Model Of Spinodal Decomposition Research Articles

Anisotropy in spinodal-like dynamics of unknown water at ice V–water interface

Experimentally demonstrating the existence of waters with local structures unlike that of common water is critical for understanding both the origin of the mysterious properties of water and liquid polymorphism in single component liquids. At the interfaces between water and ices Ih, III, and VI grown/melted under pressure, we previously discovered low- and high-density unknown waters, that are immiscible with the surrounding water. Here, we show, by in-situ optical microscopy, that an unknown water appears at the ice V–water interface via spinodal-like dynamics. The dewetting dynamics of the unknown water indicate that its characteristic velocity is ~ 90 m/s. The time evolution of the characteristic length of the spinodal-like undulation suggests that the dynamics may be described by a common model for spinodal decomposition of an immiscible liquid mixture. Spinodal-like dewetting dynamics of the unknown water transiently showed anisotropy, implying the property of a liquid crystal.

A morphological study of bicontinuous concentric lamellar silica synthesized at atmospheric pressure and its application as an internal micro-reflector in dye-sensitized solar cells.

KCC-1, a nanostructured silica material with a bicontinuous concentric lamellar (bcl) morphology, provides plenty of functional characteristics, such as an open channel structure, excellent accessibility, and a large surface area. Although bcl silica exhibits various superior properties, studies on its morphology and its application in dye-sensitized solar cells (DSSCs) are still limited. Therefore, this work aims to study the influence of the synthesis time on the morphology of bcl silica. Moreover, we used the synthesized bcl silica as internal micro-reflectors in DSSCs. The bcl silica was synthesized using the reflux method by varying synthesis times. The morphology of bcl silica was observed using FESEM and HRTEM. FESEM images show that bcl silica has bicontinuous lamellar walls arranged concentrically to form spherical particles. As the synthesis time increases, the average particle size of bcl silica increases. The quantization of bcl silica binary images shows that the average lamellar cross-sectional area ratio decreases with increasing synthesis time. The simulation of the Cahn-Hilliard's spinodal decomposition model using MATLAB also describes the lamellar cross-sectional area ratio of bcl silica. In addition, to characterize the FESEM image's texture, a Shannon entropy calculation was performed. The line and circular gray value intensity profiles of the HRTEM image show that bcl silica has a denser core than the outer part. The denser core proves that the lamellae in bcl silica are concentrically arranged towards the particle core. Furthermore, we added bcl silica to a photoanode to see the effect of bcl characteristics on the DSSC performance. The results show that the bcl silica significantly improves the light-harvesting efficiency in DSSCs due to its low refractive index and open channel structure.

Adjoint model for estimating material parameters based on microstructure evolution during spinodal decomposition

Data assimilation techniques are attracting increasing attention because they enable researchers to estimate material parameters by integrating an advanced computational model with experimental data of microstructure evolution. In this study, we develop an adjoint model to integrate a phase-field model for spinodal decomposition with time-series measurement data of compositional field maps to estimate the unknown parameters in the phase-field model. As a case study, simultaneous estimation of six parameters (Gibbs energy parameters, gradient energy coefficient, etc.) in the phase-field model is considered. To confirm the effectiveness of the developed adjoint model, numerical tests called ``twin experiments'' are conducted using synthetic measurement data prepared in advance through phase-field simulation. In the twin experiments, the optimum estimates of six model parameters of interest are shown to coincide with true values, indicating that several model parameters can be successfully estimated. Furthermore, the effects of the standard deviation of measurement noise $(\ensuremath{\sigma})$ and the time interval of measurements $(\mathrm{\ensuremath{\Delta}}{t}_{\mathrm{meas}.}^{\ensuremath{'}})$ on uncertainties of optimum estimates of parameters $({\ensuremath{\sigma}}^{\mathrm{est}})$ are examined by conducting twin experiments. It is shown that there is a positive correlation between $\ensuremath{\sigma}$ and ${\ensuremath{\sigma}}^{\mathrm{est}}$ or between $\mathrm{\ensuremath{\Delta}}{t}_{\mathrm{meas}.}^{\ensuremath{'}}$ and ${\ensuremath{\sigma}}^{\mathrm{est}}$, which is essential information for designing experiments to estimate model parameters. The developed adjoint model is assumed to be useful for estimating unknown parameters (e.g., Gibbs energy parameters of a nonequilibrium phase) using time-series measurement data of microstructure evolution during spinodal decomposition.

