The energetics of high temperature oxidation and formation mechanisms in binary lanthanide nitrides (LnN)

Abstract

Nitride-based materials present exceptional thermal and structural properties for advanced material applications, however accurate determination of their thermodynamic properties is critical to their deployment. Herein, the standard enthalpies of formation, ΔH_f^°, for all LnN compounds (Ln = La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Lu; excluding Pm) are determined via high temperature oxide melt calorimetry. These measurements are supported by high temperature oxidation studies of La, Ce, Sm, Eu, Er, Yb bearing LnN compounds using X-ray diffraction and thermogravimetric analysis, and are cross-examined against recent high temperature measurements on other LnN compounds¹. It was determined that ΔH_f^° systematically correlates with the ionic radius of Ln³⁺ cations, with smaller Ln bearing nitrides having more negative values. A discontinuity in ΔH_f^° was further observed between larger and smaller Ln bearing LnN compounds. Using the determined ΔH_f^° values with literature references, Gibbs energies of formation (ΔG_f^°), oxidation (ΔG_ox^°) and hydrolysis (ΔG_hyd^°) are calculated and compared against uranium nitride (UN) in the context of UN based nuclear fuel and related spent nuclear fuel (SNF) management. The calculations indicate that the occurrence of LnN phases within UN based SNF should lead to stabilisation of the structure and inhibit its oxidation.

Nitride-based compounds present exceptional thermal properties for advanced material applications, but an accurate determination of their thermodynamic properties is critical for their application. Here, the authors use high-temperature oxide melt calorimetry to determine the standard enthalpies of formation (ΔHf°) for all LnN compounds (Ln = La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Lu; excluding Pm), showing that ΔHf° values correlate with the ionic radius of Ln⁺³ cations, with smaller Ln-bearing nitrides exhibiting more negative values.

Introduction

Binary lanthanide nitrides (LnN) are an important class of inorganic compounds that are relevant to spintronic devices^2,3, heterogeneous catalysis^4,5, high-temperature applications^6,7 and are also expected to form an important constituent within next-generation uranium nitride (UN) based spent nuclear fuel (SNF)^8–10. The use of nitrides in nuclear energy applications arises from their improved density and higher thermal conductivity, while still providing a higher melting point over conventional oxide fuel. This has subsequently drawn considerable interest in these materials to be deployed in Generation IV fast and advanced modular reactors (AMR)^11–15, as part of general interest in advanced fuel concepts^14,16,17. Critically, mixed LnN-UN compounds are expected to form as a predominant matrix incorporated fission product phase in UN-based SNF, which may affect its chemical stability^9,18,19. Consequently, the understanding of their thermodynamic stability and precise oxidation behaviour is critical to their application and occurrence in nuclear and non-nuclear applications.

Thermodynamic investigations of LnN and UN SNF relevant materials have primarily been achieved via computational simulation-based methods^8,20,21. However, the success of computational methods requires precise experimental data, such as high-quality thermodynamic data, for benchmarking. For UN, its enthalpy of formation²² has been determined via high-temperature oxide melt calorimetry, considered the gold standard for this determination. In comparison, thermodynamic data of LnN compounds remain limited. The standard enthalpy of formation (ΔH_f^°) has been measured for some LnN compounds (Ln = La, Ce, Sm, Eu, Gd, Ho, Er, Yb) via Knudsen effusion mass spectrometry (KEMS)^22–25.

A challenging component of LnN and UN characterisation is their strong susceptibility to oxidation when in contact with atmospheric oxygen or water. This causes the materials to rapidly oxidise and compromises the measurement. It has been recently shown that under ambient conditions, UN and LnN compounds oxidise under dissimilar mechanisms in which UN follows a direct O₂ oxidation pathway, whereas LnN compounds decompose through hydrolysis (H₂O)¹. At higher temperatures, the oxidation of LnN compounds proceeds to the sesquioxide, Ln₂O₃, (Ln = Nd, Gd, Dy, Ho, Tm, Lu), or dioxide, LnO₂, (Ln = Pr, Tb)¹. In the case of UN, at high temperatures (>200 °C), it oxidises directly via ignition to U₃O₈^26,27. Despite the strong foundation of knowledge for UN, the discordant behaviour of LnN compounds in terms of their oxidation chemistry demands thorough investigation.

Considering the pertinence of LnN compounds to advanced material applications and also UN-based SNF, the present investigation has experimentally determined ΔH_f^° for all LnN compounds (Ln = La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb and Lu, excluding Pm) using high-temperature oxide melt calorimetry. The high-temperature oxidation behaviour of LnN for Ln = La, Ce, Sm, Eu, Er and Yb has been further characterised by thermogravimetric measurements and compared with recent measurements of Ln = Pr, Nd, Gd, Tb, Dy, Ho, Tm and Lu¹. Structural characterisation of synthesised LnN materials and their respective oxidation products was carried out using powder X-ray diffraction (PXRD) with Rietveld analysis. Using the ΔH_f^° values determined and combining with literature references, the Gibbs energies of formation (ΔG_f^°), oxidation (ΔG_ox^°) and hydrolysis (ΔG_hyd^°) were calculated in comparison to UN in order to gain insight into the relative stability and behaviour of LnN and UN compounds occurring in UN-based SNF. These results of the investigation are further discussed in relation to previous simulation studies and in relation to the oxidation stability of these LnN and UN compounds in relation to associated SNF.

Results and discussion

High temperature oxidation of LnN

Pristine LnN powders synthesised in this work and their respective oxidation residues after heating in synthetic air at 900 °C were measured via PXRD and analysed using the Rietveld refinement method. Pristine LnN samples could be consistently refined against a cubic face-centred structure in space group Fm$\overline{3}$m, isostructural with rock salt. The refinement profiles and diffractograms for pristine LnN compounds (Ln = La, Ce, Sm, Eu, Er, Yb) are shown in Fig. 1 with refinement results summarised in Table 1, whereas the results for LnN (Ln = Pr, Nd, Gd, Tb, Dy, Ho, Tm and Lu) have been previously reported and discussed in detail¹.

