Surface thermodynamics of yttrium titanate pyrochlore nanomaterials†

Margaret E. Reece ^ab, Jiahong Li ^a, Andrew C. Strzelecki ^bc, Juan Wen ^d, Qiang Zhang ^a and Xiaofeng Guo *^ac
aDepartment of Chemistry, Washington State University, Pullman, WA 99164, USA. E-mail: x.guo@wsu.edu; q.zhang@wsu.edu
^bEarth and Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
^cThe School of Mechanical and Materials Engineering, Washington State University, Pullman, WA 99164, USA
^dSchool of Materials and Energy, Lanzhou University, Lanzhou, Gansu 730000, China

First published on 16th February 2024

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1. Introduction

Rare earth element oxide ceramics, particularly pyrochlores, have been investigated for a wide range of applications in thermal barrier coatings,^1–7 catalytic activity,^7–11 solid oxide fuel cells,^12–15 and most extensively as host matrices for actinides in nuclear waste.^16–19 The pyrochlore family boasts a high number of compositions that have been successfully synthesized and studied for chemical durability, waste loading, radiation tolerance, and other related properties.^20–27 Having compositions of A₂B₂O₇, the ordered pyrochlore (space group, s.g. Fdm) is a derivative of the fluorite structure (s.g. Fmm) with two unique cation sites and one-eighth fewer oxygen anions. The most common pyrochlores are made up of larger trivalent cations that occupy the eight-coordinated A-site and smaller tetravalent cations in the six-coordinated B-site.^28–30 A₂B₂O₇ can also crystalize as polymorphs other than the ordered pyrochlore, and the phase is dominantly controlled by the size of the cations incorporated in the structure and their coordination environments.^31–40 This flexibility allows for fine-tuning and optimization for incorporating radioactive cations with non-ideal charges or radii through coupling mechanisms as observed in systems with uranium.^29,41

Most naturally occurring pyrochlores are metamict (partially amorphous) due to the effects of the radioactive decay of ²³⁸U, ²³⁵U, and ²³²Th and their daughter products, which can change the incorporation behaviour of actinides.^29,39,42 Radiation, such as β-decay of fission products and α-decay of the actinide elements, can induce point defects (e.g., interstitials and vacancies) that are aggregated for long-range disorder,^32,43–45 which can further cause significant degradation to the material properties (i.e., hardening, embrittlement, swelling) and limit the lifetime of the nuclear waste host.^45,46 Thus, predicting radiation response is critical in evaluating candidate waste forms. Previously, radiation resistance was found to be controlled by composition,^47–50 vacancy inclusion,^51,52 intrinsic disorder,^53–55 and grain size.⁵⁶ In this study, we focus on the size effect on the thermodynamic properties of nanoparticles by experimental calorimetry, with extended correlation with radiation resistance.

Radiation-induced point defects aggregate to form long-range disorders in crystalline materials by forming interstitial atom-vacancy pairs. The mobile interstitial atoms have been found to accumulate at crystallite surfaces in bulk materials, with recent molecular dynamics studies showing a short-range recombination of the displaced atoms with vacancies in a mechanism driven by the surface.^52,57–59 While atoms in a bulk crystalline material would be dominantly in the interior that can be better described by the crystal structure, atoms in a nanocrystal may have a substantial portion in the surface region, in which the coordination is less than ideal and the atomic bonding environment is unsatisfied.^60,61 At particle sizes decreasing to the nano-scale regime, atoms on the surfaces increasingly dominate over those that reside in the bulk-core. The consequence is that properties of nanosized particles are often different from their bulk counterparts.^62–65 From a thermodynamic point of view, the surface region has different thermodynamic parameters, which differ from that of the bulk phase by the excess free surface energy (ΔG_surface) which often contributes endothermically to the thermodynamic stability. As the size of a grain increases from the scale of a single unit cell to a larger grain diameter, the free energy accumulated from the unsatisfied bonds decreases with respect to the bulk material free energy. This results in high contribution from ΔG_surface at low grain sizes and a flattening of this effect at high grain sizes. Thus, nanoparticles due to their metastable nature, tend to reduce ΔG_surface by interacting with external substances, such as formation of agglomerates, binding to ligands and solvent, and chemical reaction with available species.⁶⁶ On the other hand, the free energy of irradiated material also depends upon the energy contribution of point defects (ΔG_defect) that have accumulated. The defect energy is directly related to the concentration of these point defects, for which there is a kinetically controlled equilibrium of defect formation and annihilation.^57,67 Recombination of interstitial atoms and vacancies is assisted by surfaces, so at small grain diameters, the rate of recombination is greater than that of vacancy formation, while at large diameters it is the opposite.^68–70 The dependence of ΔG_surface and ΔG_defect on the particle diameter has been discussed in-depth,^71,72 and is summarized in Fig. 1.

