-field method. The exploited approach is generalized by considering ballistic mixing of atoms, spatial rearrangement of point defects, and dynamics of their sinks (dislocation loops), self-consistently. Stability diagrams manifesting domains of main control parameters (irradiation temperature, damage rate, atomic relocation distance) governing precipitation are obtained. It is shown that depending on irradiation conditions a precipitation of the Cr-rich α′ -phase proceeds by either phase decomposition or composition patterning mechanism. Statistical analysis of precipitation kinetics is provided by studying precipitate number density, mean precipitate size and Chromium content in α′ -phase for a model alloy Fe-30%Cr-5%Al. A locality of point defects distribution with high concentration and dislocation loops growth are discussed. The hardening change is estimated for two possible scenarios of precipitation. Obtained results are verified with experimental observations. This study provides a deep insight into details of microstructural transformation in FeCrAl alloys during neutron irradiation.

Room-temperature pressure-induced phase separation in glassy alloys

Understanding the structural evolution of glass-forming alloys (metallic glasses) under high pressure conditions is important, on one hand, for elucidating their phase stability, and on the other, for manipulating their structure and properties. In this study, we investigate the unique pressure-induced effect leading to the phase separation phenomenon in glassy alloys, the effect which was not observed in the earlier works. By subjecting the system to various levels of external isostatic pressure, we observed the emergence of a distinct phase-separated structure within some glassy alloys. Our results shed light on the underlying mechanisms of phase separation in glassy alloys under extreme pressure conditions, providing valuable information for possible control of their structure and properties. This demonstrates that pressure can be used along or instead of temperature to produce nano-structured polyphase metallic glasses.

Composite anode for fluoride-ion batteries using alloy formation and phase separation in charge and discharge processes

For fluoride-ion batteries, (In + LaF3-based material) anodes are proposed, and reversible alloy formation during charge and discharge is demonstrated. Such formation helps shift the redox potentials of anodes to prevent electrolyte decomposition.

Thermal stability and phase separation of nanoporous high-entropy alloys containing 23 elements

This study fabricated and characterized nanoporous high-entropy alloy (HEA) catalysts containing up to 23 elements using dealloying. The thermal stabilities and phase separation behaviors of these nanostructures were investigated using scanning transmission electron microscopy and X-ray diffraction analyses. The results demonstrated the significant thermal stability of the nanoporous HEAs up to 873 K. A network visualization technique, inspired by social network analysis, was employed using elemental mapping to discern the affinity of the solid solution between different elements in extreme mixing states. The results provided valuable insights into the grouping of “precious,” “refractory,” and “cantor alloy” elements within the HEAs, facilitating the rational design of novel thermally-stable HEAs and catalysts.

Plasticity in irradiated FeCrAl nanopillars investigated using discrete dislocation dynamics

In this paper, we investigate plasticity in irradiated FeCrAl nanopillars using discrete dislocation dynamics simulations (DDD), with comparisons to transmission electron microscopic (TEM) in situ tensile tests of ion- and neutron-irradiated commercial C35M FeCrAl alloy. The effects of irradiation-induced defects, such as a/2<111> and a<100> type loops and composition fluctuations representative of phase separation in irradiated FeCrAl alloys, are investigated separately as well as superposed together in simulations. We explore the effects of defects on the stress-strain behavior, specifically yield strength and hardening response, of FeCrAl nanopillars. Our simulations confirm the widely accepted fact that irradiated alloys exhibit a stress-strain response with higher yield strength as compared to unirradiated alloys. However, our DDD calculations reveal an atypical superposition of the hardening contributions due to composition inhomogeneity and irradiation loops wherein composition inhomogeneity annihilates the hardening due to irradiation loops at small scales. As a result, we observe that the yield strength in irradiated alloys, after taking into consideration the effects of both composition inhomogeneity and irradiation loops, is smaller than the yield strength of the alloys with only irradiation loops and is approximately same for the alloy with composition inhomogeneity alone. This is referred to as “destructive interference” between the hardening contributions due to composition fluctuations and irradiation loops in the paper. We also identify this destructive interference in the superposition in our parallel TEM in situ tensile tests on unirradiated, ion-irradiated, and neutron-irradiated C35M FeCrAl alloy. This destructive interference in the hardening contributions contrasts with the dispersed barrier hardening (DBH) models widely utilized by the experimental community to model the hardening contributions due to different irradiation induced defects. The effects of the loading orientations on the yield strength and hardening are investigated and the mechanisms for the hardening in irradiated FeCrAl alloys are also reported.

