An in-depth investigation into ²³⁴U and ²³⁸U isotopes systematics in U(IV) and U(VI) phases of betafite for enhanced understanding of actinide retention

Abstract

The superior efficacy of synroc as an immobilization matrix for actinides in spent nuclear fuel has been extensively validated, positioning it as a leading candidate for long-term nuclear waste management. In this context, isotopic investigations of natural analogues are indispensable for optimizing synroc formulations, particularly regarding their capacity to incorporate and retain actinides and their decay products over geological timescales. In this study, a naturally occurring member of the pyrochlore supergroup was identified as betafite through integrated SEM, EMPA, and XRD analyses. The isotopic behavior of uranium was investigated by comparing the activity ratios of parent (²³⁸U) and daughter (²³⁴U) nuclides within U(IV) and U(VI) enriched forms of the mineral, formed and preserved over approximately 2 billion years. The ²³⁴U/²³⁸U activity ratios, 1.089 ± 0.016 in U(IV) forms and 0.956 ± 0.007 in U(VI) forms, demonstrate a preferential accumulation of radiogenic ²³⁴U in the tetravalent uranium sites. Based on the obtained findings, this may indicate a structural affinity and retention capacity of U(IV) for daughter isotopes, which might contribute to its stability under reducing conditions; however, further investigation is required to evaluate its long-term implications. Moreover, dissolution features and redox partitioning indicate that approximately 33% of U(IV) in the system results from the disproportionation of intermediate U(V), highlighting a critical redox transformation pathway relevant to actinide immobilization. These findings underscore the importance of redox-sensitive behavior and uranium isotope fractionation in pyrochlore-group minerals and reinforce the relevance of natural analogues in tailoring synroc compositions. Such analogues serve as empirical benchmarks for predicting the performance of actinide-bearing phases in nuclear waste repositories over geologic timescales.

Introduction

Immobilization of nuclear waste is the process of turning waste into a wasteform through encapsulation, solidification, or embedding that lessens the possibility of radioactive movement or dispersion during the waste lifecycle’s operational and disposal phases. Waste is immobilized by chemically incorporating it into the structure of an appropriate matrix, usually ceramic, glass, or cement, making it trapped and impossible to leave^1–5. For high-level waste (HLW), chemical immobilization is usually used. Operations related to the nuclear military industry and the reprocessing stages of spent nuclear fuel are the primary sources of high-level radioactive liquid waste⁶. Actinide waste has been proposed to be incorporated into synroc minerals related to pyrochlore, zirconolite, and phosphate because of their high irradiation stability and chemical durability⁶. The advanced crystalline phases that make up synroc are the same as those found in natural minerals, which have been shown to exist for millions of years in geological environments with high temperatures and pressures as well as potential groundwater contact^7,8. In addition to having the advantage of being less impacted by changes in the waste’s composition, synroc can hold the same waste loadings in a smaller volume than glass⁵.