Analytical Approximation for Cahn-Hillard Phase-Field Model for Spinodal Decomposition of a Binary System

Phase transformations which lead to dramatical property change are very important for engineering materials. Phase-field methods are one of the most successful and practical methods for modelling phase transformations in materials. The Cahn-Hillard phase-field model is among the most promising phase-field models. The most successful aspect of the model is that it can predict spinodal decomposition (which is essential to determining the microstructure of an alloy) in a binary system. It is used in both materials science and many other fields, such as polymer science, astrophysics, and computer science. In this study, the Cahn-Hillard phase-field model is evaluated by an analytical approach using the (1/G')-expansion method. The solutions obtained are tested for certain thermodynamic conditions, and their accuracy of predicting the spidonal decomposition of a binary system is confirmed.

Parameter estimation of phase-field model for spinodal decomposition based on the adjoint method

Parameter estimation of phase-field model for spinodal decomposition based on the adjoint method

Analytical solutions of Cahn-Hillard phase-field model for spinodal decomposition of a binary system

Spinodal decomposition is a very important and challenging issue not for only materials science but for also many other fields in science. Phase-field models, which have become very popular in recent years, are very promising for the evaluation of phase transformations such as spinodal decomposition. In this study, the Cahn-Hillard equation which is one of the most trending phase-field models is analytically solved by the double exp-function and the modified extended exp-function methods. Spatio-temporal energy and concentration distributions were evaluated by applying two of the ten obtained analytical solutions to the free energy equation. The results obtained were found to be successful in predicting spinodal decomposition as is expected from the Cahn-Hillard model.

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.

Development of a spinodal decomposition model for the example of a heterostructure based on silicon carbide polytypes

The transition region of a 3C-SiC/4H-SiC heterostructure constituted by layers of the 3C and 4H polytypes has been studied. A previously proposed spinodal decomposition model was used to estimate the thickness ratio of 4H and 3C layers in comparison with the image furnished by transmission electron microscopy.

Benchmark problems for numerical implementations of phase field models

We present the first set of benchmark problems for phase field models that are being developed by the Center for Hierarchical Materials Design (CHiMaD) and the National Institute of Standards and Technology (NIST). While many scientific research areas use a limited set of well-established software, the growing phase field community continues to develop a wide variety of codes and lacks benchmark problems to consistently evaluate the numerical performance of new implementations. Phase field modeling has become significantly more popular as computational power has increased and is now becoming mainstream, driving the need for benchmark problems to validate and verify new implementations. We follow the example set by the micromagnetics community to develop an evolving set of benchmark problems that test the usability, computational resources, numerical capabilities and physical scope of phase field simulation codes. In this paper, we propose two benchmark problems that cover the physics of solute diffusion and growth and coarsening of a second phase via a simple spinodal decomposition model and a more complex Ostwald ripening model. We demonstrate the utility of benchmark problems by comparing the results of simulations performed with two different adaptive time stepping techniques, and we discuss the needs of future benchmark problems. The development of benchmark problems will enable the results of quantitative phase field models to be confidently incorporated into integrated computational materials science and engineering (ICME), an important goal of the Materials Genome Initiative.

A benchmark for the surface Cahn–Hilliard equation

We study the surface Cahn–Hilliard equation, an often used model for spinodal decomposition and coarsening effects on surfaces. As the width of the diffuse interface shrinks to zero one expects a convergence towards a surface Hele-Shaw model. While results from formal matched asymptotic expansions confirm this conjecture, a numerical reproduction of this asymptotic behavior has not been provided, yet. It is the purpose of this contribution, to fill this gap and present a rotationally symmetric example on the standard sphere, where analytic expressions for the surface Hele-Shaw model allow a comparison with numerical results for the surface Cahn–Hilliard equation.

