Early Stage Of Spinodal Decomposition Research Articles

Fine-Tuning Melt Pools and Microstructures: Taming Cracks in Powder Bed Fusion—Laser Beam of a non-weldable Ni-base Superalloy

Powder Bed Fusion – Laser Beam (PBF-LB) of high γ’ strengthened Ni-base superalloys, such as CM247LC, is of great interest for high temperature applications in gas turbines. However, PBF-LB of CM247LC is challenging due to the high cracking susceptibility during PBF-LB processing (solidification cracking) and heat treatment (strain age cracking, mostly caused by residual stresses). This study focuses on understanding the impact of process parameters on microstructure, residual stresses and solidification cracking. Laser power (P), speed (v) and hatch spacing (h) were varied while the layer thickness (t) was fixed. The melt pool size and shape were found to be key factors in minimizing solidification cracking. Narrower and shallower melt pools, achieved using a low line energy density (LED = P/v ≤ 0.1 J/mm), gave low crack densities (0.7 mm/mm2). A tight hatch spacing (h = 0.03 mm) resulted in reduced lack of fusion porosity. Electron backscatter diffraction investigations revealed that parameters giving finer microstructure with 〈100〉 crystallographic texture had low crack densities provided they were processed with a low LED. Atom probe tomography elucidated early stages of spinodal decomposition in the as-built condition, where Cr and Al cluster separately. The extent of spinodal decomposition was found to be affected by the LED and the hatch spacing. Samples with low LED and small hatch spacing showed higher degrees of spinodal decomposition. X-ray diffraction residual stress investigations revealed that the residual stress is proportional to the volumetric energy density (VED = P/(v. h. t)). Although low residual stresses can be achieved by using low VED, there is a high risk of lack of fusion. Hence, other parameters such as modified scan strategy, build plate pre-heating and pulsed laser mode, must be further explored to minimize the residual stresses to reduce the strain age cracking susceptibility.

Exploration of spinodal decomposition in multi-principal element alloys (MPEAs) using CALPHAD modeling

Researchers attributed the orderly arranged nanoscale phases observed in many multi-principal element alloys (MPEAs) to spinodal/spinodal-mediated phase transformation pathways. However, spinodal decomposition is not well understood in multicomponent systems. Although the theoretical background is available, CALPHAD databases were not used to explore the miscibility gap in MPEAs. In this work, we develop a CALPHAD framework utilizing the Hessian of free energy to study the stability of solid solutions in MPEAs. In particular, we utilize the geometry of higher dimensional Gibbs simplex in conjunction with the Hessian to calculate concentration modulations in early stages of spinodal decomposition. We apply this framework to a diverse set of multi-phase MPEAs that have been studied in the literature including TiZrNbTa (BCC/BCC), Fe15Co15Ni20Mn20Cu30 (FCC/FCC), Al0.5NbTa0.8Ti1.5V0.2Zr (BCC/B2), AlCo0.4Cr0.6FeNi (BCC/B2) and Al0.5Cr0.9FeNi2.5V0.2 (FCC/L12). We show that the MPEA systems are unstable only to certain concentration modulations which could be further explored to design microstructurally engineered alloys.

Spinodal strain glass in Mn-Cu alloys

Strain glasses (STGs), which are characterized by nanodomains of martensite formed via a strain glass transition, can produce many unusual properties not possessed by normal martensitic alloys. These nanodomains originate from the formation of short-range strain ordering by the disruption of otherwise long-range strain ordering or normal martensitic transformation through sufficient atomic/nanoscale random stress/strain field. So far the atomic/nanoscale randomness is known to be from either point defects, dislocations, or nanoprecipitates. Here we report a spinodal STG alloy Mn60Cu40, which stems from nanoscale composition modulations (5-20 nm) formed in the early stage of spinodal decomposition, which is identified by STEM-EDS and HRTEM. For short-time (<50 min) aged sample, a strain glass transition was identified by its typical signatures including invariance of global face-centered cubic (fcc) structure with cooling, frequency dependence of elastic moduli at STG transition temperature (Tg) following a Vogel-Fulcher relationship, non-ergodicity as manifested by zero-field-colling/field-cooling curves, and the formation of martensitic face-centered tetragonal (fct) nanodomains. For long-time (≥50 min) aged sample, a normal martensitic transition from fcc to fct appears with cooling, being consistent with literatures. As the result, a temperature vs. aging-time phase diagram of spinodal STG was established and shows a crossover from STG to martensite above a critical aging time. The spinodal STG exhibits a non-magnetic Elinvar behavior, i.e., nearly constant elastic modulus over a wide temperature range, together with high-damping capacity. We anticipate that the spinodal STG and associated novel properties may also be found in other metallic and ceramic spinodal materials.

