Phase Stability of Nanocrystalline Grains of Rare-Earth Oxides (Sm2O3 and Eu2O3) Confined in Magnesia (MgO) Matrix

Rare-earth (RE) oxides are important in myriad fields, including metallurgy, catalysis, and ceramics. However, the phase diagram of RE oxides in the nanoscale might differ from the phase diagrams for bulk, thus attracting attention nowadays. We suggest that grain size in the nanoscale also determines the obtained crystallographic phase along with temperature and pressure. For this purpose, nanoparticles of Sm2O3 and Eu2O3 were mixed in an inert MgO matrix via the sol-gel method. This preparation method allowed better isolation of the oxide particles, thus hindering the grain growth process associated with increasing the temperature. The mixed oxides were compared to pure oxides, which were heat-treated using two methods: gradual heating versus direct heating to the phase transition temperature. The cubic phase in pure oxides was preserved to a higher extent in the gradual heating treatment compared to the direct heating treatment. Additionally, in MgO, even a higher extent of the cubic phase was preserved at higher temperatures compared to the pure oxide, which transformed into the monoclinic phase at the same temperature in accordance with the phase diagram for bulk. This indicates that the cubic phase is the equilibrium phase for nanosized particles and is determined also by size.


Introduction
Rare-earth (RE) oxides have gained popularity over the years owing to their versatile applications, such as the nuclear field (Sm 2 O 3 is used as an absorber in control rods), solid oxide fuel cells (Sm 2 O 3 -doped ceria electrolyte was found to have a high ionic conductivity), phosphor materials (Eu 2 O 3 is used as red or blue phosphor), catalysis, laser, optical, and more [1][2][3].
The crystallographic structure influences the physical and chemical properties of RE oxides and thus determines their functionality. Hence, achieving a better understanding of phase stability behavior has been a continuous research aim, but mainly regarding the influence of pressure and temperature rather than that of crystal size [4][5][6][7].
All the rare-earth elements form a sesquioxide of RE 2 O 3 . Regarding the polymorphism of rare-earth oxides, five different crystallographic phases are known: at temperatures lower than about placed in an ice bath in order to induce precipitation of more soluble magnesium hydroxide (Mg(OH) 2 ). After a hydrolysis of precursors and obtaining a homogeneous solution, an ammonium hydroxide solution (2 N) was dripped slowly into the mixture, which turned more milky and viscous with each drop. Finally the gel point was observed at a pH value of 10, and the dripping stopped. The gel's precipitates were dried in an air furnace at 343 K for 4 days. The powder was ground using an agate mortar and divided into different sample batches, which were gradually heated (5 K/min) in air to the desired calcination temperature (in the range of 873-1473 K) using alumina (Al 2 O 3 ) crucibles, and then calcined for 2 h in order to demonstrate the transformation of crystallographic phase transitions. Samples of pure oxides were also immediately placed in the furnace at the phase transition temperature and calcined for 2 h in order to compare this process with the previously mentioned thermal treatment.
X-ray diffraction (XRD; DMAX 2100 powder diffractometer, Rigaku, Japan) studies were performed using powder diffraction with Cu Kα 1 radiation. The XRD patterns were analyzed using the Powder-Cell program [23], and Rietveld refinement was also carried out using the FullProf/ WinPLOTR software (T. Roisnel\J. Rodriguez-Carvajal, CDIFX UMR6226 Rennes\ILL Grenoble, France) [24,25]. The morphology and chemical composition was investigated using a high-resolution scanning electron microscope (HR-SEM; JSM-7400, JEOL, Tokyo, Japan) with back scattered electrons detector (BSE) contrast and energy dispersive spectroscopy (EDS; JSM-7400, JEOL, Tokyo, Japan). The accelerating voltage and working distance were 10 kV and 6.1 mm, respectively. The samples were fixed on a graphite tape and coated with a thin layer of carbon in order to increase the electrical conductivity. The composition analysis of the sol-gel powder was also investigated by inductively coupled plasma optic emission spectroscopy (ICP-OES; Spectro Arcos, Kleve, Germany). The crystal size (below 60 nm) was evaluated based on XRD analysis using the Williamson-Hall approach and by HR-SEM using imageJ (image processing software; National Institutes of Health, Bethesda, MD, USA) in the higher nano-range (above 60 nm).

