Low-temperature heat capacity and magnetism in (U_1−yLn_y)O₂ and (U_1−yAm_y)O₂ (y = 0.01 − 0.05) solid solutions: Effects of substitution and self-irradiation

All actinide (An) dioxides from Th to Cm adopt the $MO2$ fluorite Fm$3¯$m structure, as do their mixed oxides. Moreover, the crystal structure has the capacity to incorporate metal ions with valence states other than 4+, on the one hand due to the formation of structural vacancies on the oxygen sublattice, and on the other due to charge compensation of the metals. The latter has been demonstrated for a range of $UO2$-based solid solutions, containing trivalent lanthanides¹ or americium,² showing a complex crystal chemistry with multivalent ions on the metal sublattice.

The $AnO2$ fluorite structure is known for its excellent radiation tolerance as documented by numerous studies of the effects of alpha decay in the actinide dioxides (see references in Ref. 3). The structure can accommodate a significant fraction of displaced atoms created in decay cascades, without losing the long-range crystalline order. The atomic displacements in the crystal lattice, initially present as point defects in the materials, accumulate into extended defects such as loops and dislocations with time.⁴ Such a radiation-induced disorder can have a significant influence on the physical properties of materials because the phonon dynamics are affected substantially.⁵ Therefore, thermal properties such as heat capacity and thermal diffusivity are highly sensitive to the extent of radiation exposure, but also other physical properties that are related to the crystalline order, such as magnetism.

Studying the heat capacity at very low temperatures is an excellent means to understand the relation between structural disorder, crystal chemistry, and phonon dynamics. In recent years, we have performed detailed studies of uranium dioxide samples doped with the short-lived $238$Pu isotope (U_1−y²³⁸Pu_y)O₂, which has a half-life of 87.7 years, demonstrating that the antiferromagnetic $Cp$ anomaly (around 30 K) specific to $U4+$ is affected even at a short radiation exposure time.⁶ Similar studies on (U_1−y²⁴¹Am_y)O₂ were inconclusive for Am content of $y=0.1$ and 0.2 and showed a complete absence of the magnetic transition, but a large excess heat capacity.⁷ In addition to the longer half-life of the $241$Am isotope, 432.2 years, compared to $238$Pu, the crystal chemistry of (U,Am)$O2$ is appreciably more complicated by the simultaneous presence of $U4+$⁠, $U5+$⁠, $Am3+$⁠, and $Am4+$ on the metal lattice.² Finally, results for $(U1−yThy)O2$⁠, in which radiation effects are minimal, show that the $Cp$ anomaly is strongly affected by the cation disorder resulting from the substitution.

To further resolve the effects of radiation-induced disorder, substitutional disorder, and the charge exchange on the metal lattice, we have performed an additional series of experiments with $UO2$ doped with trivalent lanthanum and neodymium as well as doped with $241$Am in significantly lower concentration compared to our previous study.

The work presented in this paper has been carried out in radiological laboratories licensed for handling actinides, partly equipped with radiation shielding and remote handling tools.

The samples used in the present study have been produced by co-precipitation, guaranteeing the homogeneity and intimate mixing (Fig. 1). U(VI), La(III), and Nd(III) aqueous solutions (2 mol/l for uranium and 0.5 mol/l for lanthanides) were obtained by direct dissolution of the corresponding nitrates in milli-Q water under ambient conditions. An Am(III) solution (0.5 mol/l) was prepared by dissolving $AmO2$ powder in $HNO3$ (6 mol/l) at 70 $°$C for 48 h. Note that, due to the aging process, the americium contains about 7% $237$Np and about 2% plutonium.⁸ 

The U(VI) and Am(III) solutions were mixed in the desired ratio in 50 ml Eppendorf test tubes. An organic thickener (Methocel 2%, Dow Chemicals) was inserted in order to increase the viscosity of the solution. The actinide solution was then added dropwise in a large excess (ten times) of 7 mol/l ammonia aqueous solution to initiate the precipitation of a mixed (U(VI),Am(III))-hydroxide. After filtration, the formed beads were washed and subjected to calcination (3 h at 800 $°$C) in air atmosphere, to remove the residual organics. The $U0.90Am0.10O2$ sample used for the magnetization measurements was from an earlier synthesis by hydrothermal decomposition, with a different flow chart.⁹ 

The resulting material was powdered in an agate mortar and further pressed uniaxially at 500 MPa to green disks (5.2 mm diameter). The disks were placed into a molybdenum crucible and sintered for 6 h at 1650 $°$C under an atmosphere of Ar/$H2$ (4%) and about 100 ppm of moisturizing water (heating and cooling ramps of 200 $°$C/h). The obtained pellets were extremely dense (i.e., >97% of the theoretical density).

