This type of phase transformation is known as spinodal decomposition, and can be illustrated on a phase diagram exhibiting a miscibility gap. Thus, phase separation occurs whenever a material transition into the unstable region of the phase diagram. The boundary of the unstable region sometimes referred to as the binodal or coexistence curve, is found by performing a common tangent construction of the free-energy diagram. Inside the binodal is a region called the spinodal, which is found by determining where the curvature of the free-energy curve is negative. The binodal and spinodal meet at the critical point. It is when a material is moved into the spinodal region of the phase diagram that spinodal decomposition can occur.
The [https://www.doitpoms.ac.uk/tlplib/phase-diagrams/freeenergy.php#:~:text=The%20phase%20with%20the%20lowest,the%20liquid%20phase%20is%20stable. free energy curve] is plotted as a function of composition for a temperature below the convolute temperature, T. Equilibrium phase compositions are those corresponding to the free energy minima. Regions of negative curvature (∂f/∂c f/∂c = 0 ) which are called the spinodes. Their locus as a function of temperature defines the spinodal curve. For compositions within the spinodal, a homogeneous solution is unstable against infinitesimal fluctuations in density or composition, and there is no thermodynamic barrier to the growth of a new phase. Thus, the spinodal represents the limit of physical and chemical stability.
To reach the spinodal region of the phase diagram, a transition must take the material through the binodal region or the critical point. Often phase separation will occur via nucleation during this transition, and spinodal decomposition will not be observed. To observe spinodal decomposition, a very fast transition, often called a quench, is required to move from the stable to the spinodal unstable region of the phase diagram.
In some systems, ordering of the material leads to a compositional instability and this is known as a conditional spinodal, e.g. in the feldspars.