Structural origin of the weak germanate anomaly in lead germanate glass properties

AbstractBinary PbO–GeO2 glasses have been studied in detail from 5 to 75 mol% PbO using high‐resolution neutron diffraction, high‐energy X‐ray diffraction, 207‐Pb NMR, pycnometry, and thermal analysis. The Ge–O coordination number displays a broad maximum nGeO = 4.14(3) close to 27 mol% PbO. This is smaller than the maximum nGeO = 4.3 reported in CaO–GeO2 glasses but occurs at a similar composition. This structural behavior appears to explain the relatively weak germanate anomaly manifest in lead germanate glasses, for example as a maximum in the measured atom number density and a plateau in the glass transition temperatures. The structural role of Pb(II) is complex. On the one hand, short covalent Pb–O bonds and small Pb–O coordination numbers of ∼3 to 4 indicate glass network former character for Pb(II), associated with a stereochemically active electron lone pair. On the other hand, the presence of some GeO5 or GeO6 units, in addition to the majority GeO4 tetrahedral species, indicates some modifier character of Pb(II) at low PbO contents, giving rise to the observed weak germanate anomaly, as well as elongation and enhanced ionicity of the Pb–O bonds. Overall, the observed structural behavior of Pb(II) in lead germanate glasses appears as intermediate between that observed in lead silicate and lead borate glasses. Despite rapid quenching, at low PbO contents, the glasses studied exhibited nanoscale heterogeneity, evidenced by small‐angle X‐ray scattering consistent with the early stages of spinodal decomposition.

Interplay between Kinetics and Dynamics of Liquid-Liquid Phase Separation in a Protein Solution Revealed by Coherent X-ray Spectroscopy.

Microscopic dynamics of complex fluids in the early stage of spinodal decomposition (SD) is strongly intertwined with the kinetics of structural evolution, which makes a quantitative characterization challenging. In this work, we use X-ray photon correlation spectroscopy to study the dynamics and kinetics of a protein solution undergoing liquid-liquid phase separation (LLPS). We demonstrate that in the early stage of SD, the kinetics relaxation is up to 40 times slower than the dynamics and thus can be decoupled. The microscopic dynamics can be well described by hyper-diffusive ballistic motions with a relaxation time exponentially growing with time in the early stage followed by a power-law increase with fluctuations. These experimental results are further supported by simulations based on the Cahn-Hilliard equation. The established framework is applicable to other condensed matter and biological systems undergoing phase transitions and may also inspire further theoretical work.

Existence and Continuity of Inertial Manifolds for the Hyperbolic Relaxation of the Viscous Cahn–Hilliard Equation

