Springer Proceedings in Physics, pages 1-8

Moving Boundary Problem for Spinodal Transformations in Thin Films

1
 
Emeritus, Mechanical Engineering, Department, JNTU, Ananthapuramu, India
Publication typeBook Chapter
Publication date2024-12-29
SJR0.135
CiteScore0.4
Impact factor
ISSN09308989, 18674941
Abstract
The equations of Spinodal Decomposition as postulated by Cahn and Hilliard involve a fourth-order partial differential equation, which to date has not been solved analytically. In this article, these equations are examined in their various versions, and solutions are obtained for the steady state and transient forms using multiple methods. Then the moving boundary associated with transformation is reviewed using a heat transfer approach, and a solution is attempted using a series and a similarity transformation approach. The equation is postulated to have two contributions, one from the usual Laplacian and Fickian contribution part for which Stefan solutions are known, and one with a Double Laplacian, which has not been examined. The thin film approximation is applied to simplify some parts of the analysis and to try to get a numerical solution. Applicability in the analysis of MGA's is discussed.
Marczewski M., Wieczerzak K., Maeder X., Lapeyre L., Hain C., Jurczyk M., Nelis T.
Journal of Materials Science scimago Q1 wos Q2
2024-05-19 citations by CoLab: 4 Abstract  
AbstractAt the interface of thin film development and powder metallurgy technologies, this study aims to characterise the mechanical properties, lattice constants and phase formation of Ti-Nb alloys (8–30 at.%) produced by different manufacturing methods, including conventional powder metallurgy (PM), mechanical alloying (MA) and high power impulse magnetron sputtering (HiPIMS). A central aspect of this research was to investigate the different energy states achievable by each synthesis method. The findings revealed that as the Nb content increased, both the hardness and Young’s modulus of the PM samples decreased (from 4 to 1.5 and 125 to 85 GPa, respectively). For the MA alloys, the hardness and Young’s modulus varied between 3.2 and 3.9 and 100 to 116 GPa, respectively, with the lowest values recorded for 20% Nb (3.2 and 96 GPa). The Young’s modulus of the HiPIMS thin film samples did not follow a specific trend and varied between 110 and 138 GPa. However, an increase in hardness (from 3.6 to 4.8 GPa) coincided with an increase in the β2 phase contribution for films with the same chemical composition (23 at.% of Nb). This study highlights the potential of using HiPIMS gradient films for high throughput analysis for PM and MA techniques. This discovery is important as it provides a way to reduce the development time for complex alloy systems in biomaterials as well as other areas of materials engineering. Graphical abstract
Belenchuk A., Shapoval O., Roddatis V., Stroh K., Vatavu S., Wawra J., Moshnyaga V.
Nanoscale scimago Q1 wos Q1
2023-06-20 citations by CoLab: 2 Abstract  
Spinodal decomposition in polycrystalline V0.65Ti0.35O2 films yields a nanocomposite with V- and Ti-rich layers. Strain-enhanced thermochromism due to compression of V-rich phase decreases both the temperature and width of metal–insulator transition.
Hoang M., Lu J., Hsieh H., Chen H.
2023-06-12 citations by CoLab: 7 Abstract  
Spinodal decomposition-based micro phase separation was found in hybrid poly(9,9-dioctylfluorene-alt-N-(4-sec-butylphenyl)-diphenylamine) (TFB) and polyvinylcarbazole (PVK) system, which is used as a hole transporting layer (HTL) in atmosphere-based quantum dot (QD) light-emitting...
Koneru S.R., Kadirvel K., Wang Y.
