Composite Forms in the REE₂O₃–ZrO₂–TiO₂ System for Minor Actinides (Am, Cm) and REE Immobilization

Abstract

The choice of efficient methods for the immobilization of high-level waste (HLW) resulting from the reprocessing of spent nuclear fuel (SNF) is an important scientific and practical task. The current policy of managing HLW within a closed nuclear fuel cycle envisages its vitrification into borosilicate (B-Si) or alumina–phosphate (Al-P) glasses. These wasteforms have rather limited waste loading and can potentially impair their retaining properties on devitrification. The optimal solution for HLW immobilization could be separating radionuclides into groups using dedicated capacious durable matrices. The phases of the Nd₂O₃–ZrO₂–TiO₂ system in this respect are promising hosts for the REE (rare earth elements: Nd, Ce, La, Pr, Sm, Gd, Y) –MA (MA: Am, Cm) fraction of HLW. In this manuscript, we present data on the composition of the samples analyzed, their durability in hot water, their behavior under irradiation, and their industrial manufacturing methods.

1. Introduction

Over the past 65 years, the concentration of CO₂ in the Earth‘s atmosphere has increased by a quarter–from 315 ppm in 1958 to 420 ppm in 2023—and continues to grow. By March 2024, its level had increased by another 5 ppm, the largest jump in the entire history of observations. A similar concentration of CO₂ in the air was reached 3–5 million years ago, when the temperature was higher by 2–3 °C, and the sea level was 10–20 meters higher than today. The increase in the amounts of climate-active gases is caused by the combustion of fossil fuels and transport. A huge contribution to environmental degradation is made by particulate matter, up to 2.5 μm in size, which causes up to 9 million premature deaths per year worldwide [1,2,3]. Low-carbon energy plays a key role in combating air pollution and global warming due to greenhouse gases [4,5]. Along with renewable sources, this also includes nuclear energy [6]. By 2026, the share of low-carbon generation in the world will reach 50%, with about a quarter of it coming from nuclear power plants [7]. The contribution of nuclear power to achieving carbon neutrality should increase by 2050, with the total capacity of nuclear power plants amounting to 890 GW(e) in the high and 458 GW(e) in the low scenario, compared to the current 369 GW(e), which is the higher of former estimations [5]. Nuclear power is statistically the cleanest source of energy in terms of CO₂ emissions and the safest along with wind and solar power, compared with coal, oil, gas, biomass, and hydropower (Figure 1).

In November 2023, the European Parliament categorized nuclear energy (NE), along with 15 other technologies, as a “clean” technology. In December 2023, at the 28th UN Climate Conference (COP28, UAE), 22 countries, including the United States, Canada, United Kingdom, France, Japan, and South Korea, committed to tripling the capacity of nuclear power plants by 2050 compared to 2020. It is expected that the share of nuclear generation in Russia will increase to 25% by 2045 from the current 20%. Investments in nuclear energy are growing worldwide; in many countries, they are either close to or have exceeded the costs of constructing hydrocarbon-fueled power plants [9]. The implementation of these plans may be hampered, however, by a shortage of uranium and the problem of handling high-level waste (HLW). Based on the growth in the capacity of nuclear power plants and under the condition of an open fuel cycle with the disposal of spent nuclear fuel (SNF), their operation will require 2–3 times more uranium than current systems, i.e., 130–200 thousand t per year. This threatens to result in the rapid depletion of available natural uranium resources if the basis of nuclear energy in the future continues to be only thermal neutron reactors and light water reactors (LWRs) [10]. These problems are solved by the transition to a two-component nuclear power system with thermal and fast neutron reactors with a closed nuclear fuel cycle–that is, the reprocessing of SNF, involving the separation of fission products, U and Pu, from HLW, which are in demand for nuclear power generation, as well as minor actinides (Am, Cm), which pose the greatest environmental hazard [11,12,13,14,15].

There are two ways of handling long-lived actinides and fission products [15,16]. The first is to separate them from HLW and then irradiate them with neutrons for transmutation into stable or short-lived isotopes. However, the implementation of this method encounters great technical difficulties and requires enormous costs [17]. The other method involves incorporating radionuclides into highly stable matrices and disposing of them [18,19,20,21,22,23,24]. In this case, the safety of HLW disposal facilities will be ensured by the presence of a bentonite-based sorption buffer, a corrosion-resistant container, and a robust HLW matrix. An additional barrier is the geological environment due to the low solubility of radionuclides in groundwater and their sorption by rocks around the disposal facility, as well as the slow flow of waters that carry radionuclides. In accordance with international standards [20] the preferred strategy for the management of radioactive waste is to contain it (i.e., to confine the radionuclides within the waste matrix, the packaging and the disposal facility) and to isolate it from the biosphere.

The current practice of isolating HLW involves its immobilization in borosilicate (B-Si) or alumina–phosphate (Al-P) glasses produced in electric furnaces or by induction melting [15,25,26,27,28,29,30,31,32,33,34,35,36,37]. The advantages of these glasses include the proven production technology and the ability to include many radioactive and stable isotopes. Their disadvantages include a low HLW load (5–20 wt.%), where the main part is made up of stable isotopes (REEs, Zr, Mo), whilst the dry residue of liquid HLW from the reprocessing of LWR spent nuclear fuel contains up to 4 wt.% actinides and 50 wt.% fission products, most of which are stable [27,38]. In addition, the glasses can crystallize over time, with the possible formation of more soluble phases; moreover colloids with high migration in the geological environment are formed when they come into contact with groundwater.

Compared with neutron-activated and fission products, such as Cl-36, Se-79, Tc-99, and I-129, the actinides are more dangerous as alpha emitters, with dose coefficients much higher than beta emitters, and because they can form colloids which will migrate in the geological environment as quickly as radionuclides in the anionic form. The partitioning of HLW will allow actinides to be included in the most durable and thermodynamically stable crystalline matrices which might be components of integral composite systems containing both crystalline and vitreous wasteforms [25,26,27,28,37,39,40]. When selecting potential materials, phases with high loading in respect of the waste are firstly identified, then their corrosion and radiation resistances are studied, and finally the possibility of their remote industrial production is assessed.

We have considered possible crystalline matrices for immobilization of the REE–minor actinides (Am, Cm) fraction. The size of the cation (Am, Cm)³⁺ is close to Nd³⁺; therefore, the Nd₂O₃–ZrO₂–TiO₂ system is of interest, which contains (Zr,Nd)O_2−x and Nd₂(Zr,Ti)₂O₇ with the fluorite or pyrochlore structure, Nd₂Ti₂O₇ of the perovskite type, as well as phases Nd₄(Ti,Zr)₉O₂₄ and Nd₂TiO₅, which have no natural structural analogues. This analysis was carried out based on the literature data and the results of our own studies. The latter were mainly published in Russian journals and are little known to the world scientific community.

2. Separation of HLW for Groups of Radionuclides Isolation

The PUREX process (extraction of Pu and U) is the basis of SNF reprocessing; it can be supplemented by operations to extract other elements, including trivalent REE and minor actinides. The TRUEX, TODGA, and DIAMEX techniques allow for the extraction of REE, Am, and Cm; they have already been tested on real HLW [41,42,43,44,45,46,47]. Both the proportion of the REE–actinide fraction in SNF and the ratio of REE and actinides in it depend on the fuel composition, burnup, and storage time of SNF before reprocessing. The burnup of LWR reactor fuel reaches 45 GW × day per t; in the future, it is expected to be increased to 55 GW × day per t [42,48]. As the burnup increases from 30 to 45 GW × day, the REE content in a ton of SNF increases from 10.2 to 13.9 kg, while the sum of Am and Cm increases from 0.52 to 0.87 kg [41,49]. A ton of SNF with a burnup of 60 GW × day contains 800 g Am (63% ²⁴¹Am, 37% ²⁴³Am), 150 g Cm (90% ²⁴⁴Cm, 8% ²⁴⁵Cm, 1% each of ²⁴³Cm, and ²⁴⁶Cm), and about 20 kg of REEs. With an increase in SNF burnup to 70 GW × day, the Am content in a ton of SNF will exceed 1 kg, and the amount of REE will be 23 kg (see

Table 1. The content of Am, Cm, and REEs in SNF (after 5 years of storage) and the proportion of Am and Cm in the mixture.