We consider the hyperbolic relaxation of the viscous Cahn–Hilliard equation 0.1 $$\begin{aligned} \varepsilon \phi _{tt}+ \phi _t-\Delta (\delta \phi _t-\Delta \phi + g(\phi ))=0, \end{aligned}$$ in a bounded domain of $${\mathbb R}^d$$ with smooth boundary when subject to Neumann boundary conditions, and on rectangular domains when subject to periodic boundary conditions. The space dimension is $$d=1,$$ 2 or 3, but it is required $$\delta =\varepsilon =0$$ when $$d=2$$ or 3; $$\delta $$ being the viscosity parameter. The constant $$\varepsilon \in (0,1]$$ is a relaxation parameter, $$\phi $$ is the order parameter and $$g:{\mathbb R}\rightarrow {\mathbb R}$$ is a nonlinear function. This equation models the early stages of spinodal decomposition in certain glasses. Assuming that $$\varepsilon $$ is dominated from above by $$\delta $$ when $$d=2$$ or 3, we construct a family of exponential attractors for Eq. (0.1) which converges as $$(\varepsilon ,\delta )$$ goes to $$(0,\delta _0),$$ for any $$\delta _0\in [0,1],$$ with respect to a metric that depends only on $$\varepsilon $$ , improving previous results where this metric also depends on $$\delta $$ . Then we introduce two change of variables and corresponding problems, in the case of rectangular domains and $$d=1$$ or 2 only. First, we set $$\tilde{\phi }(t)=\phi (\sqrt{\varepsilon } t)$$ and we rewrite Eq. (0.1) in the variables $$(\tilde{\phi },\tilde{\phi }_t).$$ We show that there exist an integer n, independent of both $$\varepsilon $$ and $$\delta $$ , a value $$0<\tilde{\varepsilon }_0(n)\le 1$$ and an inertial manifold of dimension n, for either $$\varepsilon \in (0,\tilde{\varepsilon }_0]$$ and $$\delta =2\sqrt{\varepsilon }$$ or $$\varepsilon \in (0,\tilde{\varepsilon }_0]$$ and $$\delta \in [0,3\varepsilon ]$$ . Then, we prove the existence of an inertial manifold of dimension that depends on $$\varepsilon $$ , but is independent of $$\delta $$ and $$\eta $$ , for any fixed $$\varepsilon \in (0,(\eta -2)^2]$$ and every $$\delta \in [\varepsilon ,(2-\eta )\sqrt{\varepsilon }]$$ , for an arbitrary $$\eta \in (1,2)$$ . Next, we show the existence of an inertial manifold of dimension that depends on $$\varepsilon $$ and $$\eta $$ , but is independent of $$\delta $$ , for any fixed $$\varepsilon \in (0,\frac{1}{(2+\eta )^2}]$$ and every $$\delta \in [(2+\eta )\sqrt{\varepsilon },1]$$ , where $$\eta >0$$ is arbitrary chosen. Moreover, we show the continuity of the inertial manifolds at $$\delta =\delta _0,$$ for any $$\delta _0\in [0,(2-\eta )\sqrt{\varepsilon }]\cup [(2+\eta )\sqrt{\varepsilon },1]$$ . Second, we set $$\phi _t=-(2\varepsilon )^{-1}(I-\delta \Delta )\phi +\varepsilon ^{-1/2}v$$ and we rewrite Eq. (0.1) in the variables $$(\phi ,v)$$ . Then, we prove the existence of an inertial manifold of dimension that depends on $$\delta $$ , but is independent of $$\varepsilon ,$$ for any fixed $$\delta \in (0,1]$$ and every $$\varepsilon \in (0,\frac{3}{16}\delta ^2]$$ . In addition, we prove the convergence of the inertial manifolds when $$\varepsilon \rightarrow 0^+$$ .

Quantitative Evaluation of Spinodal Decomposition in Thermally Aged Binary Fe-35 At.% Cr Alloys by Correlative APT and SANS Analyses

In this work, spinodal decomposition (SD) in Fe-35 at.% Cr alloy is quantified by correlatively combining two complimentary techniques namely, Atom Probe Tomography (APT) and Small Angle Neutron Scattering (SANS). In order to overcome the uncertainty often encountered in quantification of the characteristic SD parameters (wavelength λSD , amplitude A and volume fraction of Cr-rich α/ -phase Φ), we adopt the following: (i) utilize the unique specific attribute of a technique suitable for evaluating any particular SD parameter; (ii) incorporate such reliably extracted parameter as input for evaluating other parameters wherever applicable. This novel correlative approach builds on each other’s strength and provides improved accuracy. λSD is determined independently from APT and SANS analyses. For evaluation of A and Φ, APT analysis utilizes the value of λSD determined from SANS, whereas the phase compositions evaluated by APT are utilized in SANS analysis. With progressive phase separation, α/α/ compositional difference increases continually (from 19.8% after 10 h to 48.2% after 500 h) along with concomitant contraction of the interface (from 1.92 nm to 1.55 nm), underscoring the distinctive characteristics of SD process. Signature of rarely observed early stage of phase separation in the form of a dense population (9.78x1024 /m3 ) of extremely small (0.67 nm radius) Cr-rich nanoclusters is registered after aging only for 1 h. In addition, temporal evolution of λSD clearly distinguishes early stage of SD (time exponent of 0.15) from the coarsening stage (time exponent of 0.29, 120 h onwards).

