**3. Results**

### *3.1. Chemical Composition*

The composition was determined by microprobe analysis on laser-melted samples recovered after high temperature diffraction experiments. The measured ratios were close to nominal, indicating no preferential loss of any component on melting and laser heating during diffraction experiments. The microprobe results are reported in Table 1, with variations given as two standard deviations of the mean of 12 analyses per sample. Backscattered electron micrographs are included in Supplementary Materials (Figures S4–S6). The following stoichiometries of synthesized rare earth sesquioxides were obtained: (La0.18Sm0.20Dy0.18Er0.18Y0.26)2O3, (La0.19Sm0.21Dy0.21Er0.20Gd0.19)2O3, and (La0.20Sm0.20Dy0.21Er0.20Nd0.19)2O3. For the sake of brevity, we will refer to these compositions as HE-Y, HE-Gd, and HE-Nd, respectively, where "HE" stands for "high entropy" and element symbol is for rare earth element in (La,Sm,Dy,Er,RE)2O3 nominal composition.

**Table 1.** Atomic percent of rare earth cations in laser-melted rare earth sesquioxides from the results of wavelength dispersive microprobe analysis.


1 The average ionic radius of rare earth after Shannon [71] for RE<sup>+</sup><sup>3</sup> in octahedral coordination.

#### *3.2. Phases after Solution Combustion Synthesis and Annealing*

After 800 ◦C annealing of powders from solution combustion synthesis, the cubic C-type phase with crystallite size 20–40 nm was a major phase in all samples. The B-type phase was also detected in HE-Nd and HE-Gd samples (Table 2, Figures S7 and S8). After annealing of the powders at 1100 ◦C, only the B-type phase was identified in HE-Nd sample; the amount of B-type phase in HE-Gd sample increased to 70 wt.%. The C-type phase was retained in HE-Y composition, and its crystallite size increased to ~65 nm. The decrease in volume on C-B transformation was calculated from XRD data in HE-Nd and HE-Gd samples as 8% on average.


**Table 2.** The phase composition of powders after calcination at 800 ◦C and heat treatment at 1100 ◦C.

The numbers in brackets indicate uncertainty in the last digit from the refinement of XRD data.

#### *3.3. Phases after Laser Melting, Splat Quenching, and Annealing*

Melt processing yielded a B-type phase in all studied compositions. Room temperature XRD patterns are shown in Figure 2; the example of the whole profile refinement plot is included in Figure S9. The unit cell parameters and crystallite sizes of B-phase measured after splat quenching from ~3000 ◦C and after laser melting and 60 days annealing, are listed in Table 3.

In splat-quenching experiments, samples were heated in oxygen flow to the temperature several hundred degrees above the melting point to allow for cooling during ~100 ms drop time from the splittable nozzle to the splat-quenching plates. Sixty days annealing at 1100 ◦C was performed on the laser-melted samples, recovered after thermal analysis. The crystallite sizes of splat-quenched samples were about 80 nm. The crystallite sizes of the laser-melted samples after thermal analysis and annealing were in the range of 95–150 nm. The decrease in volume of B-type phase after annealing compared to splat-quenched samples was calculated from measured cell parameters as 0.6–0.8%. This variation is consistent with the retention of thermally induced defects in splat-quenched samples.

**Figure 2.** (**A**), (**B**), (**C**): powder X-ray diffraction patterns of three (La0.2Sm0.2Dy0.2Er0.2X0.2)2O3 compositions, where X–Y, Gd, or Nd, respectively. Patterns were collected at room temperature using CuK radiation (λ = 1.54056 Å) on samples obtained by splat quenching (s. q.) of the melts from indicated temperatures and after annealing at 800 ◦C for 60 days. All patterns identified as monoclinic (B-type) phases. Table 3 lists the results of cell parameters refinements. The typical profile refinement plot is presented in supporting information (Figure S9 in Supplementary Materials).