Element, g/t of SNF	Nuclear Fuel Burnup, GW × Day per t of SNF
	0.5	20	33	40	51	60	70
Σ Am	0.5	130	370	475	638	785	1080
Σ Cm	n.d.	n.d.	20	N.d.	78	135	n.d.
Σ REE	220	7200	11,200	~15,000	n.d.	~20,000	~23,000
(Am + Cm): REE, %	0.2 *	1.8 *	3.4	3.1 *	n.d.	4.4	4.5 *

Note: n.d.—no data, * excluding curium.

, with additional details in [50,51,52]).

During the storage of SNF, the composition of the REE–actinide fraction changes due to an increase in the proportion of ²⁴¹Am as a result of the decay of short-lived ²⁴¹Pu (half-life, T½ = 14 years) and a decrease in the proportion of ²⁴⁴Cm (T½ = 18 years). An increase in the storage period of SNF from 1 year to 30 years increases the ratio ²⁴¹Am/²⁴³Am from 1.3 to 12.1, and the proportion of actinides in the REE–MA mixture increases from 2% to almost 9% (

Table 2. Am and Cm isotopes (g/t) in SNF with a burnup of 45 GW × day per t and the proportion of MA in the REE–MA mixture depending on the SNF storage time.

Radionuclide or Mixture	After 1 Year	After 5 Years	After 30 Years
241Am	135	407	1272
243Am	105	105	105
Σ Am (ratio 241Am/243Am)	240 (1.3)	512 (3.9)	1377 (12.1)
242Cm	3.8	0.1	<0.01
244Cm	35.3	30.3	11.6
245Cm	2.2	2.2	2.2
243,246,247,248Cm	0.6	0.6	0.6
Σ total Cm	41.9	33.1	14.4
Σ MA (MA = Am and Cm)	281.9	545.1	1391.4
Cm/MA, %	14.9	6.1	1.0
MA/(REE * + MA), %	1.8	3.5	8.5

* A ton of SNF with a burnup of 45 GW × day contains about 16 kg of rare earth elements.

, with additional details in [52]).

Among the REEs in SNF and HLW, the light elements of the cerium group with a large cation radius (from La to Sm) dominate, the content of which decreases in the following sequence: Nd (about 39% of all REE), Ce (23%), La (12%), Pr (10%), Sm (8%), Y (4%), and 4% Eu, Gd, and Pm. Their isotopes are stable or have long half-lives and can be considered as stable, for example ¹⁴²Ce (5.0 × 10¹⁶ years), ¹⁴⁴Nd (2.3 × 10¹⁵ years), ¹⁴⁷Sm (1.1 × 10¹¹ years), and ¹⁵⁰Nd (6.7 × 10¹⁸ years) [53]. Only a few isotopes have a short half-life, i.e., 285 days (¹⁴⁴Ce), 2.62 years (¹⁴⁷Pm), 4.76 (¹⁵⁵Eu), 8.6 (¹⁵⁴Eu), and 90 years (¹⁵¹Sm). REE phases, especially containing Nd, are promising as matrices for the REE–actinide fraction, since it dominates among REEs (40% of their total content) in SNF and HLW, and the radii of Nd³⁺ and REE–MA cations coincide, while in terms of coordination number (c.n.), VIII are equal to 1.09 Å [54]. Let us consider the Nd₂O₃–ZrO₂–TiO₂ system, focusing first on the edge parts, and then on the entire three-component diagram.

2.1. ZrO₂–TiO₂ System

There are oxides of the composition (Ti,Zr)O₂ (tetragonal structure of rutile), (Zr,Ti)O₂ (depending on the temperature, monoclinic analogue—mineral baddeleyite or tetragonal) and ZrTiO₄ (analogue—mineral shrilankite) [55]. The content of REEs in them is low and, therefore, they are not interesting as matrices for minor actinides. However, such phases are often found in experimentally obtained samples along with titanates and zirconates of REEs. Furthermore, for simplicity and convenience, we will use their abbreviated names: Z for ZrO₂, T in the case of TiO₂, ZT instead of ZrTiO₄, and so on.

2.2. Nd₂O₃–ZrO₂ System

For the immobilisation of actinides, zirconate Nd₂Zr₂O₇, NZ with a pyrochlore structure, and oxide (Zr_2−xNd_x)₂O_2−0.5x with a fluorite structure are promising, although the latter contains less REE–actinide fraction than pyrochlore (20 and 60 wt.%, respectively). The pyrochlore field is at its maximum at 1500 °C [56], and above 2200 °C it transforms into cubic oxide (Zr_2−xNd_x)₂O_2−0.5x. These phases are also considered as inert matrix fuel for the transmutation of actinides, for example Am [16,57,58,59].

2.3. Nd₂O₃–TiO₂ System

In this system, the greatest number of compounds—potential REE–MA hosts—are formed, including Nd₂TiO₅, Nd₂Ti₂O₇, Nd₄Ti₉O₂₄, and Nd₂Ti₃O₉ [60]. Replacing Nd₂O₃ and TiO₂ with N and T, the phase formulas can be written as follows: NT (Nd₂TiO₅), NT₂ (Nd₂Ti₂O₇), N₂T₉ (Nd₄Ti₉O₂₄), and NT₃ (Nd₂Ti₃O₉). The most important in this system (

Table 3. Invariant points and phase reactions in the Nd₂O₃–TiO₂ and La₂O₃–TiO₂ systems.

Nos.	Reaction Scheme	T, K (o C)	Reaction Scheme	T, K (°C)
1	P ↔ T + N2T9	1716 (1443)	P ↔ T + L2T9	1719 (1446)
2	P + NT3 ↔ N2T9	1728 (1455)	P + LT3 ↔ L2T9	1730 (1457)
3	P + NT2 ↔ NT3	1773 (1500)	P + LT2 ↔ LT3	1933 (1660)
4	NT3 ↔ N2T9 + NT2	1472 (1199)	LT3 ↔ L2T9 + LT2	1663 (1390)
5	P ↔ NT2	2120 (1847)	P ↔ LT2	2052 (1779)
6	absent		LT2 + LT ↔ L2T3	1873 (1600)
7	P ↔ NT2 + NT	1973 (1700)	P ↔ LT2 + LT	1958 (1685)
8	P ↔ NT	1993 (1720)	P ↔ LT	1983 (1710)
9	P ↔ N + NT	1774 (1501)	P ↔ L + LT	1719 (1446)

P: molten product, T: TiO₂, N₂T₉: Nd₄Ti₉O₂₄, NT₃: Nd₂Ti₃O₉, NT₂: Nd₂Ti₂O₇, NT: Nd₂TiO₅, N: Nd₂O₃, L₂T₉: La₄Ti₉O₂₄, LT₃: La₂Ti₃O₉, LT₂: La₂Ti₂O₇, LT: La₂TiO₅, L₂T₃: La₄Ti₃O₁₂, and L: La₂O₃.

) are the eutectic of rutile and N₂T₉ (reaction No. 1), as well as incongruent (No.2) and congruent (No.5) melting of the NT₂ and N₂T₉ phases. The NT₃ phase with a perovskite structure is formed at 1200 °C according to the following reaction No. 4: 0.2 N₂T₉ + 0.6 NT₂ = NT₃. Comparatively small differences in the structure of the Nd₂O₃–TiO₂ and La₂O₃–TiO₂ systems are observed (Table 3, with details available in [60,61,62]), whereas in the Sm₂O₃–TiO₂ system, instead of the monoclinic phase, the Sm₂Ti₂O₇ compound with a cubic pyrochlore structure appears [63,64].

The REE₂Zr₂O₇ and REE₂Ti₂O₇ phases (REE = La, Nd) crystallize in a cubic (pyrochlore) or monoclinic (perovskite type) structure [65,66,67,68]. Pyrochlore is formed when the ratio of the radii of REE³⁺ and (Ti,Zr)⁴⁺ is in the range from 1.46 to 1.78 Å; in other cases, the fluorite structure of REE zirconates and the perovskite structure of titanates are stable. The REE₂Ti₂O₇ (Sm–Yb, Y) and REE₂Zr₂O₇ (La–Gd) phases have a pyrochlore structure. Depending on the REE type, the REE2TiO5 phases have an orthorhombic (La–Sm), cubic (Er–Lu, Sc), or hexagonal (Eu–Ho, Y) structure [69]. These features have a significant impact on the capacity of the phases with respect to the actinide components of the HLW.

