Impacts of Am Aggregation on the Bulk Properties of Mixed Oxides (U, Am)O₂ from First Principles

Abstract

We present a first-principles density functional theory with the Coulomb interaction U (DFT + U) investigation of the bulk properties, including structural, energetic, electronic, and mechanical properties for uranium–americium mixed oxides (U, Am)O₂. The various Am aggregation contents were investigated to better understand the impact of Am on the nuclear fuel UO₂. The supercell defect models at different scales were used to describe the solid solution (U, Am)O₂. The obtained results show that different contents of Am aggregation have a significant impact on the volume and energy of the formation of mixed oxide systems. The results of the electronic structure calculations exhibit no bandgap owing to the mixing of UO₂ and AmO₂. The mixing enthalpy of the Am aggregation systems is used to describe the phase stability of the solid solution. In particular, the mixing enthalpy of (U, Am)O₂ is significantly reduced as the Am content increases. The elastic properties of the (U, Am)O₂ mixed oxides have also been compared as a function of the Am content. Moreover, the impacts of the whole Pu aggregation content range on the bulk properties for the (U, Pu)O₂ mixed oxides are also discussed.

1. Introduction

UO₂ and uranium–plutonium mixed oxides (U, Pu)O₂ are an essential part of the nuclear fuel cycle for the current nuclear industry. Actinides such as plutonium (Pu), minor americium (Am), and neptunium (Np) are produced during UO₂ fission. The presence of these actinides has a significant impact on the structure and behavior of nuclear fuels, as well as on the cycle of nuclear fuels and reprocessing of nuclear wastes. Fast neutron reactors, such as sodium-cooled fast reactors (SFRs), can improve the recycling of Pu and the efficiency of UO₂ in the nuclear fuel cycle. In particular, under the storage conditions of PuO₂, owing to ²⁴¹Pu decaying into ²⁴¹Am and the short half-life of ²⁴¹Pu, PuO₂ contains a significant ingrowth of Am. Furthermore, uranium–americium mixed oxides (U, Am)O₂ are ideal nuclear fuel for the design of Generation IV fast neutron reactors [1,2]. Thus, it is crucial to focus on how the presence of minor actinides, especially americium in nuclear fuels, degrade the structure and properties of nuclear fuels for fast reactors.

For ideal (U, Am)O₂ mixed oxides, the random substitution of Am⁴⁺ for U⁴⁺ in the UO₂ lattice greatly affects the behavior of nuclear fuels. However, at the atomic scale of the mixed oxides systems, there are inevitably regions enriched in Am owing to the short decay period of Pu in nuclear wastes and current industrial procedures. In the nuclear fuel matrix of the mixed oxides (U, Am)O₂, Am is enriched in the crystal matrix of UO₂, and the influence on the structure and properties of nuclear materials cannot be ignored [3]. Our study focuses on the bulk properties, including structural, energetic, and mechanical properties of the mixed oxides (U, Am)O₂, especially for various Am aggregation contents in UO₂ nuclear fuel, in order to understand and predict the behavior of the fuel in the reactor.

Actinides such as U, Pu, and Am have abundant oxidation states and many interesting physical and chemical features owing to the presence of strongly correlated 5f orbital electrons. At present, there have been limited experimental and theoretical data on the ground state structure and properties of PuO₂ and AmO₂, including magnetic orders and electronic and mechanical properties. In Refs. [4,5], the authors used the method of density functional theory with the Coulomb interaction U (DFT + U) and calculated the mixed oxides (U, Pu)O₂ for the difference in the Pu content range, and reproduced lattice shrinkage with the increased Pu content, and the obtained enthalpy of formation for UO₂ and PuO₂ was consistent with the experimental values, especially the mixing enthalpy of the uranium–plutonium mixed oxides (U, Pu)O₂, which was calculated to analyze the stability of the mixed oxide systems. Reference [6] used generalized gradient approximation with the Coulomb interaction U (GGA + U) combined with the special quasirandom structures (SQSs) method to study the structural and electronic properties of U_1−yAm_yO₂ under different Am contents and the results obtained were found to be consistent with the limited experimental measurements. Although the SQS method has some advantages in constructing disordered solid solution structures, the modeling at the atomic scale and the specific impact on structure and properties for uranium–americium mixed oxides are unclear as the Am aggregation content increases in the UO₂ matrix. In the current study, the calculated results show that the structure and energy of formation of the (U, Am)O₂ mixed oxides are significantly different from those of the SQS method as the Am aggregation contents increase.

