Transformations to amorphous and X-type phases in swift heavy ion-irradiated Ln₂O₃ and Mn₂O₃

The process by which swift heavy ion (SHI) irradiation damages materials is fundamentally different from that of low-energy ions. For massive ions with specific kinetic energies in excess of ∼1 MeV/u, energy is primarily deposited along the ion track by electronic excitation and ionization, rather than collisions with atomic nuclei. The densely excited electronic system subsequently dissipates the deposited energy through electron–electron and electron–phonon interactions. The latter transfers energy to the atomic system, causing a thermal spike that locally heats the material for a few picoseconds, followed by a rapid quench that typically leaves a modified atomic structure along the ion trajectory.^1–3 Swift heavy ion irradiation is of interest as a means of modifying materials in ways unachievable by conventional processing methods and for simulating the effects of fission fragment and alpha particle irradiation, which is useful for the development of improved nuclear materials.^4–6 

Energetic ion irradiation can produce unique defect configurations^7,8 and chemical changes in materials,^9,10 yielding structural modifications in a variety of oxides, including point and clustered defects,¹¹ amorphization,^12,13 and crystalline-to-crystalline phase transformations.^14–17 Understanding the fundamental mechanisms of radiation-induced structural modifications by characterizing the radiation responses of various materials enables the manipulation of these materials to obtain specific properties or engineered nanostructures.^18,19 Processing of Ln₂O₃ materials (where Ln refers to the lanthanides, La–Lu) in this way is particularly interesting due to their applications in a variety of technologies, including ultrafast and high-power solid-state lasers,^20,21 high-κ dielectrics,^22,23 catalysts,^24,25 nanoparticles for medical imaging,^26,27 and burnable neutron absorbers in nuclear fuels.²⁸ Desirable properties, such as enhanced ionic conductivity for solid oxide fuel cell (SOFC) electrolytes and reduced propagation losses in waveguides, can be tailored by inducing disorder while also enabling the recovery of nonequilibrium crystal phases to ambient conditions.^13,14,29

Most materials in the Ln₂O₃ system are polymorphic, exhibiting different equilibrium crystal structures depending on temperature and pressure (Fig. 1). At atmospheric pressure and room temperature, Ln₂O₃ compounds with large lanthanide ionic radii (Ln = La–Nd) preferentially adopt the trigonal A-type structure (⁠$P3¯m1$⁠), in which cations are in sevenfold coordination with oxygen anions. All lanthanide sesquioxides with smaller cations (Ln = Pm–Lu) preferentially adopt the cubic C-type structure (⁠$Ia3¯$⁠), characteristic of the mineral bixbyite, at ambient conditions.^30,31 The bixbyite unit cell can be described as a 2 × 2 × 2 fluorite supercell with ordered vacancies on one-quarter of the anion sites so that cations are in sixfold coordination with anions.³² 

Phase transformations induced in these materials by increasing temperature and pressure show similar dependence on lanthanide ionic radius. Those Ln₂O₃ materials with medium-sized cations (Ln = Sm–Ho) transform to the monoclinic B-type (C2/m) at elevated temperature or pressure. Additionally, most Ln₂O₃ materials transition further to a H-type (P6₃/mmc) phase at very high temperatures, and those with large cations adopt an X-type phase (⁠$Im3¯m$⁠) within a narrow temperature range just below their melting point. The X-type unit cell has a body-centered cubic cation structure, yet the structure of the anions has been debated. Proposed anion sites include the 6b (50% occupancy), 12d (25% occupancy), and 24g sites (12.5% occupancy).^14,33 Due to this low occupancy of oxygen sites, X-type structures have been hypothesized to have high ionic conductivity typical of superionic conductors.³³ Because enhanced oxygen transport is of great importance for solid oxide fuel cells, X-type materials may prove to be excellent SOFC electrolytes.^34,35

Ample investigations of the Ln₂O₃ system have explored both high-temperature and high-pressure polymorphs,^30,36–40 but recent research has extended the understanding of Ln₂O₃ polymorphism by using ion irradiation to induce various crystalline phase transformations. These studies have found that certain high-temperature or high-pressure polymorphs can be synthesized by intense ion irradiation and quenched to ambient conditions.^14,41–43 For example, Tang et al. observed transformations from the C-type to the B-type phase in Dy₂O₃ and Er₂O₃ irradiated with low-energy ions (300 keV Kr²⁺) at cryogenic temperatures.⁴⁴ Using swift heavy ions (185 MeV Xe and 2246 MeV Au), Tracy et al. and Lang et al. have induced both the C-to-B phase transformation and a transformation from the C-type to an amorphous phase in Ln₂O₃ materials with Ln = Sm–Ho.^14,45 Through the extreme conditions of SHI irradiation, far-from-equilibrium structures that are otherwise not accessible, such as the X-type phase shown in Fig. 1, have additionally been produced and quenched to standard temperature and pressure conditions.¹⁴ Sattonnay et al. have also confirmed the C-to-B transformation for 1042 MeV Xe ion irradiation of Gd₂O₃ and Eu₂O₃, identifying a preferred crystallite orientation in the irradiation-induced phase.⁴⁶ The structural evolution and phase transformation behavior in irradiated Ln₂O₃ show a strong dependence on sesquioxide composition, ion energy, and ion energy loss.^14,43

