Preparation and Density Functional Theory Studies of Aluminosilicate-Based Ceramic Solidified Products for Sr Immobilization

Abstract

Strontium is a common radionuclide in radioactive waste, and its release into the environment can cause enormous damage to the ecosystem environment. In this study, the natural mineral allophane was selected as the substrate to prepare solidified ceramic products by cold pressing/sintering to solve the problem of the final disposal of radioactive strontium. Ceramic solidified products with various crystal structures were successfully prepared, and the microscopic morphology and energy-dispersive spectroscopy images of the samples showed a uniform distribution of Sr in the solidified products. Sr₂Al₂SiO₇ and SrAl₂Si₂O₈, which can stably solidify strontium, were formed in the solidified products, and the structural characteristics and stability of the above-mentioned substances were analyzed from the perspective of quantum chemical calculations using density functional theory. The calculation results showed that the overall deformation resistance of Sr₂Al₂SiO₇ was higher than that of SrAl₂Si₂O₈. Considering the isomorphic substitution effect of CaO impurities, we inferred that a mixed-crystalline structure of Ca_2−xSr_xAl₂SiO₇ may be present in the solidified products.

1. Introduction

Nuclear energy is a crucial high-quality energy source, and its development provides a new impetus for the progress of human society. However, nuclear energy production inevitably generates hazardous radioactive waste, posing substantial environmental and biological risks. Thus, it must be treated safely and effectively [1]. The radionuclide ⁹⁰Sr, characterized by radiotoxicity, high heat generation, and a long half-life of 28.8 years, is a β-emitter generated by uranium and plutonium fission reactions in nuclear reactors [2,3,4]. As an alkaline-earth cation with chemical properties similar to calcium, ⁹⁰Sr easily accumulates in human bones [5,6]. ⁹⁰Y, a daughter nuclide of ⁹⁰Sr, produces high-energy β particles that can damage the bone marrow. Therefore, considering environmental protection and human health, the safe disposal of ⁹⁰Sr from radioactive waste is valuable to a great extent [7].

Stabilization and solidification are considered the most promising technologies for radionuclide management [8,9]. In addition to traditional glass and cement solidification, ⁹⁰Sr solidification primarily focuses on geopolymer and ceramic solidifications. Geopolymers are amorphous inorganic binder materials that are usually composed of SiO₄ and AlO₄ tetrahedra and can be prepared from solid wastes, such as fly ash, metakaolin, and slags via alkali activation at ambient temperature [10,11,12]. These materials can be considered precursors to zeolites with different affinities toward various ions. Notably, the Si/Al ratio is the controlling factor affecting the adsorption ability of geopolymers [13,14,15,16]. In the field of radioactive waste immobilization, geopolymers that outperform Portland cement can be prepared by changing the precursor materials and activators [15]. The absorbed waste elements can be further converted into stable ceramic-phase components, thereby increasing the difficulty of ion leaching by strengthening chemical bonds. The ceramic solidification approach has received extensive research attention due to its excellent chemical stability, radiation stability, and leaching resistance [17]. At the atomic scale, radioactive elements can enter the lattice structure of ceramic matrix materials, thereby forming a safer immobilization barrier than in glass [18]. At present, various ceramic materials, such as phosphates, aluminosilicates, titanates, zirconates, and vanadates [7,17,18,19,20], have been extensively studied as matrices for immobilizing radioactive wastes through methods, such as cold pressing/sintering, microwave sintering, and spark plasma sintering [21,22,23,24].

As inorganic polymers, aluminosilicates have layered and skeletal crystal structures that endow them with high specific surface areas. These materials can achieve the selective adsorption of multiple ions through a molecular sieve mechanism; that is, certain ion sizes can enter the cavities, pores, and channels formed by the aluminosilicate framework. Allophane is a short-range order aluminosilicate and an affordable material for obtaining solid-state matrices based on aluminosilicate ceramics. It is primarily found in volcanic ash soil, and the basic structure of its skeleton comprises Al(OH)₃ and SiO₄ [25]. The special frame structure of allophane confers good radiation resistance stability and the ability to capture gases [26]. Owing to these advantages, it is one of the most promising materials for metal-ion removal and immobilization. Our group previously treated a mixture of allophane and cesium secondary waste at high temperatures, resulting in the breakdown of the allophane framework and the formation of stable crystalline phases that encapsulate cesium [27,28]. Excellent leaching resistance and mechanical properties are the main characteristics of the prepared solidified ceramic bodies. However, systematic studies on the application of allophane for the immobilization of highly radioactive ⁹⁰Sr have rarely been reported.