2022-08-01 citations by CoLab: 10 PDF Abstract  
Recent studies revealed that multiphase microstructures in Al0.5NbTa0.8Ti1.5V0.2Zr, Fe15Co15Ni20Mn20Cu30 and TiZrNbTa multi-principal element alloys (MPEAs) developed via spinodal decomposition assisted phase transformation pathways offer better properties than single-phase MPEAs. Although spinodal decomposition has been widely studied for the past six decades, it has not been explored in detail as a design strategy to develop multiphase MPEAs. In this work, we illustrate high-throughput CALPHAD calculations necessary to design MPEAs with spinodal decomposition assisted multiphase microstructures by using Fe-Co-Ni-Mn-Cu system as an example. Firstly, the MPEAs that possess single solid solution phase at high temperatures and can undergo spinodal decomposition are identified through solid solution stability analysis and phase equilibrium calculations. The spinodal temperature as a function of alloy composition is visualized through Morral’s constant core component diagrams and the MPEAs of interest are selected based on further phase equilibrium calculations at the ageing temperature. Lastly, the critical features of spinodal decomposition such as the initial compositional modulations are calculated for the chosen alloy compositions. We find that the alloying elements could be divided into three groups: (i) Fe and Co, (ii) Ni and Mn, and (iii) Cu, based on the spinodal decomposition features predicted by the PanHEA database, and the restricted solubility of Cu in Fe and Co has led to the miscibility gap in FCC solid solutions of Fe-Co-Ni-Mn-Cu MPEAs. However, the addition of Ni and Mn is crucial in attaining spinodal microstructures as they aid in shifting the miscibility gap below the solidus curve in these MPEAs.
Jáger G., Tomán J.J., Erdélyi Z.
Journal of Alloys and Compounds scimago Q1 wos Q1
2022-07-01 citations by CoLab: 5 Abstract  
With this work we attempt to raise awareness of spinodal decomposition among the members of the ion implantation researcher community. In the literature about nanoparticle formation via ion implantation, spinodal decomposition is rarely mentioned. Probably because it is not associated with individual particles which are often the desired goal of the implantation process, but with contiguous, often “labyrinth-like" nanostructures. Using a modified version of the Stochastic Kinetic Modelling Framework (SKMF), we show that spinodal decomposition can directly form nanoparticles, too. Distinguishing nucleation and growth from spinodal decomposition and coarsening based only on the result is very difficult, often impossible, and researchers regularly rely solely on morphological identification, which, as we demonstrate here, can be misleading. The authors believe that understanding nanoparticle formation during and after ion implantation is a good way to initiate a step forward in nucleation theory development, and move away from the strong distinction between nucleation and spinodal decomposition to a more general phase separation theory. • Ion implantation to produce embedded nanoparticles is a promising technology. • The ion implantation literature extremely rarely mentions spinodal decomposition. • Developed numeric model considers the occupation probability of the implanted atoms. • Results show how spinodal decomposition can form nanoparticles. • Distance between particles relates to the wavelength of spinodal decomposition.
Costa S.C., Kenisarin M.
2022-02-01 citations by CoLab: 124 Abstract  
Phase change materials provide desirable characteristics for latent heat thermal energy storage by keeping the high energy density and quasi isothermal working temperature. Along with this, the most promising phase change materials, including organics and inorganic salt hydrate, have low thermal conductivity as one of the main drawbacks. Metallic materials are attractive alternatives due to their higher thermal conductivity and high volumetric heat storage capacity. This paper presents an extensive review of the thermophysical properties of metals and alloys as the potential phase change materials for low (300 °C) temperatures. The information presented includes the fundamental thermophysical properties as melting temperature, the heat of fusion, density, specific heat, and thermal conductivity found in the published literature. The temperature dependence of critical properties as specific heat, density, thermal conductivity, expansion coefficient, viscosity is also reviewed, including mathematical theoretical predictions crucial from an engineering design point of view. Besides, the current work briefly summarizes the potential applications and main challenges of metals and alloys as phase change materials. It is intended that this review provides a database of metallic phase change materials thermophysical properties to facilitate the selection, evaluation, and potential impact in different fields as solar energy storage, heating and cooling, electronic, bioengineering, and beyond. • Supercooling and corrosion are the main challenges for low-temperature MPCMs. • Most medium-temperature MPCMs are non-compliant with RoHS directives. • Encapsulation and compatibility are key research topics for LHTES applications. • Simplified design and volume reduction could compensate the MPCMs weight penalties. • Miscibility gap binary alloy, solid-solid and composite are innovative LHTES system.