Phase-field simulation of spinodal phase separation in the Na2O-SiO2 glasses

The phase-field method was used for the kinetic simulation of the spinodal phase separation of glasses in the Na2O-SiO2 system. The miscibility gap and spinodal curve were calculated based on the previous interaction parameters of the liquid phase. The kinetic simulations showed that the resultant morphology depended on the initial concentration and the temperature. In the early stages of spinodal decomposition, the interconnected structure developed continuously and in the later stages began to coarsen. During the coarsening stage, the evolution of morphology of the microstructures could result in the discrete spherical particles as well as the interconnected structure, depending on the heat treatment condition. To analyze the phase separation rate, the amplification factors for the initial concentrations were calculated as a function of temperature and could explain the morphology developed from the present simulation. Also, the present work could explain the evolution of experimental morphologies available in the literature reasonably.

The Effect of Nonisothermality on the Early Stages of Spinodal Decomposition

A nonisothertmal model of spinodal decomposition is proposed for a binary system described by the Ginzburg–Landau energy. The initial stages of spinodal decomposition are investigated for a system of simultaneous equations describing the impurity and temperature redistribution. The dispersion equation and the instability growth rate of spinodal structures are obtained. The temperature dependence of the growth rate and the wave number corresponding to the maximum instability is found. The observed difference in the dispersion relations of isothermal and nonisothermal models shows that a criterion for the effect of temperature fluctuations on the spinodal decomposition is given by a dimensionless parameter Γ; for large values of Γ (Γ ≥ 1000), temperature fluctuations in the form of noise are certainly insufficient for spinodal decomposition due to a change in the dispersion structure of the equations, which suggests the need to take into account the nonisothermal behavior of the system.

Distinctive phase separation dynamics of polymer blends: roles of Janus nanoparticles.

Janus nanoparticles (JPs), which are anisotropic nanoparticles with at least two opposite surface regions, have been demonstrated as highly efficient compatibilizers for polymer blends. However, there are still a number of open questions concerning the mechanism behind the influence of JPs on the phase separation dynamics of polymer blends. Herein, we report a counter-intuitive feature of JPs concerning their roles during spinodal decomposition (SD); that is, they promote the decomposition of unlike polymers in the early stage of SD but retard it during the late stage. This is in remarkable contrast to traditional compatibilizers such as block copolymers and homogenous nanoparticles, which impede phase separation during both stages. We further demonstrate that the unique promoting effect of JPs at early times is due to the formation of microphase-separated homopolymer-rich regions in the vicinity of opposite JP surface regions. Our findings are expected to have important implications for the phase separation behavior of JP-compatibilized polymer blends, whose morphologies and performance could be controlled by tuning the interactions between the constituent polymers and JP-based compatibilizers.

Análisis de la descomposición espinodal en aleaciones Fe-32 y 40 %at. Cr utilizando el método de campo de fases basado en las ecuaciones lineal y no lineal de Cahn y Hilliard

La descomposición espinodal se estudió durante el envejecido de aleaciones Fe-Cr mediante la solución numérica de las ecuaciones diferenciales parciales lineal y no linear de Cahn y Hilliard usando el método de diferencias finito explícito. Los resultados de la simulación numérica permitieron describir apropiadamente el mecanismo, morfología y cinética de la descomposición de fases durante el envejecido isotérmico de estas aleaciones. La cinética de crecimiento de la descomposición de fases ocurrió muy lentamente durante las primeras etapas de envejecido, y se incrementó considerablemente con el tiempo de envejecido. La ecuación no lineal parece ser más apropiada para describir las primeras etapas de la descomposición espinodal que la ecuación lineal.