A Spinodal Decomposition Model for the Prediction of the Glass-Forming Ability of Ternary Mg Alloys

The glass-forming ability (GFA) of two alloy systems, Mg-Y-La and Mg-Zn-Nd, was investigated using thermal and microstructural analysis. Rapid solidification was found to lead to microstructural refinement and partial amorphization of the most investigated alloys. The addition of Cu to the Mg-Y-La group was found to increase its tendency to undergo amorphization during rapid solidification, exemplified by the Mg86Y9.5Cu2.5La2 alloy exhibiting a pronounced crystallization peak in the differential scanning calorimetry trace. Two Mg-Zn-Nd alloys, Mg71Zn28Nd and Mg73.6Zn22.1Nd4.3, were found to exhibit significant amorphous behavior, with the former alloy being more amorphous than the latter. An innovative model predicting the GFA of alloys based on spinodal-like decomposition of supercooled alloys is formulated herein. New generalized thermo-kinetic criteria for spinodal decomposition of ternary alloys for time/space-correlated fluctuations were formulated. The time-dependent amplification factor of concentration fluctuations in ternary systems was found to provide adequate GFA evaluation for the compositions of both alloy systems: Mg-Y-La and Mg-Zn-Nd. The model was able to pinpoint the most amorphous alloy in each alloy system, and comparison between both systems pointed to Mg71Zn28Nd as having the best GFA, while also recognizing that it has a lower GFA than the widely known and highly glass-formable Mg65Cu25Y10 alloy. This model is expected to predict the GFA of any envisaged composition, thereby avoiding cumbersome trials.

Strain Energy Effects in the Spinodal Decomposition of Cu-Ni(Fe) Nanolaminate Coatings

A model for spinodal decomposition must account for interface effects that include gradient and strain energy terms. The measurement of diffusion in the Cu-Ni(Fe) alloy for the special case of nanolaminate structured coatings is considered wherein the composition fluctuation is one-dimensional along <111>. An analytic approach is taken to model the kinetics of the transformation process that provides quantification of the strain energy dependence on the composition wavelength, as well as the intrinsic diffusivities and higher-order gradient-energy coefficients. The variation of the wave amplification factor R with wavenumber is modeled first to incorporate the boundary condition for growth at infinite wavelength. These results are used next to determine the gradient energy coefficients Kμ by modeling the interdiffusion coefficient ĎB variation with wavenumber, where a unique determination of the diffusion coefficient Ď is made. The value of the strain energy component that originates from interface strains associated with the epitaxial growth between layers is then determined by assessing the variation of wavelength-dependent amplification factors. A peak value of 9.4 × 107 J·m−3 for the strain energy is computed for Cu-Ni(Fe) nanolaminate coatings with 2–4 nm composition wavelengths.

A study of the intermediate layer in 3C–SiC/6H–SiC heterostructures

Transmission electron microscopy and the cathodoluminescence method have been used to study the transition region in 3C–SiC/6H–SiC heterostructures. It is shown that this region is, as a rule, constituted by alternating 3C–SiC and 6H–SiC layers, with possible inclusion of other silicon carbide polytypes. An assumption is made that this structure of the transition region can be explained in terms of the spinodal decomposition model.

Investigation of the transition layer in 3C-SiC/6H-SiC heterostructures

Transmission electron microscopy and the cathodoluminescence method are used to study the transition region in 3C-SiC/6H-SiC heterostructures. It is shown that this region is, as a rule, constituted by alternating 3C-SiC and 6H-SiC layers with the possible inclusion of other silicon carbide polytypes. An assumption is made that this structure of the transition region can be explained in terms of the model of spinodal decomposition.

Phase-Field Model for Spinodal Decomposition of Dilute Solute Field in Al-Ag Alloy

The typical Landau free energy functional with the fourth power of a solute composition field is not suitable for representing spinodal decomposition of a dilute Ag solute field in Al-Ag alloy. Facing this challenge, a new free energy density function is proposed for spinodal decomposition of a dilute Ag solute field of Al-Ag alloy. The evolution of the solute field in Al-4.2% Ag alloy is studied by phase-field method using this new function. The simulated results reveal that the precipitate free zone (PFZ) around the precipitated phase is an ellipse and its width is about two times that of phase, while in the region far from PFZ, a GPZ pattern of Ag solute field appears due to spinodal decomposition.