In the present study, the effects of different Am aggregation contents on the structure and properties of mixed oxides (U, Am)O₂ are calculated using the Perdew–Burke–Erzenhorf density functional (PBE) revised for solids (PBEsol) with the Coulomb interaction U (PBEsol + U) based on first principles, mainly including architecture, energy, and mechanical properties. Furthermore, as a reference, the bulk properties of the (U, Pu)O₂ mixed oxides with different Pu aggregation contents are also reported in this paper.

2. Methodology

In this study, all PBEsol + U calculations were performed using the Vienna Ab initio Simulation Package (VASP, Version 5.4) based on DFT [7,8,9,10,11]. In our previous studies [12,13] and in Ref. [14], the calculations show that the prediction of the structure, energy, and electronic properties of actinide oxide compounds using the PBEsol + U is better than that of other functional. The PBEsol + U method considers the on-site Coulomb interaction U and exchange J for the 5f electrons of actinides U, Pu, and Am [15,16,17]. In those calculations, U_U = 4.5 eV and J_U = 0.51 eV [18,19], U_Pu = 4.0 eV, and J_Pu = 0.00 eV [4,20], as well as U_Am = 6.0 eV and J_Am = 0.75 eV were used [21]. Moreover, the spin–orbit coupling (SOC) effect is neglected because of the efficiency of the calculations considered in our calculations [12,13]. As well, the calculations in the literature show that SOC has no significant effect on the structure and energy of the formation of UO₂ and PuO₂ [22,23,24,25,26,27].

Although experiments show that UO₂ is a 3k-antiferromagnetic (AFM) order, DFT + U calculations obtain a good enough description with a 1k-AFM order when SOC is not considered [4,27,28,29,30]. There is no uniform conclusion on the magnetic order for PuO₂, but usually, DFT + U calculations using a 1k-AFM order give reliable ground-state results. Thus, the calculations in this study consider the 1k-FM order and 1k-AFM order of UO₂, PuO₂, AmO₂ and the mixed oxides (U, Am)O₂ and (U, Pu)O₂ so that stable ground state structures and properties can be obtained when building these mixed oxide structures. For the different magnetic order of AnO₂ (such as UO₂, PuO₂, and AmO₂) fluorite structure (12-atom cell), including the 1k-ferromagnetic (FM) order, longitudinal 1k-collinear AFM order and transverse 3k-noncollinear AFM order, are shown in Figure S1 (in the Supplementary Materials).

The energy of formation (E_f) is calculated from the results of the DFT + U calculations as follows:

$$\Delta E_{\mathrm{f}}^{{\mathrm{AnO}}_2}=E_{\mathrm{tot}}^{{\mathrm{AnO}}_2}-E_{\mathrm{tot}}^{\mathrm{An}}-2E_{\mathrm{tot}}^{{\mathrm{O}}_2},$$

(1)

where $E_{\mathrm{f}}^{{\mathrm{AnO}}_2}$ is the PBEsol + U total energy of the UO₂, PuO₂, and AmO₂ compounds, $E_{\mathrm{tot}}^{{\mathrm{O}}_2}$ is the PBEsol + U chemical potential of oxygen in the molecular oxygen reference state, and $E_{\mathrm{tot}}^{\mathrm{An}}$ is the PBEsol + U chemical potential of metallic α-U, α-Pu, and α-Am reference state.

In order to obtain reliable defect structures at the atomic scale, we used two different supercell models, one in a 96-atom UO₂ structure that replaces U with Am (Pu) and the other in a 12-atom system. For the defect model (12-atom cell), U is replaced with Am, including 25%, 50%, and 75% Am (or Pu) in the UO₂ matrix. The supercell defect model (96-atom cell) is centered on the supercell center metal U, and in the radius region where different neighboring metal atoms are suitable, replaces U with Am to construct the computational model with different Am or Pu aggregation contents (Figure 1). In the (U, Am)O₂ defect model for various Am aggregation contents, the energetics of defects in these structures are described by the energy of formation. The energy of the formation of a replacement is expressed as follows:

$$\Delta E_{\mathrm{f}}=E_{\mathrm{rep}}^{\mathrm{MOX}}-E_{\mathrm{pure}}^{{\mathrm{UO}}_2}-E_{\mathrm{tot}}^{\mathrm{U}}+E_{\mathrm{tot}}^{\mathrm{An}},$$

(2)

where $E_{\mathrm{rep}}^{\mathrm{MOX}}$ is the PBEsol + U total energy of the lattice UO₂ with Am replacement, $E_{\mathrm{pure}}^{{\mathrm{UO}}_2}$ is the calculated total energy of the perfect lattice, $E_{\mathrm{tot}}^{\mathrm{U}}$ is the calculated chemical potential of a metallic α-U reference state, and $E_{\mathrm{tot}}^{\mathrm{An}}$ is the calculated chemical potential of metallic α-Am replacement elements.