Fig. 1. Pre- and post-oxidation PXRD comparison of investigated LnN compounds.

Rietveld profiles made against PXRD data of pristine LnN (Ln = La, Ce, Sm, Eu, Er, Yb) compounds. The insets provide corresponding Rietveld profiles for the same samples oxidised in synthetic air at 900 °C. The black crosses correspond to collected data for the pre- and post-oxidised samples. The red and pink lines correspond to the calculated and difference profiles. The vertical markers correspond to the allowed reflections according to the space group of LnN crystallising in cubic Fm$\overline{3}$m structure marked in blue, Ln₂O₃/LnO₂ crystallising in varying hexagonal, cubic and monoclinic structures marked in red and black, respectively (for details see Table 2), and La(OH)₃ observed in the LaN sample crystallising in hexagonal P6₃/m structure marked in orange. Reflexes arising from Vaseline used to fixate the powders are marked with black stars⁷⁵.

Table 1.

Lattice parameters determined from Rietveld refinements against PXRD data, associated fitting factors and literature lattice parameters for pristine LnN (Ln = La, Ce, Sm, Eu, Er, Yb) phases synthesised

Compound	Structure and space group	Lattice parameter (Å)	Fitting factors (%)	Reference lattice parameter (Å)
LaN	Cubic face centred Fm$\overline{3}$m	a = 5.299240(20)	R = 2.48 Rw = 3.47	a = 5.301(2)28
CeN		a = 5.022364(20)	R = 1.10 Rw = 1.60	a = 5.020(2)28
SmN		a = 5.047712(26)	R = 2.13 Rw = 2.81	a = 5.046(2)29
EuN		a = 5.015175(7)	R = 3.46 Rw = 4.84	a = 5.01779(6)30
ErN		a = 4.836127(14)	R = 2.24 Rw = 3.83	a = 4.8481(7)31
YbN		a = 4.783650(10)	R = 2.32 Rw = 3.95	a = 4.775(4)32

Additional refinement details are provided in Supplementary Information Note 2, Table S2. Note uncertainties are reported directly from the Rietveld analysis with no correction.

It was found that the determined lattice parameters from Rietveld analysis were in agreement with structural data reported in the literature^28–32, with small deviations attributed to non-stoichiometry in the nitrogen content of synthesised LnN phases. Slight impurities of La(OH)₃ have been observed solely in the LaN sample with 5.51 wt% and crystallising in hexagonal P6₃/m structure, which is attributed to slight oxidation arising from contact with atmospheric water during the PXRD measurement. This water-mediated oxidation behaviour of LnN compounds was recently investigated¹, where it was shown that the Ln³⁺N compounds with larger and lighter Ln’s cations oxidised faster than the nitrides with smaller and heavier Ln cations.

To accurately determine ΔH_f^° via high-temperature oxide melt calorimetry of the investigated LnN compounds, their high-temperature oxidation mechanisms are required to be established. Recent studies¹ in oxygen-containing atmospheres up to 900 °C for Ln = Pr, Nd, Gd, Tb, Dy, Ho, Tm and Lu show that these materials oxidise via two pathways to the respective Ln₂O₃ (Ln = Nd, Gd, Dy, Ho, Tm, Lu) and LnO₂ oxide compounds (Ln = Pr, Tb). Their reactions are described according to Eqs. (1) and (2).

$$LnN+\frac{3}{4}{\text{O}}_2\to \frac{1}{2}L{n}_2{\text{O}}_3+\frac{1}{2}{\text{N}}_2$$ 1

$$Ln\text{N}+{\text{O}}_2\to Ln{\text{O}}_2+\frac{1}{2}{\text{N}}_2$$ 2

With respect to the literature, LnN compounds for Ln = La, Ce, Sm, Eu, Er, Yb have not been investigated under similar conditions to those of the present investigation and necessary for a calorimetric study. It has been previously suggested that ErN forms Er₂O₃ under oxidising conditions, but details are lacking on the precise temperature at which the transformation occurs³³. To address this, coupled TGA-DSC measurements were performed on these LnN compounds (Ln = La, Ce, Sm, Eu, Er, Yb), where powder samples were heated to 900 °C in synthetic air, and the residues after oxidation were characterised via PXRD. Rietveld profiles made against the PXRD data are presented in the inset to their respective LnN phases in Fig. 1. The analysis revealed that all LnN compounds investigated follow an oxidation pathway as given by Eqs. (1) or (2). Refined lattice parameters of the oxidised LnN phases are summarised in Table 2 and are in agreement with the lattice parameters reported in the literature.

Table 2.

Summary of determined crystalline phases arising from the oxidation of LnN (Ln = La, Ce, Sm, Eu, Er and Yb) in air at 900 °C via Rietveld analysis and their respective literature lattice parameters