Exact special solutions of space–time fractional Cahn–Allen equation by beta and M-truncated derivatives

In this paper, we consider the nonlinear space–time fractional form of Cahn–Allen equation (FCAE) with beta and M-truncated derivatives. Cahn–Allen equation (CAE) is commonly used in many problems of physics and engineering, such as, solidification problems, phase separation in iron alloys and others. We apply the improved [Formula: see text]-expansion method (ITEM). We obtain four types of traveling wave solutions, including, trigonometric, hyperbolic, rational and exponential function solutions. We demonstrate some of the extracted solutions using definitions of the beta (BD) and M-truncated derivatives (MTD) to understand their dynamical behavior. We observe the fractional effects of the aforementioned derivatives on the related physical phenomena up to possible extent.

Phase-field-method-studied mechanism of Cu-rich phase precipitation in Al&lt;sub&gt;&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;CuMnNiFe high-entropy alloy

High-entropy alloys with BCC and FCC coexisting structures usually have excellent comprehensive mechanical properties, and Al element can promote the transformation of Cu-containing high-entropy alloys from FCC structure to BCC structure to obtain the BCC and FCC coexisting structures. In order to illustrate the process of phase separation of high entropy alloys, a low-cost Al-TM transition group element high-entropy alloy is selected in this work. Based on the Chan-Hilliard equation and Allen-Cahn equation, a three-dimensional phase field model of Al&lt;sub&gt;&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;CuMnNiFe high-entropy alloy is established, and the microscopic evolution of the nano-Cu-rich phase of Al&lt;sub&gt;&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;CuMnNiFe high-entropy alloy (&lt;i&gt;x&lt;/i&gt; = 0.4, 0.5, 0.6, 0.7) at 823 K isothermal aging is simulated. The results show that the Al&lt;i&gt;&lt;sub&gt;x&lt;/sub&gt;&lt;/i&gt;CuMnNiFe high-entropy alloy generates two complex core-shell structures upon aging: Cu-rich core/B2&lt;sub&gt;s&lt;/sub&gt; shell and B2&lt;sub&gt;c&lt;/sub&gt; core/FeMn shell, and it is found through discussion and analysis that the formed B2&lt;sub&gt;c&lt;/sub&gt; plays an inhibitory role in the formation of the nano-Cu-rich phase, and that this inhibitory role becomes larger with the increase of Al element. Combining the empirical formula, the curve of yield strength of the Cu-rich phase varying with the aging time is obtained for the Al&lt;sub&gt;&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;CuMnNiFe high-entropy alloy, and the overall yield strength of the high-entropy alloy has a rising-and-then-falling trend with the change of time, and the aging time of the peak yield strength and the alloy system are obtained from the change of the curve, so that the best alloy system and aging time of the high-entropy alloy can provide a reference for aging process.

Interface-Controlled Phase Separation of Liquid Metal-Based Eutectic Ternary Alloys

Interface-Controlled Phase Separation of Liquid Metal-Based Eutectic Ternary Alloys

Dislocation assisted phase separation: A phase field study

In this paper, we show the influence of dislocations on phase separation in alloys with a miscibility gap. Specifically, solute segregation to dislocations leads to spinodal phase separation even in systems with nominal compositions outside the spinodal limit. Further, when spinodal decomposition occurs along the dislocation cores, geometrically, the evolution is like that of a perturbed cylinder. Thus, unless the faster atomic mobility along the dislocation overcomes the bulk diffusion flux, the spinodal is transient and the fluctuations die down as time proceeds due to the bulk flux. We have summarised this interaction between the chemical instability and the cylindrical geometry of the instability in the form of mechanism maps. Our simulations also show the surprising phenomena of phase separation through both (i) nucleation and growth, and, (ii) spinodal decomposition, at the same time – for the case of intersecting dislocations. Finally, the prominent role played by dislocation and solute strain fields in influencing the morphology of precipitates is explored. We show that the range of parameter values chosen by us are of relevance to real alloys, and, some of the microstrucural features and morphologies agree qualitatively with recent Atom Probe Tomography (APT) results in iron based systems.