The mixing enthalpy of the (U, Am)O₂ solid solution is determined using the calculations of the total energy in the entire Am contents of the PBEsol + U method. The equation is expressed as follows:

$$\Delta H_{\mathrm{mix}}(y)=E_{\mathrm{tot}}^{{(\mathrm{U}}_{1-\mathrm{y}}{\mathrm{Am}}_{\mathrm{y}}{)\mathrm{O}}_2}-(1-y)E_{\mathrm{tot}}^{{\mathrm{UO}}_2}-y{E}_{\mathrm{tot}}^{{\mathrm{AmO}}_2}$$

(3)

where $E_{\mathrm{tot}}^{{(\mathrm{U}}_{1-\mathrm{y}}{\mathrm{Am}}_{\mathrm{y}}{)\mathrm{O}}_2}$, $E_{\mathrm{tot}}^{{\mathrm{UO}}_2}$, and $E_{\mathrm{tot}}^{{\mathrm{AmO}}_2}$ are the calculated total energies for the oxides as notified.

Our calculations were performed using a 2 × 2 × 2 k-point mesh in Brillouin zones for supercells (96-atom). The calculation of elastic constants for a range of Am or Pu contents (25%, 50%, and 75%) was performed with the use of 12-atom supercells with a 6×6×6 k-point mesh. The energy cutoff of 550 eV was used for all calculations. By performing structural relaxation until the Hellmann–Feynman force of each atom was less than 0.01 eV/Å and the convergence on energy was less than 10⁻⁵ eV/atom, the stable ground state structure of the system was obtained. Moreover, the variation in the volume of mixed oxides (U, Pu)O₂ with different Pu aggregation contents are shown in Figure S2. The structure and properties, including the lattice parameter and bandgap of the (U, Pu)O₂ defect model for various Pu aggregation contents using PBEsol + U, is shown in Tables S1 and S2. The energies of the formation of UO₂, PuO₂, and (U, Pu)O₂ using PBEsol + U are shown in Table S3. The obtained elastic constants and bulk modulus of (U, Pu)O₂ are shown in Table S4.

3. Results and Discussion

3.1. The Bulk Properties for (U, Am)O₂ Using the Supercell (96-Atom) Defect Models

For the magnetic stability in the mixed oxide (U, Am)O₂ for various Am aggregation contents for the two different magnetic configurations, the 1k-FM and 1k-AFM orders have been considered (Figure S1). In Figure 1, the (U, Am)O₂ defect model for Am aggregation contents, including single Am, 12.5% Am, 25% Am, and 50% Am, are shown. The obtained lattice parameter and bandgap of the (U, Am)O₂ using the PBEsol + U method are shown in

Table 1. Magnetic stability including the lattice parameters a₀, c/a, energy difference (E), and bandgap (Gap) of (U, Am)O₂ for various Am aggregation concentration contents using PBEsol + U. See text for details.

Am Content	AFM			FM			EFM–EAFM/Atom (eV)
	a0 (Å)	c/a	Gap (eV)	a0 (Å)	c/a	Gap (eV)
UO2	5.480	1.0	2.0	5.469	1.0	1.8	0.12
12.5%	5.221	1.0	Metal	5.223	1.0	Metal	0.00
25%	5.268	0.996	Metal	5.269	0.996	Metal	0.00
37.5%	5.368	0.995	Metal	5.305	0.995	Metal	0.00
50%	5.407	0.988	Metal	5.420	0.990	Metal	0.00
75%	5.345	0.994	Metal	5.409	0.994	Metal	0.00
AmO2	5.387	1.0	1.1	5.375	1.0	1.0	0.57

. As one can see from Table 1, the energy differences obtained between the two magnetic orders are small. There is also no difference in the lattice parameters for the two magnetic orders. In order to have a consistent comparison of the ground state properties for various americium aggregation concentration contents, the AFM order of the U-Am mixed oxides for all compositions was adopted.

