**1. Introduction**

Alloys often contain tens of elements in strictly defined ratios with one element as "the base" of the alloy (e.g., all steels have more than 70 at.% Fe). Recently, a new design approach had emerged, which is focused on "baseless" or multi-principle element alloys (MPEAs) with the concentration of each element no more than 35 at.% but not less than 5 at.% [1]. The reports on complex, concentrated alloys (CCAs) appeared in the literature since the 1960s [2]; however, the new research direction took off in 2004 after the discovery of remarkable hardness, yield strength, and resistance to annealing softening in several MPEAs made by Taiwanese metallurgists [1,3]. They also introduced the term "high entropy alloys (HEA)," arguing that in these complex compositions, the gain in configurational entropy is responsible for the formation of simple single-phase solid solutions, rather than intermetallic compounds which would have a deleterious e ffect on the properties.

The high entropy design approach was recently applied to carbides [4,5] borides [6–8], and oxides [9–18] for high temperature and battery-related applications. Most of the high entropy compositions that were successfully prepared as single phases are within the 15% limit of atomic radii di fferences known as a Hume-Rothery [19] rule to metallurgists and as a Goldschmidt [20] limit for isomorphic mixtures to mineralogists (the majority of mineral species meet HE definition! [21]). While the argumen<sup>t</sup> about the role of configurational entropy is highly contentious [2,22], the name has its merits and rightfully attracts attention to thermodynamic controls, and we use the high entropy (HE) term to refer to five component rare earth oxides studied in this work.

It soon will be a century since Goldschmidt et al. [23] published the first research on rich polymorphism in rare earth sesquioxides (R2O3, where R is a lanthanide, Y or Sc). They originally divided quenchable polymorphs into A, B, and C types (Figure 1). The A-type is trigonal (*P*-3*m*1), typical for sesquioxides of the large lanthanides, and also called La2O3-type; the B-type is monoclinic (*C*2/*m*), typical for lanthanides in the middle of series and also called Sm2O3-type [24]; the C-type is cubic (*Ia*-3), typical for small lanthanides, Y and Sc, and also called bixbyite-type after the naturally occurring (MnFe)2O3 mineral.

**Figure 1.** Phase transformations in rare earth and yttrium sesquioxides vs. ionic radii for octahedral coordination. Lines connect the best values for pure sesquioxides. The data points represent temperatures of phase transitions from thermal analysis of three (La0.2Sm0.2Dy0.2Er0.2RE0.2)2O3 compositions studied in this work, where RE–Nd, Gd, or Y, plotted vs. average ionic radius.

Most rare earth oxides can be obtained in more than one structure type (polymorph) at ambient conditions: normally an A-type La2O3 and Nd2O3 can be synthesized in a C-type structure [25] at temperatures below ~500 ◦C (and C-type was predicted [26] to be their ground state structure); while normally C-type oxides from Dy to Yb were obtained in B-type structure in nanoparticles [27]. The oxides of trivalent actinides also found in these structure types [28]. Two high temperature structures were first identified by Foex and Traverse [29,30]. The H-type is hexagonal (*P*63/*mmc*) [31] and was reported for all rare earth and Y sesquioxides except Lu and Yb [32]. For oxides from La to Dy, the transformation of the hexagonal phase to the cubic X-type (*Im*-3*m*) structure was detected before melting [33]. The X-type structure was also reported to be formed in Tm2O3 and Lu2O3 after irradiation with Xe and Au ion beams [34].

The systematic research on phase equilibria in rear earth oxides has mostly been focused on pure oxides and several binary systems. There are only a few systematic investigations of ternaries and they are limited to studies on quenched samples [35,36]. All the studied systems of trivalent rare earth oxides are characterized by wide ranges of solid solutions in the structures identified in pure oxides. Eleven interlanthanide perovskites are known to form in several systems combining large and small rare earths: LaRO3 (R = Y, Ho-Lu), CeRO3 (R = Tm-Lu), and PrRO3 (R = Yb-Lu) [37–39]. They all show an orthorhombic (*Pnma*) distortion and do not melt congruently, but decompose at 800–2000 ◦C into solid solutions of one of rear earth oxide structure types [39]. LaGdO3 in a B-type structure attracted

attention for application as high-k gate dielectric [40] and as an optical temperature sensor when doped with Er/Yb [41,42].