The use of density functional theory (DFT) to study the binding behavior of metal ions in lattice-defect structures and lattices can enable a deeper understanding of the solidification structures and bonding mechanisms at the molecular level. The lattice parameters, structural stability, mechanical properties, thermo-physical properties, and electronic structure of different materials have been extensively studied through DFT experiments to evaluate their comprehensive properties [29,30,31,32,33,34]. However, few studies have been conducted on the immobilization mechanism of Sr in high-temperature ceramics. Considering the stability and advantages of capturing Sr in ceramic matrices, it is important to explore the immobilization mechanism of solidified ceramic products at the molecular level.

In this study, the natural mineral allophane was used to synthesize solidified Sr ceramic products through cold pressing/sintering. The performance and mechanism of the allophane on Sr were explored, and the structural characteristics and stability of the sintered products were analyzed from the perspective of quantum chemical calculations using DFT.

2. Materials and Methods

2.1. Materials

Nonradioactive ⁸⁷Sr was used in all samples instead of radioactive ⁹⁰Sr. Analytical-reagent-grade strontium nitrate (Sr(NO₃)₂) was purchased from Sinopharm Chemical Reagent Co. Ltd., China. Allophane (1–2SiO₂·Al₂O₃·5–6H₂O), with an average particle size of 5.9 µm, was obtained from Hattori Company, Ltd., Japan. The smaller particle size ensured a larger specific surface area, which was conducive to improving the adsorption capacity of metal ions. The surface morphology and main components of the allophane used as matrices are shown in Figure 1.

2.2. Preparation of Solidified Products

The solidified product was prepared as follows: Allophane and Sr(NO₃)₂ were uniformly mixed in various mass ratios. Then, the uniform mixture was ground into a fine powder and molded into a disk via the cold pressing method using hydraulic pressure tablets under 4 kN with a holding time of 6 min. The resulting 10 mm diameter molded discs were placed in a muffle furnace for sintering at specific temperatures and a heating rate of 10 °C/min for 1 h.

2.3. Characterization

Scanning electron microscopy and energy-dispersive spectrometry (SEM and EDS, Mira 3, TESCAN ORSAY HOLDING a.s., Brno, Czech Republic) were used to measure the surface morphology and elemental distribution of the solidified products. The mass fractions of each element in the samples before and after sintering were determined using an X-ray fluorescence spectrometer (XRF-1800, Shimadzu Corporation, Kyoto, Japan). The crystal structures of the samples were examined using powder X-ray diffraction (XRD) spectroscopy (D8 ADVANCED DAVINCI, Bruker Corporation, Karlsruhe, Germany).

2.4. DFT Calculation

DFT is a classical quantum mechanical modeling method for calculating and predicting the electronic properties of crystal structures with high precision. It has been used extensively in computational research on ceramic materials. This method calculates the energy of the system as a function of electron density without solving the complex many-body Schrodinger equation, thereby significantly simplifying the calculation. In this study, DFT calculations were performed to analyze the crystal structure and mechanical properties of the solidified ceramic products. The gain and loss of electrons and chemical bond types of the Sr atoms were also studied to analyze the chemical stability of the solidified products. All calculations in this study were carried out based on the DFT method using the Vienna ab initio simulation package (VASP). Electron exchange and related energy were computed using the projector augmented wave (PAW) method with the Perdew–Burke–Ernzerhof generalized gradient approximation (PBE-GGA) function [35,36]. The Brillouin zone sampling was performed using a Gamma grid. The cut-off energy was set to 400 eV, as confirmed by the convergence test, and the force convergence of the structural optimization was set to be lower than 0.02 eV/Å.