Results
ICP-OES results confirmed that following the sol-gel synthesis, the powder composition was consistent with the theoretical design (maximal deviation of~5%). The results are shown in Table 1. The XRD patterns of MgO with different concentrations of Sm 2 O 3 calcined at different calcination temperatures are shown in Figure 1. All samples were gradually heated to the final temperature and were calcined for 2 h. Peaks originated from Sm 2 O 3 are marked by "S", and those originated from MgO are marked by "M". In cases where the monoclinic phase of the rare-earth oxide was apparent, it was marked by "m-S". In all compositions, for calcination temperatures of 873-1273 K, the Sm2O3 was in the cubic phase and began the c  m transition at calcination temperatures of 1373-1473 K (mixture of cubic and monoclinic). A sole monoclinic phase was observed at 1473 K (2 hours) for 40 vol % Sm2O3 in MgO only. On the other hand, according to Figure 3a, pure Sm2O3 already started the c  m transition at 1273 K (in accordance with Roth and Schneider [11]), and this transition was completed at 1473 K. Hence, the transition from the cubic to the monoclinic phase was delayed for all tested concentrations of Sm2O3 in MgO in comparison with pure Sm2O3. The crystallite size was calculated via the Williamson-Hall plot: where β is the broadening of the diffraction line measured at half of the maximum intensity, λ is the wavelength (Cu-κα), θ is the Bragg angle for a given diffraction, and k is a constant, which is in general equals 0.94 for powders. The instrumental broadening effect was estimated by subtracting the full width at half-maximum of a standard sample (LaB6) from β of the respective Bragg peaks. L represents the crystallite size, and Ԑ represents the lattice strain. The characteristic Williamson-Hall plot corresponds to the graph of β·cos(θ) versus sin(θ). After data collection, a linear regression should give a linear fit. The crystallite size was extracted from the y-intercept of the ( • L ) fit.
Regarding the grain size, grains of cubic Sm2O3 in MgO were smaller (broader peaks) in comparison with pure Sm2O3 (sharper peaks) for the same calcination temperature (for example: for 5-40 vol % Sm2O3 in MgO calcined at 1273 K, the average cubic grain size was in the range of 30-80 nm, where β is the broadening of the diffraction line measured at half of the maximum intensity, λ is the wavelength (Cu-κα), θ is the Bragg angle for a given diffraction, and k is a constant, which is in general equals 0.94 for powders. The instrumental broadening effect was estimated by subtracting the full width at half-maximum of a standard sample (LaB 6 ) from β of the respective Bragg peaks. L represents the crystallite size, and ε represents the lattice strain. The characteristic Williamson-Hall plot corresponds to the graph of β·cos(θ) versus sin(θ). After data collection, a linear regression should give a linear fit. The crystallite size was extracted from the y-intercept of the ( k·λ L ) fit. Regarding the grain size, grains of cubic Sm 2 O 3 in MgO were smaller (broader peaks) in comparison with pure Sm 2 O 3 (sharper peaks) for the same calcination temperature (for example: for 5-40 vol % Sm 2 O 3 in MgO calcined at 1273 K, the average cubic grain size was in the range of 30-80 nm, respectively, while for pure Sm 2 O 3 , the average grain size was greater than 100 nm). Table 2 summarizes the experimental results for Sm 2 O 3 :   Figure 2. All samples were gradually heated to the final temperature and were calcined for 2 h. Peaks originated from Eu 2 O 3 are marked by "E", and those originated from MgO are marked by "M". In cases where the monoclinic phase of the rare-earth oxide was apparent, it was marked by "m-E".
In temperature and were calcined for 2 hours. Peaks originated from Eu2O3 are marked by "E", and those originated from MgO are marked by "M". In cases where the monoclinic phase of the rare-earth oxide was apparent, it was marked by "m-E". In compositions of 5, 10, and 20 vol % Eu2O3 in MgO, the Eu2O3 remained cubic at each calcination temperature in the range of 873-1473 K. On the other hand, according to Figure 3b, pure Eu2O3 was mostly monoclinic at 1473 K (approximately 83%). Hence, the transition from the cubic to the monoclinic phase was delayed in the MgO-Eu2O3 systems containing 5, 10, and 20 vol % Eu2O3 in MgO. Regarding grain size, grains of cubic Eu2O3 in MgO were smaller (broader peaks) in comparison with pure Eu2O3 (sharper peaks) for the same calcination temperature (for example: for 5 vol % Eu2O3 in MgO calcined at 1473 K, the grain size was approximately 30 nm, while for pure Eu2O3, the average grain size was greater than 100 nm). Table 3 summarizes the experimental results for Eu2O3.  According to Tables 2 and 3, in general, for a given concentration of the RE 2 O 3 in MgO, crystal size increases when raising the calcination temperature. In addition, for a given calcination temperature, crystal size increases when the concentration of the RE 2 O 3 in MgO increases. Thus, crystal growth is more suppressed when a smaller amount of the RE 2 O 3 is embedded in the MgO matrix. Moreover, the monoclinic structure was obtained when large enough crystals were formed, while smaller crystals remained cubic. Thus, the presence of a mixture of the two phases (cubic and monoclinic) is due to non-uniformity in crystal size.
