Abstract
In the study presented here, the initial (that is, before the start of the process of natural hydrochemical influence) mineral formula of metamict polycrase in the composition of granite pegmatites of the Baltic Shield, applying an uranium natural halfleaching period, was calculated. To investigate the characteristics of immobilization of actinides in the studied polycrase, the absolute and relative uranium contents are compared with the corresponding uranium contents in the original betafite of the same deposit and age. It has been shown that over its geological history, betafite has lost up to 80% of its original uranium content. The proportion of uranium preserved in polycrase is twice as high. It is concluded that the difference in the relative content of uranium (27.3 wt% in polycrase and 31.6 wt% in betafite) cannot be the only reason for the complete oxidation of uranium in betafite, given that in polycrase 30% of uranium is preserved in the tetravalent state. It is more likely that the oxidation of uranium in betafite was primarily a result of the low ionicity of the chemical bonds compared to that in polycrase. This allows us to consider minerals of the euxenite group to be quite promising as matrix materials for the immobilization of actinides. At the same time, an opinion was expressed on the advisability of further comparative studies of Nb–Ta–Tioxides of the mineral groups AB_{2}O_{6} and A_{2}B_{2}O_{7} for their use at the final stage of the nuclear fuel cycle.
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Introduction
Since the commissioning of the world's first industrial nuclear power plant at Obninsk near Moscow in 1954, the nuclear industry has faced the growing problem of isolating from the biosphere the radionuclides generated during a nuclear fission chain reaction (during the operation of a nuclear reactor). The development of a reliable and costeffective method for the conservation and longterm safe storage of the highlevel waste (HLW) has become a key problem for modern nuclear energy.
At present, the concept of neutralizing highlevel radioactive waste is based on the idea of creating the multibarrier systems for their isolation from the biosphere in deep underground storage facilities (“burial grounds”). It is not a mistake to say that the most important component of multibarrier protection is the matrix, that is, the form of solidified waste in which HLW is included. Currently, two technological processes for the HLW immobilization in glass matrices have been implemented which are based on: (1) the borosilicate glass; (2) the aluminophosphate glass. However, due to the tendency of glasses to crystallize spontaneously (devitrify) at the elevated temperatures, it is impossible to guarantee the safety of the glass containing HLW over a long period of time. Crystalline matrices based on the artificial minerals, whose natural radioactive analogues have been preserved for hundreds of millions and even several billion years, have undeniable advantages over the glass. The choice of the optimal HLW matrices is associated with the need to meet the requirements for a chemical, mechanical, and radiation stability, on the one hand, and the technological and economic efficiency of their production, on the other. In the light of these requirements, a considerable attention has been paid to the study the minerals in the pyrochlore supergroup in recent decades. This is determined by several factors:

1.
The presence of natural analogues provides researchers with the necessary information about the longterm behavior of synthesized minerallike matrices in the natural environment. There are at least three stable natural minerals in the pyrochlore group, reflecting variations in the elemental composition in positions A and B^{1} and exhibiting the chemical resistance when exposed to natural fluids^{2,3,4}.

2.
The structure of pyrochlore has the feature that it can include a number of HLW radionuclides in the composition of group A cations, in particular U, Pu, and minor actinides^{5,6,7,8,9} which make the matrices based on the pyrochlore structure promising for isolating HLW from the biosphere.

3.
Minerals with the pyrochlore structure play an important role in the mechanism of nuclide immobilization in polyphase matrices of the SYNROC type. There are several modifications of SYNROC, including minerals of the pyrochlore supergroup^{10,11,12,13,14,15,16}. In this case, actinides are mainly concentrated in the structure of these minerals. The role of the other SYNROC components is to isolate the pyrochlore phase from contact with the liquid phase. Therefore, in particular, the actinide leaching rates from the polyphase ceramics are 10–100 times lower than those from the pyrochlore monophase.
However, there are reasons to think that the solidified forms of HLW based on the structures of euxenite group minerals can have no less high chemical resistance than the pyrochlore forms of HLW. This hypothesis was tested in^{17}, where the authors have studied the nuclear chemical effects in a polymineral composition based on the metamict polycrase, i.e., one of the minerals of the AB_{2}O_{6} group. In particular, the following results were obtained:

1.
The ratio of isotope activities AR(^{234}U/^{238}U) = 0.925, while in the most altered part of the mineral it drops to 0.77 in polycrase. In this case, AR(^{230}Th/^{234}U) > AR(^{230}Th/^{238}U). This means that the parent uranium exhibits a relative stability compared to the daughter isotope. The situation is different in pyrochlore. According to the data in^{18}, there is an equilibrium ratio of uranium isotopes in pyrochlore: AR(^{234}U/^{238}U) = 0.99 ± 0.01. At the same time, the activity ratios of the isotopes AR(^{230}Th/^{238}U) = 1.13 ± 0.03 and AR(^{230}Th/^{234}U) = 1.15 ± 0.03 can be considered equal within the experimental error. This means that the parent isotope in pyrochlore is also weakly bound to the metamict structure, as is the daughter isotope.

2.
An explanation for this can be found in a sharp change of the chemical state of uranium atoms in pyrochlore. According to the data in^{19}, all the uranium atoms in this sample underwent an oxidation to the U(VI) state and it is in the form of uranyl ions, which form their own phase. The same picture was observed in betafite: 95–100% of uranium was identified as the uranyl phase. The information about the samples: Pyrochlore comes from the VurriJarvi massif, North Karelia, age 517 million years; the origin of betafite is the Ilmensky mountains, Ural, age 250 million years.

3.
Unlike pyrochlore and betafite, polycrase, which is 1.8 billion years old, retains 30% of its uranium atoms in its original U(IV) valence form. In this case, the fraction of tetravalent uranium is characterized by the value of the ratio AR (^{234}U/^{238}U), which is close to the state of secular equilibrium. This indicates that tetravalent uranium in polycrase exhibits a relative resistance to the effects of natural waters and practically does not participate in isotope fractionation processes. The process of leaching radiogenic uranium occurs only after the transition of uranium to the pentavalent and hexavalent states. Thus, it can be expected that tri and tetravalent actinides included in the ceramic matrices based on the polycrase structure will be resistant to natural fluids.