Based on the characteristics and reasons mentioned in relation to the immobilization of various types of nuclear waste, it is quite evident that the immobilization of spent nuclear fuel actinides is of great importance, and the most suitable matrices for achieving high reliability in this regard are the synthesis of synroc crystalline ceramics, which can be used in this context from natural analogues, which are the best evidence for the long-term behavior of actinides. The most advanced ceramic phases for permanently immobilizing spent nuclear fuel actinides are Ti-based ceramics⁹. One sophisticated waste form that is being considered as a potential option for second-generation waste treatment is synroc, a polyphase titanate ceramic. Synroc’s main phases resemble those of naturally existing minerals that have been found to contain naturally occurring radioactive elements in a range of geological environments. Metamict minerals containing uranium and thorium isotopes that have the Ti-Ta-Nb-oxide groups are considered as natural analogues of aged HLW forms. Most of these minerals usually have a geological age of more than several billion years^10,11. Therefore, by analyzing the behavior of the parent and daughter uranium and thorium isotopes using various methods, including radiochemical analysis, useful information was obtained about the resistance of these minerals to the chemical, physical, and biochemical processes of nature. Since the natural isotopes of these analogues can represent the behavior of actinides, therefore, synroc with an optimal formulation can solve the problem of immobilizing these heavy isotopes of spent nuclear fuel with long half-lives to an acceptable level. For example, plutonium-239, plutonium-238, neptunium-237, or americium-241 and -243 isotopes with long half-lives have high activity in spent nuclear fuel. Also, the alpha decay of the aforementioned isotopes also produces daughter isotopes with long half-lives, and their preservation and stability in the matrices, like the parent isotopes, is of great importance. In natural analogues, studying the activity ratio between the parent uranium isotope (²³⁸U) and the daughter uranium isotope (²³⁴U) helps to obtain preliminary information about the behavior of these isotopes in the geological history of the mineral. Also, isotopic characterization in the U⁺⁴ and U⁺⁶ sections shows how resistant the mineral has been to natural processes. In the work¹², aegirine and albite, the crystalline members of the mineral assemblage, are distinguished by their lack of radiogenic uranium: In aegirine and albite, the parameter of the (²³⁴U/²³⁸U) activity ratio is 0.94 and 0.87, respectively. The equilibrium state of uranium isotopes, AR (²³⁴U/²³⁸U) = 0.99 ± 0.01, is what defines pyrochlore. Following the full dissolution of a metamict mineral (a Ti-Ta-Nb-oxide) within a mineral assemblage in aqua regia, the authors of work¹⁰ found AR(Σ) = 0.925 ± 0.016. This ratio indicates a considerable depletion of the radiogenic isotope of ²³⁴U in the material overall. In the betafite¹³, the difference between isotopes in relation to the influence of natural waters gradually levels off and eventually vanishes in the metamict structure of a mineral, as indicated by the value of AR (²³⁴U/²³⁸U) = 1.00. In a subsequent study¹⁴, the degree of disruption of the secular equilibrium between the parent isotope (²³⁸U) and its daughter (²³⁴U) is demonstrated by the mean value of the AR (Σ) (²³⁴U/²³⁸U) in the polycrase, which is equal to 0.963 ± 0.004. The AR (Σ) = 0.963 ± 0.004 in the original polycrase is greater than the ²³⁴U/²³⁸U activity ratios in the U(VI) section, which are 0.944 ± 0.005. In the work¹¹, following a comparison of the immobilization properties of matrix materials based on Nb-Ta-Ti-oxides of the types AB₂O₆ and A₂B₂O₇, it is determined that euxenite group minerals show great promise as matrix materials for actinide immobilization. Concurrently, a viewpoint has been presented regarding the rationale of conducting additional comparative research on Nb-Ta-Ti-oxides of the mineral groups AB₂O₆ and A₂B₂O₇ in order to determine their suitability for employment at the end of the nuclear fuel cycle.

In this research work, the natural uranium isotopic characterization of a specimen of a metamict mineral as a natural analogue of matrices for actinide immobilization has been carried out.

Experimental

It is important to note that every experiment and analysis included in this study was conducted at St. Petersburg State University’s Department of Radiochemistry.

Sample description

A specimen of a metamict mineral geologically aged 1800 ± 30 million years¹⁵, discovered in a mineral assemblage of granite pegmatites on the Nuolayniemi Peninsula in Priladozhye (the Ladoga area), Karelia, was the subject of this study. According to publication¹³, betafite is the fundamental phase of this assemblage of radioactive minerals. In the current research work, a piece of the original sample was separated and analyzed to examine the structural and isotopic characterization of the mineral assemblage. The zonal structure of the reported pegmatites is frequently one of their defining characteristics. Additionally, they are intriguing due to the presence of very uncommon minerals, including ortite, yttropyrochlor, monazite, xenotime, and others¹⁶. According to their structure, pegmatites appear to be silicate phases that significantly isolate and shield accessory minerals from the effects of natural fluids. At St. Petersburg State University, the equivalent sample was obtained from the Faculty of Geology’s Department of the Geology of Mineral Deposits.

SEM and EMP analysis

For scanning electron microscopy and electron microprobe analysis, we used two devices.