**Table 3.** Room temperature unit cell parameters and crystallite sizes of HE samples after splat quenching from ~3000 ◦C, and after laser melting and annealing at 800 ◦C for 60 days. All samples were indexed in a monoclinic B-type structure (S.G. *C*2/*<sup>m</sup>*, Sm2O3-type).


\* Cell parameters refined with internal standard on HE-Nd sample after HTXRD experiments (*a*, *b*, *c*, β): 14.244(1) Å, 3.610(2) Å, 8.852(2) Å, 100.611(5)◦.

All samples after melting show an increase in the intensity of (4, 0, −2) peak of B-phase compare with calculated from an ideal B-type structure. This variation is not related to the complex composition of the studied sample since we observed a similar effect in pure Sm2O3 (Figure S10) and it is likely due to twinning [72].

#### *3.4. Temperatures and Enthalpies of Phase Transformations from DTA Experiments*

Thermal analysis was performed on laser-melted samples to enable sealing W crucibles; thus, the initial structure for all samples was B-type. The transition temperatures detected in the samples by differential thermal analysis are plotted in Figure 1; the data are summarized in Table 4.

On heating to 2400 ◦C, three reversible heat effects were observed in all samples, which were assigned to B-A, A-H, and H-X phase transformations (Figure S11). Enthalpies of transformations obtained from endothermic peaks on heating and exothermic peaks on cooling were generally consistent and were averaged to obtain the values listed in Table 4. The range of undercooling increased with transition temperature, with maximum observed values 14, 43, and 63 ◦C for B-A, A-H, and H-X transformations, respectively. For the A-H transition, the width of DTA peaks on heating in studied samples was similar to that observed for pure Nd2O3 at the same heating rate [59]. However, the peaks corresponding to B-A and H-X transformations were substantially wider than those for A-H in HE

compositions and for H-X in pure Y2O3 and Nd2O3 (e.g., 41–44 ◦C for H-X transition in HE samples vs. 12 ◦C for pure Nd2O3).


**Table 4.** Results of thermal analysis of (La0.20Sm0.20Dy0.21Er0.20Nd0.19)2O3 (HE-Nd), (La0.19Sm0.21 Dy0.21Er0.20Gd0.19)2O3 (HE-Gd), and (La0.18Sm0.20Dy0.18Er0.18Y0.26)2O3 (HE-Y) samples.

\* The uncertainties are reported as two standard deviations of the mean with the number of experiments given in parentheses.

Temperatures and enthalpies of transitions increased with decreasing average ionic radius, from HE-Nd to HE-Gd to HE-Y, consistent with the trend among pure rare earth sesquioxides. The exception was the enthalpy of B-A transition in HE-Y sample, which, although the same within calculated uncertainties, appeared ~2 kJ/mol smaller than that for B-A transition in HE-Gd sample.

Transition entropies were calculated from trsS = trsH/T, where T is the temperature in Kelvin at the transition onset on heating. Entropies of transitions are nearly constant between compositions, with average values ~9 J/mol/K for B-A transformation; ~3.4 J/mol/K for A-H transformation, and ~11.5 J/mol/K for H-X transformation, except for ~16 J/mol/K value for H-X transformation of HE-Y at 2254 ◦C. This deviation might be related to the fact that pure Y2O3 does not undergo H-X transformation.

During DTA experiments above 2300 ◦C, the failure of the sensor is frequent, and the maximum achievable temperature is limited by magnitude and direction of temperature drift of the control WRe thermocouple. For the calibration of the DTA thermocouple in this temperature range, pure Y2O3 (Tm 2439 ± 12 ◦C) [73] was used as a standard. All studied compositions were heated to temperatures above 2450 ◦C; however, the peak corresponding to melting onset was registered only for HE-Nd sample at temperature 17 ◦C above the melting point of Y2O3 (Figure 3). Due to the significant uncertainties in baseline choice and sensitivity calibration at this range, the enthalpy and entropy of fusion were not evaluated.