Insights into propagating surface plasmons in Ag–Cu alloy thin films: Enhancement of spin angular momentum of light

Surface plasmon polaritons (SPPs) can be supported by metal–dielectric interfaces and have been exploited for various applications. Typically, most studies deal with plasmons excited in pure metallic films or homogenous alloy thin films and the understanding of plasmon behavior in films with complex microstructures is limited. In this work, we numerically study the surface plasmons that are supported at the interface of an Ag–Cu alloy film that undergoes spinodal decomposition to produce a two-phase microstructure, when an initially compositionally homogenous alloy film (with composition within spinodal limits) is processed within the miscibility gap. We use phase-field simulated spinodally decomposed microstructures for our optical simulations to study the effect of microstructure on propagating surface plasmons in Ag–Cu alloy films. We demonstrate that the far-field response is governed principally by the composition of the alloy film and is not affected by the microstructural feature size. On the contrary, near-fields are strongly dependent on the microstructure and composition of the films. The origin of inhomogenous fields is demonstrated to be the result of constructive and destructive interference of SPPs. Finally, we demonstrate the enhancement of both transverse and longitudinal components of spin angular momentum in these phase-separated alloy films. The longitudinal components can be enhanced by more than a hundred times in the alloy films as compared to the pure metal films. This study paves the way for exploiting multi-phase alloy thin films for applications in sensing, nanomanipulation, and light modulation.

The role of interfaces in governing processing and properties of stacked hot extrusion of multilayered Al composites with amorphous interlayers

In order to prepare high-strength lightweight components with aluminum alloys and Zr-based amorphous alloys and to avoid brittle fracture, the fabrication of 7075/Zr44Ti11Cu10Ni10Be25/7075 composites by stacked hot extrusion process is proposed in this study. In the supercooled liquid region (SLR) of Zr44Ti11Cu10Ni10Be25 (Vit1b), experiments were conducted with seven different temperature-velocity combinations, the effects of extrusion conditions on the connected interfaces of 7075/Vit1b/7075 composites and the thickness uniformity of Vit1b interlayers were systematically investigated. The results show that: too fast or slow extrusion speed and too high extrusion temperature can lead to crystallization or phase separation of amorphous alloys. The most uniform and continuous Vit1b interlayers can be obtained under the extrusion conditions of heating temperature 430 °C–440 °C and extrusion speed 2 mm/min-3 mm/min. The hardness of Vit1b interlayers increases with the increase of the extrusion temperature while it decreases as the extrusion speed increases. The holes at the interface between amorphous and aluminum alloys are gradually filled by element diffusion, forming discontinuous diffusion areas at the interface, allowing Vit1b and 7075 to be connected.

Segregation kinetics of immiscible alloying elements for understanding phase separation in multicomponent alloys

The diffusion and segregation rates of immiscible alloying elements in Cu-based alloys with one (V) or five refractory metals (V, Nb, Mo, Ta and W) at 300 to 500 °C were investigated for understanding the kinetics of phase separation in multicomponent alloys. At a comparable grain size and a similar influence of grain boundary diffusion (more dominant at 300 °C), the summed rate constant of segregation of the five alloying elements was higher than that of the one element, attributable to the larger entropy change for vacancy formation and atom exchange. The rate constant and time exponent of segregation depended on the melting temperature of the alloying element (W > Ta > Mo > Nb > V), while the activation energy of diffusion, 5.1 to 12.3 kJ/mole (W < Mo < V < Nb < Ta), was inversely related to the delta mixing enthalpy (to Cu) or electronegativity.

Phase Separation in Ge-Rich GeSbTe at Different Length Scales: Melt-Quenched Bulk versus Annealed Thin Films

Integration of the prototypical GeSbTe (GST) ternary alloys, especially on the GeTe-Sb2Te3 tie-line, into non-volatile memory and nanophotonic devices is a relatively mature field of study. Nevertheless, the search for the next best active material with outstanding properties is still ongoing. This search is relatively crucial for embedded memory applications where the crystallization temperature of the active material has to be higher to surpass the soldering threshold. Increasing the Ge content in the GST alloys seems promising due to the associated higher crystallization temperatures. However, homogeneous Ge-rich GST in the as-deposited condition is thermodynamically unstable, and phase separation upon annealing is unavoidable. This phase separation reduces endurance and is detrimental in fully integrating the alloys into active memory devices. This work investigated the phase separation of Ge-rich GST alloys, specifically Ge5Sb2Te3 or GST523, into multiple (meta)stable phases at different length scales in melt-quenched bulk and annealed thin film. Electron microscopy-based techniques were used in our work for chemical mapping and elemental composition analysis to show the formation of multiple phases. Our results show the formation of alloys such as GST213 and GST324 in all length scales. Furthermore, the alloy compositions and the observed phase separation pathways agree to a large extent with theoretical results from density functional theory calculations.