3. Crystal–Chemical Features of Rare Earth Zirconates and Titanates

The content of REEs and actinides is one of the important criteria for selecting a matrix for immobilization of the radionuclides of REE–MA fraction. Crystal chemistry and structural features of the phases formed in the REE₂O₃–ZrO₂–TiO₂ system were considered using the example of Nd³⁺ [70] and are briefly discussed below.

The Nd₂Zr₂O₇ phase has a cubic lattice (Figure 2a), with the space group Fd-3m. There are eight formula units in the unit cell. The Nd polyhedron is a scalenohedron (distorted cube), and contains 8 O atoms, with six equidistant from Nd³⁺ and two at a greater distance. Zr cations are surrounded by six O atoms at the vertices of a trigonal antiprism (distorted octahedron). The structure of pyrochlore can be also described through interpenetrating frameworks of BO₆ and A₂X octahedra, and is derived from a fluorite-type lattice (space group Fm-3m).

The structure of Nd₂Ti₂O₇ is derived from the perovskite-type structure (Figure 2b): TiO₆ octahedra, connecting at their vertices, form plates of four octahedra (about 12 Å) in the a and b directions, between which single-capped trigonal prisms of NdO₇ are located. Three-capped trigonal prisms of NdO₉ fill the cavities of the octahedral blocks. Two-capped prisms of NdO₈ are located inside and between the octahedral blocks. The structure of Nd₂Ti₂O₅ (Figure 2c) consists of edge-linked seven-vertex NdO₇ and chains of square pyramids of TiO₅, connected by vertices in the [010] direction. The most complex structure of Nd₄Ti₉O₂₄ is represented by a titanium–oxygen framework, and Nd polyhedra are located in its cavities (Figure 2d). Nd atoms occupy three positions: the Nd(1) polyhedron, a distorted square antiprism, Nd(2), an octahedron, and Nd(3), a distorted square prism. The Nd(1)O₈ polyhedra, connected by edges and vertices, form layers parallel to the (110) plane. The Nd(3) polyhedra are connected by edges with Nd(1) layers and form 17.5 Å-thick blocks in the channels of which Nd(2) octahedra are located.

The REE³⁺ cations are characterized by coordination numbers (c.n.) equal to VII (a one-capped trigonal prism, with a truncated cube), VIII (a cube, with a two-capped antiprism), and IX (a three-capped trigonal prism). The coordination polyhedra of the smaller Zr⁴⁺ and Ti⁴⁺ cations have the shape of an octahedron (c.n. = VI), except for Nd₂TiO₅, c.n. of Ti⁴⁺ = V, and this polyhedron is a square pyramid. The low “solubility” of impurities corresponds to the odd c. n. (VII and IX) in Nd–O polyhedra, and high solubility corresponds to the even c.n. (VIII). This explains the wide field of the pyrochlore solid solution and the narrow composition fields of the remaining phases. Pyrochlore Nd₂(Zr,Ti)₂O₇ has a high capacity in the structure with respect to actinides: up to 20 at.% U enters the Zr⁴⁺ position, and from 10 to 20 at.% U and Th enter the Nd³⁺ position. Some of the Nd³⁺ ions in Nd₄Ti₉O₂₄ have c.n. = VIII, which probably results in a higher content of impurities (Ca, U, and Zr) in this phase compared to Nd₂Ti₂O₇ and Nd₂TiO₅ [70,71,72,73,74].

Phase diagrams of the REE₂O₃–ZrO₂–TiO₂ system depend on the REE³⁺ radius (Figure 3).

The replacement of Nd³⁺ by La³⁺ has a weak effect, whereas a decrease in the ionic radius from Nd³⁺ to Sm³⁺, Gd³⁺, and Y³⁺ leads to a more significant change [74,75,76,77]. The La₂O₃–TiO₂–ZrO₂ system also contains La₂TiO₅ (LT), La₄Ti₃O₁₂ (L₂T₃), La₂Ti₂O₇ (LT₂), La₄Ti₉O₂₄ (L₂T₉), La₂Zr₂O₇ (LZ₂), ZrTiO₄ (ZT), ZrO₂ (Z), and TiO₂ (T). Systems with Nd₂O₃ and La₂O₃ are similar in terms of their set of phases; however, in the system with lanthanum, the pyrochlore region is smaller. When the large ions La³⁺ and Nd³⁺ are replaced by Y³⁺, Y₂Ti₂O₇ (pyrochlore) is formed, and a cubic oxide ((Zr,Y)O_2−x) with a fluorite structure appears. The structure of Y₂TiO₅ is cubic (sp. group Fm-3m), but Nd₂TiO₅ and La₂TiO₅ have orthorhombic symmetry (sp. group Pnma). A feature of Nd and La titanates is slight variations in composition, although the Ti–REE ratios in them are close to the values in the formulas (Figure 3). At 1350 °C, the LT₂, L₂T₃, and LT phases contain less than 2 mol.% ZrO₂, the ZrO₂ content in L₂T₉ is higher and equals 4 mol.%, and the contents of La₂O₃ and ZrO₂ in La₂Zr₂O₇ reach 35 mol.% and 69 mol.%, respectively (

Table 4. Variations in the phase composition (mol.%) in the La₂O₃–TiO₂–ZrO₂ system.

Phase and Its Designation	La2O3	TiO2	ZrO2
La2Ti2O7, LT2	32.3 ± 0.3	66.2 ± 0.2	1.5 ± 0.3
	31.7 ± 0.9	67.2 ± 1.0	1.1 ± 0.2
La4Ti9O24, L2Ti9	17.7 ± 1.0	81.1 ± 1.1	2.2 + 0.3
	16.7 ± 0.5	78.9 ± 0.6	4.4 ± 0.2
ZrTiO4, ZT	<d.l.	53.1 ± 0.4	46.9 ± 0.3
	<d.l.	41.6 ± 0.3	58.4 ± 0.3
ZrO2, Zt	<d.l.	13.5 ± 0.6	86.5 ± 0.7
TiO2, T	<d.l.	88.6 ± 0.5	11.4 ± 0.3

<d.l.—less than the detection limit of the SEM/EDS method, equal to 0.3–0.5 wt.%.

, with details in [75]). The isomorphism of La³⁺ in ZrO₂ and ZrTiO₄ is limited to 1 mol.% La₂O₃. In (Ti,Zr)O₂ and (Zr,Ti)O₂, high contents of ZrO₂ and TiO₂ (12–14 mol.%) are found, and the Zr–Ti ratio in ZrTiO₄ varies from 1.4 to 0.9.

4. Actinide Wasteforms in the REE₂O₃ (Nd₂O₃)–ZrO₂–TiO₂ System

Below, we consider the issue of matrices for the REE–actinide fraction in the REE₂O₃ (Nd₂O₃)–ZrO₂–TiO₂ system, taking into account the data of references [65,78] and the previous results from [62,70,71,72,73,74,79,80,81,82]. About 30 samples were synthesized by cold pressing and sintering (CPS) of the oxide mixture at 1400–1550 °C and by induction cold crucible melting (ICCM). These samples were analyzed on a Rigaku D/Max 2200 X-ray diffractometer (XRD, Cu Kα,) (Rigaku, Tokyo, Japan) and in a JSM–5610LV scanning electron microscope with a JED–2300 (JEOL, Tokyo, Japan) energy-dispersive spectrometer (SEM/EDS). To determine corrosion resistance, their interaction with water and brines was studied at 90–240 °C for 30–143 days. After the tests, the solutions were analyzed for REE content; to determine the colloidal form, they were filtered through membranes with pore sizes of 450, 200, 100, and 25 nm. The compositions of the solution and its filtrates were analyzed using an inductively coupled plasma–mass spectrometer (XII ICP-MS, Thermo Fisher Scientific Inc., Waltham, MA, USA). Samples were irradiated with 1 MeV Kr²⁺ (flux density of 10¹² ions/(cm² × s)) using the accelerator at Argonne National Laboratory in the US at T = 50–1023 K. Some samples were irradiated with 4.5–5 MeV electrons at JSC SRC “RIAR” (Russia) with a subsequent study of their structure and hydrolytic stability.