The calculated results show that there are two distinct variations in the volume of the (U, Am)O₂ mixed oxides as the Am aggregation concentration content increases in UO₂. First, when the Am aggregation contents in UO₂ increases from 0 to 12.5%, the lattice parameter of the (U, Am)O₂ decreases from 5.48 Å to 5.221 Å, while the lattice parameter a₀ of the systems increases from 5.221 Å to 5.407 Å when the Am content increases from 12.5% to 50% (Table 1 and Figure S2). The trends of this change are significantly different from experimental observations and predictions of U-Am mixed oxides (U, Am)O₂ using the SQS [6]. This difference may be mainly due to the finding that the ionic radius of Am⁴⁺ is somewhat smaller than that of U⁴⁺ ions in the cubic fluorite structure, which could also be further explained by the feature that the lattice size of AmO₂ is smaller than that of UO₂. The effects of different Am aggregation contents on the structure and properties of UO₂ are of great significance for improving the efficiency of the mixed oxides nuclear fuel recycling and the safe storage of nuclear waste.

For the (U, Am)O₂ mixed oxides systems, the effect of the variation in the Hubbard parameter U of Am⁴⁺ cation on the structure and properties of (U, Am)O₂ is critical. In the current study, the effect of the variations in the onsite Coulomb interaction parameter U on the lattice parameter of UO₂, (U_0.5Am_0.25)O₂, and AmO₂ were determined. The values of the J parameters were kept constant. Our results are shown in Figure 2 and compared with the experimental values. For U = 4.0 eV, an overestimation of 1% is observed in the lattice parameter of UO₂ compared to the experimental value. Furthermore, when U increases from 4.0 to 7.0 eV, the lattice constant increases by 0.7%. For U = 4.0 eV, and an overestimation of 1.5% is observed in the lattice parameter of AmO₂ compared to the experimental value. Furthermore, when U increases from 4.0 to 6.0 eV, and the lattice constant increases by 0.6%. For (U_0.5Am_0.5)O₂, when U= 6.0 eV, the overestimations compared to the experimental values are 0.5%. Thus, a small variation in the U parameter of U and Am in (U, Am)O₂ has a negligible impact on its structural properties.

3.2. The Structure and Properties of (U, Am)O₂ Using the Supercell (12-Atom) Method

The lattice parameters, energy of formation, bandgap values, and magnetic moments of the different Am contents in UO₂, including 25%, 50%, and 75%, as well as AmO₂ were calculated by the PBEsol + U method, and the results are shown in

Table 2. Lattice parameter, bandgap, magnetic moment (in Bohr magnetons μ_B), and energy difference of UO₂, AmO₂, and (U, Am)O₂ using PBEsol + U.

Compounds	Functional	a0 (Å)		Gap (eV)	μmag (μB)	EFM–EAFM/Atom (eV)
		AFM	FM	AFM	AFM
UO2	PBEsol + U	5.480	5.469	2.1	2.0	0.12
	PBE + U [5]	5.543	5.547	2.5
	Experiment [31]	5.470
(U0.75Am0.25)O2	PBEsol + U	5.221	5.223	Metal	7.2	0.00
(U0.5Am0.5)O2	PBEsol + U	5.226	5.227	Metal	7.0	0.00
(U0.25Am0.75)O2	PBEsol + U	5.236	5.236	Metal	7.1	0.00
AmO2	PBEsol + U	5.387	5.375	1.1	5.3	0.57
	Experiment [32]	5.376		1.3

. The volume of the mixed oxides (U, Am)O₂ of different supercells (12-atom and 96-atom cells) as a function of the Am contents is shown in Figure 3a. The results show that the lattice parameters of (U, Am)O₂ are reduced when Am is added to the UO₂ matrix, and the supercells of different sizes had no significant effect on the volume of (U, Am)O₂. However, compared with the calculated results of (U, Pu)O₂ (Table S2), the volume of (U, Am)O₂ showed a different trend with the Am content than that of Pu. As shown in Table S2, the volume of the (U, Pu)O₂ decreases with the increase in the Pu content, while the volume of the (U, Am)O₂ decreases with the increase in the Am content, and the volume of the (U, Am)O₂ systems decreases to the lowest when the Am content is 50%. Subsequently, there was a slight increase with the increase in the Am content. This trend is crucial for the understanding and application of the structure and properties of the two mixed oxides.

