Journal ArticleDOI
A model for diffusion on cubic lattices and its application to the early stages of ordering
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In this article, a theory for diffusion on cubic lattices is given, in which an allowance is made for the effect of sharp composition gradients on the driving force, and an expression for diffusion is derived in the form of a differential-difference equation, and a simple analytic solution for the limiting case of small composition, fluctuations.About:
This article is published in Acta Metallurgica.The article was published on 1969-06-01. It has received 208 citations till now. The article focuses on the topics: Spinodal decomposition & Diffusion (business).read more
Citations
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Book ChapterDOI
Free Energy of a Nonuniform System. I. Interfacial Free Energy and Free Energy of a Nonuniform System. III. Nucleation in a Two‐Component Incompressible Fluid
John W. Cahn,John E. Hilliard +1 more
Journal ArticleDOI
Brownian motion in spinodal decomposition
TL;DR: In this paper, the influence of Brownian motion on the rate of change of the diffuse intensity is characterized by a thermal driving force proportional to k B T where k B is Boltzmann's constant and T is the temperature.
Journal ArticleDOI
Mechanisms of phase transformations within the miscibility gap of Fe-rich Fe-Al alloys
Samuel M. Allen,John W. Cahn +1 more
TL;DR: The coherent phase diagram of the Fe-Al system possesses a tricritical point where a line of higher-order transitions ends at a miscibility gap at about 23 at.% Al and 615°C.
Journal ArticleDOI
Traveling Waves in Lattice Dynamical Systems
TL;DR: In this article, the existence and stability of traveling waves in lattice dynamical systems, in particular in coupled map lattices and in CMLs, was studied, and it was shown that the traveling wave corresponds to a periodic solution of a nonautonomous periodic differential equation.
Journal ArticleDOI
The omega phase transformation in titanium alloys as an example of displacement controlled reactions
TL;DR: In this paper, the omega phase is shown experimentally to be formed by cooling certain metastable β-Ti alloys to cryogenic temperatures, and the gradual progression from diffuse streaking in the diffraction patterns of the β phase to the sharp ω reflections is interpreted in terms of a displacive type reaction.
References
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Journal ArticleDOI
Free Energy of a Nonuniform System. I. Interfacial Free Energy
John W. Cahn,John E. Hilliard +1 more
TL;DR: In this article, it was shown 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 (T c −T) 3 2.
Journal ArticleDOI
On spinodal decomposition
TL;DR: In this article, the stability of a solid solution to all infinitesimal composition fluctuations is considered, taking surface tension and elastic energy into account, and it is found that for infinite isotropic solids, free from imperfections, the spinodal marks the limit of metastability to such fluctuations only if there is no change in molar volume with composition.
Journal ArticleDOI
On spinodal decomposition in cubic crystals
TL;DR: In this paper, the anisotropy of all factors influencing the mechanism of spinodal decomposition was considered for crystals of cubic symmetry, and it was shown that elastic aeolotropy should give rise to {100} plane waves if 2 C 44 − C 11 + C 12 > 0 or {111} plane wave if 2C 44 − c 11 + c 12
Journal ArticleDOI
A solid-solution model for inhomogeneous systems
TL;DR: In this article, a solid-solution model allowing compositional variations in one dimension is developed from the zeroth approximation of nearest-neighbor interactions, which predicts the existence of periodically modulated structures in order as well as in precipitation systems.
Journal ArticleDOI
Spinodal decomposition during continuous cooling
TL;DR: In this article, a spinodal decomposition of a binary solid solution during continuous cooling should lead to a structure similar to that resulting from isothermal decomposition, consisting of a superimposition of sinusoidally varying composition modulations clustered about a wavelength λmax that has received maximum amplification.