Compound	Oxidised phase	Structure and space group	Lattice parameters (Å)	Fitting factors (%)	Literature lattice parameter (Å)
LaN	La2O3	P63/mmc (194)	a = 3.9377(2) c = 6.1388(2)	R = 1.70 Rw = 2.57	a = 3.9381(3) c = 6.1361(6)66
CeN	CeO2	Fm$\overline{3}$m (225)	a = 5.4142(1)	R = 2.18 Rw = 3.31	a = 5.4178(1)67
SmN	Sm2O3	C2/m (12)	a = 14.175(2) b = 3.6331(2) c = 8.8574(9) β = 100.189(5)	R = 1.34 Rw = 2.02	a = 14.1975(9) b = 3.6273(3) c = 8.8561(5) β = 99.986(5)68
	Sm2O3	Ia$\overline{3}$ (206)	a = 10.931(1)		a = 10.9295(5)69
EuN	Eu2O3	C2/m (12)	a = 14.110(2) b = 3.6061(2) c = 8.8088(9) β = 100.161(5)	R = 1.39 Rw = 2.08	a = 14.1105(2) b = 3.6021(1) c = 8.8080(2) β = 100.037(1)70
	Eu2O3	Ia$\overline{3}$ (206)	a = 10.869(1)		a = 10.86831(24)71
ErN	Er2O3	Ia$\overline{3}$ (206)	a = 10.4417(2)	R = 1.89 Rw = 2.62	a = 10.5486(9)72
YbN	Yb2O3	Ia$\overline{3}$ (206)	a = 10.4378(2)	R = 2.34 Rw = 3.19	a = 10.4281(2)73

Additional refinement results provided by the Rietveld software GSAS-II are shown in Supplementary Information Note 2, Table S2. Note that uncertainties are reported directly from the Rietveld analysis with no correction.

Simultaneous TGA and DSC measurements were performed from room temperature to 900 °C under flowing air conditions for the LnN compounds with Ln = La, Ce, Sm, Eu, Er and Yb. These were performed to ensure consistency with previous measurements taken under similar conditions¹. The resulting profiles are displayed in Fig. 2, where the TGA data were normalised against the fully oxidised LnN compounds that were recovered after cooling. This has been performed since the pristine LnN exhibits varying stoichiometries at room temperature, compromising sum formula calculations based on the weight change. All determined and calculated TGA and DSC results are summarised in Table 3. It was found that all LnN compounds oxidise in a direct oxygen-mediated reaction following the reactions shown in Eqs. (1) and (2), consistent with previous investigation¹. However, it must be noted that the oxidation of CeN proceeds via an observable intermediate oxide, whose composition could be determined approximately as CeO_1.80. The formation of a distinct intermediate can be attributed to the intrinsic tendency of Ce to form mixed-valence oxidation states of +3 and +4 in oxide form, which is also observed for PrN and TbN¹.

Fig. 2. TGA profiles for investigated LnN compounds.

Combined heating and cooling black TGA- and red DSC curves of LaN, CeN. SmN, EuN, ErN and YbN heated to 900 °C in air with inset blue TGA curve of plateau performed at 900 °C.

Table 3.

Summary of TGA-DSC determined onset temperatures T_onset and temperatures of the DSC maxima T_DSC, experimental and theoretical mass changes and via PXRD analysis determined oxidation products of LnN (Ln = La, Ce, Sm, Eu, Er, Yb) oxidised in air at 900 °C

Compound	Tonset (°C) *	TDSC (°C)	Δmtotal (%)	Δmtheo (%) (oxidation product)	Oxidation product
LaN	495.9	566.3 636.41	6.97	6.52 (La2O3)	La2O3
CeN	175.0	255.7 320.7	11.38	11.66 (CeO2)	CeO2
SmN	487.3	552.6	6.14	6.07 (Sm2O3)	Sm2O3
EuN	420.5	526.3	6.38	6.01 (Eu2O3)	Eu2O3
ErN	551.7	596.4	6.18	5.50 (Er2O3)	Er2O3
YbN	603.4	612.1	6.21	5.33 (Yb2O3)	Yb2O3

All temperature values have an uncertainty of σ = ± 1 °C given by the used thermocouple type S.

^*Defined as 5% of total mass change of the nitride to oxide reaction.

High temperature oxide melt calorimetry

High-temperature oxide melt calorimetric measurements were conducted on all LnN (Ln = La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu; excluding Pm) compounds to determine their standard enthalpies of formation ΔH_f^°. Two thermochemical cycles which are provided in Table 4 and Table 5 have been developed based on the oxidation pathways shown in Eqs. (1) and (2), which were used to calculate ΔH_f^° based on the measured dissolution enthalpies, (ΔH_ds) of LnN in sodium molybdate at 973 K. Experimental ΔH_ds data are summarised in Supplementary Information Note 3, Table S3 together with literature enthalpies of the corresponding Ln oxides used for calculation. The resulting ΔH_f^° values of the LnN compounds examined in this investigation are summarised in Table 6 with their associated standard error. Error propagation with the two standard errors of the dissolution enthalpies 2σ(ΔH_ds) (summarised in Supplementary Information Note 3, and Table S3) and standard errors of the published literature data (summarised in Supplementary Information Note 3, and Table S3) has been performed for all datasets. The dataset of CeN was corrected for the TiO₂ encapsulation used to protect the sample against premature ignition using appropriate literature values³⁴.

Table 4.

Thermochemical cycle used for calculation of ΔH_f^° for the LnN compounds where Ln = La, Nd, Sm, Eu, Gd, Dy, Ho, Er, Tm, Yb and Lu oxidise to the respective Ln₂O₃, based on drop-solution calorimetric data of the LnN compounds in sodium molybdate at 973 K

Reaction		ΔH (kJ mol-1)
(1)	LnN(s, 298 K) + $\frac{3}{2}$ O2(g, 973 K) → $\frac{1}{2}$ Ln2O3(sln, 973 K) + $\frac{1}{2}$ N2(g, 973 K)	ΔH1 = ΔHds *
(2)	Ln2O3(s, 298 K) → Ln2O3(s, 973 K)	ΔH2 *
(3)	O2(g, 298 K) → O2(g, 973 K)	ΔH3 = 21.74(2)53
(4)	N2(g, 298 K) → N2(g, 973 K)	ΔH4 = 20.6574
(5)	2 Ln(s, 298 K) + $\frac{3}{2}$ O2(g, 298 K) → Ln2O3(s, 298 K)	ΔH5 = ΔHf°(Ln2O3) *
Enthalpy of Oxidation LnN → Ln2O3
(6)	LnN(s, 298 K) + $\frac{3}{2}$ O2(g, 298 K) → $\frac{1}{2}$ Ln2O3(s, 298 K) + $\frac{1}{2}$ N2(g, 298 K)
	ΔHox = ΔHds + $\frac{3}{2}$ ΔH3 - $\frac{1}{2}$ ΔH2 - $\frac{1}{2}$ ΔH4
Enthalpy of Formation LnN
(7)	Ln(s, 298 K) + $\frac{1}{2}$ N2(g, 298 K) → LnN(s, 298 K)
	ΔHf°(LnN) = - ΔHox + $\frac{1}{2}$ ΔH5