The $(U1−yLay)O2$ and $(U1−yNdy)O2$ solid solutions were produced following an identical procedure, by replacing the americium with the corresponding $Ln(NO3)3⋅6H2$O salts (Ln = La, Nd, Alfa Aesar 99.99%). The final pellets were dense but extremely fragile.

The chemical and crystallographic characterization of the samples used in this study is summarized in Table I. The exact composition of the $(U1−yAmy)O2$ solid solutions were analyzed by the JRC Karlsruhe Analytical Service. The mass of americium was measured by calorimetry relative to the total mass of the sample and the calculation was performed assuming that $241$Am was the only heat source in the samples. $237$Np is calculated as 7% of the total Am-content. The Pu-content is neglected, being not significant. For simplification, we will refer further to the target composition in the text.

X-ray diffraction analysis was performed using a Bruker D8 diffractometer mounted in a Bragg–Brentano configuration with a curved Ge (1,1,1) monochromator and a ceramic copper tube (40 kV, 40 mA) and a LinxEye position sensitive detector. The data were collected by step scanning in the angular range of $10°≤2Θ≤120°$ with a step size of $0.02°$ (2$Θ$⁠); total measuring time was about 5 h. Refinement of the data was done with Jana 2006 software.¹¹ The measurement of the lanthanides-containing samples was performed using powders dispersed with several drops of isopropanol deposited on the surface of a silicon wafer. The measurements of the Am-containing samples were performed on about 10 mg of powdered material immobilized in a two-component epoxy resin on a sample holder, to avoid any dispersion of radioactive powders in the glovebox. The swelling of the lattice as a function of time (hence radiation dose) was monitored by periodic measurements from the third day after production over a three-year timescale.

Figure 2 shows the $a$ lattice parameter of the americium samples in comparison with literature values.^2,10,12–14 For the interpretation, the results have been compared to three crystal chemistry models:¹⁰ 

• $∙$

  The continuous solid solution of stoichiometric $(U1−y4+Amy4+)O2$⁠, in which only random substitution of the tetravalent ions on the metal sublattice takes place, follows Vegard’s law.

• $∙$

  In substoichiometric $(U1−y4+Amy3+)O2−y/2$⁠, uranium is considered to be tetravalent and americium trivalent, resulting in a fully reduced material. It corresponds to the hypothetical continuous change from a fluorite $M4+O2$ dioxide to a bixbyite-like $M23+O3$ sesquioxide. Such a trend was observed in different experiments performed on mixed oxides,^15–17 but the full reduction was never reached for (U,Am)O$2$ mixed oxides, even under reducing sintering conditions.

• $∙$

  Finally, the charge transfer occurring between uranium and americium as demonstrated experimentally^2,10,12 is taken into account in the $(U1−2y4+Uy5+Amy3+)O2$ model. In this case, the average ionic radius is larger than in the tetravalent stoichiometric model for the same U/Am ratio.^18,19 Thus, the lattice parameters of stoichiometric mixed oxides (U,Am)$O2$ are systematically larger than those suggested by Vegard’s law. The presence of $Am4+$⁠, as confirmed by unpublished XANES measurements of the current samples, would further complicate this model, but has not been taken into account.

Our experimental results follow the fitted trendline for the experimental values obtained by Lebreton¹⁰ for freshly reduced mixed oxides and not the results for the same materials after natural oxidation under storage conditions. However, it should be noted that the differences in the lattice parameter between the two conditions are small at low americium content. This analysis suggest compositions close to the oxygen stoichiometry (O/M $≈$ 2) for $U0.99Am0.01O2$ and $U0.95Am0.05O2$⁠, but full stoichiometry cannot be guaranteed for the latter.