1. For ideal resolution at the nanoscale, a Zeiss Merlin scanning electron microscope equipped with a field emission cathode and a GEMINI-II electron optical column was employed. The microscope has a four-quadrant backscattered electron detector (AsB) and an energy-filtered backscattered electron detector (EsB) in addition to In-lens SE and SE2 secondary electron detectors, as previously described in our earlier work¹⁰.

2. An electron microprobe analysis system and an Oxford Instruments Swift ED3000 were utilized in conjunction with a HITACHI TM 3000 scanning electron microscope. In order to identify phases with distinct “average” atomic numbers (“compositional contrast”), a phase image was obtained in the backscattered electron diffraction region (BSE). The pieces were polished and then covered with a layer of carbon. A 15 kV accelerating voltage and a high vacuum were used for the analyses, using the instrumentation and conditions previously reported¹³.

X-ray diffraction analysis

A Bruker D2Phaser automatic powder diffractometer was used to analyze the sample’s phase composition utilizing CoKα1, λ = 1.78900 Å, and CoKα2 (λ = 1.79283 Å) radiation. We conducted isochronous thermal annealing of the sample in a vacuum at 400 and 800 °C and then X-ray diffraction monitoring of the sample phase composition at each annealing temperature.

Determination of the uranium oxidation state

Employing established methods utilized in the work^14,17, the amounts of tetravalent and hexavalent uranium in a betafite specimen were separated and measured: the incongruent dissolution of the minerals in 23M HF. The fluoride deposits, which contained U⁺⁴, thorium, and REE, were dissolved in aqua regia after the decantation isolated the resultant solution, which contained U(VI). The ideal circumstances for maintaining the original valences of uranium isotopes throughout the dissolution of geological objects in concentrated HF are provided by this method of U⁺⁴ and U⁺⁶ separation¹⁴. With every valence section, a ²³²U tracer was inserted. Following that, both valence forms of U⁺⁴ and U⁺⁶ were integrated into a solution containing 6 mol/l HCl. An anion-exchange process was then used to concentrate and purify the mixture. The object of study was first dissolved in hydrofluoric acid 23 M and subsequently in aqua regia to ascertain its complete uranium content.

Alpha spectrometric analysis

The total uranium content and the relative amounts of the U⁺⁴ and U⁺⁶ sections were ascertained by employing alpha-spectrometry. Molecular-based electrodeposition was used to prepare the alpha sources. Platinum wire served as the anode, and polished nickel discs with a radioactive area of 1.9 cm² served as the cathode. Throughout the electrolysis, the current intensity was kept between 25 and 30 mA. The electrolysis was done for 60 min at a time. The sources were measured using spectrometers equipped with 3–5 cm² silicon surface-barrier detectors. The spectrometric tracts consist of an AI-1024-95-17 4096-channel analyzer, a charge-sensitive preamplifier, a SES-13 amplifier, and a measuring chamber of the SEA-01 type. A computer software was used to examine the alpha spectra¹⁸.

Results and discussion

Elemental analysis of the mineral assemblage sample

The main phase of the mineral assemblage sample studied in this work has been identified in our previous work¹³ as metamict betafite, a Ti-Ta-Nb-oxide from the Pyrochlore supergroup. Hydrochemical processes have significantly changed the original composition of betafite. SEM and EMP analyses showed that the chemical composition of betafite at various points of the sample is varied due to leaching of primary elements, although in that research work all points were identified as betafite. Our main goal in the present work is isotopic characterization in metamict betafite, but in any case, to ensure that the tested sample is betafite, a piece of the mineral assemblage rock was separated, and after identifying the main phase, isotopic analyses were performed on this sample. Because in some cases, in mineral assemblage identification studies, due to phase diversity, the identification results through different methods do not match¹⁹.

To observe the uranium and thorium phases of the metamict sample with high resolution, SEM analysis was carried out at different scales (100 m–200 nm) of the study sample grains as displayed in Fig. 1. It is clearly visible that the bright phases indicate masses of heavy isotopes of uranium and thorium.

Fig. 1.

SEM-BSE images of the sample under study using a Zeiss Merlin scanning electron microscope on different scale bars.