The summarised values of dissolution enthalpies ΔH_ds and additional enthalpies required are provided in Supplementary Information Note 3, Table S3. Resulting standard enthalpy of formation of LnN are summarised in Table 6.

s = solid, g = gaseous, sln = solution.

^*Values summarised in Supplementary Information Note 3, Table S3.

Table 5.

Thermochemical cycle used for calculation of ΔH_f^° for the LnN compounds where Ln = Ce, Pr, Tb oxidise to the respective LnO₂, based on drop-solution calorimetric data of LnN compounds in sodium molybdate at 973 K

Reaction		ΔH (kJ mol-1)
(1)	LnN(s, 298 K) + O2(g, 973 K) → LnO2(sln, 973 K) + $\frac{1}{2}$ N2(g, 973 K)	ΔH1 = ΔHds *
(2)	LnO2(s, 298 K) → LnO2(s, 973 K)	ΔH2 *
(3)	O2(g, 298 K) → O2(g, 973 K)	ΔH3 = 21.74(2)53
(4)	N2(g, 298 K) → N2(g, 973 K)	ΔH4 = 20.6574
(5)	Ln(s, 298 K) + O2(g, 298 K) → LnO2(s, 298 K)	ΔH5 = ΔHf°(LnO2) *
Enthalpy of Oxidation LnN → LnO2
(6)	LnN(s, 298 K) + O2(g, 298 K) → LnO2(s, 298 K) + $\frac{1}{2}$ N2(g, 298 K)
	ΔHox = ΔHds + ΔH3 - ΔH2 - $\frac{1}{2}$ ΔH4
Enthalpy of Formation LnN
(7)	Ln(s, 298 K) + $\frac{1}{2}$ N2(g, 298 K) → LnN(s, 298 K)
	ΔHf°(LnN) = - ΔHox + ΔH5

The summarised values of dissolution enthalpies, ΔH_ds, and additional enthalpies required are provided in Supplementary Information Note 3, Table S3. Resulting standard enthalpy of formation of LnN are summarised in Table 6.

s = solid, g = gaseous, sln = solution.

^*Values summarised in Supplementary Information Note 3, Table S3.

Table 6.

Standard enthalpy of formation ΔH_f^° for LnN compounds

Compound	ΔHf° (kJ mol-1)	σ (ΔHf°) (kJ mol-1)
LaN	−316.92	13.1
CeN	−388.35	8.1
PrN	−321.24	15.4
NdN	−375.22	9.0
SmN	−385.98	11.5
EuN	−328.28	7.8
GdN	−368.28	19.4
TbN	−347.28	11.0
DyN	−489.26	12.9
HoN	−517.75	7.3
ErN	−566.98	16.7
TmN	−489.82	11.7
YbN	−529.08	8.1
LuN	−549.71	5.6

Enthalpies are based on performed high-temperature oxide melt calorimetry experiments and their respective two standard errors σ (ΔH_f^°).

Figure 3 provides the determined ΔH_f^° of all LnN compounds plotted against the ionic radii of Ln³⁺ cations in sixfold coordination³⁵. The Figure pertinently shows that the LnN compounds that possess smaller and heavier Ln cations exhibit lower ΔH_f^°, whereas those with larger and lighter Ln cations show less negative values. The data of heavy Ln’s contrasts significantly with previously determined ΔH_f^° values based on KEMS investigation^23–25, which suggests largely consistent values of ΔH_f^° in the range of −300 to −350 kJ mol⁻¹ and is plotted for comparison in Supplementary Information Note 3, and Fig. S2.

Fig. 3. Formation Enthalpies of LnN compounds compared against UN.

Experimentally determined ΔH_f^° of LnN (Ln = La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb and Lu) plotted against the ionic radii, r, of the Ln³⁺ cation in 6-fold coordination. The literature ΔH_f^° of UN determined by the same methodology is plotted for comparison²². Both the experimental and reference data points represent the arithmetic mean with error bars that represent ±2 standard error of the mean.

Additionally, the determined ΔH_f^° values for the LnN compounds exhibit a discontinuity in the enthalpy trend between TbN and DyN, separating the series into lighter Ln (La, Ce, Pr, Sm, Eu, Gd, Tb) with higher ΔH_f^°, and heavier Ln (Dy, Ho, Er, Tm, Yb, Lu) with lower ΔH_f^°. This break is consistent with the half-filling of the 4f orbitals, due to which LnN containing heavier Ln cations exhibit higher stability compared to LnN containing lighter Ln cations. However, Tb is a notable exception to the trend in Fig. 3. Such a deviation could be related to a potential covalent contribution to the bond in TbN, attributable to mixed ionic and covalent bonding behaviour within nitride materials³⁶. However, from the analysis of this investigation, this cannot be precisely elucidated.

Figure 3 additionally compares the ΔH_f^° for the LnN compounds with that of UN (ΔH_f^° = −288.8 kJ mol⁻¹), which was determined by the same methodology on the same experimental instrument²². It shows that UN exhibits a less negative enthalpy of formation than all LnN, which aligns well with the observed trend that larger cationic radii³⁵ of +3 cations in sixfold coordination environment correspond to less negative ΔH_f^°.