A high-resolution analytical scanning transmission electron microscopy study of the early stages of spinodal decomposition in binary Fe–Cr

Spinodal decomposition (SD) is an important phenomenon in materials science and engineering. For example, it is considered to be responsible for the 475°C embrittlement of stainless steels comprising the bcc (ferrite) or bct (martensite) phases. Structural characterization of the evolving minute nano-scale concentration fluctuations during SD in the Fe–Cr system is, however, a notable challenge, and has mainly been considered accessible via atom probe tomography (APT) and small-angle neutron scattering. The standard tool for nanostructure characterization, viz. transmission electron microscopy (TEM), has only been successfully applied to late stages of SD when embrittlement is already severe. However, we here demonstrate that the structural evolution in the early stages of SD in binary Fe–Cr, and alloys based on the binary, are accessible via analytical scanning TEM. An Fe–36wt% Cr alloy aged at 500°C for 1, 10 and 100h is investigated using an aberration-corrected microscope and it is found that highly coherent and interconnected Cr-rich regions develop. The wavelength of decomposition is rather insensitive to the sample thickness and it is quantified to 2, 3 and 6nm after ageing for 1, 10 and 100h, which is in reasonable agreement with prior APT analysis. The concentration amplitude is more sensitive to the sample thickness and acquisition parameters but the TEM analysis is in good agreement with APT analysis for the longest ageing time. These findings open up for combinatorial TEM studies where both local crystallography and chemistry is required.

Imaging chemical concentration pattern and early stages of spinodal decomposition in the AgxNa1−xBr system by scanning force microscopy

In quasi binary systems like AgBr–NaBr the demixing from the homogeneous high temperature phase into separated phases is a complex process that depends on the ageing temperature as well as on the quench rate. Spinodal decomposition and nucleation processes can be distinguished which lead, however, to the same final equilibrium state. Using frequency modulated scanning force microscopy we aimed to distinguish the demixed phases and their morphologies on a nm-scale at room temperature for samples with different concentration. While no contrast between the different phases are observed in the usual topographic mode, a modified evaluation of Kelvin experiments allows the distinction of silver- and sodium enriched phases. Moreover, direct evidence is found for concentration fluctuations which are characteristic for spinodal decomposition.

Early stages of spinodal decomposition in Fe–Cr resolved by in-situ small-angle neutron scattering

In-situ, time-resolved small-angle neutron scattering (SANS) investigations of the early stages of the spinodal decomposition process in Fe–35Cr were performed at 773 and 798 K. The kinetics of the decomposition, both in terms of characteristic distance and peak intensity, followed a power-law behaviour from the start of the heat treatment (a′ = 0.10–0.11 and a″ = 0.67–0.86). Furthermore, the method allows tracking of the high–Q slope, which is a sensitive measure of the early stages of decomposition. Ex-situ SANS and atom probe tomography were used to verify the results from the in-situ investigations. Finally, the in-situ measurement of the evolution of the characteristic distance at 773 K was compared with the predictions from the Cahn-Hilliard-Cook model, which showed good agreement with the experimental data (a′ = 0.12–0.20 depending on the assumed mobility).

溶体化処理および液体急冷した Cu-15Ni-8Sn 合金のスピノーダル分解に及ぼす初期組織の影響

We investigate early stages of spinodal decomposition in a melt-spun Cu-15Ni-8Sn alloy (melt-spun samples) by X-ray diffraction (XRD) analysis, transmission electron microscopy (TEM) and electron diffraction analysis through comparison against a quenched alloy of the same composition (quenched samples). In XRD measurements, no sidebands of (200) planes are found in the melt-spun sample after aging at 350℃ for 120 min, whereas they are found in the quenched sample after a heat treatment at 350℃ for 60 min. TEM observations of a quenched sample after aging at 350℃ for 60 min indicate the presence of a modulated structure (λ=5-10 nm) in the matrix, whereas those of a melt-spun sample after the same heat treatment also indicate the presence of a modulated structure (λ: too small to measure). Electron diffraction patterns reveal satellite structures in both samples, although with superlattice reflections from ordering phases visible in the quenched sample. These differences are presumably due to a difference in the size of clusters present in their respective quenched states; in melt-spun samples, cluster size was much smaller as a result of a high cooling rate (≈8×105℃/s).