4.
Under the selfirradiation, the change of uranium valence state (oxidation) in the pyrochlore mineral groups may facilitate the conversion of one mineral type to another. In this instance, the U(IV) integrated into the pyrochlore structure may convert to the mobile uranyl ion (UO2)^{2+} and complex (UO4)^{2−} in the conjunction with the radiation damage of the pyrochlorebased the ceramic waste form^{20}. Due to the selfradiation, the amorphization of minerals with the pyrochlore structures may be accompanied by the precipitation of certain amounts of actinides into distinct oxide phases and the disintegration of a single solid solution into many pyrochlore phases with varying the chemical compositions^{21}.
From the point of view of physical chemistry, the results obtained are easily explained since the structure of minerals in the AB_{2}O_{6} group is characterized by a higher degree of ionicity of chemical bonds compared to the structure of the A_{2}B_{2}O_{7} type. An indicator of this, in particular, is the thermal effects of the recrystallization of metamict minerals: for minerals of the AB_{2}O_{6} group, these values lie in the range of 40–85 J/g, while for the pyrochlore group, they are 125–210 J/g, depending on the degree of the amorphization of crystal structures^{22}. The activation energies for the recrystallization of metamict minerals of the AB_{2}O_{6} and A_{2}B_{2}O_{7} groups are 0.29–0.97 eV, which reflect the differences between the compounds with more and less ionic bonds, respectively.
Based on the discussed material, it can be assumed that, most likely, the euxenite group minerals and, in particular, polycrase are more stable forms of solidified waste compared to the pyrochlore supergroup minerals and, therefore, are more suitable to solve the problem of longterm immobilization of actinides. However, such a conclusion is premature because we lack knowledge of one fundamentally important parameter, namely, the content of uranium and, possibly, thorium in the corresponding mineral samples. In this case, we are discussing the original content of alpha emitters in the early stages of the geological history of Nb–Ta–Ti oxides rather than the modern ones. To get to the final conclusions about the advantages of AB_{2}O_{6} or A_{2}B_{2}O_{7} oxides, it is necessary to calculate the mineralogical formulas which correspond to the composition of minerals prior to the onset of natural leaching and compare the values of the relative contents of actinides found with each other. The methodology to calculate the corresponding formulas was developed in^{23} using a betafite sample, whose age and origin coincide with those for polycrase studied in^{17}. Therefore, the goal of this study is to calculate the initial mineralogical formula of polycrase (considered in^{17}) and compare the found content of actinides with the corresponding values for betafite (considered in^{23}). This will provide additional arguments about the advantages of one or the other form of solidified actinide waste.
Experimental
Sample description
The object of research in this work was a specimen of a metamict mineral (a TiTaNboxide of the type AB_{2}O_{6}) within a mineral association from the granite pegmatites found on the Nuolayniemi Peninsula, in Priladozhye (the Ladoga area), Karelia. In works^{17,24}, the main phase of this radioactive mineral association has been identified as polycrase. According to the Sm–Nd method of geochronology^{25}, these pegmatites were formed 1800 ± 30 million years ago and are among the pegmatites of the first postLadoga group. They contain a very large feldspar crystals—solid or sprouted with quartz. In the latter case, the socalled graphic pegmatite is formed. The pegmatites form large rectilinear veins 3–5 m thick, gradually wedging out in length and depth. Biotite forms large sabershaped plat in these pegmatites and sometimes large irregular clusters or nests. A characteristic feature of the described pegmatites is often in their zonal structure. They are also interesting because they contain relatively rare minerals such as xenotime, monazite, yttropyrochlor, ortite, and some others^{26}. The described structure of pegmatites suggests a significant isolation and protection of accessory minerals from the impact of natural fluids by silicate phases. The corresponding sample was taken from the Department of the Geology of Mineral Deposits (the Faculty of Geology) at St. Petersburg State University. The sample (laboratory code: wk7) has the following appearance: spotted color, from yellowishbrown to black; bright vitreous luster; semiconchoidal fracture. The sample was crushed in a metal mortar and separated into several granulometric fractions using a set of sieves.
SEM and EMP analysis
Scanning electron microscopy (SEM) and electron microprobe (EMP) analyses were performed utilizing a HITACHI TM 3000 scanning electron microscope with Oxford Instruments Swift ED3000 and a system of electron microprobe analysis. A phase image was acquired in the backscattered electron diffraction region (BSE), allowing for the identification of phases with different “average” atomic numbers (“compositional contrast”). After polishing, a layer of carbon was applied to the pieces. The analyses were carried out in a high vacuum with a 15 kV accelerating voltage. It is worth noting that all the experiments and analyses performed in this paper were carried out in the Department of Radiochemistry, utilizing equipment of the Center for Microscopy and Microanalysis of the Research Park at St. Petersburg State University.
Results and discussion
Calculating the kinetic parameters of uranium incongruent dissolution
It is known that the leaching of radionuclides from rocks and minerals is well described on the basis of the firstorder kinetics model developed by Latham and Schwartz^{27,28}. In accordance with this model, the leaching rates of ^{238}U and ^{234}U isotopes, denoted as c_{8} and c_{4}, respectively, are calculated by the following formulas:
where λ_{0} and λ_{4} are the rate constants for the nuclear decay of ^{230}Th and ^{234}U isotopes, respectively.
Therefore, to calculate the c_{8} and c_{4} values, it is necessary to experimentally determine the activity ratios (AR) of the ^{234}U/^{238}U and ^{230}Th/^{234}U isotopes in the studied samples of minerals, rocks, or soils. The halfleaching periods of ^{238}U and ^{234}U are calculated using the following expressions:
The activity ratios of uranium and thorium isotopes presented in^{17}, which are necessary to calculate the corresponding kinetic parameters, are given in Table 1. Throughout the radiochemical extraction, purification, and concentration of the isotope ^{230}Th, a radiotracer has not been used. Utilizing a method previously suggested in Ref.^{29}, the chemical yield was determined according to the magnitude of the ^{234}Th activity contained in the natural sample. The term "total sample" means the original polymineral composition as a whole, without dividing it into fractions. The heavy fraction isolated in the bromoform is represented mainly by grains of dark brown and black colors, which reflect that part of Ti–Ta–Nboxide was least affected by the environment. The light fraction consists of quartz crystals covered with a thin yellow–brown film of calciobetafite, which was formed from the destruction products of polycrase during a sample annealing at the temperature of 1000 °C.
Based on the data listed in Table 1, the authors of^{17} have calculated the leaching rate constants and the halfleaching of uranium for various fractions of the studied sample, which are shown in Table 2.
It should be noted that the halfleaching period of the ^{238}U isotope in the heavy fraction is 2.4 times longer than that in the light fraction. For the ^{234}U isotope, this ratio is even higher. This is mainly explained by the fact that 68% of the uranium in the heavy fraction remains in the U(IV) state, while tetravalent uranium is completely absent in the light fraction.
Comparison of uranium and calcium leaching rates
It is quite clear that, in order to reconstruct the original mineral formula of polycrase, it is necessary to know the rate of uranium leaching as well as the corresponding kinetic characteristics of other cations of group A^{19,23}. To obtain this information, an EMP analysis was performed at five points on one of the grains of the studied sample, as shown in Fig. 1.
In Table 3, the content of elements (atomic, wt%) is presented in each of the five points of the grain.
The chemical formulas for the corresponding phases of polycrase can be represented as follows:

