**5. Conclusions**

In this work, we studied three five-component compositions of trivalent rare earth sesquioxides: (La,Sm,Dy,Er,RE)2O3, with all oxides in equimolar ratios and RE either Nd or Gd or Y. All studied compositions demonstrated a C-B-A-H-X transformation sequence into structure types typical for rare earth sesquioxides. Monoclinic B-type phase was obtained in all compositions by laser melting and splat quenching and was retained after prolonged annealing at 800 ◦C. The experimentally observed phases are in good agreemen<sup>t</sup> with Calphad calculations performed using thermodynamic data for pure sesquioxides and the ideal solution model.

Compared with constituent oxides, A-type and X-type phases occur at wider temperature ranges in the studied compositions. The measured room temperature volumes of C and B phases and volume changes on C-B, B-A, and H-X transitions are in good agreemen<sup>t</sup> with those predicted from constituent oxides. No anomalies in thermal expansion of B-type solid solution and in volumes of H-type phases were detected. The obtained data on temperatures, enthalpies, and entropies of transitions can be used for benchmarking the next generation of thermodynamic databases for rare earth oxides. The observed increase in melting temperature compared with constituent oxides invites experimental and theoretical investigations of Sm2O3-Dy2O3, Dy2O3-Er2O3, Er2O3-Sm2O3 systems for which no data on melting temperatures are available.

**Supplementary Materials:** The following are available online at http://www.mdpi.com/1996-1944/13/14/3141/s1, Figure S1: The flow chart of performed experiments, Figure S2: Aerodynamic levitator with splittable nozzle and copper plates for splat quenching. Figure S3: Integration of area detector diffraction images of aerodynamically levitated bead, Figures S4–S6: Back-scattered electron micrograph of the laser-melted samples, Figure S7: Room-temperature X-ray diffraction patterns of HE-Y, HE-Gd and HE-Nd samples from solution combustion synthesis, Figure S8: Rietveld refinement plot of HE-Nd sample after calcination in air at 800 ◦C for 96 h, Figure S9: Rietveld refinement plot of HE-Nd sample after splat quenching from melt, Figure S10: Room-temperature powder XRD patterns on Sm2O3 sample after annealing at 800 ◦C and after laser melting, Figure S11: Heat flow trace vs. sample temperature for HE-Gd sample, Figure S12: Pawley refinement of unit cell parameters for B and A phases of HE-Gd sample at transition temperature, Figure S13: Pawley refinement of unit cell parameters for H and X phases of HE-Y sample at transition temperature, Figure S14: Calphad modeling of phase fractions in HE-Y, HE-Gd and HE-Nd samples.

**Author Contributions:** Conceptualization, S.V.U., S.H. and A.N.; samples synthesis and characterization, S.H. and S.V.U.; thermal analysis S.V.U.; Calphad computations, W.G.; writing—original draft preparation, S.V.U. and S.H.; writing—review and editing, W.G. and A.N.; visualization, S.V.U. and S.H. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by National Science Foundation under the award NSF-DMR 1835848 (changed to NSF-DMR 2015852 on funding moved from UC Davis to ASU). Use of the Advanced Photon Source (APS, beamline 6-ID-D), an Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory, was supported by the DOE under Contract No. DEACO2-06CH11357.

**Acknowledgments:** The authors gratefully acknowledge Matvei Zinkevich, Maren Lepple and Vladislav Gurzhiy for helpful discussions. The high temperature diffraction experiments would not be possible without Chris Benmore and Richard Weber ensuring operation and upgrades of aerodynamic levitator at beamline 6-ID-D at APS. Microprobe analysis was performed by Nicolas Botto.

**Conflicts of Interest:** The authors declare no conflict of interest.