Stochastic generalization for a hyperbolic model of spinodal decomposition

A model for diffusion and phase separation which takes into account exponential relaxation of the solute diffusion flux and its fluctuations is developed. The model describes a system undergoing phase separation governed by a partial differential equation of hyperbolic type. The analysis is done for the evolution of patterns in spinodal decomposition for the system supercooled below critical temperature. Analytical results show that relaxation processes of the solute diffusion flux lead to the selection of patterns with different wavenumbers. Considering spatial–temporal correlations of the flux fluctuations, we have found that the temporal correlations promote selecting large-period patterns, whereas the corresponding spatial correlations accelerate such processes.

Bridging length and time scales in sheared demixing systems: From the Cahn-Hilliard to the Doi-Ohta model

We develop a systematic coarse-graining procedure which establishes the connection between models of mixtures of immiscible fluids at different length and time scales. We start from the Cahn-Hilliard model of spinodal decomposition in a binary fluid mixture under flow from which we derive the coarse-grained description. The crucial step in this procedure is to identify the relevant coarse-grained variables and find the appropriate mapping which expresses them in terms of the more microscopic variables. In order to capture the physics of the Doi-Ohta level, we introduce the interfacial width as an additional variable at that level. In this way, we account for the stretching of the interface under flow and derive analytically the convective behavior of the relevant coarse-grained variables, which in the long wavelength limit recovers the familiar phenomenological Doi-Ohta model. In addition, we obtain the expression for the interfacial tension in terms of the Cahn-Hilliard parameters as a direct result of the developed coarse-graining procedure. Finally, by analyzing the numerical results obtained from the simulations on the Cahn-Hilliard level, we discuss that dissipative processes at the Doi-Ohta level are of the same origin as in the Cahn-Hilliard model. The way to estimate the interface relaxation times of the Doi-Ohta model from the underlying morphology dynamics simulated at the Cahn-Hilliard level is established.

Evolution of the structure factor in a hyperbolic model of spinodal decomposition

We consider the modification of the Cahn-Hilliard equation when a time delay process through a memory function is taken into account. The memory effects are seen to affect the dynamics of phase transition at short times. The process of fast spinodal decomposition associated with a conserved order parameter - concentration is studied numerically. Details of a semi-implicit numerical scheme used to simulate the kinetics of spinodal decomposition and evolution of the structure factor are discussed. Analysis of the modeled structure factor predicted by a hyperbolic model of spinodal decomposition is presented in comparison with the parabolic model of Cahn and Hilliard. It is shown that during initial periods of decomposition the structure factor exhibits wave behavior. Analytical treatments explain such behavior by existence of damped oscillations in structure factor at earliest stages of phase separation and at large values of the wave-number. These oscillations disappear gradually in time and the hyperbolic evolution approaches the pure dissipative parabolic evolution of spinodal decomposition.

Ordered structures of exciton condensed phases in the presence of an inhomogeneouspotential

A theory of the separation of a system of indirect excitons into a condensed and a gaseousphase with the formation of regular patterns of alternating phases in inhomogeneousexternal fields is developed. The model of spinodal decomposition of phase transitions,generalized for systems of unstable particles, is used. The theory is applied to the study ofthe non-uniform distribution of the exciton density in a double quantum wellunder a slot cut in a metallic electrode. It is shown that in a certain range ofexciton generation rates a chain of light-emitting islands periodically localizedalong the slot is developed. With increasing width of the slot, the chain splitsinto two parallel chains shifted by a half period with respect to each other. Bycreating a biased external potential along the slot, the periodical pattern couldbe forced to move along the slot. The effect of the motion of the islands shouldmanifest itself as time oscillations of the intensity of the light emitted from a fixedpoint.

Exsolution by spinodal decomposition I: Evolution equation for binary mineral solutions with anisotropic interfacial energy

Phase separation in a binary system that results from the uphill diffusion of chemical components is investigated theoretically. We reconsider the original spinodal decomposition model of Cahn and Hilliard taking into account possible intrinsic anisotropy of the underlying system. Specifically we address the effects of orientation dependent interfacial energy. Such anisotropy is of particular importance for mineral systems. The corresponding evolution equation is systematically derived. We show how the anisotropy affects the interfacial energy per unit area, the interface width, scaling laws, and the critical system size at which spinodal decomposition starts to develop. We further obtain numerical solutions and discuss coarsening dynamics for the case where the decomposition products have pronounced shape anisotropy.