The Gibbs energy of formation and oxidation stability for LnN and UN compounds in the context of UN based spent nuclear fuel

To summarise thus far, the present investigation has systematically and accurately determined ΔH_f^° and high-temperature oxidation chemical reactions of all LnN compounds except for Pm. Considering the relevance of these phases to UN-based SNF, it is salient to discuss their occurrence and associated thermodynamic chemistry with the results of this investigation considered. In UN-based SNF, LnN compounds are expected to form as a major group of fission products that are readily miscible within the UN matrix owing to their shared crystal structure^1,37 and demonstrated solid solution behaviour^9,18,19. The degree and type of solid solution, for instance, constituents and amounts, significantly impact the properties of UN. For instance, it has been shown for Ce- and Gd-doped UN solid solutions that increasing the amount of Ce-content reduces oxidation resistivity at high temperatures³⁸; whereas increasing Gd-content reduces thermal conductivity³⁹. At the same time, computational studies of Zr- and Y-doped UN indicate oxidation resistance⁴⁰. In situ steam experiments indicate that Zr-doped UN oxidation resistance also occurs⁴¹. Although from the literature, a definitive answer as to the stability of UN materials from doping is not present, it is clear that the Ln incorporation affects the stability of UN. Such effects are well known for UO₂-based SNF⁴² with a strong thermodynamic description behind it^42,43, whereby the incorporation of Ln improves resistance to oxidation. To assess analogous behaviour in UN systems, a thermodynamic framework is required. In this regard, the Gibbs energy of formation as nitrides, ΔG_f^°, the Gibbs energy of oxidation to oxide state, ΔG_ox^°, and the Gibbs energy of hydrolysis to hydroxide/oxide state, ΔG_hyd^°, are evaluated using the enthalpic data determined from this investigation. Combined with reference entropy values from literature^44–54 ΔG_f^°, ΔG_ox^° and ΔG_hyd^° can be calculated via the Gibbs equation for all investigated LnN compounds and also in reference to UN when assuming conditions of RT oxidation.

The Gibbs equation, as shown in Eq. (3), uses the reaction enthalpy, ΔH_rct^° and reaction entropy, ΔS_rct^°, of a chemical reaction, which are determined via Hess’s law shown in Eqs. (4) and (5). This is achieved by subtracting the sum of enthalpies of formation or standard entropies of the reaction products from the sum of the reactants, respectively.

$${\mathrm{\Delta }G}^{\circ }={△H}_{\mathrm{rct}}^{\circ }-{\mathrm{T}△S}_{\mathrm{rct}}^{\circ }$$ 3

$${\mathrm{\Delta }H}_{\mathrm{rct}}^{\circ }=\sum \nu {\left(\underset{\text{f}}{\overset{\circ }{\mathrm{\Delta }H}}\right)}_{\mathrm{products}}-\sum \nu {\left(\mathrm{\Delta }\underset{\mathrm{f}}{\overset{\circ }{H}}\right)}_{\mathrm{educts}}$$ 4

$$\mathrm{\Delta }{S}_{\text{rct}}^{\circ }=\sum \nu {S^{\circ }}_{\text{products}}-\sum \nu {S^{\circ }}_{\text{educts}}$$ 5

To calculate ΔG_f^°, the formation reactions of LnN and UN compounds are required, which are provided in Eqs. (6) and (7). Specifically for the formation of materials as in the present study, ΔH_rct,f^° can be replaced by the formation enthalpies determined for LnN and literature data on UN²². Reaction formation entropies ΔS_rct,f^° are calculated using literature values for all compounds, which are summarised in Supplementary Information Note 4 Table S4. Since the standard entropies S^° on pure LnN materials are scarcely known, the available values for LaN and CeN summarised in Supplementary Information Note 4 Table S4 were used as a replacement for all LnN.

$$Ln+\frac{1}{2}{\text{N}}_2\to Ln\text{N}$$ 6

$$\text{U}+\frac{1}{2}{\text{N}}_2\to \text{UN}$$ 7

In order to describe the oxidation stability of LnN and UN compounds via ΔG_ox^°, a similar thermodynamic methodology is applied. It is assumed that the oxidation occurs in a dry oxygen atmosphere for simplicity, although it was previously shown that LnN compounds react preferably with atmospheric water when contacting with air at room temperature¹. Given this assumption, the oxidation of LnN is described via the pathways in Eqs. (1) and (2). The oxidation of UN at 298.15 K can be described in a simplified form from literature observations^22,55,56 as shown in Eq. (8).

$$\text{UN}+{\text{O}}_2\to \text{U}{\text{O}}_2+\frac{1}{2}{\text{N}}_2$$ 8

ΔH_f^° values used to calculate the reaction enthalpy of oxidation ΔH_rct,ox^° are summarised in Tables 4 to 6 and Supplementary Information Note 3, Table S3. The standard entropies used to calculate the reaction entropy of oxidation ΔS_rct,ox^° for LnN and UN are summarised in Supplementary Information Note 4, Table S4. As described earlier, the standard entropies S^° on pure LnN materials are scarcely known; consequently, the available values for LaN and CeN are summarised in Supplementary Information Note 4 Table S4 were used as a replacement for all LnN.