Previous SHI studies have not covered certain compositions in the lanthanide sesquioxide series, particularly those containing relatively large lanthanide cations that form A-type phases, such as Nd₂O₃. High hygroscopy makes the measurements of irradiation-induced modifications in these materials especially challenging, limiting the comparison of Ln₂O₃ materials with different size cations. Likewise, one of the sesquioxides featuring a much smaller lanthanide cation, Yb₂O₃, has not yet been characterized under SHI irradiation. This material is of interest for its probable transformation to the X-type phase.¹⁴ Furthermore, the irradiation responses of isostructural, but chemically distinct, non-lanthanide sesquioxides such as Mn₂O₃ have not been thoroughly examined. The study of these materials is necessary to elucidate the fundamental factors governing the radiation responses of this class of oxides and systematic trends in their phase behavior as a function of cation radius. Here, we report a detailed SHI irradiation study of A-type Nd₂O₃ (large lanthanide cation), C-type Eu₂O₃ (medium-sized cation), C-type Yb₂O₃ (small cation), and C-type Mn₂O₃ (isostructural with many Ln₂O₃ materials, but with a transition metal cation) using 946 MeV Au ions. To facilitate the study of the highly hygroscopic A-type phase, structural modifications were measured using in situ x-ray diffraction (XRD) conducted in vacuo. SHI irradiation-induced material-dependent modifications include a rapid amorphous transformation in both Nd₂O₃ and Eu₂O₃, a sluggish transformation to an X-type structure in Yb₂O₃, and a minor reduction of crystallinity in Mn₂O₃.

Three lanthanide sesquioxide powders (Nd₂O₃, Eu₂O₃, and Yb₂O₃ purchased from Alfa Aesar with at least 99.9% purity) were first calcined at 800 °C for 50 h to remove any water present. Each powder was then pressed with a uniaxial pressure of 30 MPa to form a pellet with a diameter of 12 mm and a thickness of 3 mm. These pellets were sintered in air at 1100 °C for 30 h to densify and dehydrate. To prevent hydration, the Nd₂O₃ pellet was placed under vacuum immediately after sintering. MnO₂ powder (purchased from Alfa Aesar with at least 99.9% purity) was calcined and pressed under the same conditions as the lanthanide sesquioxides, but subsequent sintering differed; the pellet was sintered at 800 °C for 30 h in order to completely reduce the stoichiometry of the sample to Mn₂O₃.⁴⁷ XRD performed after sintering confirmed the crystalline phase of each sample and grain sizes greater than 1 μm. The pellets were secured to copper sample holders for irradiation and in situ x-ray characterization.

Sample irradiation was performed at the M2 UNILAC beamline of the GSI Helmholtz Centre for Heavy Ion Research in Darmstadt, Germany. All pellets were irradiated with 946 MeV ¹⁹⁷Au ions at room temperature and under vacuum. The beam spot was scanned to ensure that the entire face of the pellet was irradiated to the desired ion fluence. To limit bulk heating of the sample, the gold ion flux was held below 1.8 × 10⁹ cm⁻² s⁻¹. The samples were characterized by in situ XRD using a diffractometer integrated into the M2 beamline at the M-branch.⁴⁸ Measurements were performed before irradiation and after certain fluence steps (ranging from 10¹¹ cm⁻² to 2 × 10¹³ cm⁻²) without removal of the samples from the beamline. These specific methods allowed for the characterization of Nd₂O₃, which adsorbs water so rapidly as to render ex situ measurement in air impracticable,⁴⁹ while enabling higher ion fluences to be reached.

The x-ray diffractometer installed at the M2 beamline is a custom-built 4-circle device with a Cu-K_α source in Bragg–Brentano geometry. One-dimensional XRD patterns were collected in the range of 2θ = 25°–62° with collection times ranging from 40 to 80 s. The thickness of the damaged region was determined to be at least 27 μm in all four sesquioxides using the SRIM-2013 code.⁵⁰ The damaged region was much deeper than the penetration depth of the x rays, ensuring that only the irradiated portion of each pellet was probed, as 90% of the scattered intensity originated from the first 10 μm below the specimen surface.⁴⁸ Samples were exposed to the ion beam until each subsequent fluence step was achieved, and the XRD measurement was repeated. The extraneous signal was collected from the copper sample holders due to the relatively large size of the x-ray beam spot.

