Coherent lamellar phase decomposition of alkali feldspar studied by a microscopic approach

The Gibbs energy due to coherency strain associated with lamellar phase decomposition, including vibrational components, was investigated, using a microscopic perspective combining atomistic calculations based on density functional theory and calorimetric measurements. The model was applied to the lamellar decomposition of alkali feldspar, revealing that the coherency strain energy coefficient does not only depend on temperature and starting composition, as is the case within the macroscopic, i.e., continuum-mechanical approach, but it also depends on the chemical gradient at the lamellar interfaces and on the lamellar thickness. This difference to the macroscopic approach is caused by a realistic relaxation of the structure in the interior of the lamellae. The coherency strain energy coefficient decreases with decreasing chemical gradient. However, the lowering of the chemical gradient causes the unmixing process to be incomplete increasing the Gibbs energy of mixing, which destabilises lamellae with small chemical gradients. This incompleteness of the unmixing process was quantified in a correction procedure, which was then used to calculate the correct Gibbs energy of mixing. A minimisation procedure of the Gibbs energy that contains components from both mixing and coherency strain resulted in the determination of the equilibrium chemical gradient at lamellar interfaces and its dependence on temperature and lamellar thickness. Although the coherency strain energy coefficient depends on lamellar thickness and chemical gradient, the Gibbs energy minimisation results in a single coherent solvus, which is independent of these properties and is found to agree well with experimental data. The new method can be adapted for coherent lamellar decomposition in other binary solid solutions and alloys.