To identify the main uranium phase in this study, the mineral complex was first heated to 800 °C to grow its phases, and SEM and EMP analyses were performed on the heated sample. Figure 2 shows a SEM-BSE image of one of the grains from the study sample when the sample was annealed at a temperature of 800 °C. The results of EMP analysis of its composition specified in Fig. 2 are shown in Table 1, and the EDX spectrum of the analyzed point is illustrated in Fig. 3.

Fig. 2.

SEM-BSE image of grains of the studied mineral assemblage at a temperature of 800 °C using a HITACHI TM 3000 scanning electron microscope.

Table 1.

Elemental composition of the studied sample at a temperature of 800 °C, according to EMPA.

Element	Atomic, wt%	Atomic, σ wt%	Atomic %	Oxide, wt%	Oxide formula
Aluminum	0.906	0.162	1.182	1.713	Al2O3
Silicon	8.760	0.599	10.973	18.739	SiO2
Calcium	6.843	0.361	6.007	9.574	CaO
Titanium	5.265	0.380	3.867	8.783	TiO2
Iron	2.645	0.493	1.666	3.402	FeO
Niobium	12.049	0.795	4.563	17.236	Nb2O5
Tantalum	15.738	1.474	3.060	19.217	Ta2O5
Uranium	17.755	1.068	2.624	21.336	UO3
Oxygen	30.039	1.199	66.057

Fig. 3.

EDX spectrum of the analyzed point of the studied mineral assemblage at a temperature of 800 °C.

These two postulates were used to develop a formula for the Ti-Ta-Nb-oxide phase based on the atomic weight percentage values for the elements’ contents: According to the study of²⁰, 1. The total coefficient for group B atoms is assumed to be equal to 2.00, and 2. The total coefficient of the anions is equal to 7.

Using the data of Table 1, this formula can be shown as follows, given that position A has a substantial cation deficit:

(Ca_0.51U_0.22Fe_0.14)_(0.87)(Ti_0.33Nb_0.39 Ta_0.26Si_0.93Al_0.10)_(2.01)(O_3.77OH_3.23)₍₇₎.

The addition of the hydroxyl group in the oxygen position compensates for the formula’s lack of positive charges. The Ti-Ta-Nb-oxide research sample was initially determined to be hydroxycalciobetafite based on the standards outlined in the work of²¹.

Phase analysis of the mineral assemblage sample

Figure 4 indicates the XRD spectrum of the original sample along with the spectra when it was annealed at the temperatures of 400 and 800 °C. The important phases that formed such celadonite, chamosite, and hydroxycalciobetafite are shown in the spectrum. Considering the oxide composition in Table 1, the majority of the aluminocilicates belong to a mineral from the mica group as celadonite. Recrystallization of the metamict structure at 400 °C and more distinctly at 800 °C gives rise to the characteristic maximums in the spectrum, the origin of which can unequivocally be attributed to hydroxycalciobetafite, in accordance with the probable opinion previously put forth on the identity of the Ti-Ta-Nb-oxide being studied (Atencio et al.²¹). It is interesting to note that the betafite phase forms rather early, whereas metamict betafite recrystallization takes place between 650 and 730 °C, as noted in the monograph²². Because of the early crystallization, it can be hypothesized that the study sample had enough crystalline domains left over from the first betafit phase to produce the matching epitaxial process with a low activation energy.

Fig. 4.

XRD analysis of the mineral assemblage at temperatures of 25, 400, and 800 °C. [Cel] celadonite, [Cha] chamosite, [Bet] hydroxycalciobetafite.

According to the XRD results, the only uranium-bearing phase was determined as the betafite mineral; therefore, without phase and isotopic interference, the isotopic characterization of metamict betafite can be accurately measured.

It is worth noting that the main phase of the natural analogue identified in this work, betafite, is completely consistent with the main phase of the sample studied in our previous work¹³.