The XRD data were analyzed by Rietveld refinement⁵¹ using GSAS II software.⁵² Fits to the experimental data were obtained by refining the unit-cell parameters and microstrain based on peak shifts and peak broadening, respectively. Satisfactory fits were achieved for each material and fluence while subtracting the signal from the copper sample holder. Once refinement produced fits of sufficient quality for the crystalline (B-type or C-type) A₂O₃ diffraction pattern, the refinements were modified to include the copper peaks. The diffraction peaks from the copper sample holder remained constant in intensity and position for each fluence step due to the high radiation tolerance of copper and the immobility of the sample holder in the in situ configuration. Thus, the copper XRD peaks served as an internal standard for quantitative analysis in the irradiated samples at various ion fluences. The crystalline phase fractions of the sample and the Cu standard reported by GSAS II were used to determine the fraction (by weight) of each crystalline and amorphous phase present in the samples by the conventional internal standard method.⁵³ Besides phase fractions, shifts in unit-cell parameters and evolution of microstrain were determined as a function of ion fluence for each sample composition.

In accordance with the phase diagram reported by Coutures et al.,³⁰ Ln₂O₃ materials with cation radii greater than ∼0.97 Å preferentially adopt a trigonal (⁠$P3¯m1$⁠) A-type structure at standard temperature and pressure. Those with smaller cation radii typically adopt a cubic (⁠$Ia3¯$⁠) C-type structure, characteristic of the mineral bixbyite. Analysis of XRD patterns collected from the four materials prior to irradiation, displayed in Fig. 2, confirms that all samples exhibited the expected crystalline phases; the Nd₂O₃ pattern is representative of a phase pure A-type crystal structure, whereas the Eu₂O₃, Yb₂O₃, and Mn₂O₃ patterns indicate well-crystallized C-type structures with no impurity phases. No hydrous phases were present for Nd₂O₃, confirming that the sample treatment and experimental conditions were suitable to study this unstable compound.

The results of prior SHI irradiation experiments have indicated that amorphization, rather than a crystalline C-to-B phase transformation, can occur in C-type Ln₂O₃ materials (Sm–Er) below a threshold ion velocity (corresponding to some energy less than 2.2 GeV for Au ions).¹⁴ Thus, transformation to either the B-type or an amorphous phase can be expected for irradiation by 946 MeV Au ions. With increasing ion fluence, Φ, the Nd₂O₃ and Eu₂O₃ patterns exhibit a gradual reduction in the intensity of all crystalline diffraction maxima accompanied by the appearance of broad, low-intensity bands [Figs. 2(a) and 2(b)]. One band is visible as a bump in Fig. 2(b) at about 25°–37°, although it is obscured by a low signal-to-noise ratio, and a similar low-intensity diffuse peak exists for irradiated Nd₂O₃. These broad bands result from diffuse scattering of x rays by amorphous sample domains lacking long-range periodicity.⁵⁷ Experiments using x rays from a laboratory source tend to produce a fairly weak signal from the amorphous phase as compared with synchrotron x rays, such that scattering from the amorphous volume is expected to be extremely weak in the diffraction pattern.^12,54–56 The gradual disappearance of crystalline peaks and the emergence of amorphous scattering bands indicate an irradiation-induced crystalline-to-amorphous transformation. Broadening of all crystalline peaks is evident and is explained by strain build-up and fragmentation of crystalline sample domains associated with the amorphization process. No new, sharp diffraction maxima are seen in the XRD patterns for either Nd₂O₃ or Eu₂O₃, indicating that no well-crystallized B-type or other crystalline phase was formed by irradiation, which was confirmed by Rietveld refinement. The crystalline peak intensity of Eu₂O₃ diminishes more rapidly as a function of ion fluence than that of Nd₂O₃, indicating a larger amorphization cross section in the former. At a fluence of 10¹³ ions/cm², all crystalline peaks for both Nd₂O₃ and Eu₂O₃ have nearly disappeared, showing that both samples have become almost completely amorphous. As expected, the peak intensities from the copper sample holder remain constant throughout irradiation to all fluences.