In all samples, the lattice parameter of MgO was normal and nearly a constant (4.212 ± 0.002 Å). In general, the RE 2 O 3 -MgO systems have a lower lattice parameter compared with the pure oxides, and for a given concentration, the unit cell parameter decreased as temperature increased. The MgO matrix exerted hydrostatic pressures on the embedded oxide during cooling down caused by the higher thermal expansion coefficient of the MgO matrix [26,27].  Pure Sm2O3 started the c  m transformation at 1273 K (9% monoclinic) and completed the transition at 1473 K, while pure Eu2O3 started the transformation at 1473 K (83% monoclinic). The transition temperatures for both oxides are in accordance with the traditional phase diagram [11]. However, the low fraction of the monoclinic phase at the transition temperatures (especially for Sm2O3) indicates a possible suppression during the grain growth process that might be associated with the thermal treatment procedure. A comparison between the two different thermal treatment processes regarding pure Sm2O3 and Eu2O3 is shown in Figure 4. In the monoclinic structure, the mean distance between ions is smaller, and the bond energy is minimal. On the other hand, the cubic structure is characterized by larger distances between the ions, but this structure is isometric and therefore has higher entropy. In systems with nanosized particles (high surface area to volume ratio), the effect of surface area becomes significant and affects the Gibbs energy of each phase [19,[28][29][30]; therefore, systems of nanoparticles show different behaviour in comparison with bulk materials. Here, in powder with smaller crystallites, the cubic phase (low surface energy phase) is favoured. In other words, in nanometric crystals, the surface energy plays a more dominant role, and there is a preference for the cubic structure rather than the monoclinic. Above a certain size, the surface energy is no longer a dominant factor, and the cubic phase transforms into the monoclinic phase. A similar effect was shown regrading other oxides such as plasma sprayed films of Y 2 O 3 [31], and tetragonal ZrO 2 and gamma Al 2 O 3 synthesized from aqueous solutions [19,20]. The XRD patterns of pure Sm 2 O 3 and Eu 2 O 3 calcined at different calcination temperatures are shown in Figure 3.  The transition temperatures for both oxides are in accordance with the traditional phase diagram [11]. However, the low fraction of the monoclinic phase at the transition temperatures (especially for Sm 2 O 3 ) indicates a possible suppression during the grain growth process that might be associated with the thermal treatment procedure. A comparison between the two different thermal treatment processes regarding pure Sm 2 O 3 and Eu 2 O 3 is shown in Figure 4.
The phase composition of pure Sm 2 O 3 was 9% monoclinic and 91% cubic when heated gradually to 1273 K and then calcined for 2 h at 1273 K. However, when pure Sm 2 O 3 was placed directly in the furnace at 1273 K for 2 h, the monoclinic content increased to approximately 73%. Hence, the heat treatment parameters influence the final crystallographic phase composition. Regarding pure Eu 2 O 3 , the content of the monoclinic phase slightly increased from 80% to approximately 90% when heated directly for 2 h at 1473 K. This proves that the transition is size-dependent. In addition, according to Roth and Schneider [11], the progression of the c ⇒ m transformation is governed also by crystallinity.
A similar comparison was also executed regarding pure Sm 2 O 3 and Eu 2 O 3 calcined at temperatures below the phase transition temperature, as shown in Figure 5.
According to the phase diagram, only the cubic phase was found in both oxides [11]. Figure 5 reveals that the gradual heating method caused peak broadening and had a major effect on the particle size, as can be seen in Figure 6. The phase composition of pure Sm2O3 was 9% monoclinic and 91% cubic when heated gradually to 1273 K and then calcined for 2 hours at 1273 K. However, when pure Sm2O3 was placed directly in the furnace at 1273 K for 2 h, the monoclinic content increased to approximately 73%. Hence, the heat treatment parameters influence the final crystallographic phase composition. Regarding pure Eu2O3, the content of the monoclinic phase slightly increased from 80% to approximately 90% when heated directly for 2 hours at 1473 K. This proves that the transition is size-dependent. In addition, according to Roth and Schneider [11], the progression of the c  m transformation is governed also by crystallinity. A similar comparison was also executed regarding pure Sm2O3 and Eu2O3 calcined at temperatures below the phase transition temperature, as shown in Figure 5. According to the phase diagram, only the cubic phase was found in both oxides [11]. Figure 5 reveals that the gradual heating method caused peak broadening and had a major effect on the particle size, as can be seen in Figure 6.  A similar comparison was also executed regarding pure Sm2O3 and Eu2O3 calcined at temperatures below the phase transition temperature, as shown in Figure 5. According to the phase diagram, only the cubic phase was found in both oxides [11]. Figure 5 reveals that the gradual heating method caused peak broadening and had a major effect on the particle size, as can be seen in Figure 6.  In gradual heating, the diffusion rates are smaller, and the tendency of forming smaller grains is higher. Those small grains grow as the temperature rises but not entirely homogeneously. On the other hand, in direct heating, the kinetics are faster due to higher diffusion rates, and larger grains are mostly formed and grow. The dependency on the preparation method of the samples was also reported previously [20,32].