The lattice parameter of the two $(U1−yLay)O2$ compounds allows a more sound assessment of the O/M ratio. The charge transfer model mentioned above gives a correlation close to the experimental values. Moreover, the measured lattice parameters are in perfect agreement with those by Hinatsu and Fujino²⁰ for samples with well characterized $U5+$ content and O/M ratios, which were close to stoichiometry (evolving from 2.006 for y = 0.05 to 1.988 for y = 0.30). Based on this, we conclude that the compounds have O/M = 2. Talip et al.²¹ also reported lattice parameters of $(U1−yLay)O2−y/2$⁠, which are also in excellent agreement, but they assumed solely $U4+$ to be present, hence the O/M < 2. A similar comparison can be made for $(U1−yNdy)O2$⁠, with the results of Fukushima et al.²² on samples of defined O/M close to 2.00, from which we conclude that also these compounds are stoichiometric.

The heat capacity measurements were performed with a low-temperature vacuum calorimeter based on a hybrid adiabatic relaxation method (PPMS, Quantum Design Inc.).⁷ The measurements were carried out using small solid pieces, as summarized in Table I. The lanthanide-doped samples were measured in the traditional way, i.e., directly placed on the sample platform, thermalized by Apiezon N high vacuum grease. In this configuration of the instrument, the estimated uncertainty for the heat capacities was reported about 2% by Lashley et al.²³ Two samples were selected for each composition with masses around $∼$20 and $∼$1 mg, respectively, to better determine specific value at high temperatures (>100 K) and around the magnetic transitions where the time constant can prevent observing the specific heat capacity at the antiferromagnetic transition $TN$ correctly.

The $(U1−yAmy)O2$ samples were wrapped in a Stycast 2850FT epoxy encapsulant before the measurement, to provide a radioprotective encapsulation and ensure a good thermal conductivity.²⁴ The quantity of Stycast was precisely determined and its contribution to the global heat capacity was obtained from a calibration correlation. This increased the uncertainty to about 4%–5% since the heat capacity of the Stycast²⁴ had to be subtracted quantitatively. The samples consisted of small solid piece with mass of 15.39 mg for the 1% Am composition and 3.13 mg for the 5% Am content. Before the measurements, the samples were heated for 4 hours into Ar/$H2$ atmosphere (1 l/min.) at 1650 $°$C to anneal the lattice damage accumulated by self-irradiation during the storage at room temperature in the period between fabrication and measurement. As self-heating of $241$Am is significatively important at T < 20 K (101 $μ$W/mg), the mass of americium had to be optimized for the different pieces to achieve the low temperature needed for the measurements, $∼$10 K. Corrections for the decay heat of $241$Am have been applied for the 5% sample.

D.C. magnetic susceptibility measurements were also carried out, in the temperature range of 2–300 K, with an external magnetic field up to $μoHmax=7$ T with a MPMS-3 superconducting quantum interference device (SQUID) from Quantum Design Inc. Samples were measured in Plexiglas containers calibrated at a precision below 1% for temperature and magnetic fields dependencies. The contributions of the paramagnetic containers were subtracted after the measurements leading to a precision of around 2% for the samples in full temperature and magnetic field ranges. In the case of the americium-based compounds, the container was sealed by Araldite® adhesive glue to prevent contamination giving an extra error below 0.5%.

The heat-capacity measurements of $UO2$ doped with a few percent of the lanthanides La and Nd are shown in Fig. 3(a) and compared to $UO2$⁠.²⁵ In high-purity $UO2$⁠, the antiferromagnetic transition occurs at 30.44 K²⁵ as a prominent $λ$-peak in the heat capacity. It is now well established by neutron diffraction measurements that below the Néel temperature the oxygen atoms in the antiferromagnetic state of $UO2$ are slightly displaced, resulting in a change from a Fm$3¯$m to a Pa$3¯$ symmetry.^26,27

