The role of precursor decomposition in the formation of samarium doped ceria nanoparticles via solid-state microwave synthesis

The impact on the final morphology of ceria (CeO2) nanoparticles made from different precursors (commercial: cerium acetate/nitrate) and in house: cerium tri(methylsilyl)amide (Ce-TMSA)) via a microwave solid state reaction has been determined. In all instances, powder X-ray diffraction indicated that the cubic fluorite CeO2 phase (PDF# 04–004-9150, with the space group Fm-3 m) had formed. Scanning electron microscopy (SEM) images revealed spherical nanoparticles were produced from the Ce-TMSA precursor. The commercial acetate and nitrate precursors produced particles with irregular morphology. The roles of the precursor decomposition and binding energy in the synthesis of the nanocrystals with various morphologies, as well as a possible growth mechanism, were evaluated based on experimental and computational data. The formation of spherical shaped nanoparticles was determined to be due to the preferential single-step decomposition of the Ce-TMSA as well as the low activation energy to overcome decomposition. Due to the complicated decomposition of the commercial precursors and high activation energy the resulting particles adopted an irregular morphology. Highly uniform samarium doped ceria (SmxCe1-xO2-δ) nanospheres were also synthesized from Ce-TMSA and samarium tri(methylsilyl)amide (Sm-TMSA). The effects of reaction time and temperature, on the final morphology were observed through SEM. The rapid single-step decomposition of TMSA-based precursors as observed through thermogravimetric analysis (TGA) and confirmed through the calculation of potential energy surfaces and binding energies from density functional theory (DFT) calculations, indicated that nanoparticle formation follows LaMer’s classical nucleation theory.

(1.09 Å); this allows for easy solid solution formation. Upon successful doping, Sm x Ce 1-x O 2-δ has reported one of the higher ionic conductivities and particularly low operating temperature requirements [12]. For example, Huang et al. showed a nearly two order of magnitude increase in ionic conductivity at 600 °C by doping CeO 2 with 23% samarium [13].
It has been reported that the properties of CeO 2 -based ceramics are highly dependent on the size, shape, and crystalline phase of the particles [14][15][16]. For instance, Mai et al. observed an oxygen storage content of 554 μmol O g −1 for CeO 2 nanorods compared to an oxygen storage content of 318 μmol O g −1 for CeO 2 nanopolyhedra [16]. Ma et al. utilized a novel hydrothermal method to synthesize Sm x Ce 1-x O 2-δ nanorods, which due to their increased surface area, displayed a very high power density of 522 mW cm −2 [17]. Since the shape-phase-property relationship is important for various applications, it is critical to establish control over the morphology of CeO 2 based materials (i.e., morphology, phase, shape, etc.) as a function of Ln 3+ doping. Previous efforts to tailor the morphology of various CeO 2 -based nanoparticles have been investigated using commercially available precursors by altering specific synthesis variables, such as pH [18], precursors [19], and surfactants [20]. Recently, Wang et al. demonstrated the synthesis of CeO 2 in the form of stacked nanoplatelets, nanorods, nanosquares, and round nanoplatelets using a solution-based synthesis in the presence of different mineralizers [21]. While morphological control of neat CeO 2 and trivalent doped CeO 2 has been realized by varying the pH, surfactant, and precursors in solution, to the best of our knowledge there has been no report on the systematic comparison of nonvolatile (commercial/ hydrate/air-stable) vs volatile (in-house/non-hydrate/ air-unstable) precursors for the production of neat and Ln 3+ -doped CeO 2 nanoparticles.
A broad variety of synthesis processes has been utilized to make CeO 2 -based nanomaterials including: hydrothermal methods [22], solvothermal methods [23], co-precipitation [24], sol-gel [23], and microemulsion [25]. While many of these methods have produced high quality materials with good shape and size control, they are reliant on secondary mechanisms/catalysts such as surfactants and pH. Furthermore, they can involve aging steps or complex surfactant washing procedures that make them unattractive for large scale synthesis. As an alternative to solutionbased techniques, solid-state reactions have the potential for direct preparation of economically viable, high-purity, stoichiometric metal oxide nanoparticles while avoiding many of the aforementioned complexities [26]. Solidstate reactions can also be improved upon by utilizing microwave heating. Compared to conventional heating methods, microwave heating is more efficient, has a more homogenous heating profile, and can lead to higher yields [27].
Given the limited investigations of traditional vs nontraditional precursors to produce faceted nanoparticles, a systematic approach was taken to produce CeO 2 and Sm x Ce 1-x O 2-δ nanoparticles by decomposing traditional cerium/samarium acetate hydrate (Ln-acetate) and cerium/samarium nitrate hexahydrate (Ln-nitrate) precursors, as well as nontraditional samarium/cerium tri(methylsilyl)amide (Ln-TMSA) precursors via microwaveassisted solid state in ambient conditions. This report details the synthesis, characterization, and growth mechanism of CeO 2 and Sm x Ce 1-x O 2-δ nanoparticles. The effect of different precursors to produce Sm x Ce 1-x O 2-δ nanoparticles as well as the effects of reaction temperature, time, and initial molar ratio were investigated. Details of the possible growth mechanism of spherical nanoparticle of CeO 2 and Sm x Ce 1-x O 2-δ nanoparticles are explained through thermogravimetric analysis (TGA) and density functional theory (DFT) calculations that reinforce the classic LaMer growth mechanism.