Previously conducted oxidation experiments of LnN in air at RT conditions have revealed that these compounds react via a water-mediated oxidation pathway, resulting in the formation of the complementary Ln(OH)₃ as shown in Eq. (9)¹. Thus, to establish a thermodynamic framework of their oxidation behaviour, the hydrolysis of LnN and UN via ΔG_hyd^° must also be considered. In this regard, the hydrolysis of UN can be described with respect to the literature as shown Eq. (10)^57–59.

$$Ln\text{N}+3{\text{H}}_2\text{O}\to Ln{\left(\text{OH}\right)}_3+\text{N}{\text{H}}_3$$ 9

$$\text{UN}+2{\text{H}}_2\text{O}\to \text{U}{\text{O}}_2+\text{N}{\text{H}}_3+\frac{1}{2}{\text{H}}_2$$ 10

All hydrolysis calculations were performed assuming that water participating in the hydrolysis was in the gaseous state. The reaction enthalpy of hydrolysis ΔH_rct,hyd^° was derived using the formation enthalpies summarised in Tables 4 to 6 and Supplementary Information Note 3, Table S3. The standard entropies used to calculate the reaction entropy of hydrolysis ΔS_rct,hyd^° are summarised in Supplementary Information Note 4, Table S4. Once again, given that standard entropies S^° on pure LnN materials are scarcely known, entropy values for LaN and CeN were used as a replacement for all LnN. Additionally, S^° for Lu(OH)₃ was replaced by the available literature S^° of Tm(OH)₃⁶⁰. All thermodynamic data that were calculated via the methodology described are summarised in Table 7 and Supplementary Information Note 4, Table S5.

Table 7.

Gibb’s energies of formation ΔG_f^° for LnN and UN, their oxidation ΔG_ox^° and their hydrolysis ΔG_hyd^° at 298.15 K

Compound	ΔGf° (kJ mol-1)	rionic (Ln/U in oxide) (Å)35	ΔGox° (kJ mol-1)	rionic (Ln/U in hydoxide) (Å)35	ΔGhyd° (kJ mol-1)
LaN	−303.90	1.16	−573.31	1.16	−330.12
CeN	−371.59	0.87	−686.21	1.143	−262.14
PrN	−303.15	0.85	−622.64	1.126	−327.63
NdN	−357.97	1.109	−530.44	1.109	−274.91
SmN	−369.21	0.958	−523.42	1.079	−253.94
EuN	−309.03	0.947	−493.76	1.066	−222.37
GdN	−351.97	0.938	−540.43	1.053	−274.18
TbN	−329.37	0.76	−605.45	1.04	−301.60
DyN	−470.88	0.912	−440.22	1.027	−173.80
HoN	−499.33	0.901	−422.66	1.015	−147.93
ErN	−549.11	0.89	−381.35	1.004	−99.67
TmN	−471.71	0.88	−451.10	0.994	−164.80
YbN	−515.19	0.868	−373.46	0.985	−97.59
LuN	−538.47	0.861	−380.63	0.861	−110.81
UN	−283.08	1.00	−779.34	1.00*	−327.17

Calculated using Eqs. (3) to (5), based on the reactions shown in Eqs. (1), (2), and (6) to Eq. (10). Additionally, literature ionic radii³⁵ of Ln/U cations in the oxide/hydroxide materials after oxidation/hydrolysis used to plot the Gibbs energies in Fig. 5 are summarised. Note that the respective ionic radii of the cations were chosen according to their coordination numbers and oxidation states (Ln⁴⁺ for Ln = Ce, Pr, Tb and U⁴⁺) in the resulting oxidation product.

^* Hydrolysis reaction product = UO₂, see Eq. (10).

Comparison of the calculated Gibbs energies allows evaluation of the aforementioned stability case scenarios: (a) relative stability of LnN compounds formed within and compared to UN within UN-based SNF, (b) the subsequent stability of UN SNF against oxidation and (c) the stability of UN SNF against hydrolysis, such as what may occur during an unexpected cladding breach. These scenarios are illustrated in Fig. 4a–c, and the calculated ΔG_f^°, ΔG_ox^° and ΔG_hyd^° values are plotted as a function of ionic radii in Fig. 5a–c, respectively. Note that the schemes assume ideal reaction scenarios, without passivation of phases.

Fig. 4. Stability scenarios for UN based SNF.

Schematic illustration of ideal stability case scenarios comparing (a) formation of LnN against UN in UN based SNF during irradiation, (b) oxidation of LnN against UN in a cladding breach scenario involving oxygen-fuel contact and (c) hydrolysis of LnN against UN in a cladding breach scenario involving water-fuel contact under RT conditions.

Fig. 5. Comparison of Gibbs energies for formation ΔG_f^°, oxidation ΔG_ox^° and hydrolysis ΔG_hyd^° of investigated LnN compounds against UN.

Gibbs energies of (a) formation ΔG_f^° for LnN and UN, (b) oxidation ΔG_ox^° for Ln/U oxides (Ln₂O₃ for Ln = La, Nd, Sm, Eu, Gd, Dy, Ho, Er, Tm, Lu; LnO₂ for Ln = Ce, Pr, Tb) and (c) hydrolysis ΔG_hyd^° for Ln(OH)₃/UO₂ plotted against the ionic radii³⁵ of the Ln/U cation in the respective compound. All Gibbs energies are calculated for 298.15 K as shown in Eqs. (3) to (5), based on the chemical reactions described for the formation of LnN and UN see Eqs. (6) and (7), as well as their oxidation in Eqs. (1), (2), (8) and Eqs. (9) to (10). The Gibbs energies and literature ionic radii of varying oxide/hydroxide structures used for plotting are summarised in Table 7. Note that the respective ionic radii of the cations were chosen according to their coordination numbers and oxidation states (Ln⁴⁺ for Ln = Ce, Pr, Tb and U⁴⁺) in the resulting oxidation product.