The evolution of the Yb₂O₃ XRD patterns with ion fluence [Fig. 2(c)] exhibits an irradiation behavior markedly different from that of the previous two materials. Retention of the C-type peaks indicates that Yb₂O₃ largely maintains its initial structure up to a fluence of 2 × 10¹³ ions/cm², although a reduction in crystalline peak intensity is observed. Broadening of the crystalline diffraction peaks with increasing ion fluence can be attributed to strain from accumulated defects.⁵⁸ At fluences above 3 × 10¹² ions/cm², two new diffraction features become visible in the patterns: a peak at 31.2° and a shoulder at 44.7° on the (431) C-type peak. These new peaks fit well to the X-type structure model (Fig. 1), which was observed previously in swift heavy ion-irradiated Tm₂O₃ and Lu₂O₃.¹⁴ 

XRD patterns of the Mn₂O₃ sample show retention of the initial C-type peaks up to the highest fluence, indicating that no distinct structural transformation is induced in this material by SHI irradiation. All diffraction peaks reduce in intensity upon increasing fluence and show significant broadening that could be a consequence of defect formation or amorphization, although no diffuse scattering band is apparent up to 10¹³ ions/cm².

For the three materials whose XRD patterns clearly show large-scale irradiation-induced phase transformations (Nd₂O₃, Eu₂O₃, and Yb₂O₃), the loss of the starting phase and growth of the new phase as a function of ion fluence were analyzed to yield information about the phase transformation mechanisms. The crystalline phase fractions of amorphizable Nd₂O₃ and Eu₂O₃ for a given fluence were obtained by Rietveld refinement of XRD patterns representing the remaining C-type sesquioxide phase and the (constant) copper phase. Subtle diffuse scattering from the amorphous phase was subtracted with the background prior to the refinement. The crystalline phase fractions for both Nd₂O₃ and Eu₂O₃ decrease noticeably as a function of increasing ion fluence, at a much faster rate for Eu₂O₃, and appear to saturate at ∼4% at higher fluences (Fig. 3). This behavior can be best described by a direct-impact (i.e., single-impact) model, which assumes that each incident ion produces an amorphous track along the ion's path and that no track overlap is required to create an amorphous region in the target material. An equation for the unmodified crystalline sample volume remaining after irradiation to a given fluence was derived from Poisson statistics. Because some small crystalline peaks persist even at the highest fluences studied, indicating possible saturation of the amorphous fraction, the direct-impact model was adjusted to allow non-zero crystalline fractions at high fluences,⁵⁹ 

in which $fc$ is the remaining crystalline fraction by weight, ϕ is the ion fluence, and σ is the cross-sectional area of the amorphous region of the ion track. The constant b represents the remaining crystalline fraction at infinite ion fluence. A Levenberg–Marquardt (damped least squares) fit was obtained for Eq. (1) and plotted alongside the refined remaining crystalline fractions in Fig. 3.

The crystalline fractions of both Nd₂O₃ and Eu₂O₃ are fit well by the direct-impact model described in Eq. (1). A multi-impact mechanism, wherein multiple ions must traverse a given volume of material in order for it to transform, would produce sigmoidal loss of the crystalline phase. Though a multi-impact mechanism has been observed for SHI irradiation-induced transformations in other binary oxides,¹⁶ there is no evidence of sigmoidal behavior seen within the uncertainties of experimental data for Nd₂O₃ and Eu₂O₃. Track diameters of 8.9 ± 0.7 and 14.1 ± 0.6 nm were calculated from the cross-sectional area, σ, for Nd₂O₃ and Eu₂O₃, respectively; saturation values, b, deduced from Eq. (1) were 5% and 4%, respectively. As qualitatively observed from the XRD data in Fig. 2, the crystalline fraction of Eu₂O₃ decreased more distinctly with fluence than that of Nd₂O₃ (Fig. 3) due to the larger cross-sectional area of the amorphous ion tracks produced in Eu₂O₃.

In contrast to ion-beam-induced amorphization of Nd₂O₃ and Eu₂O₃, two new diffraction maxima are visible in the XRD patterns of Yb₂O₃ [Fig. 2(c)] and were indexed to the (110) and (200) peaks of the X-type phase. Rietveld refinement of the XRD patterns with mixed C-type and X-type phases provided a very good fit to the experimental data for each fluence, confirming that C-type Yb₂O₃ transforms to an X-type phase rather than an amorphous phase in response to SHI irradiation. Although X-type maxima are only visually apparent in the XRD patterns at fluences of 5 × 10¹² ions/cm² and higher, refinements indicated the accumulation of an X-type phase fraction at lower fluences [Fig. 4(a)]. The X-type phase fraction, f_X, increases with ion fluence after an initial latent period and appears to saturate at the maximum fluence at f_X = ∼15%. The pronounced sigmoidal growth of the X-type phase fraction with increasing ion fluence indicates a multi-impact mechanism. This means that multiple ion tracks must overlap to induce C-to-X transformation in Yb₂O₃,⁶⁰ suggesting a stepwise transformation process wherein structural defects produced by previous ion impacts facilitate a gradual transformation of a given volume of material.