Spectrum 1: (Ca_{0.17}Y_{0.38}U_{0.31})_{(0.86)} (Nb_{0.93}Ta_{0.03}Fe_{0.19}Si_{0.54}Ti_{0.31})_{(2.00)}(O_{5.49}OH_{0.51})_{(6)}.

Spectrum 2: (Ca_{0.15}Y_{0.41}U_{0.24})_{(0.81)} (Nb_{0.93}Ta_{0.01}Fe_{0.16}Si_{0.55}Ti_{0.35})_{(2.00)}(O_{5.27}OH_{0.73})_{(6)}.

Spectrum 3: (Ca_{0.14}Y_{0.37}U_{0.22})_{(0.73)} (Nb_{0.87}Ta_{0.03}Fe_{0.25}Si_{0.55}Ti_{0.30})_{(2.00)}(O_{4.92}OH_{1.08})_{(6)}.

Spectrum 4: (Ca_{0.13}Y_{0.41}U_{0.20})_{(0.74)} (Nb_{0.94}Ta_{0.06}Fe_{0.22}Si_{0.44}Ti_{0.34})_{(2.00)}(O_{5.07}OH_{0.93})_{(6)}.

Spectrum 5: (Ca_{0.12}Y_{0.38}U_{0.17})_{(0.67)} (Nb_{0.89}Ta_{0.04}Fe_{0.17}Si_{0.52}Ti_{0.38})_{(2.00)}(O_{4.82}OH_{1.18})_{(6)}.
The obtained mineral formulas illustrate the gradual decrease in the content of uranium and calcium from point 1 to point 5. Based on these data, in Table 4, the ratios of the leaching rates (L.r.) of uranium and calcium were calculated. The mean value of the ratio U L.r./Ca L.r. = 1.19 ± 0.03. It is noteworthy that the same value has been obtained for betafite, 1.19 ± 0.02^{23}.
To expand the collection of experimental data on the elemental composition of the studied sample and on the corresponding leaching rates, EMP analysis of one more grain of the mineral composition was performed. The analysis points are shown in Fig. 2, whereas the data in Table 5 indicate the elemental composition. Turning to the mineral formulas of polycrase calculated below at each of points from 1 to 8, then, one can state that the yttrium content varies widely in contrast to the data in Table 3 and the corresponding mineral formulas of spectra 1–5. It is quite clear that this is the result of endogenous rather than hydrochemical processes. Therefore, to compare the contents of uranium and calcium, we chose only those points, in which the content of yttrium was close. These points are listed in Table 6.
The chemical formulas for the corresponding phases of polycrase can be expressed as follows:

Spectrum 1: (Ca_{0.27}Y_{0.15}U_{0.12})_{(0.54)} (Nb_{0.35}Ta_{0.17}Fe_{0.13}Si_{0.96}Ti_{0.39})_{(2.00)}(O_{3.86}OH_{2.14})_{(6)}.