As before, we will use mineral names or designations for the phases based on their formulas, where Nd₂O₃, ZrO₂, and TiO₂ are replaced by N, Z, and T, respectively. In the Nd₂O₃–TiO₂–ZrO₂ system, there are [65,78] the following phases: Nd₂(Ti,Zr)₂O₇ (NTZ) with a pyrochlore structure, TiO₂ (T), ZrTiO₄ (ZT), and tetragonal ZrO₂ (Z). Nd titanates are represented by Nd₂TiO₅ (NT), Nd₂Ti₂O₇ (NT₂), Nd₂Ti₄O₁₁ (NT₄), and Nd₄Ti₉O₂₄ (N₂T₉). In [60], the identities of Nd₂Ti₄O₁₁ and Nd₄Ti₉O₂₄ were proven, and the Nd₂Ti₃O₉ (NT₃) phase was found. The largest field in the Nd₂O₃–ZrO₂–TiO₂ diagram is occupied by pyrochlore; smaller variations in composition are characteristic of Nd₄Ti₉O₂ (Figure 3a), which makes these phases promising hosts for the REE–actinide fraction. Data on samples prepared by CPS or ICCM routes composed of the pyrochlore or orthorhombic REE titanate are discussed below.

4.1. Samples of the Composition (REE)₂(Zr,Ti)₂O₇ with a Pyrochlore Structure

To check the pyrochlore region boundaries, samples whose composition points lie on the REE₂Zr₂O₇–REE₂Ti₂O₇ line (Figure 4) were studied. They were obtained by sintering for 5 h at 1400 °C (Zr–Ti ratio ≤ 1) or 1550 °C (Zr–Ti ratio > 1). The batch charge was prepared from TiO₂, ZrO₂, and REE₂O₃ in quantities corresponding to the formula REE₂Zr_2−xTi_xO₇, where “x” varies from 0 (sample T0) to 2 (T20), with a step of 0.1 or 0.2. The proportions of REE oxides corresponded to the contents in the SNF and were in wt.% as follows: 11.8 La₂O₃, 23.0 Ce₂O₃, 10.7 Pr₂O₃, 38.9 Nd₂O₃, 8.1 Sm₂O₃, 1.3 Eu₂O₃, 1.5 Gd₂O₃, and 4.7 Y₂O₃. Up to x = 0.8 (T0–T8), the samples consist of pyrochlore; however, at a higher titanium content, monoclinic REE titanate with a perovskite structure appears. This phase becomes the main one at x > 1.2, i.e., in samples T12–T20. The content of total REE oxides in titanate is approximately 10% higher than in pyrochlore, as the values are 65 and 55 wt.%, respectively (

Table 5. Compositions (wt.%) and formulas of the pyrochlore (p) and monoclinic phases (m).

№	TiO2	ZrO2	Y2O3	La2O3	Ce2O3	Pr2O3	Nd2O3	Sm2O3	Eu2O3	Gd2O3
T0 (p)	0	45.7	2.6	7.5	12.6	5.1	19.2	3.7	1.7	1.9
	(Y0.12La0.25Ce0.41Pr0.17Nd0.62Sm0.11Eu0.05Gd0.06)Zr2.0O6.69
T15 (p)	19.8	23.7	5.8	4.2	12.6	5.1	20.3	5.4	1.2	1.9
	(Y0.23La0.12Ce0.35Pr0.14Nd0.55Sm0.14Eu0.03Gd0.05)(Ti1.21Zr0.79)O6.42
T15 (m)	33.0	1.6	2.4	11.6	16.2	6.5	23.3	3.8	0.7	0.9
	(Y0.10La0.33Ce0.46Pr0.19Nd0.65Sm0.10Eu0.02Gd0.02)(Ti1.94Zr0.06)O6.82
T18 (m)	33.1	0.7	2.2	10.4	17.0	6.4	23.6	4.2	1.1	1.3
	(Y0.09La0.31Ce0.50Pr0.19Nd0.67Sm0.12Eu0.03Gd0.03)(Ti1.97Zr0.03)O6.89
T20 (m)	33.4	0	2.9	8.9	16.0	6.0	25.1	5.2	1.4	1.2
	(Y0.12La0.26Ce0.47Pr0.17Nd0.71Sm0.14Eu0.04Gd0.03)Ti2.0O6.92

).

Samples P1 and P2 (Figure 4) were obtained using the ICCM method with neodymium (P1) or a mixture of lanthanum, cerium, and gadolinium (P2) as waste simulants. The synthesis was carried out in air with a zirconium ring placed in the batch to start the melting. After the melt was formed and the batch was loaded, it was kept melted for 0.5 h, and then the setup was turned off for cooling and the material formed a ceramic block. The composition of sample P1 (formula Nd₂Zr_1.5Ti_0.5O₇) lies in the pyrochlore field (Figure 4). According to XRD and SEM/EDS data, it is composed of pyrochlore, the composition of which varies within the sample (

Table 6. Phase compositions (wt.%) and atomic quantities of elements based on 7 O²⁻.

Oxide/Cation	Sample P1: Pyrochlore, Light–Dark	Sample P2: Pyrochlore, Center–Edge (Average)	Sample P2: Monoclinic REE Titanate
TiO2	3.7–8.4	4.6–14.1 (9.1)	31.8
ZrO2	41.5–36.6	36.1–23.2 (30.0)	No
La2O3	No	6.9–11.6 (10.2)	25.5
Nd2O3	54.8–55.0	No	No
Ce2O3	No	11.9–12.4 (11.7)	17.1
Gd2O3	No	38.2–35.5 (37.8)	23.9
Ti4+	0.26–0.57	0.34–0.99 (0.65)	2.01
Zr4+	1.88–1.61	1.72–1.06 (1.39)	No
La3+	No	0.25–0.40 (0.36)	0.79
Nd3+	1.82–1.77	No	No
Ce3+	No	0.43–0.43 (0.41)	0.53
Gd3+	No	1.24–1.10 (1.19)	0.67

). Light areas are enriched in Zr (on average 41.5% ZrO₂) compared to dark ones (36.6%), although the Nd₂O₃ contents are similar.

The composition of sample P2, wt.%, is 14.6 TiO₂, 22.4 ZrO₂, 14.9 La₂O₃, 15.0 Ce₂O₃, and 33.1 Gd₂O₃, its formula is (La_0.5Ce_0.5Gd)TiZrO₇, and it is located at the edge of the pyrochlore field. Pyrochlore dominates in it (85–90%), although REE titanate is also present (Figure 4). From the center to the edges of the pyrochlore grains, the concentration of zirconium and lanthanum decreases (Table 6), and that of gadolinium and titanium increases. Pyrochlore is enriched in ZrO₂ and Gd₂O₃ but contains less La₂O₃ and Ce₂O₃ relative to REE titanate. REE titanate is located between the pyrochlore grains, which indicates its late formation. Another phase of the composition, wt.%, is 18.7 TiO₂, 5.1 ZrO₂, 26.7 La₂O₃, 15.0 Ce₂O₃, 13.5 Gd₂O₃, 18.6 SiO₂, and 2.4 Fe₂O₃ with the following ratio of REEs: (Ti + Zr + Fe), while Si is close to the mineral perrierite (La,Ce)₂Ti₂Si₂O₁₁. It is formed due to the partial dissolution of the crucible coating, which explains the localization in the marginal parts and the presence of Si and Fe.

4.2. Samples of the Composition (REE)₄(Zr,Ti)₉O₂₄ with a Pyrochlore Structure

Samples with the (REE)₄Ti₉O₂₄ phase containing 48 wt.% of the REE–actinide fraction were obtained by sintering and melting–crystallization. The points of the bulk compositions of the samples lie near or in the field of this phase, as shown in Figure 3a. Sample RT-1 (Figure 5,

Table 7. Compositions (wt.%) and formulas of the rare earth titanate (dash—element not entered).