The total ²³⁴U/²³⁸U activity ratios in the original betafite

A fundamental characteristic of any chain of radioactive decay is that the isotopes that are produced follow a secular equilibrium. At the level of the parent decay rate and the rate of the daughter half-life, radioactive equilibrium is created between the parent and daughter isotopes in the decay chain. In contrast, the secular equilibrium states that the ratio of the precursor radioisotope’s activities to those of its radiogenic nuclides is equal to unity. One can use the determined AR(²³⁴U/²³⁸U) ratio, i.e., isotope activity ratio, for the total uranium section as well as for the sections of U⁺⁴ and U⁺⁶ to reason about a mineral’s ability and chemical durability as natural analogues of matrices for immobilizing actinides, where it is affected by different factors of physical, chemical, and biochemical weathering. Thus, the first step is to ascertain the secular equilibrium between the ²³⁸U and ²³⁴U isotopes in the mineral being studied. The results of four experiments performed by radiochemical analysis, after complete dissolution of the betafite and separation of the total uranium section done in parallel, are shown in Table 2.

Table 2.

The total ²³⁴U/²³⁸U activity ratios in the original betafite.

N	AR(Σ) (234U/238U) (Bq/Bq)
1	1.005 0.012
2	1.002 0.013
3	1.000 0.007
4	1.001 0.006
Mean value	1.002 0.005

One standard mean square error is represented by the error margins in Table 2. In every instance, the sum rule for quantities of unequal accuracy measurements has been used to get the average activity ratio value and associated margin of error.

As presented in Table 2, the average activity ratio AR(Σ) of 1.002 ± 0.005 indicates that secular equilibrium between ²³⁸U and its decay product ²³⁴U has been effectively sustained over the geological timescale in the studied betafite. However, this equilibrium condition alone cannot be regarded as definitive evidence of betafite’s superior performance as a natural analogue for actinide immobilization. Supporting this view, previous investigations¹³ reported a mean AR(²³⁰Th/²³⁴U) of 1.305 and assessed the leaching kinetics of both ²³⁴U and ²³⁸U in the same sample. The comparable half-leaching times derived for these isotopes suggest that long-term retention is governed not merely by isotopic equilibrium but also by the intrinsic geochemical behavior of uranium under alteration conditions. Thus, the AR(²³⁴U/²³⁸U)(Σ) in mineral formed under natural conditions generally reflects a state of secular equilibrium. However, deviations from this equilibrium can be indicative of uranium mobilization or alteration processes. As demonstrated in a previous study¹⁰, the polycrase-bearing mineral assemblage exhibits a disrupted equilibrium, with an overall AR(Σ) value of 0.925 ± 0.016, and a markedly lower value of 0.770 ± 0.014 observed in the light-colored zones of polycrase. These reduced ratios suggest a depletion of the radiogenic ²³⁴U isotope in the altered domains, likely due to preferential leaching or recoil-induced loss. When ²³⁸U half-life and ²³⁴U half-leaching time are analyzed, it is clear that the AR(²³⁴U/²³⁸U) = 0.77 in the light section is exclusively due to leaching of ²³⁴U atoms. This is because the rate constant of leaching ²³⁴U atoms, l₄, is more than 20,000 times greater than the rate constant of radioactive decay of ²³⁸U, λ₈. Comparing the half-leaching times of ²³⁴U and ²³⁸U yields the same result: ⁴T_l/⁸T_l = 0.76, while the half-leaching durations of ²³⁸U and ²³⁴U are ⁸T_l and ⁴T_l, respectively, which nearly correspond to AR(²³⁴U/²³⁸U) = 0.77 for the light section. Thereby, the ²³⁴U and ²³⁸U leaching rate constants closely correlate to the degree of disruption of the secular equilibrium in Ti-Ta-niobate. Considering the AR(²³⁴U/²³⁸U)(Σ) = 1 in the currently studied betafite and the data related to the leaching of this mineral,: ⁴T_l/⁸T_l = 1, the above hypothesis is supported.

It is interesting that in pyrochlore¹², another mineral from the group of Nb-Ta-Ti-oxides of the types A₂B₂O₇, AR(²³⁴U/²³⁸U) = 0.99 ± 0.01. It seems that throughout the geological lifetime of group A₂B₂O₇ minerals, the parent and daughter isotopes of uranium have followed similar paths in the face of natural interactions.