Characterization methods
Analytical data were collected on dry, free-flowing powders. Powder X-ray diffraction (PXRD) of the products were conducted on a zero-background holder by a Siemens D500 Diffractometer equipped with a graphite monochromator with Cu Kα radiation operating at 45 kV and 40 mA. The samples were scanned at a rate of 4°/s in the 2θ range of 20°-100°. The patterns were analyzed with the JADE 9.6.0 software with ICDD PDF-4 database. Raman spectra were obtained using a Witec Raman Confocal Microscope with an excitation laser operating at 532 nm. X-ray fluorescence (XRF) spectra were obtained using a Thermo Scientific ARL Quant'X EDXRF Analyzer. For all scanning electron microscopy (SEM) analyses, the samples were dispersed on carbon tape and examined with a Hitachi S-5200 Scanning Electron Microscope under an accelerating voltage of 5 kV and a current of 7A. Differential scanning calorimetry (DSC) and TGA were measured using a Mettler Toledo TGA/ DSC 3 + Thermogravimetric Analyzer equipped with a high temperature (HT) furnace. The samples were heated a rate of 5 °C/min in the temperature range of 25-500 °C.

Computational Details
To complement experimental TGA analysis, gas-phase electronic structure calculations were performed for Ln-TMSA and Ln-acetate (representative of the commercial precursors) using Gaussian 09 [29] at the DFT level with the hybrid B3LYP functional (Becke's three parameter hybrid exchange functional with Lee-Yang-Parr correlation function) [30][31][32]. The small-core effective core potential (ECP) MWB28 was used for the Ce and Sm atoms [33]. All other atoms were described using the 6-31G basis set [32,34,35] as part of the complete basis set model described by Petersson et al. [36]. The ECP MWB28 core potentials include a scalar relativistic correction and has been previously applied to Ce-and Sm-based molecules resulting in agreement with experimental structures [37,38]. Molecular structures were selected from solved crystal structures and optimized in unrestricted calculations. All atoms were allowed to relax during optimization. Agreement in the metrical data between the crystal structures and DFT optimized molecules (Table S1) validates the quality of the DFT models and is discussed in the results. Potential energy surface (PES) scans were performed to identify the strength of the Ln-TMSA interaction and the presence of intermediate states during disassociation. The Ln-N distance was stretched by 0.05 Å, and then the structure was relaxed. No other constraints were placed on the system during relaxation. This process was repeated iteratively until the Ln-N distance reached 5.0 Å. In addition to the PES scans, dissociation energy (E D ) data was collected for complete removal of the trimethylsilyl amide (TMSA) ligand. E D data was calculated by removing a TMSA ligand from the Ln-TMSA molecule and relaxing the resulting structure as well as the lone TMSA ligand. E D was calculated as the difference between the molecule (E Ln-TMSA ), the energy of a lone TMSA ligand (E TMSA ), and the energy of the precursor without a third TMSA ligand (E Ln-TMSA-TMSA ):

Preparation of Ln-TMSA precursors
Separate solutions of LnCl 3 in THF and KNR 2 in THF were prepared in inert atmosphere. The LnCl 3 solution was cooled and progressively treated with the KNR 2 solution. The final mixture was stirred overnight, filtered with hexanes, extracted with toluene, and then stripped again to yield Ln-TMSA powder.