Spectrum 2: (Ca_{0.27}Y_{0.16}U_{0.10})_{(0.53)} (Nb_{0.31}Ta_{0.08}Fe_{0.23}Si_{0.84}Ti_{0.54})_{(2.00)}(O_{3.58}OH_{2.42})_{(6)}.

Spectrum 3: (Ca_{0.19}Y_{0.25}U_{0.09})_{(0.53)} (Nb_{0.41}Ta_{0.09}Fe_{0.17}Si_{0.73}Ti_{0.60})_{(2.00)}(O_{3.82}OH_{2.18})_{(6)}.

Spectrum 4: (Ca_{0.19}Y_{0.22}U_{0.08})_{(0.49)} (Nb_{0.39}Ta_{0.10}Fe_{0.17}Si_{0.74}Ti_{0.60})_{(2.00)}(O_{3.68}OH_{2.32})_{(6)}.

Spectrum 5: (Ca_{0.20}Y_{0.22}U_{0.06})_{(0.48)} (Nb_{0.38}Ta_{0.07}Fe_{0.23}Si_{0.74}Ti_{0.58})_{(2.00)}(O_{3.52}OH_{2.48})_{(6)}.

Spectrum 6: (Ca_{0.16}Y_{0.25}U_{0.06})_{(0.47)} (Nb_{0.41}Ta_{0.08}Fe_{0.19}Si_{0.72}Ti_{0.66})_{(2.00)}(O_{3.85}OH_{2.15})_{(6)}.

Spectrum 7: (Ca_{0.21}Y_{0.19}U_{0.05})_{(0.45)} (Nb_{0.45}Ta_{0.12}Fe_{0.14}Si_{0.67}Ti_{0.62})_{(2.00)}(O_{3.62}OH_{2.38})_{(6)}.

