Thermal and Microstructural Simulations of Photonic Sintering of Oxide Ceramics: A Two-Scale Scheme

TL;DR

The paper develops a two-scale, non-isothermal framework to simulate photonic sintering of oxide ceramics by coupling macro-scale heat transfer with micro-scale phase-field densification. The method transfers the macroscopic temperature field to microscopic domains via Hill-Mandel consistent BCs and uses asynchronous time stepping to resolve coupled thermo-structural evolution efficiently. The work demonstrates that macro-scale thermal profiles, material transport pathways, and potential transient liquid-phase mechanisms jointly govern densification and porosity gradients, achieving quantitative agreement with depth-resolved porosity data when surface diffusion is enhanced and depth-dependent mobility is calibrated (e.g., $Q_{a}^{\text{sf}}=10\,Q_{a}^{\text{gb}}$ gives $R^2=85.12\%$). Overall, the framework provides a predictive tool for optimizing PS parameters to tailor microstructure in BaZrO3-based protonic ceramics, with potential extension to fully two-way coupled simulations and in-situ validation.

Abstract

Photonic sintering (PS) offers an ultra-fast, contact-free alternative to conventional sintering and has demonstrated its potential for enhancing the sinterability of acceptor-doped barium zirconate (BZY) ceramics. However, a central challenge in the PS process lies in achieving precise control over thermal self-stabilization in the presence of complex microstructural effects arising from photonic-ray--induced thermal profiles. To elucidate the interplay among thermal fields, microstructural evolution, and PS process parameters, this study establishes a two-scale, non-isothermal simulation framework. The framework integrates macroscopic heat-transfer simulations, incorporating effective heat conduction and photonic-ray--induced volumetric heating in the porous media, with microscopic non-isothermal phase-field sintering simulations that resolve microstructure evolution under local thermal profile. Scale bridging is achieved through a temperature field transferring and mapping that satisfies Hill-Mandel condition between the macroscopic and microscopic simulations, while maintaining synchronization between their asynchronous time-stepping schemes. After calibrating model parameters against experimental measurements, the framework successfully reproduces the experimentally observed porosity inhomogeneity along the sample depth. The influence of enhanced localized mass transport is further examined through a parametric investigation of surface and grain boundary diffusivities. Overall, the proposed framework demonstrates its feasibility and physical interpretability in establishing process-microstructure relationships for the scalable fabrication of high-performance protonic ceramics.

Figures (7)

• Figure 1: (a) Experimental setup for PS, image is reprinted with permission from Porz et al.porzBlacklightSinteringCeramics2022 under the terms of the Creative Commons Attribution 3.0 Unported Licence. (b) The schematic of the proposed two-scale simulation. (c) The workflow of the proposed two-scale scheme on every sampled point.
• Figure 2: (a) Macroscopic mesh configuration showing element size and distribution, with insets illustrating the heat absorption profile and domain boundaries. (b) Microscopic initial powder stack with corresponding local mesh refinement.
• Figure 3: (a) Densification analysis: left - SEM image; right - thresholded image. (b) Isothermal densification curve at 1873 K, annotated with the degree of densification and corresponding times. Here the degree of densification $\theta$ is calculated from the porosity $\varphi$ as $\theta=1-\varphi$. (c) Workflow for calibrating the surface diffusivity.
• Figure 4: (a) Thermal history at the top central point $\mathrm{P}_1$ for varying powder absorptivity and light transfer efficiency, based on the ZSS model. Inset: schematic showing the location of $\mathrm{P}1$. (b) Thermal history at point $\mathrm{P}_1$ using different analytical effective thermal conductivity ($K_\text{eff}$) models, assuming constant porosity and fixed parameters ($A = 0.7$, $\eta = 0.1$). (c) Thermal history at point $\mathrm{P}_1$ under different maximum incident power flux $J_\mathrm{d}$. Inset: energy input profile, where $r_1$ and $r_2$ represent the power increasing and decreasing rates, respectively. (d) Thermal history at point $\mathrm{P}_1$ under various power loading paths.
• Figure 5: ($\mathrm{a}_1$)–($\mathrm{a}_4$) Temperature distribution within the domain at different times. (b) Temperature and temperature gradient distributions along the radial direction ($r$). (c) Temperature and temperature gradient distributions along the thickness direction ($z$).