Distribution of ²³⁴U and ²³⁸U in U⁺⁴ and U⁺⁶ sections of the original betafite

The distribution of ²³⁴U and ²³⁸U between uranium valence forms of U⁺⁴ and U⁺⁶ is given in Table 3. The mean AR(IV) and AR(VI) values are calculated from 3 experiments done in parallel. As seen from Table 3, the mean value of the ²³⁴U/²³⁸U activity ratios in the U(IV), 1.089 ± 0.016, is greater than the mean value of the AR(²³⁴U/²³⁸U) in the U(VI) section, 0.956 ± 0.007, in the original betafite under study. Since the uranium in the mineral was in a tetravalent state when it formed, we can conclude that the cause of the U(VI) in the mineral was the result of U(IV) autoxidation throughout the betafite’s geological history. In fact, the highest proportion of ²³⁴U is in the valence form of U(IV), and the highest proportion of ²³⁸U is in the U(VI) section. It indicates that the secular equilibrium in both valence forms of U⁺⁴ and U⁺⁶ of the betafite is disturbed. This observation aligns well with the widely recognized notion of natural fractionation of even ²³⁴U and ²³⁸U isotopes²³. In a mineral assemblage based on polycrase¹⁰, where the values of AR(IV) and AR(VI) have been found, 0.943 ± 0.017 and 0.903 ± 0.017, respectively, it shows that the sample of polycrase is distinguished by the missing of the radiogenic uranium isotope (²³⁴U) in both sections of U⁺⁴ and U⁺⁶.

Table 3.

The ²³⁴U/²³⁸U activity ratios in the U(VI) and U(IV) sections of the original betafite.

N	AR234U/238U (IV) (Bq/Bq)	AR234U/238U (VI) (Bq/Bq)	Relative content				AR(IV)/AR(VI) (Bq/Bq)
			Mass balance, %		Radiochemistry (mean values)
			P4	P6	U(IV)	U(VI)
1	1.091 0.017	0.957 0.014	32.1	67.9	40	60	1.140 0.024
2	1.087 0.008	0.954 0.012	34.6	65.4	–	–	1.139 0.017
3	1.088 0.045	0.956 0.012	33.3	66.7	30	70	1.138 0.049
Mean value	1.089 0.016	0.956 0.007	33.1	66.9	35	65	1.139 0.019

¹N is the number of parallel experiments.

²One standard mean square error is represented by the error margins provided here.

³AR(Σ) = AR(IV) × P₄ + AR(VI) × P₆.

Where AR(Σ) is the total ²³⁴U/²³⁸U activity ratio; P₄ and P₆ are the relative contents of the sections of U⁺⁴ and U⁺⁶, respectively; AR(IV) and AR(VI) are the 234U/238U activity ratio in the sections of U⁺⁴ and U⁺⁶, respectively.

The following formula can be used to determine the value of the U⁺⁴ and U⁺⁶sections: AR(Σ) = AR(IV)P₄ + AR(VI)P₆, where P₄ and P₆ are the relative contents of the U⁺⁴ and U⁺⁶ sections, so that P₄ and P₆ are attributed to ²³⁸U.

According to the data in Table 3, at room temperature:

Quantitative analysis performed at room temperature under the applied dissolution and uranium speciation protocol indicate that approximately 33% of the uranium occurs in the tetravalent [U(IV)] form, while 67% is present as hexavalent [U(VI)]. Given that uranium is initially incorporated into the mineral structure in the U(IV) oxidation state, the substantial proportion of U(VI) observed is most likely the result of gradual autoxidation of U(IV) throughout the long-term geochemical evolution of the betafite. This transformation highlights the long-term oxidative evolution of uranium within the mineral matrix under natural conditions. The oxygen coefficient 2 + X in the UO_2+X, obtained by the chemical shift of the Lα₁-line¹³ in the original betafite, (2.657) is virtually identical to the oxygen coefficient of the uranium in the U₃O₈ oxide, which is equal to 2.666. It is believed that the uranium in U₃O₈ has an oxidation state that combines penta- and hexavalent uranium (U₂O₅ + UO₃). Hence, according to the chemical shift of the Lα₁-line, U(IV) is not present in the original mineral composition. Based on these facts, we deduce that the U(IV) content of 33%, as determined by the radiochemical method, results from U(V) disproportionation when the mineral is treated with an HF solution, as indicated by the equation below:

The relative contents of U⁺⁴ and U⁺⁶ were ascertained by radiochemistry procedures at room temperature utilizing the ²³²U isotope as a standard radiotracer. It is evident from Table 3 that the values determined for the relative contents of U⁺⁴ and U⁺⁶sections using the mass balance equation and radiochemical tracing with ²³²U are nearly identical.