Figure 3 shows that already at a low concentration of 1 mol% of La and Nd, a significant change in the magnetic anomaly is observed. These samples are characterized by multiple peaks close but lower to the reported ordering temperature of $UO2$⁠, partially overlapping but with a strong similarity in shape to the pure compound. With increasing concentration of the dopant, the peaks shift to lower temperatures and loose intensity, but not to the same extent, as summarized in Table III. The variation in the peak at the highest temperature, indicated as $TN2$⁠, remains within 2 K for the composition range studied, that of the lower temperature peak is close to 7 K. SQUID magnetization measurements confirmed the antiferromagnetic character of the materials and the change in Néel temperature at the same positions. As can be seen in Fig. 4, the DC magnetic susceptibility $χDC=M/H$ for the La and Nd doped systems follows a Curie–Weiss law. This is confirmed by plotting 1/$χDC=H/M≈C/(T−ΘP)$⁠, with $ΘP$ being the paramagnetic temperature, which is fitted well with linear relations for each material [Figs. 4(a) and 4(b)]. Magnetic transitions are also clearly visible in Figs. 4(c) and 4(d), supporting the results of the heat capacity measurements. However, the split is difficult to discriminate but nevertheless the estimated positions of the Néel temperatures are close to the $TN2$ temperature (Table II).

We attribute the split to the fact that in these compounds effectively two ions are diluted on the metal sublattice of the stoichiometric fluorite structure, $La3+$ or $Nd3+$ and $U5+$⁠, the latter because of charge compensation. This has been clearly demonstrated by XANES measurements^28,29 and also inferred in earlier magnetization measurements.³⁰ The alignment of the $U4+$ spin moments in the antiferromagnetic state is consequently affected by the interruption of the nearest-neighbor interactions in the fluorite structure, impacting the magnetic ordering. The difference in the positions and intensity of the two peaks for the La- and Nd-compounds can be attributed to the fact that the free $La3+$ ion has a $4f0$ electronic configuration (non-magnetic) and $Nd3+$ a $4f3$ (magnetic). The spin moments of the $4f$ electrons in the latter thus can interact with $U4+$ (⁠$5f2$⁠), whereas that effect is absent for the former. Also the spin moments of $U5+$ (⁠$5f1$⁠) will couple, but this effect will be the same in the two compounds. We exclude that the double peak is the effect of inhomogeneity in the samples, since they were produced by coprecipitation from solution, thus resulting in a near-to-atomic scale mixing.

The entropy of transition was calculated from the heat capacity by subtraction of the lattice heat capacity curve of $UO2$⁠,²⁵ which is a reasonable approximation for these low concentrations, and numerically integrating the resulting excess heat capacity. The results show that the full $Rln⁡(3)$ value for the $U4+$ ground state is not reached (neglecting the structural contribution for the Fm$3¯$m to Pa$3¯$ transition), as is the case in $UO2$ and also (U,Th)$O2$⁶ and is often attributed to magnetoelastic effects.³¹ The combined entropy of the two anomalies is even substantially lower than for the (U,Th)$O2$ solid solution, as measured by us in the past.⁶ As discussed by Huntzicker and Westrum²⁵, the anomaly in $UO2$ is atypical with a considerable portion of the enthalpy developed in the premonitory region, resulting from magnon–phonon interaction. Also, a considerable fraction of the magnetic entropy is developed above the Néel temperature, indicating some residual magnetic ordering. The presence of La and Nd in the structure thus enhances this effect strongly.

The heat capacity measurements of the annealed $(U0.99Am0.01)O2$ and $(U0.95Am0.05)O2$ samples revealed a similar splitting of the anomaly as for the La- and Nd-doped UO$2$ samples, as shown in Fig. 5. For the $(U0.99Am0.01)O2$ sample, two overlapping peaks were found at about T = 29 K, the one at lower temperatures being much more intense, similar to $(U0.99Nd0.01)O2$⁠. In the $(U0.95Am0.05)O2$ sample, the peaks have shifted further to lower temperature and their intensity has decreased substantially, again in line with the observations for the lanthanide-doped samples. This is not surprising as also in this system $U5+$ is formed as charge compensation for $Am3+$⁠, as evidenced by XANES analysis.² The shifts of the peak temperatures and intensities may probably be enhanced by the effect of radiation in view of the higher Am content (vide infra). For comparison, we also displayed the results for $U0.92Am0.08O2$ from our earlier work,⁷ in which the antiferromagnetic peak was not obvious.

