Theory of spinodal decomposition in alloys

A statistical theory of the thermally driven composition fluctuations in a binary alloy is developed for the purpose of studying the phenomenon of spinodal decomposition. The theory can be stated in the form of a Fokker-Planck equation, which reduces, upon taking a suitable moment, to the nonlinear generalized diffusion equation which has been the basis of recent work in this field. Using the full Fokker-Planck equation, it is possible to compute the lifetime of the stationary solutions of the diffusion equation, and thus to study the rate at which the structure of the alloy coarsens during aging.     

The spinodal decomposition of Cu-Ti alloys

The wave length of periodic modulated microstructure in an aged Cu-Ti alloy has been measured. Simultaneously the microstructure changes and development were studied in dependence on the ageing time at 573 K.     

Surface spinodal decomposition in coherent metal-hydrogen and other alloys

Spinodal decomposition in metal hydrides and alloys near a surface under the influence of elastic interactions is investigated. As long as the crystals remain coherent this process sets in prior to spinodal decomposition in the bulk. A statistical theory containing thermal fluctuations and nonlinear effects is developed and solutions are found in a mean field approximation. The theory is applied to niobium-hydride and a possible explanation for the appearance of quasiperiodic-phase precipitates in quenched probes is given.     

Early stages of decomposition of alloys (spinodal or nucleation)

Progress in theory and experiment on the early stage of decomposition of alloys is reviewed. In the first half of this paper, theoretical treatments on decomposition of alloys by spinodal and nucleation mechanism and also continuum theories and the discrete lattice theories are comparatively reviewed. In the latter half of this paper, experimental results on Al-Zn, Ni-Al, Cu-Co and Al-Ag alloys are discussed.     

Magnetism in amorphous Fe-Si alloys

Fe-Si alloys have been obtained by the vapor quenching technique. Resistance measurements, electron microscopy and diffraction results are typical of an amorphous system. The Mössbauer spectra of these amorphous alloys, fitted in terms of a distribution of hyperfine fields, show the existence of a local magnetic order with, however, a proportion of weakly or even no coupled Fe atoms which is temperature and Fe-concentration dependent.     

Diffusion in ordered Fe-Si alloys

The measurement of the diffusional Mössbauer line broadening in single crystalline samples at high temperatures provides microscopic information about atomic jumps. We can separate jumps of iron atoms between the various sublattices of Fe-Si intermetallic alloys (D0₃ structure) and measure their frequencies. The diffusion of iron in Fe-Si samples with Fe concentrations between 75 and 82 at% shows a drastic composition dependence: the jump frequency and the proportion between jumps on Fe sublattices and into antistructure (Si) sublattice positions change greatly. Close to Fe₃Si stoichiometry iron diffusion is extremely fast and jumps are performed exclusively between the three Fe sublattices. The change in the diffusion process when changing the alloy composition from stoichiometric Fe₃Si to the iron-rich side is discussed.     

Interactions between grain boundary and compositional domain boundary during spinodal decomposition in nanocrystalline alloys

Due to the large grain boundary (GB) volume fraction in nanocrystalline materials, interactions between GB and compositional domain boundary (CDB) play an important role in determining the nanoscale-modulated domain structures during spinodal decomposition. In the present paper, the phase field crystal model is employed to investigate the interactions between GB and CDB. Simulation results show that CDB coarsening can drive the GB migration and bring the impingement of particles with different orientations; the large volume fraction of GB can increase the dislocation volume fraction in CDBs but does not change its proportion in the whole defects number; the crossover point of the coarsening dynamic comes from the block effect of GB with large volume fraction.     

Asymptotic behaviour of spinodal decomposition

We report a numerical study of the asymptotic regime of spinodal decomposition. Specifically, we find (a) that the characteristic pattern size shows a power-law growth with exponent 0.33; and (b) that the effect of noise is asymptotically irrelevant.     

Non-linear dynamics of spinodal decomposition

We develop a new technique describing the non linear growth of interfaces. We apply this analytical approach to the one dimensional Cahn-Hilliard equation. The dynamics is captured through a solvability condition performed over a particular family of quasi-static solutions. The main result is that the dynamics along this particular class of solutions can be expressed in terms of a simple ordinary differential equation. The density profile of the stationary regime found at the end of the non-linear growth is also well characterized. Numerical simulations are compared in a satisfactory way with the analytical results through three different fitting methods and asymptotic dynamics are well recovered, even far from the region where the approximations hold. Received 16 October 2001 / Received in final form 15 March 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: josseran@lmm.jussieu.fr RID="b" ID="b"UMR CNRS 7607     

Dynamical spinodal: The transition between nucleation and spinodal decomposition

The nonclassical regime in the two phase region between nucleation and spinodal decomposition of a binary model with medium range interaction has been investigated. The Monte Carlo results indicate a dynamical spinodal. At this dynamical spinodal a transient percolating structure occurs. However, the mean droplet size remains finite there.     

Characterization of the spinodal decomposition of Fe−Cr alloys by Mössbauer spectroscopy

Addition of 5%Ni to an Fe?28%Cr alloy causes a transition of the aging behavior from the nucleation and growth to the spinodal decomposition. Very rapid increase in the average internal magnetic field and a broadening of the internal magnetic field distribution occur in the spinodal decomposition. Mössbauer spectra are synthesized by assuming a rectangular and a sinusoidal wave for the composition fluctuation, and the internal magnetic field distributions obtained from those are compared with the experimental results to estimate a time evolution of the amplitude of the composition wave.     

Morphological characterization of spinodal decomposition kinetics

The time evolution of the morphology of homogeneous phases during spinodal decomposition is described using a family of morphological measures known as Minkowski functionals. They provide the characteristic length scale L of patterns in a convenient, statistically robust, and computationally inexpensive way. They also allow one to study the scaling behavior of the content, shape, and connectivity of spatial structures and to define the crossover from the early stage decomposition to the late stage domain growth. We observe the scaling behavior with , , and depending on the viscosity of the fluid. When approaching the spinodal density , we recover the prediction for the early time spinodal decomposition. Received 3 March 1998     

Asymmetric landscapes of early spinodal decomposition

We address the effect of an asymmetric concentration-dependent mobility on the early stages of spinodal decomposition in polymer blends and solutions, and characterise it quantitatively. This is particularly important when one of the components has a slower dynamics than the other, e.g., because it is closer to its glass transition, or is weakly cross-linked. Composition mode coupling is proposed as the underlying physical mechanism, and then investigated by means of numerical simulations of the Cahn-Hilliard equation in one (1d) and two (2d) dimensions. In general, this coupling broadens the peak in the structure factor: in 1d an asymmetric concentration profile is obtained, with sharpened interfaces, whereas in 2d the formation is favoured of sharp peaks of the phase rich in the more mobile component. It is shown how the changing morphology of this phase-separating system can be described with the aid of Minkowski functionals. Received 28 August 2000 and Received in final form 18 July 2001     

On the kinetics of spinodal decomposition

We discuss the kinetics of phase separation based on the mechanism of spinodal decomposition. The starting point is Boltzmann's transport equation. A perturbation theory will be developed leading to a hierarchy of differential equations for the local density. The first member of this hierarchy is a nonlinear wave-type equation, which linearized version will be solved in order to discuss the behaviour of the amplification factor. Additionally, we compare our results with those of standard diffusion-type approximations and molecular dynamics calculations.Research supported in part by National Science Foundation, Grant ENG-7 515 882-A01