The Cahn–Hilliard model of coherent lamellar microstructure: application to alkali feldspar

Abstract The temporal evolution of coherent lamellar microstructures is significantly influenced by their elastic properties, particularly when the exsolved phases are coherent. This research utilizes the Cahn–Hilliard model to examine the morphological and energetic evolution of binary alkali feldspar, integrating anisotropic elastic energy into the Gibbs energy equation. The Cahn–Hilliard model successfully simulated the orientation of lamellae observed in natural samples and the elastic strain was consistent with previous research. We also computed the coherent solvus from the annealing simulation of various precursor compositions and temperatures. The temperature difference ( $$\Delta T$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:mi>T</mml:mi> </mml:mrow> </mml:math> ) between the strain-free solvus and the coherent solvus was $$\Delta T = 85\,{}^\circ \text {C}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:mi>T</mml:mi> <mml:mo>=</mml:mo> <mml:mn>85</mml:mn> <mml:mspace/> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mo>∘</mml:mo> </mml:mmultiscripts> <mml:mtext>C</mml:mtext> </mml:mrow> </mml:math> , which is slightly lower than previously reported values obtained from similar parameters. This discrepancy is likely due to the presence of non-planar lamellae at the onset of phase separation, which are more stable than planar ones. We also simulated the binodal curves of the coherent solvi for different precursor phase compositions. The computed solvi were not unique but varied depending on the precursor composition. Our model is flexible because it does not assume any specific shapes for the lamellar interfaces and is applicable to various coherent binary systems.