Mixed three-four valent Ce, Tb, and Pr oxides with cubic defect fluorite related structures have been studied for gas sensor and catalyst applications [43]. Following the high entropy approach, Tseng et al. [44] studied thermal expansion and magnetic susceptibility of (Gd,Tb,Dy,Ho,Er)2O3 composition, which formed solid solution in a C-type structure. Djenadic et al. [11] reported that the presence of Ce4+ in several HE rare earth oxide compositions produced defect fluorite solid solutions.

In this work, we studied three compositions containing five rare earth sesquioxides in equiatomic ratios: (La,Sm,Dy,Er,RE)2O3, with RE either Nd or Gd or Y. All chosen rare earths are trivalent in the solid state, and their sesquioxides represent all polymorphs: A-type (La, Nd), B-type (Sm, Gd, Dy), and C-type (Er, Gd). However, they all form a H-type structure at high temperatures (Figure 1) with very intriguing properties, such as fast oxygen ion conductivity and superplasticity [45], but was never quenched to room temperature.

We performed laser melting, splat quenching, and annealing of the samples and characterized their high temperature phase transformations and thermal expansion by a combination of in situ differential thermal analysis and synchrotron diffraction on laser-heated samples. An unexpected and surprising finding was the substantial (>100 ◦C) increase in melting temperatures compared to those expected from consideration of melting points of constituent oxides.

#### **2. Materials and Methods**

The intimately mixed rare rear earth oxides of desired stoichiometry were first synthesized by the solution combustion method [46] and characterized by X-ray diffraction (XRD). Then, samples were laser melted in the hearth and in aerodynamic levitator and used for high temperature synchrotron XRD, differential thermal analysis (DTA), splat quenching, and prolonged annealing experiments. The experiment flow chart is provided in the Supplementary Materials (Figure S1).

## *2.1. Sample Synthesis*

Aqueous solutions of rare earth nitrates (Sigma-Aldrich 99.9% metals base) were mixed in desired stoichiometry. Ethylene glycol and citric acid were mixed at a molar ratio of 1 to 2 and added to the nitrate water solution. The mixed nitrate–citrate solution was evaporated at 150 ◦C under agitation by magnetic stirring until a highly viscous foam-like colloid was formed. This colloid was annealed in air at 800 ◦C for 96 h. An additional heat treatment was performed at 1100 ◦C for 12 h. The samples were analyzed by room temperature powder X-ray diffraction after each treatment.

#### *2.2. Laser Melting and Splat Quenching*

Powders after heat treatment at 1100 ◦C were laser melted in air on the copper hearth with 400 W CO2 laser and remelted in an argon flow in the aerodynamic levitator. The resulting samples were oblate spheroids 2.6–2.9 mm in diameter, with a flattening of ~0.1. The structure and phase transformations in obtained samples were studied by XRD and DTA. Sample composition and homogeneity were characterized by electron microprobe analysis. Laser-melted spheroids were further processed by splat quenching using a splittable nozzle aerodynamic levitator. The employed device is part of a drop-and-catch (DnC) calorimeter, described in detail earlier [47]. For quenching experiments, solid copper plates were installed in place of the calorimeter sensors (Figure S2). The samples produced by splat quenching were analyzed by room temperature XRD.

## *2.3. Microprobe Analysis*

A Cameca SX-100 electron microprobe was used for imaging and analysis of the chemical composition of laser-melted samples. Energy dispersive spectroscopy and backscattered electron imaging (BSE) were used for the characterization of sample homogeneity. Quantitative chemical analysis was performed by wavelength dispersive spectroscopy (WDS) using synthetic rare earth orthophosphate crystals for calibration standards for all rare earths except Y, for which synthetic Y3Al5O12 (YAG) was used due to flux originated Pb contamination detected in YPO4 standard.

#### *2.4. Room Temperature X-ray Di*ff*raction*

Room temperature powder XRD was used to characterize samples after precipitation, laser melting, splat quenching, differential thermal analysis, and synchrotron diffraction experiments. The measurements were performed using Bruker D8 Advance diffractometer (Bruker, Madison, WI, USA) with CuKa radiation and a rotating sample holder. The operating parameters were 40 kV and 40 mA, with a step size of 0.01◦ and dwell 3 s/step. Lattice parameters, phase fractions, and crystallite sizes of powders after annealing were refined using whole profile refinement as implemented in MDI Jade 2010 software package (Materials Data, Livermore, CA, USA). GSAS-II [48] was used for Rietveld [49] refinement of lattice parameters and phase fractions in laser-melted samples.

