The existence of the spinodal and its relation to spinodal decomposition

The most well-known theory of spinodal decomposition depends on the existence of a free energy versus composition curve for a binary solution which exhibits a maximum within the region of the miscibility gap of its phase diagram. Such a maximum cannot exist unless special constraints are applied to the thermodynamic system. The role of these constraints, their clear specification, and the possible confusion associated with the use of mean field models are discussed. Attention is drawn to the fact that the conventional criterion of stability against decomposition is only true in an asymptotic limit.     

Nonlinear diffusion in spinodal decomposition: a numerical solution

The numerical solution of the one-dimensional nonlinear diffusion equation with a negative diffusion coefficient (up-hill diffusion) by a five-point approximation central difference scheme is considered. The stability criteria are discussed in detail and a numerical solution is provided for a specific case in which the time evolution of a periodic composition wave is presented with growth eventually leading to a stationary configuration. A critical comparison of the numerical solution with existing analytical solutions is shown. This leads to a simple semi-empirical growth law for studying the kinetics of spinodal decomposition in alloys.     

Coherency strains in the elastic free energy

A semi-discrete model for the elastic free energy of systems with coherent composition fluctuation has been developed. It applies to systems of orthorhombic and higher symmetry. The treatment is carried through the continuous theory of elasticity and hence involves the elastic constants which makes it readily applicable to any system. Moreover, the distortions may assume isotropic as well as anisotropic form in this model. The total strain may be isotropic but the (stress-free) coherency strain and subsequently the elastic strain tensors will in general be anisotropic. This results in the anisotropic kinetics of the mechanism of the spinodal decomposition.This treatment can be applied to study strain-dependent physical properties through a Green's function method and the mathematical formalism presented here. It is currently being applied to study the effect of the coherency strains on the structure of compositionally modulated systems of various symmetries. Calculations of the biaxial elastic modulus of these modulated systems as well as application of the present development to spinodal decomposition in systems with orthorhombic, tetragonal and hexagonal symmetry will be presented in a future report.     

Finite size effect in spinodal decomposition of nanograined materials

Decomposition of solid solution taking into account the grain boundaries segregations is considered in the framework of generalized Cahn-Hilliard model for finite systems. Two types—“stripe” and “drop-wise”—of the surface-directed decomposition found below spinodal depend on concentration of a wetting component. We demonstrate that grain boundaries segregations are able to drastically change the phase equilibrium inside the grain when its size becomes less than the critical value. As a result, decomposition of the solid solutions easily appears for nanograined materials.     

Comparative study of spinodal decomposition in symmetric and asymmetric Cu-Ni-Cr alloys

Spinodal decomposition in three alloys of nominal compositions 71Cu-27Ni-2Cr, 45Cu-45Ni-10Cr and 33Cu-52Ni-15Cr were studied by X-ray diffraction technique and transmission electron microscopy. It was found that the first and third alloys are asymmetric in nature while the second is symmetric. The symmetric alloy was found to decompose faster than the asymmetric ones. The asymmetry of the side bands was found to be related to the proportion of phases in the alloy. Electron microscopic studies revealed that during coarsening the major phase increases its connectivity by isolating the minor phase.     

Preparation and x-ray diffraction studies of compositionally modulated PbTe/Bi films

A technique is described for preparing compositionally modulated PbTe/Bi films on mica with a well-defined [111] epitaxy by evaporation. For short wavelengths or a large ratio of PbTe to bismuth, the bismuth layers of the film approached a quasi-simple-cubic structure.     

Surface-directed spinodal decomposition in a stressed, two-dimensional, thin film

Two-dimensional simulations of the spinodal decomposition of self-stressed, binary thin films using a Cahn-Hilliard model are presented. Two different sets of mechanical boundary conditions are considered, and compositional strains for a cubic-anisotropic system under plane strain are treated. A composition-dependent interaction energy is assumed at the free surface. Numerical solution of the coupled Cahn-Hilliard and elastic equilibrium equations are obtained using an efficient nonlinear multigrid method. Results of simulations show that, for large enough compositional strain, surface-directed decomposition occurs at the traction-free surface, even when there is negligible surface interaction energy initially attracting one of the components. This decomposition is controlled by elasticity, and results in a local alignment of phases perpendicular to the free surface, in contrast to the parallel alignment produced by surface energy in stress-free systems.     

Studies on spinodal decomposition in Cu-27Ni-2Cr alloy

Transformation characteristics of a Cu-27Ni-2Cr alloy were studied on ageing in the temperature range of 773 to 1073 K, by means of X-ray diffraction and transmission electron microscopy. It was concluded from morphological features that the alloy undergoes spinodal decomposition and the coherent spinodal was estimated to be 946 K. Yield stress increment on ageing was found to follow monotonically the strain amplitude and to be independent of the wavelength of composition modulation.     

