14:45 〜 15:00
[SMP24-15] Synergistic numerical and analytical approaches for elucidating lamellae texture evolution in metamorphic and plutonic rocks
キーワード：ラメラ組織、フェーズフィールド法、ランダウ理論
The premise that local equilibrium is a robust and pertinent assumption for the mathematical analysis of textures in metamorphic and plutonic rocks holds considerable merit. in principal, local equilibrium suggests that thermodynamic equilibrium is maintained within minuscule areas of rock textures. With this assumption, the Gibbs free energy function, G(ni, ∇ni, ...), alongside the phenomenological diffusion equation, ∂tni=-divΣjLijgradμj, aptly characterizes the temporal evolution of rock textures. In order to conduct numerical simulations of lamellar textures, it is imperative to employ a model depicting a two-phase and two-component system, with particular attention to the elastic effects within binary solid solutions. This consideration is particularly critical for exsolved lamellae that maintain coherence, where coherence denotes the continuous lattice connection between the host and the exsolved lamellae.
In this study, we focused on Na-K alkali feldspar binary, which forms a microperthite texture in immiscibility region. Note that lattice strain resulting from Na-K interdiffusion, coupled with their significant difference in ionic radii, leads to the accumulation of elastic energy; in addition, the impact of elastic energy, influenced by factors such as chemical strain and stiffness coefficients, is notably pronounced in these coherent systems.
We derived numerical and analytical results by solving the phenomenological diffusion equation (see Figure 1). From a numerical standpoint, our simulations successfully demonstrated the textual formation processes. These simulations visually demonstrate that the presence of elastic energy disrupts phase separation, consequently destabilizing the two-phase coexistence region. From an analytical standpoint, we adapted the Gibbs free energy into a Ginzburg-Landau type free energy expression. This formulation elucidates the origins of phase anisotropy and the elastic effect on solvus temperature. In essence, the combined utilization of analytical and numerical methodologies furnishes a comprehensive comprehension of the mechanisms steering the formation and evolution of lamellar textures, thereby offering insights into their structural and compositional intricacies.
In this study, we focused on Na-K alkali feldspar binary, which forms a microperthite texture in immiscibility region. Note that lattice strain resulting from Na-K interdiffusion, coupled with their significant difference in ionic radii, leads to the accumulation of elastic energy; in addition, the impact of elastic energy, influenced by factors such as chemical strain and stiffness coefficients, is notably pronounced in these coherent systems.
We derived numerical and analytical results by solving the phenomenological diffusion equation (see Figure 1). From a numerical standpoint, our simulations successfully demonstrated the textual formation processes. These simulations visually demonstrate that the presence of elastic energy disrupts phase separation, consequently destabilizing the two-phase coexistence region. From an analytical standpoint, we adapted the Gibbs free energy into a Ginzburg-Landau type free energy expression. This formulation elucidates the origins of phase anisotropy and the elastic effect on solvus temperature. In essence, the combined utilization of analytical and numerical methodologies furnishes a comprehensive comprehension of the mechanisms steering the formation and evolution of lamellar textures, thereby offering insights into their structural and compositional intricacies.