We also observe magnetic transitions for the 1, 5, and 10% Am doping (Fig. 5) by SQUID magnetometry, confirming the magnetic character of the materials, and the change in temperature as a function of $y$⁠. As can be seen in Fig. 6(a), the magnetization curves also follow the Curie–Weiss law for the paramagnetic range, as for La- and Nd-doped systems, and show a gradual decrease of the Néel temperature with the Am content, in line with the heat capacity measurements [Fig. 6(b)]. This is clearly in contrast to what was previously reported⁷ where no magnetic order was visible for the heat capacity at 8% Am.

The free $Am3+$ ion has a $5f6$ configuration, and since the spin and orbital moments have the same magnitude and opposite direction, the resulting ground state is nonmagnetic (J = 0),³² but with strongly polarized spins. Moreover, the $5f$ electrons have a larger radial extent compared to the $4f$ electrons, and thus participate more strongly in the bonding. The closer spacing between the two peaks could be related to this.

The presence of the small quantity of $237$Np, the product of the radioactive decay of $241$Am, is considered to have a negligible effect. Np (5$f3$⁠) will have a tetravalent state in the dioxide and substitute for $U4+$ without charge transfer.

Finally, we have monitored the evolution of the magnetic anomaly in $(U0.95Am0.05)O2$ with increasing radiation dose in further detail, with a series of heat capacity and SQUID measurements between 11 days and 473 days of aging time. The $Cp$ results, shown in Fig. 7, indicate a gradual loss of intensity of the double peak and a shift to lower temperatures, corresponding to a steady decrease of the magnetic entropy with time and accumulated dose. In both samples, the heat capacity below the Néel temperature increases with time, indicating an excess resulting from the increase of the defect density in the structure that leads to accumulation of enthalpy. The magnetization measurements confirm that the magnetic order exists during this period [Fig. 8(a)], and the shift in the Néel temperature is in line with the heat capacity anomaly [Fig. 8(b)]. The measurements of $(U0.99Am0.01)O2$ have been repeated on two further moments in time, 6 weeks and 16 months. Figure 7 shows that after 6 weeks the peak has slightly shifted and its height decreased and that after 16 months it has shifted down to T = 26.6 K with an intensity of only 25% of the peak at $t0$⁠.

The difference in extent of accumulated damage between the two samples is well exemplified by the evolution of the lattice parameter measured by XRD as a function of aging time, shown in Fig. 9. The damage accumulation in the two samples follows a similar trend, almost independent of the initial concentration. The results can be described well by the following exponential equation as a function of dose (⁠$D$ in $α$/g):

From the graph, it can be seen that the $(U0.99Am0.01)O2$ sample did not reach the saturation of radiation effects at the moment of the last heat capacity and SQUID measurements (16 months $∼5×1016$ $α$/g), whereas the $(U0.95Am0.05)O2$ sample reached $2×1017$ $α$/g at the last measurement, where the saturation is approached.

Ionic substitution on the $U4+$ sublattice of the $UO2$ fluorite structure by other $f$-elements leads to spin exchange and frustration of the magnetic ordering. Whereas the effect of the dilution of the non-magnetic $Th4+$ leads to a simple shift in the temperature and intensity/entropy of the antiferromagnetic transition,⁶ the effect of the trivalent lanthanides $La3+$ and $Nd3+$ is more complex. Dilution with diamagnetic $La3+$ causes splitting of the AF-peak in two, which we attribute to the presence of a second diluent, $U5+$ that forms due to charge compensation and exchanges with the $U4+$ spins. Dilution with $Nd3+$ and $Am3+$ also causes splitting of the peak, but results in different intensities, probably due to additional $f$–$f$ exchange interaction (⁠$4f3$ in $Nd3+$ and $5f6$ in $Am3+$⁠).