In the electronic structure calculations (Figure 4), the results show that the UO₂ bandgap value at 1k-AFM is 2.0 eV, which is significantly closer to the experimental value [31]. than other results. Moreover, the calculated results of the bandgap of AmO₂ are in a reasonable agreement with the experimental values [32]. As Table 1 and Table 2 show, the bandgap of the mixed oxides (U, Am)O₂ is significantly reduced to 0 eV. As well, with the increase in the Am content, the bandgap of (U, Am)O₂ almost does not change. Compared with the bandgap results of (U, Pu)O₂ (Tables S1 and S2), the characteristics of the reduced bandgap of (U, Am)O₂ are consistent. A close comparison of the electronic structure changes in the two mixed oxides shows that the reduction in the bandgap in the structure of the mixed oxides is mainly determined by the size of the bandgap between UO₂ and AmO₂, such as the strong Coulomb interaction of the 5f orbital electrons.

In Table 2, the spin magnetic moments of UO₂ calculated by the PBEsol + U method are 2.0μ_B, which is close enough to the experimental observations. Although there is no experimental result for the spin magnetic moment of AmO₂, the calculated result is 5.3μ_B, which is consistent with the calculated results of the hybrid density functional (HSE). In the calculated results of the mixed oxides (U, Am)O₂, the spin magnetic moment is 7.1μ_B, which is significantly higher than that of UO₂ and AmO₂. Therefore, the magnetic moment of UO₂ and AmO₂ calculated using 1k-AFM is also closer to the experimental values, which also provides a reference for the prediction of the magnetic moment for the mixed oxides (U, Am)O₂.

3.3. Energetic Properties for (U, Am)O₂ Using PBEsol + U

The results of the energy formation of UO₂, AmO₂, and the mixed oxides (U, Am)O₂ with different Am aggregation contents obtained using the PBEsol + U method are listed in

Table 3. Energy of formation of UO₂, AmO₂, and (U, Am)O₂ using PBEsol + U.

Compound	Ef (eV)
	Experiment	CALPHAD	PBE + U	vdW-optPBE + U	PBEsol + U
UO2	−11.24 [33]	−11.23 [34]	−10.86 [5]	−11.27 [5]	−11.78
(U0.75Am0.25)O2					−15.39
(U0.5Am0.5)O2					−15.67
(U0.25Am0.75)O2					−15.95
AmO2	−9.51 [35]		−8.29 [21]		−10.46

. Figure 3b shows the relation between the energy of formation of different supercell sizes and the Am aggregation contents of (U, Am)O₂. According to the calculated results of the energy of formation, the value of (U, Am)O₂ reduces at different Am aggregation contents. Compared with the different Pu aggregation contents for the (U, Pu)O₂ (Table S3), the energy of formation of (U, Am)O₂ is lower.

In the defect model, with the accumulation of Am in UO₂, the energy of formation of the mixed oxide system is significantly lower than that using the SQS method [5]. In the mixed oxides (U, Pu)O₂, when the Pu content is 25%, the energy of formation of (U, Pu)O₂ is the lowest. However, in the mixed oxides (U, Am)O₂, the energy of formation of (U, Am)O₂ can continue to decrease with the increase in Am content. Although the results of different supercell sizes in calculating the energy of formation of the two mixed oxides are different, the calculated results of 2 × 2 × 2 supercells are reliable.

The obtained mixing enthalpy of mixed oxides (U, Am)O₂ in the entire range of Am contents using the PBEsol + U method is shown in Figure 5. The mixing enthalpy of (U, Am)O₂ was found to be negative in the entire range of Am contents using the PBEsol + U calculations. The calculated result suggests that there is no phase separation related to the variation in Am content in the solid solution. The mixing enthalpy of (U, Am)O₂ displays a regular evolution as a function of the Am content. For the Am content equal to 0.75, the mixed oxide is more stable than all the other compositions.

3.4. Elastic Properties of the (U, Am)O₂ Using PBEsol + U

As listed in

Table 4. Elastic constants and bulk modulus of (U, Am)O₂ using PBEsol + U.

	Functional	UO2	(U0.75Am0.25)O2	(U0.5Am0.5)O2	(U0.25Am0.75)O2	AmO2
C11 (GPa)	PBEsol + U	383	358	325	274	321
	PBE + U [5]	364				363
	LDA + U [4]	401
	experiment [33]	389
C12 (GPa)	PBEsol + U	126	92	80	75	161
	PBE + U [5]	112				102
	LDA + U [4]	132
	experiment [33]	119
C44 (GPa)	PBEsol + U	72.3	25	43	37	58
	PBE + U [5]	58				71
	LDA + U [4]	94
	experiment [33]	60
B0 (GPa)	PBEsol + U	212	181	162	141	215
	PBE + U [5]	196				189
	LDA + U [4]	222
	experiment [33]	207