Spectrum 8: (Ca_{0.13}Y_{0.23}U_{0.05})_{(0.41)} (Nb_{0.42}Ta_{0.04}Fe_{0.18}Si_{0.76}Ti_{0.60})_{(2.00)}(O_{3.43}OH_{2.57})_{(6)}.
As follows from the data in Table 6, the average value of the U/Ca leaching rate ratio is 1.30 ± 0.19. However, for further calculations, we will use the previously obtained value of 1.19 ± 0.03, which is characterized by a smaller standard deviation. It is quite obvious that the influence of “original compositional heterogeneity”^{30} prevents obtaining correct results. This effect is reflected not only in the content of yttrium but also in the content of elements of group B. The mineral formulas presented in spectra 1–8 convincingly confirm this.
Calculation of the original (initial) mineral formula of polycrase
Based on the data on the individual behavior of atoms in group A during hydrochemical impacts on the mineral, let us turn to the calculation of the chemical formula of polycrase at the early stages of its geological history according to the methodology employed in Ref.^{23}. First consider the formula for polycrase at point 1, the elemental composition of which is shown in Table 3. At present, as we have seen, the mineral formula looks like this:
First of all, it is necessary to determine the sum of the charges of atoms in groups A and B. The charge of atoms in group B is 8.77. Therefore, in group A, the charge should be 3.23. Thus, our task comes down to selection of the time interval at which the sum of the charges of atoms in group A becomes equal to 3.23. Having gone through several options, we come to the conclusion that the time when the charge of atoms in group A was close to 3.23 lies in the interval (0.45 ÷ 0.46)T_{1/2}. The number of atoms in group A may be determined using the value of t = 0.453T_{1/2}. Since 2^{0.453} = 1.36888 and the uranium content during this time decreased by 1.36888 times. 0.453·T_{1/2} years ago, the coefficient of the uranium atom in group A was equal to: 0.31·1.36888 = 0.4243. The content of calcium decreased by 1.36888/1.19 = 1.15 times; hence, the previous value was 0.17·1.15 = 0.1955. Thus, the sample corresponding to spectrum 1 (Table 3), (0.45 ÷ 0.46)T_{1/2} years ago had a mineral formula close to the following:
Next, we perform similar calculations for spectrum 5 (Table 3). The modern content of elements is reflected in the corresponding mineral formula:
However, the coefficients of the calcium and uranium atoms in group A indicate a more significant hydrochemical change in the corresponding polycrase grain compared to the phase at point No 1. Since the charge of atoms in group B is 8.76, the charge in group A should be 3.24. (Note that both values are very close to those which characterized the spectrum No 1.) Given that the degree of the change in the composition of the mineral at point No 5 is significantly greater than at point No 1, the exposure time of the liquid phase is much longer than at point No 1. Therefore, we use the duration t = 1.2·T_{1/2} for our calculations. Then 2^{1.2} = 2.297. Next, the coefficients of calcium and uranium atoms are calculated: Ca: 0.12·2.297/1.19 = 0.2316. U: 0.17·2.297 = 0.3905. Rounding up to the second decimal place, we obtain the original phase formula at point 5. It looks like this:
In terms of the number of atoms, it corresponds exactly to the formula for yttrium polycrase, but the charge of atoms in group A turned out to be 3.16 (instead of 3.24). Thus, it is necessary to increase the charge in group A by 0.08. To do this, we replace 0.04 calcium atoms with 0.04 uranium atoms. As a result, we derive to the final initial polycrase formula in the phase corresponding to point No 5:
A comparison of formulas (I) and (II) shows that they almost coincide in the coefficients of Ca and U atoms in group A, although the first refers to the least leached phase and the second one to the most altered one. Thus, we can conclude that the original polycrase formula in the entire given grain is the only one, as reflected by formulas (I) or (II). From a methodological point of view, this is rather important conclusion. Below we explain what it means. If we did not set a goal to calculate the initial polycrase formula but only tried to determine the periods of uranium halfleaching at different points of the grain, then we would inevitably encounter the following dependence: the rate constant c8 in passing from point 1 to point 5 would gradually increase (due to an increase in the ^{230}Th/^{234}U ratio) and, accordingly, the uranium halfleaching period would decrease. In reality, in view of the complete identity of the composition of polycrase, we are not talking about different kinetic parameters. We can only talk about different durations of contact t of polycrase with the liquid phase at different points. At the point 1 t = (0.45–0.46) T_{1/2}; at the point 5 t = 1.2 T_{1/2}.