3. Results and Discussion

3.1. Characterization and Self-Sintering Behavior of Allophane

Self-sintering experiments were performed on the allophanes at different temperatures. The XRD patterns of allophanes with different sintering temperatures are shown in Figure 2. No obvious diffraction peaks were observed in the XRD patterns of fresh allophane, indicating that allophane was an amorphous substance. Two weak diffraction peaks were observed at 26.6° and 28°, which may be attributed to the spherical shell structure of allophane, comprising silica and alumina, characterized by short-range ordering. When the sintering temperature was lower than 1000 °C, wide and diffuse peaks were observed in the XRD pattern, suggesting no mineral-phase transformation or crystal-phase substance formation under these experimental conditions. After sintering at 1200 °C, the main crystal phases in the self-sintering products of allophane were primarily transformed into two phases, namely, mullite (Al₆Si₂O₁₃) and cristobalite (SiO₂). The increase in the sintering temperature may have caused the Si–O–Si and Si–O–Al bonds to break and the allophane framework to collapse. The decomposition products Al₂O₃ and SiO₂ with high chemical reaction activity also recrystallize at high temperatures to yield a mullite crystal phase [26,37]. The content of the cristobalite crystal phase was relatively low, and the cristobalite phase may be attributed to the high-temperature calcination of excessive SiO₂ [38]. Moreover, the volume reduction rate of the sintered solidified body increased from 20.6% to 52.2% with increased sintering temperature from 700 °C to 1000 °C. This phenomenon has benefited waste minimization and improved economic efficiency. Hence, the formation of stable crystalline phases and good volume reduction rates indicate that allophane has excellent self-sintering properties, making it a potential matrix material for the solidification of radionuclide ceramics.

3.2. Sr Immobilization Ratio and Solidification

Figure 3 shows the Sr immobilization ratios obtained via XRF for various mixtures of Sr(NO₃)₂–allophane sintered at 600–1200 °C, with a gradual increase in Sr content from 10wt% to 20 wt%, the immobilization ratio of Sr remained at approximately 100% at all sintering temperatures. This finding indicates that allophane can be effectively used for the immobilization treatment of Sr.

XRD was used to study the crystal phases of the sintered products and to understand the immobilization mechanism of Sr. Figure 4 shows the XRD patterns of various mixtures of Sr(NO₃)₂–allophane sintered at 1200 °C. The crystal structure of the solidified products changed after sintering. When the Sr content was 1 wt%, no obvious crystal phase of Sr was detected in the solidified product; it had primarily mullite and cristobalite crystal phases. Thus, the self-sintering behavior of allophane dominated the immobilization when the Sr content was low. When the Sr content ranged from 5 wt% to 30 wt%, in addition to the mullite phase, strontium feldspar (SrAl₂Si₂O₈) and strontium aluminum silicate oxide (Sr₂Al₂SiO₇) crystal phases that can stably solidify Sr also formed in the solidified product. With increasing Sr content in the solidified product, the proportion of the mullite phase gradually decreased and that of Sr₂Al₂SiO₇ gradually increased; however, the proportion of SrAl₂Si₂O₈ initially increased and then decreased. This finding may be related to the value of Si/Al in the solidified product. The deflection of the diffraction peaks can also be observed in the solidified products with different compositions. According to the Scherrer formula, the decreased interplanar spacing led to an increased diffraction angle, indicating that the crystal-phase structure of the solidification products changed to a certain extent.

The surface morphologies and main elemental compositions of the solidified products after sintering at 1200 °C are shown in Figure 5. The surface of the solidified product appeared to melt and transform into a ceramic phase, and a non-uniform porous surface was formed. Si, Al, and Sr were detected and uniformly distributed on the surface of the solidified product, indicating that well-crystallized phases containing Sr were produced, which is consistent with the XRD results.

3.3. Calculation of Elastic Properties of Solidified Product

Sr was primarily immobilized in the solidified product in the form of SrAl₂Si₂O₈ and Sr₂Al₂SiO₇. Therefore, the Young’s modulus, shear modulus, and other parameters of the two phases were simulated and calculated using DFT to analyze the change in mechanical properties of the solidified product with increased Sr content. The crystal-structure parameters of SrAl₂Si₂O₈ and Sr₂Al₂SiO₇ after optimization are listed in

Table 1. The cell parameters of SrAl₂Si₂O₈ and Sr₂Al₂SiO₇ after optimization.

Crystal	Crystal System	Space Group	Lattice Parameter
			a (Å)	b (Å)	c (Å)	α	β	γ
SrAl2Si2O8	Monoclinic	C2/c	9.385	9.385	9.650	81.056°	81.056°	74.481°
Sr2Al2SiO7	Triclinic	P1	7.837	5.264	7.848	90.231°	90.000°	90.000°

, and the structures of SrAl₂Si₂O₈ and Sr₂Al₂SiO₇ are shown in Figure 6. The calculated elastic-tensor parameters of the two crystals after optimizing the cell structure are listed in

Table 2. The stiffness tensor parameters of SrAl₂Si₂O₈ and Sr₂Al₂SiO₇ after optimization.