Our observations are overall in line with the results of the magnetic susceptibility study by Hinatsu and Fujino^20,30,35 for the $(U1−yLay)O2−x$ solid solution in a wider composition range (⁠$0.05≤y≤0.30$⁠), but we observe a slight discrepancy. The paramagnetic state behavior is very similar but no splitting at $TN$ was detected by them. We can stress that the low density of acquisition points by the authors could have prevented observation of the splitting. Nevertheless, the antiferromagnetic state was much higher (⁠$χDC$⁠) and the ordering temperature was shifted to a lower value $∼$21 K corresponding to $TN1$⁠, while $TN2$ was maybe not detectable. From their results, Hinatsu et al.³⁰ concluded that both oxygen vacancies and interstitials weaken the magnetic interactions on the U sublattice. Similar to our heat capacity results, they observed the different behavior compared to Th substitution, which they attributed to the presence of $U5+$⁠. Hinatsu and Fujino³⁶ also studied the magnetic susceptibility of the $(U1−yNdy)O2$ solid solution in the (⁠$0.01≤y≤0.30$⁠) composition range. They found no change in the temperature at which the discontinuity in the curves took place, 30–31 K, comparable to their work on $(U1−yPry)O2$⁠,³⁷ for which they could not give a clear explanation: “these phenomena are considered to be not due to the effect of $U4+$⁠, but due to the effect of $U5+$ and $Nd3+$ [$⋯$] which are Kramers' ions with odd unpaired electrons.” This contrasts with our results, as we clearly see the Néel temperatures in heat capacity and magnetization measurements. One can only speculate about the reasons for this. Based on our results for the heat capacity of the $(U1−yNdy)O2$ solid solution [Fig. 3(b)], it cannot be excluded that the convolute of unresolved double peaks did not change position as a result of the changing intensities of the magnetic anomalies in combination with insufficient resolution of the work of Hinatsu and Fujino.

Another valuable comparison can be made with $(U1−yNpy)O2$⁠. Tabuteau et al.³⁸ studied the magnetic susceptibility of this solid solution in the composition range 0.15 $≤y≤$ 0.75 and also observed a lower Néel temperature, with magnetization curves very similar to (U,Pu)$O2$ samples.³⁹ $237$Np Mössbauer spectroscopy by the same authors³⁸ evidenced the tetravalent state of Np (also confirmed by XANES⁴⁰), and showed that the $Np4+$ ions order at a lower temperature than the observed $TN$ for the solid solution but as well below that for $NpO2$⁠.⁴¹ The low-temperature neutron diffraction measurements of the $(U0.50Np0.50)O2$ composition indicated that the magnetic structure of this solid solution is different from that of the $UO2$ low-temperature phase.⁴² These observations support the attribution of the splitting of the C$p$ anomaly to ordering of different ions, but call for an experimental check whether two anomalies can be observed as well in the low-temperature heat capacity of $(U1−yNpy)O2$ at Np concentrations comparable to those studied in our work for the trivalent lanthanide and tetravalent actinide elements.

As can be seen in Fig. 10(a), the $TN2$ peak positions for the lanthanide-doped are slightly higher than the trendline for temperature vs composition (⁠$y$⁠) for Th-doped $UO2$⁠,⁶ and close to the isotropic Heisenberg model for small $x$ in dilute magnetic systems, which is represented by $TN(x)/TN(0)=(0.75−x)/0.75$⁠.³⁹ The $TN2$ values of the Am-doped compounds are lower, which may be due to rapid build-up of some damage in the time between sample annealing and measurement. Also shown is the value for (U_0.98²³⁸Pu_0.02)O₂ from our earlier work,⁶ which fits the Th trendline as well. $Pu4+$ has a non-magnetic ground state,⁴³ so its effect on the magnetic behavior is expected to be similar to $Th4+$⁠.

The $TN1$ temperatures for (U,$241$Am)$O2$ and (U,Ln)$O2$ clearly follow a different trendline, with a stronger dependence on $y$⁠. It is tempting to link $TN1$ to the presence of $U5+$⁠, which, with an ionic radius of 0.88 Å,¹⁹ is substantially smaller than $U4+$⁠, 1.00 Å,¹⁸ and thus decreases the distance between the uranium ions. However, the intensity of $TN1$ compared to $TN2$ is clearly correlated to the trivalent dopant ion.

