High-entropy fluorite oxides (HEFOs) show significant potential for thermal protection applications due to their advantageous combination of low thermal conductivity and high Yong’s modulus. However, the factors influencing its formation have not been well studied and the systematic method for compositional design has not yet been established. In this paper, effects of oxygen vacancy concentration (O_vac) and mean cation radius ( ) on the formability of HEFOs have been investigated aiming to develop a compositional design approach. The results indicate that an appropriate  and O_vac are crucial for promoting the formability of single-phase (Ca_xCe_y1Zr_y2Hf_zSn_zTi_z)O_2-δ HEFOs. High mass/size disorder and appropriate O_vac (10%) result in (Ca_0.2Ce_0.14Zr_0.12Hf_0.18Sn_0.18Ti_0.18)O_2-δ exhibiting the lowest thermal conductivity of 1.24 W·m^-1·K^-1. Building upon these insights and employing a valence combination strategy, three new single-phase HEFOs with low thermal conductivity were successfully designed and synthesized, including (La_0.28Y_0.28Ce_0.18Zr_0.18W_0.08)O_2-δ, (La_0.3Y_0.3Ce_0.2Nb_0.1Ta_0.1)O_2-δ, and (Yb_0.52Ce_0.12Zr_0.12Sn_0.12Nb_0.12)O_2-δ. The design approach will provide a valuable reference for the design of other high-entropy oxides.

In this paper, cordierite-based porous ceramics with magnetic properties have been firstly in-situ synthesized by using MgO, Al₂O₃, and SiO₂ powders as raw materials and Fe₃O₄ as a functional additive. Combining with the foam freeze casting method, near net size fabrication (total linear shrinkage < 2.86%) of the magnetic porous materials was realized by adjusting the amount of Fe₃O₄. The porosity, compressive strength, and saturation magnetization of the prepared materials were 83.9%–87.8%, 1.51–2.65 MPa, and 1.2–5.8 emu/g, respectively. The phase composition and microstructure evolutions during sintering were investigated briefly. The results showed that the synthesis temperature of cordierite was lowered about 100 ℃ due to the addition of Fe₃O₄. Except for the main phase-cordierite, Mg–Al–Fe spinel and α-Fe₂O₃ also existed in the final materials. The lattice parameters of the Mg–Al–Fe spinel and the amount of α-Fe₂O₃ changed obviously with the change in the sintering temperature and Fe₃O₄ amount, which mainly influenced the magnetic properties of the prepared materials. Thus, a facile fabrication method of the cordierite-based porous ceramics with the magnetic properties has been put forward in this paper.