Fig. 6: Entropy and enthalpy descriptors for five-component oxides.
From: Phase stability of entropy stabilized oxides with the α-PbO2 structure
Entropy and enthalpy descriptors (μ and σ of \(\Delta {H}_{{{{{{{{\rm{mix}}}}}}}}+{{{{{{{\rm{trans}}}}}}}}}[A{A}^{{\prime} },P]\) respectively) including the penalty on Pb for all the possible five-component oxides in the four crystal structures: a α-PbO2, b rutile, c baddeleyite, and d fluorite. The green shaded region indicates empirical synthesizability. Most compositions are far outside of the green region, but some of our attempted syntheses are quite close. The three compositions marked with stars, (Ti, Zr, Hf, Sn, Pb)O2 (red star), (Ti, Zr, Hf, Sn, Ce)O2 (maroon star), and (Ti, Zr, Hf, Sn Ge)O2 (pink star) are identical to the successfully synthesized four-component phase with the addition of Pb, Ce, and Ge, respectively. We find that none of these compositions form as single phase materials under solid state synthesis conditions, supporting the empirical range of stability for the enthalpy and entropy descriptors.