In the original polycrase belonging to the group of euxenite-like minerals¹⁴, ²³⁴U/²³⁸U activity ratios in the U(VI) have a mean value of 0.944 ± 0.005, which is lower than the AR (Σ) = 0.963 ± 0.004. Interestingly, the secular equilibrium between ²³⁴U and ²³⁸U isotopes is created in the U(IV) proportion of the original polycrase. In the U(IV) section, 32% of the uranium stabilizes, while in the U(VI) section, 68% does so. However, it appears that ²³⁸U and ²³⁴U have interacted with each other to preserve the natural secular equilibrium between them in the polycrase, even when a portion of them is oxidized and leached due to natural geological circumstances.

As mentioned above, in the betafite under study, the amount of U(IV) section obtained is related to U(V) disproportionation process when the mineral is treated with an HF solution because, according to the Chemical Shift of the Lα₁-line method, the oxygen coefficient 2 + X in the UO_2+X is equal to 2.657. However, in polycrase¹⁴, it is unlikely that U(IV) section is due to U(V) disproportionation process because the oxygen coefficient 2 + X in the UO_2+X calculated by the Chemical Shift of the Lα₁-line method is equal to 2.454, which indicates that a relatively large percentage of U(IV) has been preserved in the polycrase structure relative to the geological age of the mineral.

Natural analogues, due to their high geological age, are suitable references for predicting the long-term behavior of actinides such as ²³⁹Pu, ²³⁸Pu, ²⁴⁴Cm, ²⁴⁵Cm, ²⁴¹Am, etc., loaded in modeled matrices. Because obtaining independent information on the behavior of the parent and daughter actinides immobilized in matrices is not possible due to the long half-lives of these isotopes. Therefore, by examining the behavior of the parent and daughter isotopes of natural uranium and thorium elements in natural analogues, an optimal matrix for immobilization can be prioritized.

Conclusion

Natural analogues are suitable evidence for modeling the formulation of spent nuclear fuel actinide synroc matrices; hence, investigating the behavior of uranium isotopes in such natural analogues as traces of synthetic actinides provides essential information on the future behavior of waste actinides. The composition of the mineral assemblage (a Ti-Ta-Nb-oxide) investigated here has altered significantly under the hydrochemical processes so that the main phase of this mineral assemblage has been identified in our previous work as metamict betafite¹³. Since, due to phase diversity, the identification results of mineral assemblage through different methods occasionally do not match¹⁹, it was agreed that before isotopic characterization, a piece of the original sample should be separated, and the mineral assemblage phases should be identified. The results of SEM, EMP, and XRD analyses confirmed the main phase of the mineral assemblage as metamict betafite. The mean value of the ²³⁴U/²³⁸U activity ratios in the U(IV), 1.089 ± 0.016, is greater than AR(²³⁴U/²³⁸U) in the U(VI) section, 0.956 ± 0.007; it indicates that the secular equilibrium in both valence forms is disturbed. The relative content of U⁺⁴ and U⁺⁶ sections, 33% and 67%, respectively, using the mass balance equation and radiochemical, are nearly identical. Based on the results of the Chemical Shift of the Lα₁-line method in determining the chemical composition of uranium oxide (U₃O₈)¹³ in the original sample, it is not unlikely that the U(IV) content of 33% results from U(V) disproportionation when the mineral is treated with an HF solution under incongruent dissolution of the sample. A higher proportion of daughter uranium than the parent isotope is stabilized in the form of U(IV).

Author contributions

Mohammad Hosseinpour Khanmiri: Formal analysis, Methodology, Conceptualization, Writing—original draft, Project administration, Review & editing and Investigation.

Funding

This research received no specific grant from any funding agency.

Data availability

The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.

Declarations

Competing interests

The authors declare no competing interests.