Effects of Initial States on the Spinodal Decomposition of Quenched and Melt-Spun Cu-15Ni-8Sn Alloy

We investigate early stages of spinodal decomposition in a melt-spun Cu-15Ni-8Sn alloy (melt-spun samples) by X-ray diffraction (XRD) analysis, transmission electron microscopy (TEM) and electron diffraction analysis through comparison against a non-melt-spun alloy of the same composition (quenched samples). In XRD measurements, no sidebands of (200) planes are found in the melt-spun sample after aging at 350°C for 120 min, whereas they are found in the quenched sample after a heat treatment at 350°C for 60 min. TEM observations of a quenched sample after aging at 350°C for 60 min indicate the presence of a modulated structure (λ = 5–10 nm) in the matrix, whereas those of a melt-spun sample after the same heat treatment also indicate the presence of a modulated structure (λ: too small to measure). Electron diffraction patterns reveal satellite structures in both samples, although with superlattice reflections from ordering phases visible in the quenched sample. These differences are presumably due to a difference in the size of clusters present in their respective quenched states; in melt-spun samples, cluster size was much smaller as a result of a high cooling rate (≈8 × 105°C/s).

Mesoscopic Dynamics of Laser-induced Phase Separation in Water and 2-Butoxyethanol Mixtures Revealed by Nanosecond Time-resolved Light Scattering

Abstract For the first time, we have succeeded in observing the dynamics of laser-induced phase separation in a water/2-butoxyethanol mixture by applying nanosecond time-resolved light scattering on a submicron scale. The scattering revealed that the domain size of the mixture during phase separation was almost constant at 300 nm for 10 µs after a laser T-jump, and the light scattering intensity increased exponentially with time. The results clearly indicate that the early stage of spinodal decomposition described by Cahn–Hilliard theory occurred in the mixture for 10 µs.

Phase separation in Zr56-xGdxCo28Al16 metallic glasses (0 ⩽ x ⩽ 20)

The influence of Gd addition on the microstructure of Zr56Co28Al16 metallic glasses was investigated for the exchange of Zr by up to 20 at.% Gd. Due to the large positive enthalpy of mixing between Zr and Gd, liquid–liquid phase separation occurs during rapid quenching of the melt. For a low concentration of Gd (x=2 at.%), a homogeneous amorphous structure is obtained for the as-quenched state. Early stages of spinodal decomposition are observed in the as-quenched state of the glasses with x=5 and 10 at.% Gd. Gd-enriched clusters 4–7nm in size are formed, as shown by atom probe tomography (APT). Annealing below the crystallization temperature Tx leads to an increase in the amplitude of compositional fluctuations and the analysis of the spatial atomic distribution by APT provides direct evidence of the spinodal character of the decomposition by uphill diffusion of Gd into the clusters. For higher Gd content (x=15 and 20 at.%), a coarsened microstructure of the phase-separated glass is obtained due to growth and coalescence while quenching the melt. The microstructure formation is essentially determined by the thermodynamic properties of the metastable undercooled liquid.

Quantitative Evaluation of Spinodal Decomposition in Fe-Cr by Atom Probe Tomography and Radial Distribution Function Analysis

Nanostructure evolution during low temperature aging of three binary Fe-Cr alloys has been investigated by atom probe tomography. A new method based on radial distribution function (RDF) analysis to quantify the composition wavelength and amplitude of spinodal decomposition is proposed. Wavelengths estimated from RDF have a power-law type evolution and are in reasonable agreement with wavelengths estimated using other more conventional methods. The main advantages of the proposed method are the following: (1) Selecting a box size to generate the frequency diagram, which is known to generate bias in the evaluation of amplitude, is avoided. (2) The determination of amplitude is systematic and utilizes the wavelength evaluated first to subsequently evaluate the amplitude. (3) The RDF is capable of representing very subtle decomposition, which is not possible using frequency diagrams, and thus a proposed theoretical treatment of the experimental RDF creates the possibility to determine amplitude at very early stages of spinodal decomposition.

Phase separation in thick InGaN layers – A quantitative, nanoscale study by pulsed laser atom probe tomography

Pulsed laser atom probe tomography was employed to study 300nm thick In0.25Ga0.75N layers grown on a GaN buffer layer. The unique three-dimensional data provided by atom probe tomography revealed a complex microstructure in the InGaN formed by indium-rich columns and plates adjacent to strongly indium-depleted regions. This complex indium-related domain structure is likely to represent the early stages of spinodal decomposition occurring during layer growth. The interface with the buffer layer is characterized by the absence of this microstructure and a generally more homogeneous indium distribution. Also, a significantly reduced InN mole fraction was found in that region. Both are believed to be a result of the interfacial misfit strain, which suppresses phase separation and impedes indium incorporation during growth, which is termed the compositional pulling effect.