As a result of such an interplay between surface energy and energy related to radiation-induced point defects, the radiation resistance of a nanoparticle can be effectively controlled by tuning size.⁷¹ According to Fig. 1, thermodynamics of small particles with diameters in regions 1 and 2 is dominated by ΔG_surface, with the overall Gibbs free energy higher than the energy barrier for amorphization (ΔG_{amorphization}). For bulk sized particles that reside beyond region 3, the surface energy contribution is not significant and there are insufficient surfaces acting as point defect sinks to prevent cascades, and so the amorphization process is driven by ΔG_defect. Thus, with the energetic competition between ΔG_surface and ΔG_defect, it is then possible to engineer nanosized ceramics with desired stability within the region 3, such that the total energies, ΔG_surface + ΔG_defect, is smaller than ΔG_{amorphization}. In this diameter range, the amorphization of the nanomaterial is thermodynamically unfavourable and hindered.

For solids, the contribution from entropy and excess volume terms are negligible, and so ΔG_surface can be determined by the production of the specific surface free energy (γ) and the surface area (SA).⁷³

ΔGsurface = γ × SA.

Thus, obtaining the specific surface free energy is critical for understanding how a waste form, such as pyrochlore, in the repository responds to irradiation. In this study, we experimentally determined the surface free energy of nanosized Y₂Ti₂O₇ pyrochlores by performing high temperature oxide melt drop solution calorimetry. Yttrium was chosen because it is the fourth most abundant rare earth element (REE) and the most abundant heavy rare earth element (HREE),⁷⁴ with an ionic radius near the middle of the HREE range.⁷⁵ In order to ensure the ordered pyrochlore crystal structure of the material, titanium was selected as the B-site cation. Although zirconium, hafnium, and tin are also common B-site cations, the A/B cationic ratio of yttrium to any of them is below or only just within the stable range to form ordered pyrochlore.^{28,29,35,37,75} Additionally, the thermodynamic properties of bulk-sized Y₂Ti₂O₇ have been determined thoroughly,⁴⁷ yet there are very limited thermodynamic studies of these nanocrystalline pyrochlores.^{45,65,76–78} This work represents one of the efforts to experimentally determine surface effects on the thermodynamic stability of pyrochlore, which can shed light on designing novel nanoceramic materials aimed at forming durable nuclear waste hosts.

2. Experimental

2.1 Sample synthesis

Yttrium titanate pyrochlore can be prepared by traditional solid-state reaction methods,⁷⁹ coprecipitation,⁸⁰ hydrothermal approaches,^81,82 and sol–gel methods.⁸³ Among these, sol–gel methods adapting the Pechini approach based on polymeric precursors has resulted in a large body of published work with pyrochlore nanomaterials of small size and high phase purity.^45,84–89 Nanocrystalline Y₂Ti₂O₇ pyrochlore powders were synthesized according to previously published methods using a modified citric acid sol–gel route described by Chen and Wen (Fig. S1†).^45,85 Starting materials of yttrium oxide (Y₂O₃, 99.99%) was dissolved in nitric acid with slow heating to remove the excess nitrate. A 1:1 stoichiometric molar ratio (Y/Ti) of tetrabutyl titanate was dispersed in a citric acid (CA)–absolute ethanol mixture. The amount of citric acid chelator was calculated such that nCA/(nY + nTi) = 2.5. This solution was stirred until homogenous and then combined with the aqueous yttrium nitrate solution under heat and stirring conditions. The mixture became highly viscous and finally changed into a glossy gel that was then allowed to air dry. Heat treatment of the samples was performed in air with the same dwelling time of 1 h at different temperatures from 700–850 °C (one batch every 50 degrees) for obtaining particles with different sizes.