Sun G., Cao X., Yue Y., Gao X., Long S., Li N., Li R., Luo H., Jin P.
Scientific Reports scimago Q1 wos Q1 Open Access
2018-03-28 citations by CoLab: 18 PDF Abstract  
Coating of VO2-based thin film has been extensively studied for fabricating energy-saving smart windows. One of the most efficient ways for fabricating high performance films is to create multi-nanolayered structure. However, it has been highly challenge to make such layers in the VO2-based films using conventional methods. In this work, a facile two-step approach is established to fabricate multilayered VO2-TiO2 thin films. We first deposited the amorphous thin films upon sputtering, and then anneal them to transform the amorphous phase into alternating Ti- and V-rich multilayered nanostructure via a spinodal decomposition mechanism. In particular, we take advantage of different sapphire substrate planes (A-plane (11–20), R-plane (1–102), C-plane (0001), and M-plane (10-10)) to achieve different decomposition modes. The new approach has made it possible to tailoring the microstructure of the thin films for optimized performances by controlling the disorder-order transition in terms of both kinetic and thermodynamic aspects. The derived thin films exhibit superior optical modulation upon phase transition, significantly reduced transition temperature and hysteresis loop width, and high degradation resistance, these improvements indicate a high potential to be used for fabricating the next generation of energy saving smart windows.
Chen Z., Chen Y.
Computational Materials Science scimago Q1 wos Q2
2018-01-01 citations by CoLab: 8 Abstract  
We study materials with spatial gradients in nanoscale grain size (5–120 nm), and quantitatively examine the effect of spatial gradient on microstructure evolution and thermal stability using mesoscale Monte Carlo modeling and statistical analysis. The spatial grain size gradient weakens and the grain size distribution widens at elevated temperatures, accompanied by grain rounding and movement of grains along the gradient direction. Introducing heterogeneous grain boundary networks into gradient materials leads to better preservation of the spatial grain size gradient but less equiaxed grains. Coarsening in small grain regions is accompanied by an increase in the local fraction of low-energy grain boundaries, as these are competing mechanisms for reducing total energy, and spatial gradients in grain boundary character distribution and triple junction character distribution develop in the material. We further compare concave, linear, and convex gradient materials with increasing grain size gradient for small grains. Grains in convex gradient materials have the highest grain growth rate compared to grains of the same size in linear and concave gradient materials. The accelerated grain growth in the presence of a steeper grain size gradient is attributed to a change in local grain neighbor environment that promotes grain boundary curvature (and pressure) and enhances the driving force for grain growth.
Artemev A., Roytburd A.
Acta Materialia scimago Q1 wos Q1
2010-02-01 citations by CoLab: 11 Abstract  
This study investigates the spinodal mechanism of domain formation and switching through the loss of stability of a single-domain (SD) state with respect to a polydomain (PD) state in thin ferroelectric films with dead layers. The macroscopic thermodynamic model of a homogenized domain structure (DS) is used to analyze the depolarizing field effect on the transitions between SD and PD states and the shape of the P(E) hysteresis loop. Phase field modeling is used to study the inhomogeneities and film thickness effects on DS and P(E) hysteresis. Such modeling of relatively thick films produces P(E) hysteresis loops of a shape similar to that predicted by the macroscopic model. The results of the analysis demonstrate that the SD → PD transition can proceed by the spinodal mechanism in thin films, while the nucleation and growth mechanism should operate in thick films. It is shown that columnar and stripe DS can be produced in thin films.
Chen L.
2002-08-11 citations by CoLab: 2310 Abstract  
▪ Abstract  The phase-field method has recently emerged as a powerful computational approach to modeling and predicting mesoscale morphological and microstructure evolution in materials. It describes a microstructure using a set of conserved and nonconserved field variables that are continuous across the interfacial regions. The temporal and spatial evolution of the field variables is governed by the Cahn-Hilliard nonlinear diffusion equation and the Allen-Cahn relaxation equation. With the fundamental thermodynamic and kinetic information as the input, the phase-field method is able to predict the evolution of arbitrary morphologies and complex microstructures without explicitly tracking the positions of interfaces. This paper briefly reviews the recent advances in developing phase-field models for various materials processes including solidification, solid-state structural phase transformations, grain growth and coarsening, domain evolution in thin films, pattern formation on surfaces, dislocation microstructures, crack propagation, and electromigration.