Microwave-assisted solid-state synthesis of Sm x Ce 1-x O 2-δ powders
CeO 2 and Sm x Ce 1-x O 2-δ nanoparticles were prepared via solid state microwave radiation of the respective metal precursors (Ln-nitrate, Ln-acetate, Ln-TMSA) in the presence of atmospheric air. All reactions involving acetate and nitrate precursors were prepared and performed in ambient conditions, while the Ln-TMSA precursors were handled in a glove box prior to heating in ambient conditions. In a standard synthesis method, the precursor was ground in a mortar to insure a homogenous mixture. After mixing the necessary precursors, the reaction was heated in a Microwave Research and Application BP-210 microwave oven under atmospheric conditions at 750 °C, using air as the reaction media. For the formation of Sm x Ce 1-x O 2-δ various ratios and reaction conditions of Ce-TMSA and Sm-TMSA, shown in Table 1, were attempted to increase the Sm 3+ dopant concentration and control the physical nature of the material (size, morphology, and crystallinity). After the reactions were conducted as described the isolated materials were collected and analyzed without further modifications.

Results and discussion
The robust and diverse physical properties of CeO 2 and Sm x Ce 1-x O 2-δ have led to numerous investigations detailing the morphological impact on their optical and electronic properties [39,40]; however, there are no reports on understanding the generation of the aforementioned materials using traditional vs non-traditional precursors in a microwave without the presence of a liquid solution or surfactant. Due to the shape-dependent properties of nanomaterials and the void in literature on microwaveassisted solid-state synthesis of various precursors, it was of interest to investigate the effect of traditional and nontraditional precursors, on the properties of the resultant CeO 2 and Sm x Ce 1-x O 2-δ nanoparticles. Therefore, a systematic study was undertaken, and the results discussed below focus on the crystal structure and particle morphology of resulting nanoparticles. A growth mechanism is also described based on the (i) decomposition profiles, (ii) calculated dissociation energies, and (iii) calculated potential surfaces of precursor materials.

Formation of spherical cerium oxide nanoparticles
PXRD data, shown in Fig. 1a, was collected on the powders isolated from reacting the Ce-precursors (acetate, nitrate, and TMSA) at 750 °C for 10 min. For each sample the major peaks of the PXRD patterns were indexed to the cubic fluorite CeO 2 phase (PDF# 04-004-9150) with the space group Fm-3 m and no other impurities can be observed in the patterns. SEM images of products generated from the microwave reaction of the individual Ce-precursors are shown in Fig. 1b-d. Figure 1b, c show SEM images of the product formed from Ce-acetate and Ce-nitrate, respectively. For these systems, highly irregular CeO 2 nanoparticles are present as well as agglomerated particles. The irregular morphology of the acetate and nitrate-based CeO 2 indicates that there are adsorbed surface species during the conversion reaction, and that transport of ions on the surfaces is not rapid enough to form regular facets based on crystal symmetry. However, Fig. 1d shows that decomposition of the Ce-TMSA precursor yields CeO 2 nanoparticles with a highly defined spherical morphology. In contrast, Ce-TMSA processed in a conventional furnace with identical conditions yielded a minute amount of spherical nanoparticles with the majority exhibiting  Figure S1. The round spherical morphology agrees with a rapid decomposition process achieved through rapid microwave heating, where cation transport to the nuclei is diffusion limited. These variations in growth kinetics and nucleation will be discussed more in depth in the growth mechanism section.