Microstrain in Yb₂O₃, determined from “peak broadening” through Rietveld refinements of the remaining C-type phase, reveals a correlation with the onset/saturation of X-type phase formation, illustrating the role that defect accumulation and structural distortion play in this transformation process [Fig. 4(b)]. With increasing ion irradiation, the microstrain accumulates monotonically at three distinct rates of increase, as indicated by the linear slope lines in Fig. 4(b). The initial accumulation of microstrain at low ion fluences is rapid as (largely isolated) point defects and small defect clusters are produced up to a fluence of ∼3 × 10¹² ions/cm², at which point the rate of accumulation decreases. Above this fluence, defect-rich ion tracks begin to overlap, and diffraction maxima of the X-type phase become visible in the XRD patterns [Fig. 2(c)]. The accumulation rate further decreases at a fluence of ∼10¹³ ions/cm² as the X-type fraction nears saturation. Saturation of the X-type fraction below unity implies a steady-state regime of ion-beam-induced X-type phase formation and replacement by the C-type phase in the absence of any detectable amorphization.

Figure 5(a) presents stacked XRD patterns for Yb₂O₃ in detail with increasing ion fluence, emphasizing the emerging (110) X-type peak at fluences greater than 3 × 10¹² ions/cm². The C-type structure remains mostly intact, and there is no evidence of amorphization or transformation to the B-type phase, as commonly observed in sesquioxides with larger lanthanide elements. The inset reveals a polytonic shift in C-type peak positions, shown for the (222) peak, and a gradual increase in peak width. This most intense C-type diffraction maximum exhibits complex behavior in 2θ position during irradiation, corresponding to both unit-cell contraction and expansion.

The shift of the C-type Yb₂O₃ unit-cell parameter indicates a complex interplay between irradiation-induced defect accumulation within the C-type matrix and stresses induced by X-type domain formation. The initial expansion of the unit cell [Fig. 5(b)] is interpreted as swelling from the production of defects, corresponding to the pronounced buildup of microstrain at low fluences [Fig. 4(b)]. The contraction that follows at higher fluences may be explained by the formation of X-type domains, which are less dense than the C-type phase per the X-type phase model (Fig. 1),¹⁴ exerting compressive stresses on the remaining C-type volume.⁵⁵ The reversion to unit-cell expansion at the highest fluences achieved “coincides” with the saturation of the X-type fraction. This suggests that defect accumulation in the remaining C-type volume persists after X-type creation and removal has reached steady state, which is in agreement with the continued increase in microstrain across the same fluence range [Fig. 4(b)]. These distinct polytonic trends observed in X-type phase fraction as well as in C-type microstrain and unit-cell parameter provide further evidence of a multi-impact transformation mechanism in Yb₂O₃. The transformation to the X-type phase appears to be driven by the accumulation of a critical defect density that is reached after multiple ion impacts, in agreement with previous studies on other binary oxides.¹⁶ 

No new crystalline phases were observed in the irradiated Mn₂O₃ [Fig. 2(d)]. Instead, minor amorphization is indirectly evident based on the reduction in peak intensity with no apparent diffuse scattering background. All diffraction maxima broaden considerably while the total integrated peak intensity diminishes with increasing ion irradiation. This sesquioxide compound is comparatively resistant to amorphization by SHI irradiation, as the refined C-type phase fraction reduces gradually to only ∼80% at the maximum fluence [Fig. 6(a)]. The direct-impact model was used to fit the data and determine the cross-sectional track area and diameter using Eq. (1). The same procedure was applied as for Nd₂O₃ and Eu₂O₃, but the fit parameter b was adjusted to zero since no phase saturation is apparent up to the maximum fluence achieved. The amorphous track area and diameter were determined to be 3.1 nm² and 2.0 nm, respectively, far smaller than the values obtained for the two other amorphizable sesquioxide compositions.