Sample	TiO2	ZrO2	Y2O3	La2O3	Ce2O3	Pr2O3	Nd2O3	Sm2O3	Eu2O3	Gd2O3
RT-1	51.8	–	–	–	–	–	44.9	3.3	–	–
	Nd3.72Sm0.26Ti9O24
IM-9	51.2	1.0	–	–	–	–	47.8	–	–	–
	Nd3.94(Ti8.88 Zr0.12)O23.91
RT-2	51.1	1.4	–	–	–	–	47.5	–	–	–
	Nd3.95(Ti8.86Zr0.16)O24
MLM-1	51.5	2.9	1.4	5.2	11.4	3.1	20.1	2.4	1.1	0.9
	(Y0.17La0.44Ce0.95Pr0.26Nd1.63Sm0.19Eu0.09Gd0.07)(Ti8.83Zr0.32)O24
IM-2	50.5	3.0	1.9	4.9	10.9	3.5	19.8	3.1	1.2	1.2
	(Y0.23La0.42Ce0.92Pr0.30Nd1.63Sm0.25Eu0.10Gd0.09)(Ti8.71Zr0.34)O24

), composed of REE titanate (light) and titanium oxide with a rutile structure (dark), was obtained by sintering the following mixture for 4 h at 1375 °C, wt.%: 52 TiO₂, 45 Nd₂O₃, and 3 Sm₂O₃ (formula Nd_3.75Sm_0.25Ti₉O₂₄). Several samples (IM-1, IM-2, RT-2, and MPM-1) were obtained by the ICCM method at 1500 °C. They are composed of orthorhombic titanate and rutile, the proportion of which depends on the composition of the batch and varies from 10 to 50% (Figure 5). Rutile contains 3–8 wt.% ZrO₂, where Zr⁴⁺ replaces Ti⁴⁺ due to the close radii (0.72 Å and 0.61 Å). The formula of REE titanate is calculated for 24 O²⁻, and the sum of Ti⁴⁺ and Zr⁴⁺ is close to 13 (Table 7). It contains up to 3 wt.% ZrO₂. Analysis of the samples in a high-resolution electron microscope (Figure 5f) confirmed the orthorhombic symmetry (sp. gr. Fddd) and the unit cell parameters, Å: “a” = 14.0, “b” = 35.5, and “c” = 14.6.

Samples obtained via melting have larger grain sizes than those obtained by sintering. The melting temperatures of samples with orthorhombic titanate are about 1500 °C. This is 100–250 °C lower than that of Ti-Zr pyrochlore, which simplifies the synthesis.

5. On the Pseudo-Ternary Nature of the Nd₂O₃–ZrO₂–TiO₂ System

The Nd₂O₃–ZrO₂–TiO₂ system was previously considered to be ternary; however, in the case of the partial reduction of Ti⁴⁺ (TiO₂) to Ti³⁺ (Ti₂O₃), it becomes quaternary. A sample of the composition (mol.% 21 Nd₂O₃, 16 ZrO₂, and 63 TiO₂) was synthesized by melting in a glass–carbon crucible [82]. According to the data [65,78], it should consist of Nd₂Ti₂O₇ and ZrTiO₄; however, according to the results of the X-ray diffraction and SEM/EDS studies, the sample is composed of two Nd titano-zirconates of different colors and compositions (Figure 6,

Table 8. Compositions (wt.%) and phases formulae; for zirconolite, the option with Ti³⁺ is shown.

Phase		Ti	Zr	Nd	O	Only Ti4+	With Ti3+ Also
Pyrochlore		16.5	13.1	46.9	23.5	Nd1.35Zr0.59Ti1.41O6.02	Nd1.35Zr0.59Ti1.41O6.02
Zirco-nolite	Center	21.5	14.6	38.1	25.8	Nd1.22Zr0.74Ti2.04O7.4	Nd1.22Zr0.74Ti4+1.26Ti3+0.78O7
	Edge	23.5	11.8	38.5	26.2	Nd1.20Zr0.60Ti2.20O7.4	Nd1.20Zr0.60Ti4+1.40Ti3+0.80O7
Rutile		46.8	7.0	10.7	35.5	Ti0.86Zr0.07Nd0.07O1.97	Ti0.86Zr0.07Nd0.07O1.97

) and rutile. Electron back-scatter diffraction (EBSD) confirmed the structure of pyrochlore for the light phase and zirconolite for the dark one (Figure 6). When the melt interacts with the glass–carbon crucible, the following reaction occurs: 2Ti⁴⁺O₂ + C = Ti³⁺₂O₃ + CO. Ti³⁺ ions serve as charge compensators during the following exchange: Nd³⁺ + Ti³⁺ → Ca²⁺ + Ti⁴⁺, which leads to the formation of zirconolite (ideally CaZrTi₂O₇), in which Ca²⁺ is fully replaced by Nd³⁺. Based on the composition of the phases (Table 8), their formulas were calculated with Ti⁴⁺ only and taking into account Ti³⁺. Reducing conditions are necessary for Ti³⁺ appearance, but only Ti⁴⁺ is stable at the synthesis in air, and the system is ternary.

6. Behavior of the Matrices with a REE–Actinide Fraction in Hot Aqueous Solutions

Along with the waste capacity, a very important characteristic of actinide matrices is their resistance to leaching. Several standard test protocols have been developed to determine this parameter [25,26,28,36,39,83]. The behavior of pyrochlore has been studied in static and dynamic tests [64,66,68,73,84,85,86,87]. The normalized leaching rate of U and REE from titanate pyrochlore under near-neutral conditions is 10⁻⁴–10⁻⁵ g/(m² × day), and it increases by an order of magnitude in alkaline (pH > 9) or acidic solutions (pH < 5). This is three orders of magnitude lower compared to the leaching rates of HLW glasses under similar conditions [88,89]. The rates of actinide and REE leaching from zirconate pyrochlores are lower than from titanate ones. For pyrochlore La₂Zr₂O₇ in static tests in water and alkaline solution (pH = 10) at 90–150 °C, the leaching rates of La are below 10⁻⁴ g/m² × day, and for Zr, they are equal to 10⁻⁶ g/(m² × day) [90,91,92]. The rate of plutonium leaching from titanate pyrochlores before their amorphization (MCC-1, water, 90 °C, 14–28 days) varies from ~10⁻² to 10⁻⁴ g/(m² × day). The spread of values is probably due to the presence of other phases in addition to pyrochlore in the samples. After amorphization, the rate of Pu leaching increases to 7 × 10⁻²–9 × 10⁻³ g/(m² × day). Leaching of Cm from pyrochlore (Gd,Cm)₂Ti₂O₇ after amorphization increased from 10⁻² to 2 × 10⁻¹ g/(m² × day) [89,93,94]. For pyrochlore (Gd,Cm)₂(TiZr)O₇, leaching rates as low as 1.7 × 10⁻² and 4.7 × 10⁻² g/(m² × day) were obtained [94]. Amorphization increases the rate of actinide leaching by a factor of 3–10, and, rarely, reaches 50 times the original rate [66,87,89,93,94,95,96,97]. Therefore, in runs with short-lived actinides (²⁴⁴Cm), the rate of actinide leaching increases due to phase amorphization, as well as due to an increase in the acidity of the solution to pH = 4 due to its radiolysis.

Studies of the corrosion resistance of the REE₂Ti₂O₇ and REE₄Ti₉O₂₄ phases are rare [64,73,79,80,98,99]. The leaching rates of La and Nd (95–240 °C, water, brine, 30–143 days) are close to those of pyrochlore and vary from 10⁻³ to 10⁻⁵ g/(m² × day), which corresponds to the dissolution of a matrix layer a few microns thick in a year. Taking into account previous studies [66,72,73,80], we conclude that pyrochlore and Nd titanates are rather resistant to corrosion in hot waters. Incongruent dissolution with a higher leaching rate of REEs and actinides compared to Ti and Zr is typical for them. This leads to the formation of a surface layer, tens of nm thick, enriched with these elements, which complicates the leaching of actinides [64,92,96]. After 40 days of contact of the pyrochlore with a solution of 0.5 M CaCl₂ + 0.5 M NaCl (T = 200 °C), no changes were detected in the SEM (Figure 7).

7. Behavior of the Matrices with a REE–Actinide Fraction Under Irradiation

The sources of radiation in the HLW forms are β- and α-decay, γ-radiation, and spontaneous fission of actinides (

Table 9. Composition and properties of a mixture of Am and Cm isotopes isolated from a t of SNF of a PWR-type reactor with a burnup of 50 GW × day after 6 years of storage.