Quantifying microstructural evolution via time-dependent reduced-dimension metrics based on hierarchical n-point polytope functions.

We devise reduced-dimension metrics for effectively measuring the distance between two points (i.e., microstructures) in the microstructure space and quantifying the pathway associated with microstructural evolution, based on a recently introduced set of hierarchical n-point polytope functions P_{n}. The P_{n} functions provide the probability of finding particular n-point configurations associated with regular n polytopes in the material system, and are a special subset of the standard n-point correlation functions S_{n} that effectively decompose the structural features in the system into regular polyhedral basis with different symmetries. The nth order metric Ω_{n} is defined as the L_{1} norm associated with the P_{n} functions of two distinct microstructures. By choosing a reference initial state (i.e., a microstructure associated with t_{0}=0), the Ω_{n}(t) metrics quantify the evolution of distinct polyhedral symmetries and can in principle capture emerging polyhedral symmetries that are not apparent in the initial state. To demonstrate their utility, we apply the Ω_{n} metrics to a two-dimensional binary system undergoing spinodal decomposition to extract the phase separation dynamics via the temporal scaling behavior of the corresponding Ω_{n}(t), which reveals mechanisms governing the evolution. Moreover, we employ Ω_{n}(t) to analyze pattern evolution during vapor deposition of phase-separating alloy films with different surface contact angles, which exhibit rich evolution dynamics including both unstable and oscillating patterns. The Ω_{n} metrics have potential applications in establishing quantitative processing-structure-property relationships, as well as real-time processing control and optimization of complex heterogeneous material systems.

In situ de-wetting of liquid–solid interface to fabricate spherical Ag@Ni immiscible alloys

Spherical Ag@Ni immiscible alloy powders were successfully fabricated combining in situ de-wetting of metal droplets from a metalloid solid medium with phase separation of immiscible alloys. The effects of atom ratio and temperature on morphology, structure, and phase separation were investigated. The spherical morphology of alloy powders confirmed the de-wetting of the liquid–solid interface between the liquid Ni–Ag immiscible alloy and the solid alumina powder medium. The Ni-rich phase was scattered in the Ag-rich phase matrix at 1673 K while the spherical Ni-core at the center was surrounded by a ring-shaped shell of Ag at the outer layer with an egg-type structure at 1753 K. The egg-type microstructure of the Ni–Ag particle resulted from the liquid–liquid immiscible phase separation. Such spherical Ag@Ni alloy powders with an egg-type microstructure have a good combination of a high strength Ni-rich phase core and a high electric and thermal conductivity Ag-rich phase shell with many potential advanced applications in electronic packaging.

Single atom alloys vs. phase separated alloys in Cu, Ag, and Au atoms with Ni(111) and Ni, Pd, and Pt atoms with Cu(111): a theoretical exploration.

A single-atom alloy (SAA) consisting of an abundant metal host and a precious metal guest is a promising catalyst to reduce the cost without a loss of activity. DFT calculations of Ni- and Cu-based alloys nX/M(111) (X = Cu, Ag, or Au for M = Ni; X = Ni, Pd, or Pt for M = Cu; n = 1-4) reveal that a phase-separated alloy (PSA) is produced by Cu atoms with Ni(111) but an SAA is produced by Au atoms with Ni(111) and Pd and Pt atoms with Cu(111). In the Ni(111)-based Ag alloy and Cu(111)-based Ni alloy, the relative stabilities of the SAA and PSA depend on coverages of Ag on Ni(111) and Ni on Cu(111). The interaction energy (Eint) between the Xn cluster and M(111) host is larger than that between one X atom and the M(111) host, because the Xn cluster forms more bonding interactions with the M(111) host than does one X atom. When going from one X atom to the X4 cluster, the Eint values of Au and Pt clusters respectively with Ni(111) and Cu(111) increase to a lesser extent than those of Cu and Ni clusters respectively with Ni(111) and Cu(111). Consequently, Au and Pt atoms tend to form SAAs respectively with Ni(111) and Cu(111) hosts compared to Cu and Ni atoms. This trend in the Eint value is determined by the valence orbital energies of the X atom and the Xn cluster. Cu atoms in nCu/Ni(111) have a slightly positive charge but Ag atoms in nAg/Ni(111), Au atoms in nAu/Ni(111), and Ni, Pd, and Pt atoms in nX/Cu(111) (X = Ni, Pd, or Pt) have a negative charge. The negative charge increases in the order Ag < Au in nX/Ni(111) and Ni < Pd < Pt in nX/Cu(111). The Fermi level decreases in energy in the order nCu/Ni(111) ≥ Ni(111) > nAg/Ni(111) > nAu/Ni(111) and Cu(111) ≥ nNi/Cu(111) > nPd/Cu(111) > nPt/Cu(111). The d valence band center decreases in energy in almost the same order. The CO adsorption energy decreases in the order Ni(111) ∼ nCu/Ni(111) > nAg/Ni(111) ∼ nAu/Ni(111) and Cu(111) > nNi/Cu(111) > nPd/Cu(111) > nPt/Cu(111). These properties are explained based on the electronic structures.

