Optimizing the directional solidification process of nickel-based superalloys is pivotal for enhancing the quality of hot-end castings in aero-engines. Traditional process optimization methods have heavily relied on empirical trial-and-error approaches, whereas numerical simulation technology is increasingly emerging as a pivotal tool. This paper presents a comprehensive review of the latest advancements in numerical simulation pertaining to the directional solidification process of nickel-based superalloys. It emphasizes modeling methodologies, simulation outcomes, and their practical applications in process optimization and defect control（such as stray grains and freckles） across various multi-physics fields, encompassing temperature fields, fluid flow and solute transport, stress-strain fields, and microstructural aspects（grains and dendrites）. A synthesis of current research reveals that numerical simulation studies still grapple with several shortcomings: a high degree of dependence on approximate boundary conditions in models; inadequate refinement and limited global optimization capabilities within process windows; incomplete numerical representations of certain crystalline defects and complex defect interactions; and substantial computational resource demands for high-fidelity microstructural simulations. To tackle these challenges, future research trends are anticipated to concentrate on deepening and integrating multi-physics and cross-scale coupling models, leveraging artificial intelligence-driven simulation and optimization, enhancing the precise characterization of solidification mechanisms in multi-component alloys, and strengthening experimental-simulation collaborative validation systems through the integration of in-situ characterization techniques with simulations. By advancing in these areas, numerical simulation technology is poised to play a pivotal role in achieving precise control over the morphology and properties of complex castings, while effectively mitigating defects.

Rare-earth phosphates (REPO₄) are regarded as one of the promising thermal/environmental barrier coating (T/EBC) materials for SiC_f/SiC ceramic matrix composites (SiC-CMCs) owing to their excellent resistance to water vapor and CaO–MgO–Al₂O₃–SiO₂ (CMAS). Nevertheless, a relatively high thermal conductivity (κ) of the REPO₄ becomes the bottleneck for their practical applications. In this work, novel xenotime-type high-entropy (Dy_1/7Ho_1/7Er_1/7Tm_1/7Yb_1/7Lu_1/7Y_1/7)PO₄ (HE (7RE_1/7)PO₄) has been designed and synthesized for the first time to solve this issue. HE (7RE_1/7)PO₄ with a homogeneous rare-earth element distribution exhibits high thermal stability up to 1750 ℃ and good chemical compatibility with SiO₂ up to 1400 ℃. In addition, the thermal expansion coefficient (TEC) of HE (7RE_1/7)PO₄ (5.96×10⁻⁶ ℃⁻¹ from room temperature (RT) to 900 ℃) is close to that of the SiC-CMCs. What is more, the thermal conductivities of HE (7RE_1/7)PO₄ (from 4.38 W·m⁻¹·K⁻¹ at 100 ℃ to 2.25 W·m⁻¹·K⁻¹ at 1300 ℃) are significantly decreased compared to those of single-component REPO₄ with the minimum value ranging from 9.90 to 4.76 W·m⁻¹·K⁻¹. These results suggest that HE (7RE_1/7)PO₄ has the potential to be applied as the T/EBC materials for the SiC-CMCs in the future.