But obviously, the question arises: what the halfleaching period should be used for calculations, since in Ref.^{17} three halfleaching periods of uranium from polycrase were determined: 2.59∙10^{5}, 4.34∙10^{5}, and 6.14∙10^{5} years for the light, mixed, and heavy fractions of the studied sample, respectively (see Table 2). There is only one essential criterion for the selection: the analysis of the initial mineral formulas of phases 1 and 5. We will pay attention to the content of silicon in them. The light fraction, being the most destroyed, consists mainly of silicon, oxygen, and iron (the content of polycrase in the light fraction is 24 times less than that in the heavy fraction). The content of silicon in the heavy fraction does not exceed 4.79 wt%, including the silicon contained in celadonite. (Wt% of the celadonite phase in the heavy fraction is 7.3%.) The relative content of silicon in the formulas of phases 1 and 5 is 3.91and 4.08 wt%, correspondingly. Therefore, points 1–5 are precisely located in the heavy fraction of the sample under study, and for the corresponding calculations, we can use quite reasonably the value T_{1/2} = 614 thousand years and take the duration of the impact of natural fluid on the phase at point 5 to be approximately equal to 740 thousand years. On the other hand, the beginning of the betafite leaching process, according to^{23}, refers to the time interval 690–770 thousand years ago. The fact that the values of these time intervals are quite close to each other should not surprise us since both TiTaniobates under study come from the granitic pegmatites of the Baltic Shield, geographically located on the Nuolayniemi Peninsula, Priladozhye. The age of the minerals is also approximately the same, about 1800 million years.
The rhetorical question that arises naturally in this situation can be formulated as follows: the age of minerals is 1800 million years. Why did the process of hydrochemical action begins only in the last million years of the existence of minerals? Until that time, there was no rain on the earth; did gravitational or pressure waters appear in the earth’s crust? What emergency could have happened in the area of Lake Ladoga 700–800 thousand years ago to initiate suddenly an intense interaction “water—rock”?—We do not exclude a possibility that the answers to these questions may lie on a different level. As we have seen, the mathematical model for calculating the original mineral formula of polycrase is based on the hypothesis of uranium leaching in accord to the firstorder kinetics. (We exclude from consideration the unlikely process described by zeroorder kinetics, the introduction of any significant amount of uranium into the accessory minerals of pegmatites^{31}.) However, for the calculation, it is sufficient to use only the T_{1/2} symbol without indicating a specific value of the halfleaching period since, as can be assumed, the cumulative effect of hydrochemical exposure manifested itself and accumulated at the different rates with the different intensities in different periods of the geological history of pegmatites in accordance with the evolution of rock porosity or various environmental conditions^{32}. When the impact of natural fluids on the pegmatite minerals is weakened or there is a long pause in this impact under changed geological conditions, the disturbed secular equilibrium between the nuclides of the uranium series is fully or partially restored. It cannot be ruled out that over a period of time close to 2 billion years, the alternating process of “equilibrium disturbance—equilibrium restoration” is repeated more than once. The activity ratios of ^{230}Th/^{234}U and ^{234}U/^{238}U nuclides observed by us, both in betafite and polycrase, reflect the leaching processes over the last 1–1.5 million years and do not provide information about the real halfleaching period of uranium isotopes. Note that the possible deviation of the ^{230}Th isotope content from the equilibrium one is not so much the result of its leaching as the consequence of the leaching of the parent ^{234}U nuclide.
After this remark, let us turn to the main subject of this work, namely, the comparison of oxides of the types AB_{2}O_{6} and A_{2}B_{2}O_{7} as possible matrix materials for the immobilization of actinides. Recall that polycrase retained in its composition at least 30% of uranium in the tetravalent state. In betafite, according to^{23}, all the available uranium was oxidized to the states of U^{5+} and U^{6+}, while losing any differences in properties between the parent and daughter isotopes. For the matrix, such changes can have catastrophic consequences. Therefore, the question arose about the uranium content that polycrase and betafite had at the time of their formation. To answer this question, we need to compare the relative content of uranium in betafite, which was described in^{23} by formula (XVI):
and that in polycrase according to this work, formulas (I) and (II):
We will make the necessary calculations of the molar masses of minerals (in grams).
Polycrase (point 1):
The atomic mass of group A is 141.775 g. The atomic mass of group B is 132.404 g. The mass of oxygen is 96 g. The molar mass of the mineral is 370.179 g. The mass fraction of uranium in polycrase (point 1) is:
Polycrase (point 5):
The atomic mass of group A is 143.75 g. The atomic mass of group B is 132.17 g. The mass of oxygen is 96 g. The molar mass of the mineral is 371.92 g. The mass fraction of uranium in polycrase (point 5) is:
The average value of the relative content of uranium in polycrase is 27.27 wt%.
Betafite:
The atomic mass of group A is 212.6766 g. The atomic mass of group B is 142.60 g. The mass of oxygen is 112 g. The molar mass of the mineral is 467.2766 g. The mass fraction of uranium in polycrase (point 5) is:
Thus, the mass fraction of uranium in betafite is actually higher than that in polycrase. And if, in terms of relative content, this difference is small (~ 4.3%), then in absolute terms, the capacity of betafite with respect to uranium is almost one and a half times higher than the capacity of polycrase: 147.6 g versus 100 g. Therefore, we must give a positive answer to the question posed at the beginning of the article: yes, the effect of complete oxidation of uranium in betafite can be associated with a higher content of uranium in it. But still, such an answer is largely formalized. It basically means that the reasoning scheme may be different taking into account the specific contents of uranium in the compared Nb–TaTi oxides. Indeed, with a uranium content of 27.3 wt%, polycrase retained 30% of uranium in the U(IV) form. Since the uranium content in betafite is 4.3 wt% higher, betafite would have to retain a smaller amount of uranium in the U(IV) form, for example, 25%, 20%, or 15%, and such a result would be understandable. However, it is difficult to explain why the difference of 4.3 wt% in the relative content of uranium has played such a dramatic role in the chemical fate of uranium in betafite. We cannot reject the assumption that the effect of the complete uranium oxidation in betafite is still based on the lower degree of ionicity of the chemical bonds Nb–O in betafite compared to polycrase and not on the difference in uranium content. As a result, more serious changes in the atomic and electronic subsystems of a mineral in metamictization processes can be expected. Of course, significant hydrochemical changes in betafite are also associated with this process: under the action of the natural fluids, betafite lost 116.6 g of its initial uranium content, which is almost twice as much as the corresponding losses in polycrase. The basic differences between the metamict polycrase (AB_{2}O_{6}) and metamict betafite (A_{2}B_{2}O_{7}) as matrix materials for actinide immobilization are shown schematically in Fig. 3.
Conclusion
The consequences of introducing spent nuclear fuel actinides into the biosphere can be controlled to a large extent by examining natural analogues as the matrix of actinides. Calculating the initial mineral formula of metamict polycrase and its comparison with the initial mineral formula of metamict betafite is widening our choice in prioritizing the appropriate matrix. Examining the initial formulas obtained for the metamict polycrase (AB_{2}O_{6}) and metamict betafite (A_{2}B_{2}O_{7}) through a model designed based on the natural halfleaching period of uranium showed that polycrase, compared to betafite, had the ability to maintain its original uranium content twice as much in the face of the natural processes throughout the geological history. On the other hand, almost all tetravalent uranium in betafite has been oxidized, while in polycrase, 30% of U(IV) has been preserved in the mineral composition, which is another significant advantage of polycrase. Also, the isotopic ratiometric in the mentioned minerals gives the result that, the relative to the daughter isotope, the parent uranium in polycrase exhibits a relative stability compared to betafite. However, it is difficult to unconditionally prefer a Nb–Ta–Ti oxide for this purpose. The only circumstance that makes it possible to indicate a certain perspective of polycrase is that such parameters as the “mass” of the nuclide or the “capacity” of the matrix in relation to the mass fraction of the nuclide during actinide immobilization do not act as critical parameters. The specific activity of actinide in the matrix and the requirement for the radiation resistance in materials come to the fore. In such a situation, the oxides of the AB_{2}O_{6} group have an unconditional advantage over the oxides of the A_{2}B_{2}O_{7} group. Nevertheless, we believe that further studies of oxides of the AB_{2}O_{6} and A_{2}B_{2}O_{7} types as matrix materials for actinide immobilization remain relevant.
Data availability
The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.
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Acknowledgements
We are grateful to the professors and staff of the Radiochemistry Department of St. Petersburg State University.
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Mohammad Hosseinpour Khanmiri: Methodology, Formal analysis, Writing – original draft, Project administration. Roman Bogdanov: Conceptualization, Methodology, Writing – original draft, Investigation. Elena Puchkova: Investigation. Anatoly Titov: Investigation. Ali Yadollahi: Review & editing.
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Hosseinpour Khanmiri, M., Bogdanov, R., Puchkova, E. et al. On the issue of comparing the immobilization characteristics of matrix materials based on Nb–Ta–Tioxides of the types AB_{2}O_{6} and A_{2}B_{2}O_{7}. Sci Rep 14, 17992 (2024). https://doi.org/10.1038/s41598024689846
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DOI: https://doi.org/10.1038/s41598024689846
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