Formation of Samarium-Doped Ceria Nanospheres
Due to the serendipitous generation of spherical CeO 2 nanoparticle from microwave irradiation of the Ce-TMSA precursor, Sm x Ce 1-x O 2-δ was synthesized by combining Ce-TMSA and Sm-TMSA precursors. Sm x Ce 1-x O 2-δ was generated with an initial Ce:Sm molar ratio of 4:1,3:1, 2:1 and a reaction time of 10 min at 1000 °C. PXRD data, shown in Fig. 2a, were collected on the powders isolated from the different reaction conditions. The crystalline product was indexed to the cubic fluorite phase (PDF# 04-004-9150), with no secondary phase present (Sm 2 O 3 ; cubic la-3 phase). Upon addition of Sm 3+ , the PXRD patterns exhibit a Sm 3+ concentration-dependent downfield shift relative to CeO 2 for all the major reflections, which can be seen clearly in Fig. 2b. The shift to lower angles is due to lattice strain from size mismatch cause by the uptake of differently sized Sm 3+ ions, suggesting the successful incorporation of Sm 3+ in the cubie lattice of CeO 2 [41]. As shown in Fig. 2c, production of Sm x Ce 1-x O 2-δ yielded spherical nanoparticles, indicating that uptake of Sm 3+ ions does not affect the final morphology. In order to confirm the uptake of Sm 3+ ions in the cubic fluorite CeO 2 lattice as well as to ascertain any structural changes, Sm x Ce 1-x O 2-δ powders were analyzed via Raman spectroscopy and XRF ( Figure S2). Representative Raman spectra for as synthesized CeO 2 and Sm x Ce 1-x O 2-δ are shown in Fig. 3. The major peak for both powders is the triply degenerate F 2g band at ~ 460 cm −1 which is assigned to the CeO 2 cubic fluorite structure [42]. This Raman active mode is attributed to the symmetric breathing of oxygen around the central cerium ions [43]. The symmetry of this breathing mode means that they are sensitive to disorder in the oxygen lattice that can occur through doping. Upon Sm 3+ incorporation in CeO 2 , a broad absorption band in the region of 520-630 cm −1 emerges as oxygen vacancies are introduced and disorder is introduced into the oxygen sublattice. Additionally, the F 2g peak becomes asymmetric, broadens, and shifts to lower frequencies due to increased oxygen vacancy and changes in the lattice structure [44]. This result is consistent with other reports of Sm x Ce 1-x O 2-δ [45,46].

Effect of synthesis parameters on nanoparticles size
To understand the effect of temperature on the formation of Sm x Ce 1-x O 2-δ, Ln-TMSA based nanoparticles with at 750 °C the average diameter increases to 75-125 nm, and at 1000 °C most particles have diameters between 175-250 nm. It is worth noting that the particle distributions follow a log-normal distribution as illustrated by the overlays on the histograms. Additionally, the effect of reaction time on the formation of Sm x Ce 1-x O 2-δ nanoparticles generated with an initial Ce:Sm ratio of 2:1 at 750 °C was investigated for 5, 10, and 20 min, respectively. SEM images of the final products are shown in Fig. 5a-c. After analyzing > 200 nanoparticles, it is evident that longer reaction times increases the average final nanoparticle size, shown visually in Fig. 5d-f. With all other conditions kept constant, there should be identical nucleation events and the particle size distribution should be identical upon reaching the final dwell temperature. However, if the longer the reaction proceeds at the final reaction temperature, more growth will occur, particularly in the form of Ostwald ripening [47]. According to the Gibbs-Thompson description of nucleation, dissolution can occur as the reaction proceeds due to the curvature radius of formed particles. These smaller particles can then be re-dissolved into solution and incorporated into larger particles [48].