#### *2.5. High Temperature X-ray Di*ff*raction*

High-temperature X-ray diffraction experiments were performed on an aerodynamic levitator at beamline 6-ID-D at the Advanced Photon Source (APS), Argonne National Laboratory. The levitator at the beamline provided by Materials Developments, Inc. (Evanston, IL, USA) and described in detail elsewhere [50]. The samples 63–70 mg in weight, were prepared by laser melting as described above.

The diffraction experiments were performed in transmission geometry with X-ray wavelength 0.1236 Å (100.3 keV energy). The beam was collimated in a "letterbox" shape, 500 μm wide and 200 μm tall. The samples were levitated in argon flow and heated from the top with a 400-W CO2 laser. The levitator software provided manual control of the levitation gas flow rate and manual or automated laser power control for sample heating. Diffraction data were collected in 100-◦C increments based on the surface temperature of the levitated bead, which was monitored with a single color pyrometer (875–925 nm spectral band, IR-CAS3CS, Chino Co., Tokyo, Japan) with emissivity set to 0.92. Emissivities for rare earth oxides above 2000 ◦C are unknown [51], and thermal gradient in laser-heated aerodynamically levitated bead exceeds 100 ◦C [52–54]. In this work, the temperatures of diffracted volume were assigned based on phase transformation temperatures obtained from DTA measurements.

The diffraction images were recorded with a Perkin-Elmer XRD 1621 area detector positioned at a distance 1099 mm from the sample. The exposure time was set to 0.1 s to avoid detector saturation; 100 exposures were summed and recorded into a single image used for further processing with GSAS-II software [48]. The sample to detector distance, detector tilt, and beam center coordinates was calibrated using NIST CeO2 powder standard available at the beamline and with Y2O3 bead prepared by laser melting. The images from area detector were integrated from 1 to 7◦ 2Θ at 70–120 ◦ azimuth into diffraction patterns with 1600 points (0.00375 steps in 2Θ) (see Figure S3). Room temperature diffraction images were collected from every bead before and after laser heating. During the processing of diffraction data from the levitator, sample displacement was refined at room temperature from known cell parameters and kept constant during further refinements. Pawley [49,55] method, as implemented in GSAS-II, was used for refinement of unit cell parameters at high temperatures.

#### *2.6. Di*ff*erential Thermal Analysis*

Differential thermal analysis was performed with a Setaram Setsys 2400 instrument modified to enable excursions to 2500 ◦C. The experiments were conducted in Ar flow at heating and cooling rates 20 ◦C/min using WRe differential heat flow sensor and thermocouple for furnace temperature control.

Laser-melted beads, 100–140 mg in weight were placed in tungsten crucibles and sealed under Ar atmosphere to avoid the possibility of sample and standards contamination with carbon vapor from vitreous carbon protection tube. Multiple measurements were performed on each sample. Temperatures of phase transformations were determined as average from the onset [56] of endothermic peaks on heating. Enthalpies of phase transformation were calculated as the averages of absolute values of endothermic heat effects on heating and exothermic heat effects on cooling. The instrument and

methodology were described in detail elsewhere [53,57–59]. Temperature and sensitivity calibrations were performed using melting and phase transition temperatures and enthalpies of Au (1064 ◦C), Al2O3 (2054 ◦C), Nd2O3 (A-H, H-X, and X-L at 2077, 2201 and 2308 ◦C, respectively), and Y2O3 (C-H and H-L at 2348 ◦C and 2439 ◦C, respectively). It must be noted that international temperature scale ITS-90 [60] defines no fixed points above the freezing point of gold, albeit alumina melting temperature 2054 ± 6 ◦C was recommended to be included as a secondary reference point on the ITS [61,62].

## *2.7. Calphad Modeling*

Calphad [63–66] modeling was performed to compare with experimental results. Calphad-type thermodynamic database for rare earth sesquioxides was created by Zinkevich [67]. He critically reviewed all relevant experimental data available before 2006 and evaluated missing fusion enthalpies values based on measured enthalpy of fusion and volume change on melting for Y2O3. In a more recent evaluation by Zhang and Jung [68] evaluation, missing data were estimated from liquidus in RE2O3-Al2O3 phase diagrams. However, new measurements for fusion enthalpies [53] are in better agreemen<sup>t</sup> with Zinkevich's assessment. Zhang and Jung's evaluation varies largely with the values proposed by Konings et al. [69]. Zinkevich [67] database for rare earth sesquioxides is openly available at the NIST website [70] and was used in this work without any modifications. Thermo-Calc (Stockholm, Sweden) software was used for calculations.