Fischer H.P., Maass P., Dieterich W.
Europhysics Letters scimago Q2 wos Q2
1998-04-01 citations by CoLab: 52 Abstract  
We study the early-time spinodal decomposition of binary mixtures in thin slabs of thickness L on the basis of a Ginzburg-Landau–type treatment. After deriving a general classification of the linear demixing modes, we calculate explicitly the L-dependent mode spectrum for a symmetric slab with wall-induced interactions that tend to stabilize the mixture. We show that there exists a critical thickness Lc below which no spontaneous demixing takes place. Both the wavelength 2π/k∥,m and the inverse growth rate ω∥,m−1 of the most unstable modes diverge when L approaches Lc.
Chen L.Q., Shen J.
Computer Physics Communications scimago Q1 wos Q1
1998-02-01 citations by CoLab: 932 Abstract  
An efficient and accurate numerical method is implemented for solving the time-dependent Ginzburg—Landau equation and the Cahn—Hilliard equation. The time variable is discretized by using semi-implicit schemes which allow much larger time step sizes than explicit schemes; the space variables are discretized by using a Fourier-spectral method whose convergence rate is exponential in contrast to second order by a usual finite-difference method. We have applied our method to predict the equilibrium profiles of an order parameter across a stationary planar interface and the velocity of a moving interface by solving the time-dependent Ginzburg—Landau equation, and compared the accuracy and efficiency of our results with those obtained by others. We demonstrate that, for a specified accuracy of 0.5%, the speedup of using semi-implicit Fourier-spectral method, when compared with the explicit finite-difference schemes, is at least two orders of magnitude in two dimensions, and close to three orders of magnitude in three dimensions. The method is shown to be particularly powerful for systems in which the morphologies and microstructures are dominated by long-range elastic interactions.
Voorhees P.W.
Journal of Statistical Physics scimago Q2 wos Q3
1985-01-01 citations by CoLab: 1607 Abstract  
Developments in the theory of Ostwald ripening since the classic work of I. M. Lifshitz and V. V. Slyozov (LS) are reviewed and directions for future work are suggested. Recent theoretical work on the role of a finite volume fraction of coarsening phase on the ripening behavior of two-phase systems is reformulated in terms of a consistent set of notation through which each of the theories can be compared and contrasted. Although more theoretical work is necessary, these theories are in general agreement on the effects of a finite volume fraction of coarsening phase on the coarsening behavior of two-phase systems. New work on transient Ostwald ripening is presented which illustrates the broad range of behavior which is possible in this regime. The conditions responsible for the presence of the asymptotic state first discovered by LS, as well as the manner in which this state is approached, are also discussed. The role of elastic fields during Ostwald ripening in solid-solid mixtures is reviewed, and it is shown that these fields can play a dominant role in determining the coarsening behavior of a solid-solid system.
Cahn J.W., Hilliard J.E.
Journal of Chemical Physics scimago Q1 wos Q1
1958-02-01 citations by CoLab: 8240 PDF Abstract  
It is shown that the free energy of a volume V of an isotropic system of nonuniform composition or density is given by : NV∫V [f0(c)+κ(▿c)2]dV, where NV is the number of molecules per unit volume, ▿c the composition or density gradient, f0 the free energy per molecule of a homogeneous system, and κ a parameter which, in general, may be dependent on c and temperature, but for a regular solution is a constant which can be evaluated. This expression is used to determine the properties of a flat interface between two coexisting phases. In particular, we find that the thickness of the interface increases with increasing temperature and becomes infinite at the critical temperature Tc, and that at a temperature T just below Tc the interfacial free energy σ is proportional to (Tc−T)32. The predicted interfacial free energy and its temperature dependence are found to be in agreement with existing experimental data. The possibility of using optical measurements of the interface thickness to provide an additional check of our treatment is briefly discussed.

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