Magnetic-field-induced phase separation via spinodal decomposition in epitaxial manganese ferrite thin films

In this study, we report about the occurrence of phase separation through spinodal decomposition (SD) in spinel manganese ferrite (Mn ferrite) thin films grown by Dynamic Aurora pulsed laser deposition. The driving force behind this SD in Mn ferrite films is considered to be an ion-impingement-enhanced diffusion that is induced by the application of magnetic field during film growth. The phase separation to Mn-rich and Fe-rich phases in Mn ferrite films is confirmed from the Bragg’s peak splitting and the appearance of the patterned checkerboard-like domain in the surface. In the cross-sectional microstructure analysis, the distribution of Mn and Fe-signals alternately changes along the lateral (x and y) directions, while it is almost homogeneous in the z-direction. The result suggests that columnar-type phase separation occurs by the up-hill diffusion only along the in-plane directions. The propagation of a quasi-sinusoidal compositional wave in the lateral directions is confirmed from spatially resolved chemical composition analysis, which strongly demonstrates the occurrence of phase separation via SD. It is also found that the composition of Mn-rich and Fe-rich phases in phase-separated Mn ferrite thin films deposited at higher growth temperature and in situ magnetic field does not depend on the corresponding average film composition.     

The phase diagram and spinodal decomposition of metastable states of Lennard-Jones system

The method of molecular dynamics is used to treat the metastable states of Lennard-Jones crystal and liquid at different temperatures and pressures, including the negative-pressure region. Analysis is made of the pattern of relative position of surfaces of the equation of state of the crystal and liquid phases in the metastable region. The limits of stability of metastable states of liquid and crystal on the phase diagram are determined. The mechanism of crystal decomposition in the vicinity of the stability limit is treated. The stochastic properties of a many-particle system are investigated in the region in the vicinity of the spinodal, and the dynamic memory time and K-entropy are calculated.     

Anisotropic spinodal decomposition of a polar dielectric in a strong electric field: Molecular dynamics simulation

The evolution of a one-component, initially single-phase, dielectric medium that represents a two-dimensional system of dipole molecules has been studied by the molecular dynamics method after the application of a uniform electric field. It is shown that the initially homogeneous medium under the action of the applied field can separate into two phases, liquid and gaseous. In the two-dimensional model system, these phases appear as bands extended along the field direction.     

Age-hardening associated with ordering and spinodal decomposition in a AgCu-40 at % Au pseudobinary alloy

The age-hardening mechanism in an AgCu-40 at% Au alloy was studied by means of electrical resistivity measurement, hardness tests, X-ray diffraction and electron microscopy. Two stages of hardening were found by isothermal ageing below 648 K, which was higher than the critical temperature of ordering, T _c=620 K, in the present alloy. The first stage of hardening took place by formation of a modulated structure resulting from spinodal decomposition. Further hardening was brought about by ordering, yielding metastable AuCu I and/or AuCu II ordered platelets grown from the copper-rich portion of the modulated structure. Transitional ordering which gave rise to a marked hardening of the second stage was found, even though the temperature of below 648 K was higher than the T _c of the present alloy. Drastic softening was also found on disappearance of the transitional ordered phases. Although the modulated structure was observed by ageing at 773 K, there was no age-hardening.     

On the various stages of spinodal decomposition in an Al-38 at % Zn alloy

Spinodal decomposition of an Al-38 at % Zn alloy in the temperature range 293 to 573 K has been studied by transmission electron microscopy. Microstructural evidences for the existence of various stages of spinodal decomposition, namely, the initial, the corsening and the particulate stages have been established. The morphological characteristics and the different diffusion regimes under which these stages are operative are explained.     

Mössbauer spectrometry study of early stage spinodal decomposition in Fe-Cr-Co alloy under high magnetic field

Local structure in a low-cobalt-type Fe-25Cr-12Co-1Si ferromagnetic alloy spinodal decomposed under an external magnetic field up to 120 kOe was investigated by Mössbauer spectrometry. The high magnetic field was found to significantly affect the local structure in the alloy formed at the early stage of phase decomposition. It was found that high magnetic field favors the acceleration of phase decomposition of ferromagnetic alloy at the early stage, resulting in the enhancement of average hyperfine field. The effect of high magnetic field on spinodal decomposition in ferromagnetic alloy was initially interpreted based on the free energy analyses.     

Preparation of spherical TiO2/SnO2 powders by ultrasonic spray pyrolysis and its spinodal decomposition

Spherical TiO₂/SnO₂ powders were prepared from the TiCl₄-SnCl₄ aqueous solution by ultrasonic spray pyrolysis. The particle size, particle-size distribution and morphology of the powders were studied in relation to concentration of source solutions and reaction temperatures. The width of the compositional undulation induced by spinodal decomposition in the sintered bodies increased with increasing starting particle sizes, which resulted from micro-compositional heterogeneity in the form of a solid solution within a TiO₂/SnO₂ secondary sphere.