Nuclide (T1/2, Years)	Share, wt.%	Heat Release, W/kg	Decay and Its Probability	Emission, Particles/s		Daughter Nuclide T1/2, Years
				α-Particles	Neutrons
241Am (433)	63.85	114.7	α + SF (3.8 × 10−12)	1.3 × 1011	2752	237Np (2.1 × 106)
243Am * (7.3 × 103)	25.35	6.4	α + SF (3.7 × 10−11)	7.4 × 109	139	239Pu (2.4 × 104)
243Cm (29.1)	0.09	1860.7	α (0.9976) + β+ (0.0024)	1.9 × 1012	48,690	239Pu (2.4 × 104)
244Cm (18.1)	9.78	2841.8	α + SF (1.4 × 10−6)	3.0 × 1012	10.9 × 106	240Pu (6537)
245Cm (8.5 × 103)	0.82	5.8	α (1.0)	6.4 × 109	123	241Pu (14.4)
246Cm (4.76 × 103)	0.11	10.2	α + SF (2.6 × 10−4)	1.1 × 1010	8.76 × 106	242Pu (3.8 × 105)

The content of isotopes ²⁴²Am and ²⁴²Cm is less than 0.01 wt.%. * ²³⁹Np is formed (T_1/2 = 2.36 days), which is converted into ²³⁹Pu. α—alpha decay, SF—spontaneous fission, β⁺—positron decay. A t of SNF contains about 17 kg of REE and 0.7 kg of MA (Am and Cm).

and

Table 10. Radiation effects in solidified forms of HLW according to references [25,50,93,95,97,101].

Type of Radiation (Decay)	Range of Defects, m	Irradiation Dose, Gray * After 104/106 Years	Atomic Displacements per Decay (dpa)
α-particle	~2 × 10−5	3 × 109/1010	130–200
recoil nucleus	~3 × 10−8	~6 × 107/~3 × 109	120–2000
β-particle	~10−3	~3 × 109/~4 × 109	0.1–1
γ-radiation	~2 × 10−2	~2 × 109/~2 × 109	<<1
Spontaneous decay	~10−5	103–104 **/No data	2.5 × 104–5 × 105

Gray *, unit of absorbed dose of radiation, Gy = J/kg; ** for the first 100 years.

). The disordering of the crystalline structure is mainly due to the formation of α-particles and heavy recoil nuclei during actinide decay. α-particles (He²⁺ with an energy of 4.5–5.5 MeV) account for up to 98% of the decay energy. At the end of a range of 10–20 μm, they collide with hundreds of atoms, knocking them out of their original position (Table 10, with additional data in [100]). Recoil nuclei with an energy of 70–100 keV collide with 1000–2000 atoms on a path of 10–40 nm. The role of beta particles, gamma radiation, and neutrons in this aspect is small. The influence of spontaneous fission of heavy actinides increases starting from ²⁴⁴Cm, but this effect is weak due to their low content.

The synthesis of actinide matrices is a labor-intensive and complicated process due to the need for protection from radiation, as well as the high cost of Pu, Am, and Cm isotopes. To study radiation damage, simulation techniques are typically used, such as irradiation with neutral or charged particles [25,26,28,50,66,68,69,85,86,93,97,99,101,102,103,104,105,106,107,108,109,110,111]. These techniques allow radiation doses that a matrix with real HLW will accumulate over many thousands of years to be achieved in a very short time (minutes). The most common method for studying the radiation resistance of actinide matrices is irradiation with heavy ions. The goal of such works is to determine the critical radiation dose (D_cr), leading to amorphization of the structure, and the critical temperature (T_cr), above which amorphization does not occur at any dose. The higher the first value and the lower the second, the more resistant the phase structure is to radiation. The main advantages of irradiation with ions are its short duration; lack of induced activity, which simplifies the study of matrices; the fact that the critical doses and temperatures of all phases in the sample can be determined simultaneously; and the fact that disordering is observed in an electron microscope during irradiation. Matrices are usually irradiated with 1 MeV Kr^+/2+, in which case the amorphization doses in units of displacements per atom (dpa) are close to the values during the decay of actinides [66,68,87,88,89,93,95,97,101].

In the REE₂O₃–ZrO₂–TiO₂ system, the phases with the pyrochlore structure have been intensely studied [66,95,97,101,102,103,104,105], there is a lot of data on the behavior of REE₂TiO₅ and REE₂Ti₂O₇ under irradiation [69,87,97,101,102,103,104,105,106,107,108,109,110,111], and for REE₄Ti₉O₂₄ there are scarce data [111]. For the A₂B₂O₇ phases (A = La–Lu, B = Ti, Zr), the critical temperature decreases (the resistance to radiation increases) upon transition from REE phases with the perovskite structure to compounds with the pyrochlore structure [103,104,105]. We studied samples consisting of pyrochlore only (T0), as well as pyrochlore and monoclinic titanate (T15, T18, T20), and orthorhombic REE titanate and rutile (IM-2, IM-9), the compositions of which are given in the Table 5, Table 6 and Table 7. When irradiated with 1 MeV Kr²⁺ to a dose of 25 × 10¹⁴ ion/cm², the structure of the zirconate phase is transformed into the fluorite lattice (Figure 8), and for the monoclinic perovskite phase, amorphization is already observed at 2.5 × 10¹⁴ ion/cm². This proves the resistance of zirconate pyrochlore (T0) to irradiation. Zirconate–titanate pyrochlore (T15) has intermediate values of D_cr, while low resistance is typical for monoclinic and orthorhombic rare earth titanates (Figure 9). For a specific type of irradiation, the T_cr is constant (Figure 9), and the D_cr increases with the rise in temperature, since the amorphous state is unstable. Heating leads to the healing of defects, so higher doses of irradiation are required to disorder the atoms in the lattice with increasing temperature.

The composition of A_1.94Ti_2.00O_6.92 (where A is a mixture of REE as in HLW) has the following D_cr and T_cr values: D_cr = 2.5 × 10¹⁴ Kr²⁺/cm², and T_cr = 900 K. Critical doses (T = 298 K) of the phases Nd_3.96(Ti_8.92Zr_0.12)O_23.94 and REE_3.95(Ti_8.71Zr_0.34)O_24.01 (REE = 0.43La + 0.92Ce + 0.30Pr + 1.63Nd + 0.25Sm + 0.10Eu + 0.09Gd + 0.23Y) are determined as 3 × 10¹⁴ Kr²⁺/cm² (0.2 dpa), and their T_cr is 900 K. Similar values were obtained for monoclinic titanates: for La₂Ti₂O₇, the critical dose is defined as 2.16 × 10¹⁴ Kr²⁺/cm², while the critical temperature, T_cr, is 840 K.

A sample consisting of Nd₄(Ti,Zr)₉O₂₄ and rutile (Ti,Zr)O₂ was obtained by the ICCM method [99] and irradiated with an electron beam (energy 4.5–5 MeV, beam power 20 kW, current 17 mA) to a dose of 5 × 10⁹ Gray. Irradiation did not affect the cell parameters of the neodymium titanate and rutile phases (Figure 10), but the leaching rate of Nd and Ti from the irradiated sample with water on the 28th day increased from 10⁻⁵ to 10⁻⁴ g/(m² × day).

When irradiated with 1 MeV Kr²⁺ ions, the critical temperatures of the Nd phases change from 135 and 685 K for the pyrochlores Nd₂Zr₂O₇ and Nd₂Ti_0.8Zr_1.2O₇ to 918 K for the perovskite Nd₂Ti₂O₇ and 1200 K for Nd₂TiO₅, respectively [108]. At a disposal facility, temperatures of 300–350 K (in mines) or 400–550 K (in deep boreholes) are expected, so only pyrochlores with a Zr–Ti ratio > 1 will retain crystallinity, while the remaining compositions will be amorphized due to actinide decay. Nevertheless, the actinide leaching rate increases by only one order of magnitude in this case. Radiation has direct (amorphization) and indirect (increase in acidity during radiolysis, heating) effects on the properties of actinide matrices and their behavior in the disposal facility. The influence of amorphization on leaching rates is usually limited to less than one order of magnitude. The acid pH of the solution is quickly neutralized by interaction with the container materials and the bentonite-based buffer. Temperature causes an increase in the leaching rate, but slows down the process of disordering the structure, preserving the original properties of the matrix. In general, radiation resistance is significantly less important for the selection of matrices than their corrosion resistance. Deep groundwater is represented by brines, so the leaching resistance of matrices must be studied under conditions close to these settings. Calculations were made of the thermal field of a borehole repository for the REE–actinide fraction. The estimates have considered the container diameter, waste content, and holding time before disposal [53]. The decay of minor actinides (Am, Cm) will result in the heating of the wasteforms of up to 300–500 °C for decades, while REE decay has a rather short-term effect on the matrix heating. With a waste content of 30 wt.% in the immobilizing matrix, the temperature increase in 10 years will be less than 40 °C.