The microstrain increases and the unit-cell parameter in C-type Mn₂O₃ decreases with ion fluence approaching saturation, a behavior that is well-represented by a single-impact mechanism. The relative changes in strain and unit-cell parameter proceed at a much higher rate than the amorphization process as represented by much larger cross sections. This phenomenon that has also been observed in Au-irradiated Ga₂O₃ was attributed to the production of isolated defects within a larger shell region surrounding a more highly damaged ion track core.⁵⁵ Interestingly, the unit-cell parameter does not expand under swift heavy ion irradiation but contracts with saturation at ∼0.17%. This behavior is not commonly observed in amorphizable materials and may be attributed to compressive stresses from an under-dense amorphous phase or to irradiation-induced redox effects in the remaining C-type phase. Similar unit-cell contraction was previously observed in redox-sensitive binary oxides following SHI irradiation⁶¹ and was attributed to irradiation-induced oxidation processes. Manganese has more accessible oxidation states than any other transition metal, which may present a high redox activity under extremely ionizing irradiation. If oxidation of Mn³⁺ occurs with swift heavy ions, the decrease of ionic radius may lead to unit-cell compression that overshadows possible defect-induced swelling.

The precise in situ experimental design allowed the Cu sample holder to function as an internal standard, which was crucial for the quantitative analysis of the remaining crystalline phase and the induced amorphous phase in each sample. Using an internal standard in XRD measurements is a standard technique that has been applied extensively for quantitative phase analysis in mixed-phase polycrystalline materials since the 1940s.^{53,56,62–64} Likewise, irradiation studies have regularly used crystalline peak analysis of diffraction patterns measured in situ to diagnose and quantify amorphization; TEM has confirmed the efficacy of this method to quantify amorphization by observation of crystalline peak attenuation.^{5,12,48,54,65} Therefore, the amorphous phase fraction was determined in this study by diffraction pattern analysis of attenuated integrated peak intensities with respect to the internal copper standard diffraction peaks.

Irradiation by 946 MeV Au ions produced very similar behavior in both A-type Nd₂O₃ and C-type Eu₂O₃. Rietveld refinements using the internal copper standard showed a near-complete loss of the crystalline peak intensity which cannot be explained by defect-induced strain broadening or a transformation to a different crystalline phase. Direct amorphization within individual ion tracks was shown to be the dominant transformation mechanism for both compositions, despite their distinct initial structures (Fig. 3). Incomplete amorphization with non-unity saturation of the amorphous fraction suggests an ion-track morphology more complex than a simple cylindrical amorphous volume in both materials. Heterogeneous ion tracks have previously been observed in A₂B₂O₇ pyrochlore oxides, which exhibit concentric defective regions around amorphous cores.⁵ This core–shell morphology was explained by recrystallization processes that may also form epitaxial A-type (Nd₂O₃) and C-type (Eu₂O₃) shells surrounding amorphous ion track cores in Nd₂O₃ and Eu₂O₃. If crystalline shells repeatedly form, complete amorphization cannot be reached; such shells must be thin for Ln₂O₃ materials, as the direct-impact model approximates the phase fraction evolution quite well.

It has previously been observed that ion track diameters and phase transformation rates in C-type Ln₂O₃ materials decrease monotonically as the atomic number of the lanthanide increases (and thus as the ionic radius decreases); a smaller cation radius typically corresponds to greater phase stability.^14,44 This rule is confirmed for the C-type lanthanide sesquioxides in the present study, as the remaining C-type fraction is greater in Yb₂O₃ compared to Eu₂O₃ for any given fluence (e.g., 85% vs 4% at 2 × 10¹³ ions/cm²). However, the heightened amorphization resistance of Nd₂O₃ relative to Eu₂O₃, indicated by the smaller amorphous track diameter of Nd₂O₃, shows that the trend of increased phase stability for smaller lanthanide cations cannot be extended to A-type sequioxides (whose cations have the largest ionic radii), despite their qualitatively similar response to SHI irradiation. Furthermore, Mn₂O₃, with the smallest cation, retains a lower C-type phase fraction (80% at 10¹³ ions/cm²) compared to Yb₂O₃, indicating that this rule cannot be extended to non-lanthanide C-type oxides either. The underlying mechanism for this behavior remains unclear, but it indicates that either the Ln₂O₃ starting structure or the accessible phase space plays a role in swift heavy ion irradiations. It has been shown that C-type to B-type transformation is critical for the irradiation of most sequioxides, and the B-type phase is absent in the equilibrium phase diagram for A-type compositions such as Nd₂O₃.¹⁴ 