2.2 Characterization

Synchrotron powder X-ray diffraction was conducted at beamline 11-ID-C of the Advanced Photon Source (APS) at Argonne National Laboratory (ANL). The wavelength of the X-ray beam was 0.1173 Å, with a distance of 1610 mm from the sample to the detector. Collected two-dimensional (2D) images were calibrated, integrated, and refined by the Rietveld method using the General Structure Analysis System software version II (GSAS-II),⁹⁰ where instrument parameters were obtained using a CeO₂ standard. Backgrounds of these spectra were modelled by the Chebyshev function with 6 coefficients. Procedures for the above Rietveld refinement are referenced elsewhere.^91–95 Brunauer–Emmett–Teller (BET) surface area of the nanosized samples were obtained from the measured nitrogen adsorption–desorption isotherms collected on a Micromeritics ASAP 2020Plus instrument at 77 K. Samples were degassed under vacuum at 150 °C for 10 h before analysis. Transmission electron microscopy (TEM) pictures were acquired using a FEI Tecnai F30 instrument after preparing the samples by dispersing the sample into absolute ethanol with ultrasonic treatment, then dropping the solution onto the carbon-coated TEM grids and naturally drying in air.

2.3 Thermogravimetric analysis

Thermogravimetric analysis coupled with differential scanning calorimetry (TGA-DSC) was performed on a Setaram SetSYS 2400 thermogravimetric differential scanning calorimeter, where 5–20 mg of the sample was heated from 28 to 1000 °C in an alumina crucible with a heating rate of 10 °C min⁻¹ under a flowing N₂ atmosphere (20 mL min⁻¹). The temperature and sensitivity of the instrument were calibrated by heating indium, tin, lead, zinc, aluminium, silver, and gold across their fusion point repeatedly at temperature change rates of 5, 10, 15, and 20 °C min⁻¹.^92,96–100

2.4 High temperature oxide melt solution calorimetry

The enthalpy of drop solution (ΔH_ds) was measured directly by a Setaram AlexSYS-1000 Calvet-type microcalorimeter. The calibration of the instrument was conducted by performing transpose temperature drops using solid pieces of α-Al₂O₃. The powdered nanoparticle samples were hand pressed into pellets with masses between 2 and 6 mg, and dropped from room temperature into a molten solvent of sodium molybdate (Na₂O·MoO₃) contained in a Pt crucible at 700 °C with bubbling O₂ through the solvent at a rate of 5 mL min⁻¹. The calorimeter chambers were continuously flushed with O₂ gas at a rate of ∼100 mL min⁻¹ to facilitate a constant gas environment above the solvent. Methods for determination of enthalpies of formation by high temperature oxide melt solution calorimetry employed in this work from enthalpy of drop solution have been previously described in more detail.^101–107

3. Results and discussion

3.1 Characterization of nanosized particles

X-ray diffraction patterns of the four as-prepared samples clearly show diffraction related to pyrochlore with peaks (Fig. 2 and S2–S4†) such as the (111), (311), (331), and (511). Rietveld refinements were performed using the Fdm space group. The resulting refinements yielded R_wp values between 4.1 to 8.5% with average crystallite sizes in the 30–135 nm range. The calculated size was visually confirmed for the 34 and 131 nm size samples by TEM (Fig. S5†). A representative fit of the 131 nm sample is shown in Fig. 2, with all refined results summarized in Table 1. The atomic displacement parameter (U_iso) increases as crystallite size decreases for all atoms in the structure. Surface atoms of the material have higher thermal displacement parameters due to their locally unsatisfied bonding environments. The increase in the ratio of surface atoms to bulk atoms as crystallite diameter decreases leads to a greater number of atoms with this lattice distortion in the material, and can be seen in the trend of the atomic displacement parameters. Surface area data determined by BET are also included in Table 1.