8. On the Synthesis of Matrices in the REE₂O₃ (Nd₂O₃)–TiO₂–ZrO₂ System

A material with the best properties will not become a matrix of real HLW unless it can be effectively obtained in the required volumes remotely. Given the high radiation, the availability of industrial wasteform production technology is especially important [15,28,29,30,31,32,33,34,35,36,37,39,86,112,113,114,115,116]. Due to the absence of such a technology, the ceramics Synroc and the super-calcine proposed in the 1970s did not find practical application [25,26,28,114]. Only now, 50 years later, is the technology for producing Synroc by hot pressing close to implementation at a radiochemical plant in Australia [115]. The technologies already tested on real actinide-containing materials (waste) include melting in electric furnaces or induction crucibles, and sintering [15,37,39,86,116]. Melting has been used for over 40 years at the radiochemical plants in France, UK, USA, Russia and other countries to vitrify high-level waste [25,26,27,28,29,30,31,32,33,34,35,36,37,112,113], while sintering—for the synthesis of fuel with Pu, Np, and Am—is carried out using the MOX, REMIX, and MNUP processes [117,118,119]. The cold pressing and sintering route was developed to produce Synrocs and pyrochlore-based ceramics for weapons-based plutonium [15,26,28,39]. The hot pressing method was proposed in Australia to produce Synroc ceramics [25,114,115].

Melting methods are preferable to industrial technologies, as they are less sensitive to the quality of the batch and do not require the use of pressure. In the 1970s, induction melting technology was proposed for the vitrification of high-level waste [25,26,27,28,29,30,31,32,33,34,35]. Its advantages are a contactless energy supply and skull melting under active hydrodynamic conditions. In Russia, research has been conducted for over 20 years on the synthesis of induction melting in a cold crucible, as well as on the ICCM of vitreous matrices and ceramics, including Synroc, zirconolite, pyrochlore, murataite, brannerite, etc. [80,81,86,99,120,121]. Abroad, the ICCM method is widely used to obtain ceramic and glass–ceramic forms with HLW simulants [28,30,39,122,123,124,125]. It allows for obtaining matrices of the REE–actinide fraction at temperatures up to 2200 °C, although high temperatures require large energy costs. The REE zirconates are refractory phases, while the liquidus temperatures are above 2000 °C. In titanate systems, the melting temperatures are lower: for La₂Ti₂O₇ and Nd₂Ti₂O₇, they are 1790 and 1650 °C, but for Nd₄Ti₉O₂₄ and the eutectic mixture composed of 85 mol.% Nd₄Ti₉O₂₄ and 5 mol.% TiO₂, they are below 1500 °C (Table 3), which makes ICCM a promising technique for their manufacture.

9. Discussion

The prevention of the negative ecological impact of nuclear power waste is a fundamental scientific task and a practical problem. The main threat is associated with high-level waste containing long-lived actinides and fission products. Two approaches have been proposed to solve this problem, namely P&T (partitioning and transmutation) and P&C (partitioning and conditioning) [58,125]. The P&C approach is being developed by physicists and radiochemists; it is based on the separation of radioisotopes and their conversion into stable and short-lived isotopes upon neutron irradiation. This scheme includes the separation of HLW onto radionuclides or their groups, transmutation in a fast neutron flux, and disposal of the remaining waste. The first information on transmutation dates back to 1964 [126,127] and concerned fission products (⁹⁰Sr, ¹³⁷Cs). The transmutation of actinides in thermal light water-cooled reactors (LWRs) was proposed in 1972 [128], but later fast neutron reactors and subcritical installations, such as accelerators, were chosen for this purpose, as these are more promising [129,130,131]. The alternative approach (P&C) is being developed by geologists (mineralogists, geochemists), materials scientists, and some radiochemists; it involves the inclusion of waste in matrices, followed by their disposal. This method is more economical, since it requires less isotope separation and there is no need to build very complex expensive installations for the deep partitioning of HLW, fuel fabrication, multiple irradiations, and SNF reprocessing.

The purpose of transmutation is to reduce the environmental hazard posed by SNF and HLW [11,12,41,43,59,132,133,134,135,136,137,138,139,140,141] in order to achieve radiation (radioecological) equivalence of HLW and the uranium ore used to manufacture nuclear fuel as quickly as possible. Calculations have shown that extraction and transmutation of 99.9% of actinides reduces this time to 100–300 years, which eliminates the need to construct deep geological disposal facilities. The obvious mistake in this calculations is connected with the assumption of complete dissolution of HLW and uranium ore in water and the subsequent entry of radionuclides into the human body [142]. The shortcomings of the radiation equivalence concept are discussed in [143,144]. Many studies have noted the difficulties in implementing industrial separation of radionuclides, MA-loaded fuel production, its irradiation in fast reactors, and SNF reprocessing to extract actinides again [41,43,58,125,135,136,137,138,139,141,145,146,147].

For the transmutation of minor actinides, installations with accelerators [131,148,149,150] and molten salt reactors [151,152,153,154] are also proposed. The latter do not require actinide separation, but their problems are associated with their high cost and lack of operating experience, as well as the requirement of isotopically pure ⁷Li, the need to remove fission products, the high corrosive activity of the fluoride melt, etc. [153]. It can be assumed that the announced ambitious task of implementing large-scale transmutation in the first half of the 21st century [149] will not be realized. Due to the need for large volumes of scientific and experimental design work in the field of creating new types of reactors, fuel, and materials, the use of this technology is shifted to the distant future [17]. Another problem with this approach is that in this case, it will be necessary to deal with large volumes of highly active materials for many years, which creates a high risk of accidents, such as the irradiation of personnel and the population. Therefore, the question of using transmutation comes down to the choice between risks and consequences for current (transmutation) and future (disposal of HLW) generations.

The possibility of the geological isolation of actinide-containing waste is beyond doubt. There are over 2000 uranium deposits with an age of many millions of years and total resources of over 10 million t [155]. Numerous data prove the absence of uranium migration in reducing environments, which determines the preservation of uranium ores, as well as uranium and thorium retention, in natural vitreous and crystalline materials for hundreds of millions of years [50,66,85,87,101,156]. Such environments are realized at depths of up to several hundreds of meters. Arguments in favor of long-term conservation of radionuclides include the results of studies of radioactive minerals and ores, laboratory and field experiments, thermodynamic calculations, and computer modelling. The world has already accumulated 30–35 thousand t of vitrified HLW from the reprocessing of SNF (the main volumes are stored in France, Russia, the UK, and the US) [7,15,37,157], which will be disposed of in underground disposal facilities. In countries with an open nuclear fuel cycle without reprocessing of SNF, its geological disposal is also assumed. The protective properties of geological environments are due to the low solubility of radionuclides in water and the high sorption capacity of rocks. This is facilitated by the slow movement of underground waters, which are carriers of radionuclides. A contribution to safety will be provided by sorptive bentonite buffer swelling in water, corrosion-resistant containers, and durable matrices immobilizing nuclear waste. Their main characteristics are high loading for waste, a low leaching rate in water, and the possibility of remote fabrication on an industrial scale.

Extraction and precipitation methods are used to separate liquid HLW onto fractions [13,17,24,38,41,42,43,44,45,46,47,52,125,130,139,157]. In France, a pilot reprocessing of 15 kg of SNF was conducted with the separation of the REE–actinide group of elements [158]. In Russia, a plant for the separation of the Cs-Sr fraction from liquid HLW was in operation from 1996 to 2007, and the separation of the REE–actinide fraction was began there in 1999 [159]. From 1996 to 2003, 1630 m³ of HLW were processed there and 1.73 million Curies of the REE–actinide fraction (Am, Cm) were separated by precipitation of oxalate.

During one year of operation of an LWR with a capacity of 1000 MW, 20 t of SNF are formed. A plant for the reprocessing of 800 t of irradiated fuel generates about 4000 m³ of liquid HLW per year, with 1 m³ of such waste containing up to 90 g of Am and Cm. A fleet of reactors with a total capacity of 100 GW(e), as in the USA or Western Europe, produces up to 3 t of minor actinides per year, with almost equal amounts of Np and the sum of Am and Cm; the annual accumulation of the REE–actinide fraction during the reprocessing of SNF will be about 30 t. In France, 350–400 billion kWh of electricity are produced per year at nuclear power plants [160]. This leads to an annual production of SNF containing up to 300 kg of Am and 150 kg of Cm [43], and the mass of the REE–actinide fraction will be about 10 t. In 2022, Russian NPPs generated more than 220 billion kWh of electricity [161], or ~60% of that produced in France.