#### *3.5. Volume Changes and Thermal Expansion from High-Temperature XRD*

In diffraction experiments on levitated samples, powder-like diffraction patterns are obtained by ensuring the rotation of the solid sample in the gas flow [53,54,58]. When sample spheroids are prepared by melt solidification, as in this study, the exact shape of each bead depends on the surface tension of the particular composition, volume change on melting, and stochastic nature of nucleation. Due to these variations and crystal growth at high temperature, the rotation does not always produce the required random orientation of crystallites. In some cases, data are amenable to structure refinement [32,52]; however, in the present study, variations in intensities only allowed unambiguous identification of B-A and H-X transformations and refinement of the unit cell parameters of corresponding phases.

**Figure 3.** (**A**) The schematic of differential thermal analyzer and samples placement. (**B**) Heat flow trace (no baseline subtraction), showing heat effects on heating from HE-Nd ((La0.20Sm0.20Dy0.21Er0.20Nd0.19)2O3) and Y2O3 samples. Endothermic B-A-H-X-Liquid transformations for HE-Nd are labeled in black. Endothermic C-H-Liquid transformations for Y2O2 are labeled in red. The assignment of the exothermic direction of the heat flow signal for HE-Nd and Y2O3 is the opposite due to the placement of the samples. Melting temperatures for Y2O3 and HE-Nd are marked on the temperature trace. The Y2O3 melting point (2439 ◦C) was used for calibration.

The A-H transformation shows well pronounced peaks in DTA measurements (Figure S11); however, the diffraction patterns of A and H phases are very similar (Figure 4). In our experiments, the data quality did not allow us to unambiguously identify the A-H transition from diffraction on levitated samples. Volume changes on B-A and H-X transformations were calculated from unit cell parameters at phase transformation temperatures. The data are presented in Table 5, and examples of refinements are included in Supplementary Materials (Figures S12 and S13). Both transitions are accompanied by volume contraction. The volume change on B-A transition was refined for all samples and found to be −2.5 ± 0.1% for HE-Nd and HE-Gd and −3.1 ± 0.1% for HE-Y (Table 5).

**Figure 4.** (**A**) Calculated X-ray diffraction patterns for different structure types for (La, Sm, Dy, Er, Nd)2O3 composition and instrument parameters corresponding to the experimental condition (λ = 0.1236 Å). Note the similarity of diffraction patterns for A and H structures. (**B**) GSAS-II contour plot of experimental diffraction patterns collected at 1800–2200 ◦C on laser-heated HE-Nd bead. See Figures S11 and S12 for refinement plots.


**Table 5.** High-temperature unit cell parameters and volume changes on B-A and H-X transformation in HE samples from synchrotron diffraction on laser-heated levitated samples.

The thermal expansion of the B-type phase from room temperature to the B-A transition was calculated from room temperature cell parameters of annealed samples (Table 3) and cell parameters at the transition temperature (Table 5). The thermal expansion is anisotropic and similar for all three compositions. The smallest expansion is observed in *a* parameter (7.8 ± 0.7) × <sup>10</sup>−<sup>6</sup>/K, linear thermal expansion coefficients along *b* and *c* directions are (1.6 ± 0.2) × <sup>10</sup>−<sup>5</sup>/<sup>K</sup> and (1.2 ± 0.5) × <sup>10</sup>−<sup>5</sup>/K, respectively. The average volume thermal expansion coefficient for all studied compositions in the B-type structure is (3.5 ± 0.2) × <sup>10</sup>−<sup>5</sup>/K.

Due to the narrow temperature range of stability of A and H phases, the accurate calculation of thermal expansion is not possible. For HE-Nd sample, the average volume thermal expansion of A and H phases appears to be similar to that for the B phase, but for HE-Y an increase in thermal expansion is observed. The volume change on H-X transformation was refined for HE-Nd and HE-Y compositions as −1.2 ± 0.1% and −0.6 ± 0.1%, respectively.