Figure 5a compares calculated ΔG_f^° of LnN with UN by plotting them against the ionic radii of the Ln³⁺/U³⁺ cation in a sixfold coordination environment in the isostructural nitrides crystallising in Fm$\overline{3}$m structure. At 298.15 K, all LnN exhibit comparable more negative ΔG_f^° values than UN, indicating thermodynamically favourable formation of nitrides as described in Eqs. (6) and (7). Consequently, it can be inferred that all LnN compounds examined exhibit a higher stability than UN, implying that a solid solution with UN in UN-based SNF will be stabilised by the presence of secondary fission product LnN phases under the given conditions. It is, however, stressed that this investigation is directed at end member compositions where solid solution measurements are necessary to test the veracity of this postulate. Additionally, LnN compounds with heavier and smaller Ln cations exhibit comparable lower ΔG_f^° values than LnN compounds with lighter and larger Ln cations, which are more closely related to the ΔG_f^° calculated for UN. Hence, LnN fission product phases with heavier and smaller Ln cations are expected to provide a greater stabilisation effect on the UN matrix. These results also suggest that burnup of UN fuel, through the accumulation of Ln-based fission products that are lattice matrix soluble, will affect the thermodynamic stability of UN and suggest an enhancement in the energetic stability of the UN-based SNF matrix.

Scenario b) compares the oxidation of LnN and UN as described in Eqs. (1), (2), and (8) shift the focus to the decomposition of the nitrides in the presence of oxygen. A measure to describe this chemical behaviour is presented by the calculated ΔG_ox^° plotted in Fig. 5b against the ionic radii of the Ln/U cations in the oxide compounds. Unlike Scenario a), the comparison is more complex as the oxides are not isostructural; consequently Table 5 additionally provides the literature ionic radii³⁵ values of Ln/U cations in their respective oxide structures, considered for plotting ΔG_ox^° against³⁵. From Fig. 5b, it is observed that all LnN compounds have less negative ΔG_ox^° values than UN, specifically under the given conditions, equivalent to a preferred oxidation of UN over LnN. This result implies that a solid solution of UN with LnN will be stabilised against oxidation, consistent with previous findings¹. Consistent with Scenario a), heavier Ln cations provide an increased stabilising effect, indicating that increasing fission product accumulation from higher burnup enhances the oxidation resistance of UN-based SNF. It should be emphasized that these implications depend on the stated assumptions, particularly variation in temperature and composition of the exposed atmosphere, both of which can have significant effects upon ΔG_ox^°. Nevertheless, the results of the investigation are consistent with experimental investigations on the stability of doped UN materials^40,41, pointing towards increased thermodynamic and oxidation stability in the occurrence of Ln-doped UN.

Recent investigations have shown that in the presence of air containing both atmospheric oxygen and water, LnN compounds oxidise via water to form the respective Ln(OH)₃ instead of oxides. Therefore, the hydrolysis reaction must also be considered to establish a thermodynamic perspective on the oxidation behaviour of these compounds. Scenario c) compares the hydrolysis of LnN against UN, as described by Eqs. (9) and (10). As a measure for comparison, the Gibbs energies of hydrolysis ΔG_hyd^° are presented and plotted in Fig. 5c against the literature ionic radii³⁵ of Ln/U cations in the respective Ln(OH)₃ and UO₂. Note that it was shown that Ln(OH)₃ resulting from LnN air oxidation forms crystalline structures only for Ln = Pr, Nd, while the Ln = Gd, Tb, Dy, Ho, Tm, Lu were observed to form amorphous structures¹. For the present comparison of ΔG_hyd^° it was assumed that all Ln(OH)₃ will be crystallising isostructural in the hexagonal P6₃/m (#176) space group, as observed for Pr(OH)₃ and Nd(OH)₃¹, in order to choose the ionic radii³⁵ from literature for the respective Ln cation to plot against. From Fig. 5c, it becomes apparent that ΔG_hyd^° for LnN is comparably higher than for UN, which, given the stated conditions, is equivalent to a preferred hydrolysis of UN over LnN. Similar to the oxidation scenario b), this implies that LnN will have a stabilising effect on the UN matrix. Consistent with scenarios a) and b), the results imply that a higher content of fission products, particularly with heavier Ln cations, will increase the hydrolysis stability of UN SNF. This effect correlates with the burnup of the fuel, indicating that a higher burnup increases the hydrolysis resistance. Notably, these implications are strongly based on the stated assumptions and are influenced by the temperature and exact composition of the exposed atmosphere, which can significantly affect ΔG_hyd^°.

Conclusions

High-temperature oxide melt calorimetry experiments were performed to determine ΔH_f^° for all LnN compounds (Ln = La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu; excluding Pm) which are isostructural. A clear trend is observed whereby the ΔH_f^° of LnN compounds with larger and lighter Ln exhibits more negative values than those of LnN with smaller and heavier Ln. A distinct discontinuity observed in ΔH_f^° further highlights the role of 4 f electrons in governing thermodynamic stability. Comparison with isostructural UN, for which ΔH_f^° was determined using the same methodology previously²², further supports these trends. Due to the relevance of UN and LnN compounds to UN-based SNF, ΔG_f^°, ΔG_ox^° and ΔG_hyd^° were derived based on the results of this work and literature data. These analyses suggest that LnN compounds exhibit generally higher chemical stability compared to UN, and the presence of potential UN-LnN solid-solution phases within SNF will enhance structural stability and oxidation resistance during irradiated and air-cladding breach scenarios. Moreover, the work provides critical thermodynamic data for LnN systems, advancing the understanding of UN-based SNF, and offering broader insights into general nitride materials that can be found in advanced technology applications like fusion energy and thermoelectric in which LnN compounds play a fundamental role.

Methods

Synthesis

The synthesis and utilisation of the LnN powders used in the investigation are derived from a previous study¹. A direct nitridation approach was used, in which fine pieces of lanthanide metals (Hunan Rare Earth Metals Materials Co, 99.9%) were heated in a flowing nitrogen atmosphere (Nippon Gases, 99.999%, purified with an oxysorb cartridge) utilising a custom water-cooled radio frequency furnace⁶¹. After the complete reaction of the samples, they were crushed and sieved through a 100 mesh. The preparation of samples was carried out in a protective argon atmosphere.