In the case of the reprocessing of all discharged SNF and fractionation of HLW, up to 6 t of the REE–actinide fraction will be formed per year. Its immobilization will require 10–20 t (2–4 m³) of matrix with a 50–25 wt.% REE–actinide fraction. According to estimates, a cluster of horizontal boreholes drilled from a vertical wellbore, known as SuperLAT technology (Figure 11), will accommodate up to 1000 t of SNF [162] or 500 t of HLW.

Placing solidified actinide waste in deep disposal facilities is obviously less dangerous than injecting liquid radioactive waste (LRW), which has been practiced in Russia for about 60 years [164,165,166]. This technology involves injecting it into porous collectors at depths of 180 to 500 m, isolated from aquifers by clays. The total volume of LRW by 2014 exceeded 60 million m³, and the activity was 7 × 10¹⁹ Bq or ≈ 2 billion Curie. The actinide content in water at a distance of 100–150 m from the injection wells decreases by 10⁴, which is 10⁶ times compared to the initial values, i.e., the bulk of the radionuclides was quickly precipitated.

The very low migration ability of actinides in underground water at reducing conditions, which are already dominant at depths of the first hundreds of meters, is evidence in favor of the geological isolation of actinide wastes [125,167,168]. Programs for the geological disposal of HLW exist in many countries, including Russia [22,23,24,167,168,169,170,171,172]. The main contribution to human exposure will be made not only by the actinides, but also by long-lived fission products (⁷⁹Se, ⁹⁹Tc, ¹²⁹I) due to their weak sorption by rocks and high migration rates in the geological environment [168,171]. Along with the traditional ultimate disposal of SNF and solidified HLW in mine-type disposal facilities [18,19,20,21,22,23,24,172], more and more attention is being paid to deep boreholes, which are vertical, with a depth of 3 to 5 km [173,174,175], or initially vertical and then horizontal, at depths of 1–3 km [162,163,176,177,178].

10. Conclusions

Two technologies have been proposed for handling actinide-containing fractions: transmutation and immobilization. The purpose of transmutation is to reduce the amounts of long-lived radionuclides by irradiation in nuclear reactors or accelerators. The first works on this topic devoted to fission products are about 60 years old [126]; this method was first proposed for actinides 50 years ago [128]. At practically the same time, the study of crystalline matrices for HLW began [25]. The principles of transmutation are developed theoretically [41,137,179], and experiments on irradiation of targets with actinides have been conducted [140]. Practical implementation of the approach faces a lot of technical difficulties and high costs. Reducing the amounts of radionuclides requires multiple irradiations of actinide-loaded fuel [43]. Due to the increased amounts of heavy actinides, mainly ^244,245Cm [179], the irradiated targets will possess high levels of radioactivity, neutron fluxes, and temperature, which complicate reprocessing and the production of new fuel. For these purposes, fast neutron reactors are needed, in which the actinide fission dominates over neutron capture. Reasonable doubts on the benefits of minor actinides transmutation are discussed in [180]. As can be seen, many questions concerning the technical feasibility of the effective transmutation of minor actinides, raised more than 30 years ago [181], are still relevant. The extraction and accumulation of minor actinides (Am, Cm) with relatively low (tens kg) critical masses is a threat to the policy of nuclear weapons non-proliferation [182,183].

Another approach to solving the problem of long-lived radionuclides is to incorporate them into stable matrices for placement in deep geological disposal facilities. This approach’s feasibility is demonstrated by the study of natural analogues of matrices, i.e., minerals that have retained actinides (Th,U) and REEs with properties similar to minor actinides for millions of years [50,85,87,184,185,186]. The presence of geological environments with a very low actinide migration is demonstrated by data on the preservation of U and Th deposits, their behavior in the natural nuclear reactor Oklo (Gabon), and studies on the solubility and sorption of actinides in laboratories and in natural (field) tests. This research is supported by data on volcanic rocks confining uranium and thorium for over 140–145 million years [156].

Let us summarize the analysis of the phases of the REE₂O₃–ZrO₂–TiO₂ system as applied to the problem of REE–actinide fraction immobilization. It is known that Nd³⁺ serves as an analogue of trivalent actinides (Am, Cm); therefore, the Nd₂O₃–TiO₂–ZrO₂ system is relevant when searching hosts for REE–MA. It contains Nd₂(Zr,Ti)₂O_7−x, Nd₂TiO₅, Nd₂Ti₂O₇, Nd₂Ti₃O₉, and Nd₄Ti₉O₂₄ phases, containing from 48 to 73 wt.% Nd₂O₃. Pyrochlore Nd₂(Zr,Ti)₂O_7−x and titanate Nd₄Ti₉O₂₄ are of the greatest interest as matrices: their stability fields (impurity content) are larger than those of other Nd titanates. With an excess of titanium, an additional phase of rutile (TiO₂) is formed, as a result of which the melting temperature decreases to 1450–1500 °C, which facilitates synthesis. Unlike pyrochlore, the Nd₄Ti₉O₂₄ compound has no analogues in nature. The content of Nd₂O₃ (actinide imitator) in it varies from 48 wt.% (only Nd₄Ti₉O₂₄) to 35 wt.% (70% Nd₄Ti₉O₂₄ and 30% rutile). The leaching rates of actinides and REE from Ti-Zr pyrochlore and REE titanates matrices in a wide range of temperatures (50–240 °C), compositions, and pH of solutions (water, brines) varied in the range of 10⁻³–10⁻⁵ g/(m² × day) and decreased with increasing interaction time. This is due to the formation of a thin surface layer enriched with zirconium and titanium, which prevents the release of REE and actinides into the solution. As for the other types of matrices [187], the leaching rate in the first days is determined by their solubility; then, due to the formation of an surface layer of alterations, the mode changes to diffusion exchange with low velocity.

Phases of the Nd₂O₃–TiO₂–ZrO₂ system are considered as matrices for isolating Pu and the REE–actinide fraction [62,65,68,188]. In addition to Ti-Zr pyrochlore, Nd₄Ti₉O₂₄ is of interest due to its higher content of impurities (Ca²⁺, Zr⁴⁺, U⁴⁺) compared to Nd₂TiO₅ and Nd₂Ti₂O₇. With an excess of titanium, rutile (TiO₂) is formed, which reduces the melting temperature by 200–300 °C, which facilitates the synthesis of such a composite matrix.

Durable stable crystalline phases hosting long-lived radionuclides might be components of integral composite systems containing both crystalline and vitreous nuclear wasteforms. The vitreous systems are not necessarily limited to the B-Si and Al-P glasses currently in use [8,37,142] and may include Fe-P, Al-Si, Fe-Pb-P, and other materials known for their high durability [39,189,190,191]. There is a notable trend to use durable composite materials containing both crystalline and vitreous phases in nuclear waste immobilization practices. The content of the crystalline phases is now being increased in the glass formulations used for nuclear waste vitrification [116,192,193,194], which is schematically shown by the red arrow originating in the left side of the diagram (Figure 12). It is worth noting that the first industrial plant which uses hot pressing in Australia is now designed to synthesize composite materials with Synroc-type crystalline and mineral-like phases distributed within a glass matrix, together forming a durable glass–crystalline material [115,194,195,196,197].

Matrices of HLW are currently supposed to be placed at depths of 500–700 m in mine-type disposal facilities or in super-deep (3–5 km) boreholes. For the REE–actinide fraction, the borehole option is preferable; in this case, due to the increase in temperature with depth, the rocks can be heated to 200 °C and even higher values [198]. High temperature slows down the radiation destruction of the crystalline structure of actinide hosts and reduces the effect of amorphization on the leaching of radionuclides. Both the large distance to the surface and low velocity of water movement will also serve as important safety factors for HLW disposal.

Progress in the field of methods for separating HLW [47], their incorporation into matrices [39,196], and recent achievements on geological disposal of the spent nuclear fuel and solidified high-level waste [23,199,200] allows us to expect a solution to the problem of handling the REE–minor actinide fractions within the coming decades. The use of transmutation for this purpose appears to be, essentially, a much more complex technological approach, and requires significantly more financial resources and time for implementation [17].