Effect of Zr addition on metastable Liquid-Liquid Phase Separation of Cu-Fe alloys

The liquid-liquid phase separation (LLPS) behavior was investigated in Cu-Fe alloys that consisted of 60 wt % or 80 wt % Cu and balance iron, without or with addition of 1 wt% Zr. Both Zr-free alloys clearly showed LLPS at metastable spinodal temperatures prior to γ-Fe nucleation, whereas Zr-added showed γ-Fe phase evolution without LLPS. Addition of Zr was highly effective to activate γ-Fe nucleation by decreasing the mixing enthalpy and also accelerating heterogeneous nucleation. A combination of thermal instrumental analysis and classical nucleation theory yielded an effective assessment made of LLPS behavior below the liquidus temperature of Cu-Fe alloys. Furthermore, it was possible to control the solidification mechanism of Cu-Fe alloy by zirconium addition.

Achieving fast hydrogenation by hydrogen-induced phase separation in Mg-based amorphous alloys

Mg-based amorphous alloys are one of the potential hydrogen storage materials. The challenges which are blocking application of such alloys involve unfavorable crystallization of amorphous phase in hydrogenation and dehydrogenation and sluggish low-temperature de/hydrogenation kinetics. To solve those challenges, the Mg60RExNi30−xCu10 (RE=La and Ce; x = 5, 7.5, 10 and 15) amorphous alloys were prepared by melt spinning and the structural transformation of amorphous phase and its correlation to hydrogenation kinetics has been investigated. It is observed that all the amorphous powders are able to absorb more than 3.0 wt%-H at 130 °C under 4.5 MPa-H2, and the hydrogen absorption rate of the Mg60RE10Ni20Cu10 amorphous alloys is much faster than other alloys by forming a dual amorphous phase structure during hydrogenation. XRD characterization of Mg60Ce10Ni20Cu10 hydrides proved that such dual amorphous phase structure is resulted by hydrogen-induced amorphous phase separation. According to EDX results, the dual amorphous phase structure consists of Ce-rich and Ni-Cu-rich domains with a size of about 5 nm which gradually form by element aggregation during hydrogen absorption. Meanwhile, it is also confirmed that the element aggregation is the precursor of hydrogen-induced crystallization as crystallization is observed in the Ni–Cu-rich domain. It is verified that the hydrogen-induced amorphous phase separation of the Mg-based amorphous alloys is tunable and can be used for obtaining superior hydrogenation performance. The hydrogen-induced structural evolution revealed in this work might inspire the development of new Mg-based hydrogen storage amorphous alloys.

Multiphysics approaches for modeling nanostructural evolution during physical vapor deposition of phase-separating alloy films

Physical vapor deposition of phase-separating alloy films yields a rich variety of distinct self-assembled nanostructures depending on the deposition rate and temperature. However, the role of grain boundaries, elastic imhomogeneity, and anisotropy, and surface tension, in the formation of such nanostructures is currently not well understood. Here, we employ a phase-field approach that couples the multiphysics of elemental diffusion, elastic misfit and anisotropy, surface tension, and grain boundaries with processing parameters, namely deposition rate and temperature, to investigate phase separation and grain boundary evolution in binary alloy films. We develop phase-field deposition models of increasing complexity to isolate and analyze the influence of processing parameters on nanostructural transitions in vapor co-deposited films. While it is found that such transitions are primarily guided by a minimization of total free energy, our simulation-based insights strongly indicate the phenomena of nanostructure selection at faster deposition rates. It is anticipated that the insights gained from this study will provide the much-required knowledgebase for establishing nanostructure-level control in the physical vapor deposition of alloy films.