Powder X-ray diffraction

PXRD data of finely ground LnN powders was collected on a Huber G670 imaging plate Guinier camera (2Θ_max = 100°) using a curved germanium (111) monochromator and Cu-K_α1 (Ln = La, Ce, Sm, Er, Yb) or Co-K_α1 radiation (Ln = Eu) at 293(1) K. Co-K_α1 radiation was used for EuN to avoid fluorescence effects that are caused by the Cu-K_α1 energy alike L₁-edge of Eu, hence improving the signal to noise ratio of the diffraction data^62,63. The powder samples were placed between Kapton foils to avoid oxidation in air. PXRD data of the high-temperature oxidised LnN (Ln = La, Ce, Sm, Eu, Er, Yb) compounds in this investigation were collected on a Bruker D8 diffractometer equipped with a Lynxeye XE-T detector in Bragg–Brentano configuration using Cu-K_α1,2 radiation (λ = 1.54184 Å) at room temperature. The powder samples were placed on a thin Vaseline layer on Si-zero background holders closed by an airtight Kapton dome. Measurements were performed in the range of 20° ≤ 2θ ≤ 85° with a step size of (2θ) = 0.02° and a counting time of 2 s per step. Data analysis was performed via the Rietveld method as implemented in the program GSAS-II⁶⁴. The PXRD characterisation of pristine and high-temperature oxidised LnN powders (Ln = Pr, Nd, Gd, Tb, Dy, Ho, Tm, Lu) was reported previously¹.

Thermogravimetric analysis

The thermogravimetric characterisation of the high-temperature oxidation behaviour of LnN (Ln = La, Ce, Sm, Eu, Er, Yb) powders with a NETZSCH STA 449C in thermogravimetric and differential scanning calorimetry setup (TGA-DSC) equipped with a thermocouple type S (σ_T = ± 1 °C) has been adapted from previous works¹. Powder samples of 20 mg were heated in Pt/Rh crucibles (NETZSCH) to 900 °C under flowing synthetic air at 10 °C/min rate. The oxidation residues were analysed by PXRD.

High temperature oxide melt drop solution calorimetry

High temperature calorimetry experiments were performed using a Calvet Calorimeter (Setaram AlexSys 1000)^34,65, where each of the two calorimeter chambers was maintained at 973 K and contained a quartz crucible with 30 g of molten sodium molybdate solvent (3 NaO · 4 MO₃). The sample chambers were kept under flowing oxygen gas (A-L Compressed Gases, 99.5%) with ~60 mL/min, which was also bubbled through molten salt solvents at 4 mL/min to maintain oxidising conditions. Prior to sample measurements, the calorimeter was calibrated using Al₂O₃ calibrants, which were dropped into empty quartz crucibles in separate experimental runs. Pellets of around 5 mg LnN (Ln = La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu) with a diameter of 1 mm were prepared before each respective experiment and sealed in plastic bags under a protective nitrogen atmosphere. In order to minimise air contact of the sample pellets, the bags were cut open right before the drop into the calorimeter, where they dissolved in the molten salt solvent. During the initial drop experiments of CeN, visible light flashes were observed, indicating ignition before dissolution. To prevent unintended oxidation, CeN samples were encapsulated in Rutile-structured TiO₂ pellets (1.5 mm diameter), isolating them from air contact until dissolution. PXRD structure analysis of TiO₂ is provided in Supplementary Information Note 1, Fig. S1 with Rietveld analysis results summarised in Table S1. The standard enthalpy of formation was calculated by two constructed thermocycles which were based on the observed high-temperature oxidation behaviour for the respective LnN compounds described in this investigation and elsewhere¹.

Author contributions

The research methodology, experimental planning and formal analysis was developed and conducted by Pascal Uhlemann, Xiaofeng Guo and Gabriel L. Murphy. Funding acquisition and project management was performed by Pascal Uhlemann, C. Schreinemachers, Giuseppe Modolo and Gabriel L. Murphy. The materials were synthesised by Pascal Uhlemann and Peter Höhn. PXRD measurements and analysis were performed by Pascal Uhlemann, Philip Kegler and Peter Höhn. Thermogravimetric measurements were performed by Pascal Uhlemann and Christian Schreinemachers. High temperature calorimetry experiments were conducted by Pascal Uhlemann, Will Vance with support and guidance provided by Matthew P. Heaney and Natalie Yaw. Data analysis and visualisation of the calorimetry experiments, as well as calculations were performed by Pascal Uhlemann, Will Vance and Xiaofeng Guo. Manuscript writing, review and editing was performed by Pascal Uhlemann and Gabriel L. Murphy with input from all authors.

Peer review

Peer review information

Communications Chemistry thanks all reviewer(s) for their contribution to the peer review of this work. A peer review file is available.

Funding

Financial support for this research was provided by European Commission through the “Fuel Recycle and Experimentally Demonstrated Manufacturing of Advanced Nuclear Solutions for Safety” (FREDMANS) project, grant agreement number 101060800. Views and opinions expressed are those of the authors only and do not necessarily reflect those of the European Union, European Commission or European Atomic Energy Community (granting authority). Neither the European Union nor the granting authority can be held responsible for them. Funding for P. Uhlemann to perform the experimental work in the facilities of Washington State University (WSU) was provided by the HITEC Graduate School of Forschungszentrum Jülich GmbH. Calorimetric work performed at WSU were supported by the United States Nuclear Regulatory Commission, Office of Nuclear Regulatory Research (RES) under award No. 31310023M0011. Open Access funding enabled and organized by Projekt DEAL.

Data availability

The data that support the findings of this study is available in an open access Zenodo repository, https://doi.org/10.5281/zenodo.22296171.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at https://doi.org/10.1038/s42004-026-02236-8.