Thermodynamics of dual-phase compositionally complex ceramics: A case study of ultrahigh-entropy fluorite-bixbyite refractory oxides
Heidy Vega, Mingde Qin, Jian Luo
Abstract
A set of 8-, 10-, 12-, and 14-component compositionally complex refractory oxides (CCROs, containing Nb, Ta, Ti, Zr, Hf, Ce, Yb, Tm, Er, Ho, Y, Dy, Tb, and Gd) have been successfully fabricated. In addition to five single-phase high- and ultrahigh-entropy CCROs in either bixbyite or defect fluorite structure, nine dual-phase CCROs have been made with co-existing fluorite and bixbyite phases in a thermodynamic equilibrium one another, representing a new class of dual-phase compositionally complex ceramics (DP-CCCs). A thermodynamic relation dictating the dual-phase equilibria is discovered, where the ratio of the atomic fractions in the two equilibrium phases remains roughly a constant. Interestingly, this ratio for eight different trivalent rare-earth cations linearly depends on the ionic radius (ri). A further analysis showed that the differential enthalpy of solution in the bixbyite versus fluorite phase approximately follows ΔHi (eV) = –0.80·(ri – 1.06 Å). Such thermodynamic relations are important for designing DP-CCCs.