, three elastic constants C₁₁, C₁₂, and C₄₄ of UO₂, (U_0.25Am_0.75)O₂, (U_0.5Am_0.5)O₂ and (U_0.75Am_0.25)O₂ and AmO₂ cubic structures were calculated. Compared with the limited experimental and theoretical results [19], our calculations using the PBEsol + U method are close to those of GGA at a U value of 4.0 eV. The incorporation of different amounts of Am into UO₂ significantly reduced C₁₁ and approached the value of AmO₂ at 75%, while C₁₂ also decreased and C₄₄ did not change significantly. In the (U, Am)O₂ system, with the increase in the Am content in the UO₂ matrix, the calculated elastic constants in the C₁₁ and C₁₂ directions decreased significantly, especially in the C₁₁ direction, while the C₄₄ direction increased slightly. At the same time, the obtained bulk modulus B₀ decreased significantly with the increase in the Am content in the (U, Am)O₂ system. Since there are no experimental measurements of the mechanics of the (U, Am)O₂ mixed oxides, we could only compare and analyze the calculated results of DFT + U with the experimental values of UO₂.

The bulk modulus of UO₂ calculated by the PBEsol + U method is 212 GPa, which is very close to the experimental results. The calculated results of the bulk modulus of AmO₂ are the same as the results of Ref. [5]. and somewhat higher than the experimental value [33]. However, it is crucial to obtain the elastic constants of these oxide systems in different functional forms. The elastic constants C₁₁, C₁₂, and C₄₄ and bulk modulus B₀ of UO₂, PuO₂, and the mixed oxides (U, Pu)O₂ are listed in Table S4. Compared with the experimental values of UO₂ [7], the calculated results of C₁₁ and C₁₂ are 383 GPa and 126 GPa, respectively, which are close enough to the experimental results, and C₄₄ (72 GPa) is somewhat higher than the experimental value (60 GPa).

In Table 4 and Table S4, comparing the contents of different Pu and Am in UO₂, the influence of the elastic constants of the mixed oxide (U, Pu)O₂ and (U, Am)O₂ structures in different directions is different; that is, the incorporation of Pu into the UO₂ structure increases the elastic constants of (U, Pu)O₂, while the incorporation of Am into the UO₂ structure decreases the elastic constants of (U, Am)O₂, especially in the direction of C₁₁, and has little effect on the direction of C₁₂ and C₄₄. Thus, the elastic properties of (U, Am)O₂ mixed oxides are reported for the first time by means of theoretical simulations, which provide theoretical support for further experimental verification and the further development of nuclear fuel U-Am mixed oxides.

4. Conclusions

In this paper, we calculated and analyzed the changes in the structure, energy, and elastic properties of UO₂, AmO₂, and mixed oxides (U, Am)O₂ using the PBEsol + U method. Actually, we use the first-principles approach to explore the influence of different defect structures of Am aggregation on the atomic-scale crystal structure of the fuel in the mixed oxide systems. First of all, we used the PBEsol + U method to ascertain whether the structural and energetic properties of UO₂ and AmO₂ are consistent with the experimental results. In the calculation of the mixed oxides (U, Am)O₂, the results showed that the substitution of Am in the UO₂ matrix reduced the volume of the nuclear fuel and seriously affected the energy of the nuclear fuel.

Actually, when the volume of the (U, Am)O₂ structure with 25% Am content is about 4.7% lower than that of UO₂, the energy of formation of (U, Am)O₂ is about 30% lower than that of UO₂. In particular, with the increase in the Am contents, there are clear differences in the properties of the mixed oxides, especially the changing trend of energy formation. For the (U, Am)O₂ mixed oxides, the lattice parameters and the energy of formation were reduced as the Pu aggregation content increased in the UO₂ matrix, especially the energy of formation for these mixed oxide systems.

Meanwhile, the results of electronic structure calculations show that the bandgap value in the mixed oxide systems decreased with the increase in Am, which is crucial for the thermodynamic transport of mixed oxide fuels. The mixing enthalpy calculations show that (U, Am)O₂ mixed oxides are a stable solid solution for all Am contents. Finally, we discussed the elastic properties of the mixed oxides (U, Am)O₂, and the results show that with the increase in the content of Am in the UO₂ matrix, the elasticity of the system C₁₁ and C₄₄ decreases significantly. Moreover, the bulk modulus also shows the same decreasing trend.