No clear effect of the ionic radius on $TN$ is evident from Fig. 10(a), although this property ranges from 1.16 Å for $La3+$ to 0.96 Å for $Pu4+$⁠. However, when considering the $TN$ temperatures for dilute solid solutions of the same concentration of dopant (⁠$y=0.05$⁠) of La, Nd from this work, Y,⁴⁴ Th,⁶ Pu,³⁹ Ce,⁴⁵ Mg⁴⁶ and Ca,⁴⁷ a systematic decrease with decreasing ionic radius, expressed as R(⁠$Mn+$/R(⁠$U4+)$⁠, becomes evident within the chemical groups IV-valence actinides/lanthanide, III-valence rare-earth elements, and the II-valence alkaline-earth elements (Fig. 11). The value for Y-doped $UO2$ reported by Hinatsu and Fujino⁴⁴ was considered as a $TN1$⁠, and it fits well those for La- and Nd-doping. This observation is consistent with the notion of weakening the magnetic interactions between the $U4+$ ions, represented by the Néel temperature, when the size of the dopant ion increases (and the lattice expands). However, in the $M3+$ and $M2+$ systems the charge compensation also introduces $U5+$⁠, in a 1:1 and 1:2 ratio, respectively. This means that although $y$ is the same, the total number of “dopant” ions is not the same. The differences in the graph thus may be related to that, and/or the concomitant possibility that the $M3+/M2+$ and $U5+$ ions are not randomly distributed in the material, but are paired in clusters, potentially also involving oxygen ions, and as such affect the magnetic ordering of the $U4+$ ions differently compared to random diluted atoms. In this respect, it would be highly valuable to resolve whether the solid solutions with $Mg2+$ and $Ca2+$ show similar splitting of the antiferromagnetic anomaly as we observed for the lanthanide-doped systems, which remained undetected by Hinatsu and Fujino.

Similarly, the magnetic entropy (⁠$Sexs$⁠), calculated as the total of the two anomalies, decreases with composition (⁠$y$⁠), but the Ln-doped and Th-doped materials⁶ have a different dependence [Fig. 10(b)]. The value for the $238$Pu-doped⁶ sample fits the Ln-trendline, however, this may be fortuitous since the sample was not free from radiation damage resulting from the period between annealing and measurement, during which some entropy may be “lost” (vide infra).

On first sight, the effects of radiation are very similar for (U,$241$Am)$O2$ and (U,$238$Pu)$O2$ obtained in an earlier study:⁶ a gradual shift of the antiferromagnetic transition to lower temperatures and a substantial decrease in intensity. This can be understood from the fact that the magnetic interaction in $UO2$ is governed by superexchange (SE) through the oxygen atoms. Radiation will displace oxygen and metal atoms from their positions creating oxygen-Frenkel pairs, uranium-Frenkel pairs and vacancies, expanding the lattice and thus the distance between two $U4+$ ions.⁴⁸ As shown in Fig. 9, the relative lattice expansion, has a similar evolution and is almost independent of the initial concentration of the metal dopant for both compounds. However, the extent and kinetics of the lattice swelling, and hence the damage process, seem to be different for both materials, evident from slightly different saturating values: $Δ$a/a$0$ = 0.0030 for the $238$Pu-doped material (2% and 6% doping) at $∼5×1017$ $α$/g and $Δa/a0=0.0027$ for the $241$Am-doped material (1% and 5% doping) at $∼7×1017$ $α$/g. We interpret this as differences in the disorder on the oxygen sublattice, either an O/M ratio slightly lower than 2 in the $241$Am-doped material resulting in oxygen vacancies, or a local distortion of the oxygen around the $Ln3+$ and $U5+$ lattice sites. Overall, the observed saturation is in line with the values for pure $241AmO2$⁴⁹ and $238PuO2$⁠.^50–52 

The shift in the position of $TN2$ in (U,$241$Am)$O2$ and $TN$ in (U,$238$Pu)$O2$ as a function of accumulated dose is different, as shown in Fig. 12(a), being larger in the case of the (U_0.98²³⁸Pu_0.02)O₂ sample. The two (U,$241$Am)$O2$ samples (⁠$y=0.01$ and 0.05) plot on a single trendline, similar to the (U_0.98²³⁸Pu_0.02)O₂ results, suggesting that dopant concentration is not a key factor affecting the damage kinetics, which is in line with the observed evolution of the lattice expansion with accumulated dose (Fig. 9). The variation in the magnetic entropy with accumulated dose in (U,$241$Am)$O2$ and (U,$238$Pu)$O2$ is similar, showing almost parallel relationships [Fig. 12(b)], the values in the Am-doped sample being about 0.7 $JK−1mol−1$ lower. When plotted as the change in the excess magnetic entropy relative to the zero dose value [Fig. 12(c)], all values follow a single linear trendline.