A Rietveld refinement was performed for each curve in Figures 1-4. Representative cases of measured XRD pattern (Yobs), Rietveld refinement (Ycalc), and difference (Yobs-Ycalc) are shown in Figure 7. are mostly formed and grow. The dependency on the preparation method of the samples was also reported previously [20,32].
A Rietveld refinement was performed for each curve in Figures 1-4. Representative cases of measured XRD pattern (Yobs), Rietveld refinement (Ycalc), and difference (Yobs-Ycalc) are shown in Figure 7. HR-SEM images, presented in Figure 8, demonstrate the unique morphology of confided RE2O3 in a magnesia matrix. In all of the investigated samples, RE2O3 was mostly found as isolated grains HR-SEM images, presented in Figure 8, demonstrate the unique morphology of confided RE 2 O 3 in a magnesia matrix. In all of the investigated samples, RE 2 O 3 was mostly found as isolated grains embedded in the MgO matrix. A representative case, as shown in Figure 8, indicates that following 1473 K, nano-agglomerated particles with irregular shapes were observed. Energy dispersive X-ray spectroscopy (EDS) of these micrographs indicated the presence of nearly two separated pure phases: RE 2 O 3 phase (brighter phase in Figure 8) and magnesia phase (darker phase in Figure 8), and a noteworthy phase boundary similar to previous reports [33]. These results are in agreement with the XRD results in Figures 1 and 2, and indicate two distinct non-interacting phases of MgO and RE 2 O 3 .
1473 K, nano-agglomerated particles with irregular shapes were observed. Energy dispersive X-ray spectroscopy (EDS) of these micrographs indicated the presence of nearly two separated pure phases: RE2O3 phase (brighter phase in Figure 8) and magnesia phase (darker phase in Figure 8), and a noteworthy phase boundary similar to previous reports [33]. These results are in agreement with the XRD results in Figures 1 and 2, and indicate two distinct non-interacting phases of MgO and RE2O3.

Conclusions
This research investigated the crystallographic phase transformation of some rare-earth oxides in two different conditions: as embedded particles in MgO matrix and as pure oxides. XRD analysis allowed to demonstrate the transformation of crystallographic phase transitions and to approximate the relative amount of each phase as a function of concentration, temperature, and crystal size. From a practical perspective, it was possible to observe the differences between two situations (unhindered and hindered grain growth process) when embedding the desired phase in MgO in small amounts. It can be concluded that once the grain growth process is suppressed, the transition to monoclinic phase is delayed for the same calcination temperature compared with the pure oxide. Two methods to control the crystal growth process by changing the thermal treatment parameters were also investigated. Performing a direct heat treatment led to larger crystals, while a gradual heat treatment showed similar results to the RE2O3-MgO systems. In general, both suppression methods (embedding particles in MgO matrix or performing a gradual heat treatment process) ended in diverting the cubic-to-monoclinic transition towards higher temperatures. This indicates that grain size has a role in determining the crystallographic phase obtained.

Conclusions
This research investigated the crystallographic phase transformation of some rare-earth oxides in two different conditions: as embedded particles in MgO matrix and as pure oxides. XRD analysis allowed to demonstrate the transformation of crystallographic phase transitions and to approximate the relative amount of each phase as a function of concentration, temperature, and crystal size. From a practical perspective, it was possible to observe the differences between two situations (unhindered and hindered grain growth process) when embedding the desired phase in MgO in small amounts. It can be concluded that once the grain growth process is suppressed, the transition to monoclinic phase is delayed for the same calcination temperature compared with the pure oxide. Two methods to control the crystal growth process by changing the thermal treatment parameters were also investigated. Performing a direct heat treatment led to larger crystals, while a gradual heat treatment showed similar results to the RE 2 O 3 -MgO systems. In general, both suppression methods (embedding particles in MgO matrix or performing a gradual heat treatment process) ended in diverting the cubic-to-monoclinic transition towards higher temperatures. This indicates that grain size has a role in determining the crystallographic phase obtained.