Decomposition mechanism of Sm x Ce 1-x O 2-δ precursors
In solid-state reactions, the mechanism by which precursors breakdown plays a major role in the final morphology and properties of the resulting product. To help understand the effect of different precursors on final nanoparticle morphology, the thermolysis properties of Ln-precursors were studied using TGA, shown in Fig. 6. The commercial Ln-acetate/nitrate precursors display multi-step decomposition steps as reported in literature and displayed in Table S2 [ [49][50][51][52]; Ln-TMSA precursors display a single step decomposition. Additionally, Ln-TMSA exhibits a much lower decomposition temperature; Sm-TMSA decomposes at ~ 200 °C, but Sm-acetate and Smnitrate do not decompose fully until > 400 °C. The simpler decomposition mechanism and lower decomposition temperature of Ln-TMSA are indicators for classical nucleation behavior that can ultimately lead to well defined spherical nanoparticles.
To help identify particle nucleation mechanisms, DFT calculations can provide insight into the breakdown mechanism of Ln-precursors. The presence of a single step decomposition in Ln-TMSA precursors suggests that TMSA ligands are removed from the Ce/Sm center without the formation of intermediate states. To evaluate the effect of TMSA ligand removal, a potential energy scan (PES) scan was performed on Ce-TMSA by iteratively stretching the Ce-N bond in 0.05 Å steps and allowing the structure to completely relax. The PES shown in Fig. 7, does not indicate the formation of significant intermediate states as indicated by the Lorentz potential like behavior. The small change in slope at ~ 3.6 Å is a result of the methyl groups loosely interacting with the Ce center but is not a strong  Table 2 are the pathways and E D for the first decomposition step of Ln-TMSA and Ln-acetate precursors calculated as the difference between the relaxed energies of the products and reactants shown schematically in Fig. 8. For the cerium precursors, Ce-TMSA displays a lower binding energy of -4.348 eV as compared to -1.574 for Ce-acetate. Similarly, Sm-TMSA displays a lower binding energy of -3.334 as compared to -1.598 for Sm-acetate. The intermediate structures formed during acetate decomposition result in higher binding energies that make it difficult for molecular species to become available for particle nucleation. Nitrate decomposition also displays a multi-step profile; nitrates are known in molten salt chemistry to break down into nitrite ions before complete decomposition. Due to this behavior, it is expected that the binding energies would be in a similar range as that of the Ln-acetate precursors.
According to the TGA data and relevant calculations, it is apparent that the single step decomposition of Ln-TMSA and subsequent formation of spherical nanoparticles falls in line with LaMer's classical nucleation theory, shown schematically in Fig. 9. In step 1, the concentration of Ln monomers increases at a steady rate as TMSA ligands begin to separate from the metal center. In step 2, the saturation of monomers overcomes the energy barrier at some critical solute concentration ( C nu min ) to achieve a burst nucleation event. In step 3, crystallization occurs as  the concentration of monomers decreases due to continued growth of stable nuclei. In step 4, nuclei continue to grow due to continued monomer diffusion and Ostwald ripening. Spherical nanoparticles are formed due to rapid nucleation followed by the diffusion of readily available monomer species leaving no time for faceted surfaces to form around nuclei. In the case of nitrate and acetatebased precursors, the multi-step decomposition profiles are indicative of a sol-gel polymerization nucleation mechanism that leads to irregular morphologies as facets form semi-randomly on nuclei surfaces [48].

Conclusions
In conclusion Sm x Ce 1-x O 2-δ nanoparticles were produced using a microwave-assisted solid-state synthesis. By varying reaction conditions like the molar ratio of reactants, the reaction temperature, and reaction time, spherical nanoparticles with sizes ranging from 20 nm up to 600 nm were produced. Based on TGA analysis and DFT calculations, Sm x Ce 1-x O 2-δ nanoparticles produced with TMSA based precursors grow according to classical LaMer nucleation theory leading to the formation of spherical nanoparticles. The results of this research indicate that microwave-assisted solid-state synthesis can be used to make doped Ceria nanoparticles, but more research is needed in order to control the homogeneity of these particles. Solid state synthesis can be readily scaled up, easily controlled, and does not need solvent or washing, making it an attractive option for producing rare earth oxide-based materials. Future studies will focus on the optimization of Sm x Ce 1-x O 2-δ nanoparticles as well as the introduction of additional rare earths. Funding Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA0003525. SAND2020-7474 C.

Compliance with ethical standards
Conflict of interest The authors declare no competing financial interest.
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