Also, the comparison of the residual heat capacity $Cp(T=0K)$⁠, derived from the results by extrapolating the results at low temperatures using a linear $Cp/T=α(T/K)2$ equations, shows differences between (U,$241$Am)$O2$ and (U,$238$Pu)$O2$ [Fig. 12(d)]. The increase with accumulated dose indicates that the anharmonicity of the system increases with defect concentration resulting from the $α$-self-irradiation. The evolution with accumulated dose is very similar for the two materials, but the zero dose values are strikingly different, being close to zero for the $238$Pu-doped compound, and strongly positive for the $U0.95Am0.05O2$ compound. This may indicate a difference in the initial ordering in the compounds. From the fact that the (U,$238$Pu)$O2$ has the lowest residual $Cp$ in spite of a four times higher dose rate, we conclude that differences in the initial oxygen content are the likely cause. As shown in Fig. 2, the slight deviation in lattice parameter from the ideal line for the stoichiometric composition could suggest a slightly oxygen-substoichiometric composition.

In conclusion, we have firmly demonstrated that the magnetic transition in $UO2$-based solid solutions is affected by several factors that have strong coupling: crystal chemistry, defect structure including radiation effects, and electron interaction. Whereas our earlier work showed that $Pu4+$ and $Th4+$ substitution on the uranium sublattice has a straightforward effect on the magnetic ordering, reducing Néel temperature, peak intensity, and magnetic entropy, we now evidenced that the substitution of trivalent ions (⁠$La3+$⁠, $Nd3+$⁠, $Am3+$⁠) leads to more complex changes. The antiferromagnetic transition splits into two in the heat capacity measurements, and this effect is also evident in magnetization measurements, but was not observed in the magnetization measurements reported in literature.^30,35 We suggest that this is due to the presence of $U5+$ charge compensator in the stoichiometric compounds, and hypothesize that clustering of $U5+$ with the trivalent ions with the pentavalent can play a role explaining the differences in intensities of the anomalies. The observed differences between $La3+$⁠, $Nd3+$⁠, and $Am3+$ are attributed to the $f$–$f$ exchange interaction.

Americium substitution causes in addition radiation effects (point defects) that also reduce Néel temperature, peak intensity, and magnetic entropy. With the evidence presented here, it can be concluded that the Am concentrations in the samples of our previous measurements⁷ were too high to detect the changes as the combined effects of substitution and radiation-induced defects almost completely removed/spread the magnetic anomaly. Comparison between the new results for (U,$241$Am)$O2$ and our earlier results for (U,$238$Pu)$O2$ suggests similar damage accumulation mechanisms. The slight differences in the evolution with accumulated dose is explained by the higher degree of disorder in the Am material, from the $Am3+/U5+$ substitution and possible also from the fact that this chemical system is more susceptible to substoichiometric compositions.

The authors acknowledge the Analytical Service of the JRC-Karlsruhe for the chemical and isotopic characterization of the samples. The technical support of Daniel Bouëxière, Eckhart Dahms, Co Boshoven, Sebastien Gardeur and Patrick Lajarge is highly appreciated.

The authors have no conflicts to disclose.

Jean-Christophe Griveau: Conceptualization (equal); Formal analysis (equal); Investigation (equal); Writing – review & editing (equal). Jean-François Vigier: Conceptualization (equal); Formal analysis (equal); Investigation (equal); Writing – review & editing (equal). Karin Popa: Conceptualization (equal); Formal analysis (equal); Investigation (equal); Writing – review & editing (equal). Sorin-Octavian Vălu: Formal analysis (equal); Writing – review & editing (equal). Eric Colineau: Conceptualization (equal); Investigation (equal); Writing – review & editing (equal). Rudy J. M. Konings: Conceptualization (equal); Writing – original draft (equal).

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