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TGA of the Y₂Ti₂O₇ samples under nitrogen (Fig. S6†) show an extended region of mass loss from 100–500 °C. This extended region of mass loss is expected to attribute to the removal of physically adsorbed species (e.g., water) on the high surface area. Coupled DSC (Fig. S7†) revealed coarsening of nanocrystallites by the endothermic signal from 600–900 °C with negligible mass loss at the same temperature.¹⁰⁸

3.2 Enthalpy of formation of nanosized Y₂Ti₂O₇

Y₂Ti₂O₇ samples were used in the drop calorimetric experiments without pre-treatment. The thermochemical cycle used for determining the enthalpy of formation of yttrium titanate pyrochlore materials is outlined in Table 2. For nanomaterials, the enthalpy of drop solution (ΔH_ds) is the sum of the heat content of the sample, the enthalpy of solution in the oxide-melt solvent, the enthalpy of dehydration of the surface water with its associated heat content, and the excess enthalpy related to the surface.⁷³ By assuming that all water is physically adsorbed on the surface and is energetically equivalent to liquid water when condensed to solid ice (−44 kJ mol⁻¹),^30,109,110 ΔH_ds can be corrected for obtaining the drop solution enthalpy of nanosized Y₂Ti₂O₇ with a hydrated surface^30,73,109 (ΔH′_ds), further used for deriving ΔH_f,ox and (Table S1†).

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All samples in this study were enthalpically favourable to form from the oxides, with ΔH_f,ox positively correlated with surface area (Fig. 3). Insignificant agglomeration was found in three of the sample series and these were used to extrapolate linear trends in energetics, while the sample that deviates from these trends (34 nm) is discussed in-depth in the following sections. Extrapolating the linear trend to the zero enthalpy of formation from the oxides yields a surface area of 50 m² g⁻¹, which corresponds to a particle diameter of 1.8 nm (approximately 1.75 unit cell). This suggests that nanosized Y₂Ti₂O₇ smaller than 1.8 nm is thermodynamically metastable and unlikely to form or persist. Although such an implication is based on the hypothesis that physical properties of sub-nano particles still correlate linearly with those of nano-sized and bulk-sized phases, that assumption is sometimes untrue.⁶¹ This is mostly because when the size decreases to below 5 nm (with surface area ∼38 m² g⁻¹), the percentage of atoms on the surface dominates, which may further cause excess free energy to significantly deviate from the linear trend.^114,115 After all, the linear trend still gives a good estimation in the size that one can use to predict the stability of nanoparticles. On the other hand, as surface area decreases (with increasing particle size), enthalpy of formation from oxides of the nanosized phase typically approaches that of the bulk value. The extrapolated enthalpy value with particle size zero is −85.1 ± 1.6 kJ mol⁻¹, consistent with ΔH_f,ox = −86.2 ± 1.5 kJ mol⁻¹ of the bulk-sized Y₂Ti₂O₇.⁴⁷ Such a good agreement also suggests the high reliability of the size-dependent enthalpy of formation data we measured experimentally.

3.3 Derivation of surface energy from calorimetry

The excess enthalpic contribution to the nanoparticles can be written as

ΔHexcess = ΔH′ds(bulk) − ΔH′ds(nano).

In the case of nonaggregated nanoparticles that have negligible interface area, this excess enthalpy directly attributes to the excess energy originated at the termination of the crystal (surface energy, γ)¹¹⁶ and the total area of the surface of the sample (SA) as

ΔHexcess = γ × SA.

In order to derive γ, the corrected drop solution enthalpies were fitted as a linear function of the BET surface area (Fig. 4).^30,110,117 The slope of this line corresponds to the enthalpy of the free particle surface, which was determined to be 4.07 ± 0.32 J m⁻² (R² = 0.987). This value agrees well with theoretically determined values of the surface energy of titanate pyrochlore materials, as discussed in-depth below. In the case of agglomerated nanoparticles, the grain boundary has additional interfacial energy (γ′) that contributes to the excess enthalpy that is proportional to interfacial area (IA).^110,118 Thus, the total excess enthalpy is

ΔHexcess = γ × SA + γ′ × IA.

