The spinodal is the boundary where a metastable phase loses local stability. In a mean-field free-energy description the relevant curvature vanishes there, separating local minima from unstable configurations.
Spinodal decomposition is spontaneous growth of composition fluctuations in a homogeneous mixture whose local mixing free energy has negative composition curvature. For a mean , equal regions at change the mean free energy by , which is negative inside the spinodal. Interfacial costs suppress sufficiently short wavelengths, while conservation of composition constrains the dynamics. Outside the spinodal but inside the binodal, the uniform state is instead metastable and requires nucleation to begin separation.
A spinodal point is the limit of local metastability of a phase. At a mean-field spinodal, a local minimum merges with a neighboring maximum and the corresponding second derivative of the free energy vanishes.
For the Landau free energy with and , stationary branches satisfy . Their local stability requires . At a spinodal point, and , giving the displayed field magnitude. Following local minima without nucleation produces a hysteresis loop switching at these limits. Equilibrium instead switches between the two global minima at .
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The term "spinodal" is primarily used in the context of thermodynamics, specifically in phase separation processes in materials science and physical chemistry. It refers to a specific type of phase transition that occurs when a mixture is unstable and can separate into two or more distinct phases. In a broader sense, spinodal decomposition is a mechanism that describes how a homogeneous mixture becomes unstable. The spinodal curve defines the limits within which phase separation can occur spontaneously, even without nucleation.