Interestingly, there is no evidence of ion-beam-induced B-type phase formation in any Ln₂O₃ composition under irradiation with 946 MeV Au ions. While prior SHI studies of C-type Ln₂O₃ materials reported transformations to the B-type (Ln = Sm–Er) and minor X-type (Ln = Tm–Lu) phases induced by irradiation with high ion energies (e.g., 2.2 GeV Au), lower ion energies (e.g., 185 MeV Xe) predominantly caused amorphization with minor B-type phase formation (Ln = Sm–Er) and substantial X-type formation (Ln = Tm–Lu).^14,45,46 This discrepancy in which more extensive damage results from irradiation with ions of lower energy and mass (i.e., lower dE/dx) was explained by the swift heavy ion velocity effect and associated energy density differences along ion tracks.^14,66 The distance that excited electrons travel from the ion–solid interaction region before thermalizing is proportional to the energy initially transmitted to them and thus to the ion irradiation energy. Therefore, the energy deposited to a material by high-energy ions is spread over a much larger volume than that deposited by lower energy ions, yielding lower energy densities.^1,3 Based on the results reported here, 946 MeV Au ions have sufficiently reduced velocity compared to 2.2 GeV Au ions to generate energy densities above the threshold for amorphization. Amorphization appears to be complete for Eu₂O₃, which was not the case for the two neighboring compositions (Sm₂O₃ and Gd₂O₃) irradiated with 185 MeV Xe ions, where a minor C-type to B-type transformation was reported.¹⁴ This can be explained by a combined effect of ion velocity and energy loss. The velocity of 946 MeV Au ions is lower than that of 2.2 GeV Au ions, resulting in an increased energy density within the track region. Compared to 185 MeV Xe ions, however, the energy loss (dE/dx) is still higher, which further increases the energy density and yields complete amorphization of Eu₂O₃.

The X-type phase, which was accessible in Yb₂O₃ by 946 MeV Au irradiation, is particularly interesting because of its highly nonequilibrium nature and predicted superionic conductivity. Neither temperature nor pressure has been demonstrated to induce the formation of an X-type phase in Yb₂O₃ or other Ln₂O₃ materials with similarly small cations. Moreover, for larger cations where the X-phase can be produced at very high temperatures, attempts to quench this phase to ambient conditions were unsuccessful. However, stresses resulting from radiation-induced defects have been shown to stabilize certain high-pressure polymorphs in oxides.^67–69 Considering that numerous high-pressure phase transformations have been reported for Ln₂O₃ materials,³¹ irradiation-induced strain may play a role in stabilizing the X-type phase to ambient conditions. The fact that the X-type phase has never been reported for Yb₂O₃ in the equilibrium phase diagram emphasizes the far-from-equilibrium conditions that are accessible through SHI irradiation. Consistent results have previously been reported for Tm₂O₃ and Lu₂O₃ irradiated with energetic 185 MeV Xe ions.¹⁴ Given that the atomic number and ionic radius of Yb are intermediate to those of Tm and Lu, the observed formation of X-type Yb₂O₃ agrees well with this prior work. Interestingly, a direct-impact transformation was proposed for Tm₂O₃ and Lu₂O₃,¹⁴ while a multi-impact mechanism best describes the accumulation of the X-type phase in Yb₂O₃. Overlapping tracks of 946 MeV Au ions are required to reach defect concentrations necessary to drive the C-to-X transformation, which is produced directly in 185 MeV Xe ion tracks. This discrepancy may be related to the difference in the ion velocity, energy loss, or a combination of both.

Saturation of X-type phase fraction in Yb₂O₃ was determined to be about 15% for 946 MeV Au ions (Fig. 4), unlike previous results that have found no such X-type saturation in Tm₂O₃ and Lu₂O₃ by direct impact. This finding depends disproportionally on the highest fluence data point, and further irradiation experiments to much higher fluences are required to unambiguously confirm that X-type transformation saturates at such a low phase fraction. If accurate, this finding is intriguing as it suggests that a pure X-type phase cannot be produced by this particular ion species and energy. Similarly, to the incomplete amorphization of Eu₂O₃, this behavior can be explained by a core–shell morphology. While the X-type phase forms by track overlap, a C-type shell is continuously formed. Given the low saturation value, the shell size must dominate the cross-sectional area of ion tracks. An X-type phase has also been shown to form in Er₂TiO₅ at extreme pressure⁷⁰ and in Gd₂Zr₂O₇ under simultaneous pressure and SHI irradiation.⁷¹ Park et al. reported only a partial recovery to ambient conditions for Er₂TiO₅,⁷⁰ while Lang et al. confirmed a complete quenching to atmospheric pressure for Gd₂Zr₂O₇.⁷¹ Further work should evaluate whether synergistic effects of pressure and irradiation are required for complete X-type formation and recovery. Once experimental protocols have been established and a sufficient quantity of the X-type phase is available for broadband dielectric spectroscopy measurements, its unique ionic properties should be explored.