Given that [23 m² g⁻¹] has a similar XRD particle diameter to [29 m² g⁻¹] but a lower BET surface area, it can be assumed that this sample has significant grain boundaries and additional excess enthalpy that leads to the deviation from the ΔH′_ds-SA relationship shown in Fig. 4. If the difference in measured surface area between [23 m² g⁻¹] and [29 m² g⁻¹] is twice the total interface area of that sample,^110,118 then γ′ can be estimated as 3.04 ± 0.70 J m⁻² for Y₂Ti₂O₇ materials.

Previously, surface energies of REE titanate pyrochlores were mostly studied by computational calculations.^119,120 Average surface energies calculated for the specific (100), (110), (111), and (112) planes for REE = Y, Gd, and Lu are summarized in Table 3 with these planes highlighted in the general pyrochlore structure in Fig. 5. The average values of the four planes are in excellent agreement with our experimental results. Nanostructures that are not spherical are expected to have a preferential exposure of certain planes to minimize the free energy. The surface energy determined by calorimetry being closer to the high-energy (111) surface instead of the lowest-energy (112) surface indicates the nucleation of these materials by the employed synthetic route as either kinetically controlled or ligand-stabilized instead of thermodynamically driven.

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The bulk thermodynamic properties of pyrochlores have been found to be primarily controlled by the incorporated cations. For a given A (or B) cation, there are established trends in the enthalpy of formation from the oxides that can be predicted based on the A/B radius ratio over a range of B (or A) cations.^47,54,121 Cation size also controls nanoscale energetics. For instance, the calculated minimized surface energy of Gd₂B₂O₇ (B = Pb, Zr, Hf, Sn, and Ti) has a negative correlation with the ionic size of B cation.^75,120 The most stable surface reported in that study (the (110)-a₁) for Gd₂Ti₂O₇ has a surface energy value of ∼2.52 J m⁻², compared to ∼1.87 J m⁻² for Gd₂Pb₂O₇.¹²⁰ Also, the average surface energy of Lu₂Ti₂O₇ was reported to be higher than that of La₂Zr₂O₇ by about 1 J m⁻². Because the pyrochlore structure is a derivative of the defect fluorite and fluorite structures, we also summarize surface energy of the latter in Table 4. The B site in pyrochlore is disordered from the defect fluorite with a changed coordination environment from six- to eight-coordinated. With such a change in B site, defect fluorite in general has a small surface energy compared to its pyrochlore counterpart (Table 4). However, within the defect fluorite or fluorite structure, the surface energy increases with increase of cation size, different from the relation seen in pyrochlore that larger B cation suggests smaller surface energy.

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3.4 Implication of radiation resistance of nanosized Y₂Ti₂O₇

While some data is still unknown for the nanoscale effect on irradiation of pyrochlores, we can create a preliminary lower limit of particle size that should have an increased tolerance to radiation-induced amorphization for the yttrium titanate pyrochlore. The enthalpy of amorphization for Gd₂Ti₂O₇ (ΔH_{amorphization} = 236.6 kJ mol⁻¹)¹²² Dy₂Ti₂O₇ (ΔH_{amorphization} = 243.3 kJ mol⁻¹)¹²³ and Dy₂Sn₂O₇ (ΔH_{amorphization} = 283.6 kJ mol⁻¹)¹²⁴ pyrochlores have been experimentally determined. As this is describing a solid phase system, the entropy contribution to ΔG is considered to be negligible at room temperature or moderately high temperatures. To predict a reasonable ΔG_{amorphization} value for Y₂Ti₂O₇, we correlated the amorphization energy trends with the ionic radii ratio of the pyrochlore compounds (Fig. S8†).

Using this empirical correlation, the amorphization energy of Y₂Ti₂O₇ is predicted to be 246.5 ± 4.3 kJ mol⁻¹. Fig. 6 shows this ΔG_{amorphization} estimate of Y₂Ti₂O₇ (black solid line) and the experimentally determined amorphization energy thresholds of two titanium pyrochlores (grey lines). Assuming nanoparticles to be spherical, the contribution from the surfaces to meeting this energy of amorphization can be displayed for many pyrochlore systems as a function of particle diameter. ΔG_surface of Y₂Ti₂O₇ (red lines) are average values using the experimentally determined (red solid) and the computationally derived (red dashed) γ values from this study and Yang.¹¹⁹ The average surface energy is most applicable to spherical nanoparticles as all surfaces are equally exposed, however synthetic methods that tailor synthesis to shapes with a single surface exposed, such as cubes, can minimize the free energy contribution by preferential exposure of the lowest energy surface. A series of cube-shaped gadolinium pyrochlores using the lowest computationally derived surface energy with diameter equal to the length of the side is also shown for comparison in dotted blue lines.¹²⁰ These get darker in colour as the size of the B cation decreases.

From Fig. 6, one can estimate that the smallest particle size of Y₂Ti₂O₇ that begins to favour crystallinity over amorphization under radiation is approximately 5.0 nm in diameter (considered here as the critical particle size). This is the upper limit of the region one in Fig. 1.⁷¹ With increasing particle size from 5 nm while remaining nanosized, Y₂Ti₂O₇ is expected to have enhanced radiation resistance. Furthermore, the effect of the A/B radius ratio on the surface energy contribution can also be seen in Fig. 6, but it is unknown whether the changes to the amorphization energy decrease at a similar rate as the surface energy for a given composition. Characterization of these radiation resistance effects as trends of cation size will help identify the minimization region of the energetics to be determined, which in turn will allow highly radiation-tolerant pyrochlore nanomaterials to be engineered. On the other hand, the size-dependent defect accumulation in pyrochlore materials has not been sufficiently published at this time to elucidate the ΔG_defect contribution which would provide insight into the lower and upper limits of particle diameter in the stable region three, if one exists.

4. Conclusions

Yttrium titanate pyrochlore nanomaterials were synthesized by a modified sol–gel method. The phase crystallinity and particle morphology were confirmed by synchrotron powder X-ray diffraction analysis and transmission electron microscopy, and surface area was determined by BET liquid nitrogen adsorption. Average particle size of samples ranged from 31 nm (29.0 m² g⁻¹) to 131 nm (10.6 m² g⁻¹) and were loosely spherical in shape. Using high temperature oxide melt drop solution calorimetry, we determined the surface enthalpy for the pyrochlore (4.07 ± 0.32 J m⁻²) which indicates preferential exposure of the (111) surface, and have estimated interfacial energy (3.04 ± 0.70 J m⁻²). This information was further used to estimate the critical particle size for Y₂Ti₂O₇ at ∼5.0 nm, with smaller particles predicted to spontaneously amorphize or agglomerate. The impact of radiation accumulation and self-healing of nanomaterials was also discussed in this work. It is expected that tunability of exposed particle surfaces for nano-sized ceramic waste hosts will be a key characteristic in the engineering of radiation-resistant materials in the future.

Author contributions

MR and XG conceptualized and designed the study. JW provided samples for the study and collected TEM images. JL and QZ performed the BET experiments and analysed the data. AS collected the XRD data that was analysed by AS and MR. MR and XG performed the high temperature melt drop solution calorimetry and analysed the data. MR and XG interpreted the data. All participated in writing the manuscript.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by the institutional funds from the Department of Chemistry at Washington State University in the early stage, and later supported by the National Science Foundation (NSF), Division of Materials Research, under award No. 2144792. Portions of this research were also supported by collaboration, services, and infrastructure through the Nuclear Science Center User Facility, and the Alexandra Navrotsky Institute for Experimental Thermodynamics at WSU. Portions of this research used Beamline 11-ID-C (XSD-SRS) of the Advance Photon Source (APS), a U.S. DOE Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory (ANL) under Contract No. DE-AC02-06CH11357.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d3nr05605h

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