Since Mn₂O₃ exhibits the smallest cation radius among the studied C-type materials, it is expected to be most stable under SHI irradiation. Despite its high resistance to amorphization relative to Eu₂O₃, Mn₂O₃ retains less of its C-type phase than Yb₂O₃ and amorphizes somewhat. Fitting a direct-impact model to the phase fractions indicates a small amorphous core only 2 nm in diameter, surrounded by a strained C-type region (11 nm diameter), which is part of a larger defective C-type region (16 nm diameter). Mn₂O₃ may reasonably be expected to form an X-type phase, as is typical of Ln₂O₃ materials with smaller cations, yet Mn₂O₃ forms no detectable X-type under the same irradiation conditions for which Yb₂O₃ transforms. Instead, minor amorphization is evident and the relative stability of the C-type phase under irradiation with 946 MeV Au ions is intermediate of Eu₂O₃ and Yb₂O₃. This behavior may be related to the 23% lower ion energy loss of Mn₂O₃ (∼37 keV/nm) relative to Yb₂O₃ (∼48 keV/nm) resulting from the lower density of the former. The induced energy density may not be sufficiently high to form the X-type phase or cause more substantial amorphization as shown for Eu₂O₃. The distinct behavior of Mn₂O₃ may also suggest that irradiation-induced modifications in sesquioxides depend not only on cation size but also on the electronic structure. X-type phase formation may be specific to A₂O₃ materials with lanthanide cations. Different effects may come into play for other cations, such as redox behavior, which is absent for many lanthanide elements. Reduction and oxidation processes can be triggered by highly ionizing radiation,⁹ and partial oxidation in Mn₂O₃ from Mn³⁺ to Mn⁴⁺ can explain the unusual unit-cell contraction (Fig. 6). Possible changes in stoichiometry and excess oxygen may render the highly anion-deficient X-type phase inaccessible in this sesquioxide composition.

Irradiation of Nd₂O₃, Eu₂O₃, Yb₂O₃, and Mn₂O₃ with 946 MeV Au ions over a range of fluences and subsequent XRD characterization provided new insight into the radiation responses and compositional trends in various sesquioxides. The structural responses were analyzed in vacuo at the beamline, which allowed the analysis of an air-sensitive A-type phase for the first time with a dense array of fluence steps to determine detailed phase-transformation mechanisms. The crystalline-to-amorphous transformation proceeds by a direct-impact mechanism for A-type Nd₂O₃ and C-type Eu₂O₃. Amorphization consistent with a direct-impact mechanism is also evident in C-type Mn₂O₃, but at a much slower rate than in Nd₂O₃ and Eu₂O₃. The formation of an X-type phase, as expected for small cation ionic radii, was not confirmed in Mn₂O₃ up to the highest fluence studied. Amorphous track diameters in Nd₂O₃, Eu₂O₃, and Mn₂O₃ are approximately 8.9, 14.1, and 2.0 nm, respectively, and saturation of amorphous phase fractions below 100% is indicative of a core–shell morphology. The A-type phase with the largest cation ionic radius is relatively more radiation tolerant than a C-type phase with medium-sized cations. C-type Mn₂O₃ is much more resistant against amorphization than the other two amorphizable compositions, which can be explained by electronic structure effects. Partial oxidation may be induced in this non-lanthanide sesquioxide by extremely ionizing radiation, leading to an unusual unit-cell contraction. The C-type sesquioxide with the smallest lanthanide cation (Yb₂O₃) undergoes a C-to-X phase transformation by a multi-impact mechanism with saturation at ∼15% X-type phase. This agrees well with earlier work reporting the formation of this phase in similar lanthanide sesquioxides. However, the results shown here differ from the prior analysis with respect to the observed saturation of the X-type phase fraction below 20% and the type of transformation mechanism (multi-impact in this study vs direct impact in previous studies). Further research is needed to fully understand the formation and quenching of this far-from-equilibrium phase by swift heavy ion irradiation and a possible synthesis route for a phase pure X-type material at ambient conditions. Neutron scattering experiments coupled with impedance spectroscopy can then be used to elucidate details regarding the oxygen ions’ structural role in the irradiated material, obtain additional information about the predicted superionic conductivity properties, and assess potential use in solid oxide fuel cell electrolytes.

This work was supported by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences, under Award No. DE-SC0020321. A.P.S. acknowledges support from the Integrated University Program Graduate Fellowship program. Any opinions, findings, conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the Department of Energy Office of Nuclear Energy. The results presented here are based on a UMAT experiment, which was performed at the M1-beamline of the UNILAC at the GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt (Germany) in the frame of FAIR Phase-0. We thank Dr. Siegfried Klaumünzer for assistance with x-ray diffraction experiments.

The data that support the findings of this study are available from the corresponding author upon reasonable request.