Crystal	Stiffness Tensor Cij/GPa
SrAl2Si2O8	C11	C12	C13	C15	C22	C23	C25
	154.742	43.414	72.793	13.905	187.346	52.2	−16.89
	C33	C35	C44	C46	C55	C66
	129.94	−0.01	14.429	9.931	45.872	13.305
Sr2Al2SiO7	C11	C12	C13	C14	C15	C16	C22
	193.271	63.599	78.3	1.878	0	0	160.477
	C23	C24	C25	C26	C33	C34	C35
	62.674	0.001	0	0	191.154	−1.141	0
	C36	C44	C45	C46	C55	C56	C66
	0	46.079	0	0	68.894	−0.546	45.721

.

In general, the hardness of a material increases with an increase in Young’s modulus (E). Conversely, a smaller shear modulus (G) corresponds to more easily formed dislocation slips, causing the material to become ductile [36]. The bulk modulus (B) of polycrystalline crystals was used to measure the relationship between the bulk strain and the average stress of the crystal. The bulk modulus decreased with an increase in the crystal volume. The bulk modulus, shear modulus, Young’s modulus, and Poisson’s ratio $\nu$ were evaluated using the Voigt–Reuss–Hill approximation (Equations (1)–(3)) [36].

$$\begin{array}{cc}{B}_V=\frac{1}{9}\left(C_{11}+C_{22}+C_{33}\right)+\frac{2}{9}\left(C_{12}+C_{13}+C_{23}\right)& \\ B_R=\frac{1}{\left(S_{11}+S_{22}+S_{33}\right)+2\left(S_{12}+S_{13}+S_{23}\right)}& \end{array}$$

(1)

$$G_V=\frac{1}{15}\left(C_{11}+C_{22}+C_{33}-C_{12}-C_{13}-C_{23}\right)+\frac{1}{5}\left(C_{44}+C_{55}+C_{66}\right)$$

$$G_R=\frac{15}{4\left(S_{11}+S_{22}+S_{33}\right)-4\left(S_{12}+S_{13}+S_{23}\right)+3\left(S_{44}+S_{55}+S_{66}\right)}$$

(2)

$$B=\frac{B_V+B_R}{2},G=\frac{G_V+G_R}{2},$$

$$E=\frac{9BG}{3B+G},\nu =\frac{3B-E}{6B}$$

(3)

where C_ij and S_ij represent the elastic constant and elastic compliance, respectively.

The anisotropy indices of the bulk and shear moduli can be expressed using the following formula [39]:

$$A_B=\frac{B_V-B_R}{B_V+B_R},A_G=\frac{G_V-G_R}{G_V+G_R}$$

(4)

The calculated bulk, shear, and Young’s moduli of the SrAl₂Si₂O₈ and Sr₂Al₂SiO₇ polycrystals are shown in Figure 7. The results showed that the overall anti-deformation ability of Sr₂Al₂SiO₇ was better than that of SrAl₂Si₂O₈. Moreover, a larger value of A corresponds to greater anisotropy of the system, whereas when A is equal to zero, it is completely isotropic [36]. The anisotropy percentages of the bulk and shear moduli of Sr₂Al₂SiO₇ are close to 0, further indicating that this crystalline phase is isotropic. By contrast, SrAl₂Si₂O₈ showed obvious anisotropy.

To observe the anisotropy property more clearly, the three-dimensional distributions of Young’s modulus and shear modulus were obtained through further calculation [40], and the results are displayed in Figure 8 and Figure 9, respectively. The closer the three-dimensional figure was to a spherical shape, the more isotropic the system. Obviously, SrAl₂Si₂O₈ was more anisotropic than Sr₂Al₂SiO₇ in terms of Young’s modulus and shear modulus.

3.4. Simulation and Calculation of Sr/Ca Mixed-Crystal Structures

Given that allophane contains some CaO impurities, considering the isomorphism substitution, a Sr-Ca mixed-crystal phase may have existed in the solidified product after sintering. According to the doping levels of different Ca atoms, the XRD patterns of Ca_1−xSr_xAl₂Si₂O₈ and Ca_2−xSr_xAl₂SiO₇ after optimization are shown in Figure 10A,B. As shown in Figure 10A, for the Sr/Ca mixed-crystal structure of SrAl₂Si₂O₈ (simulated), an obvious diffraction peak was observed at 2θ = 6.8° with a change in the Ca/Sr ratio. The intensity of the diffraction peak increased as the Ca/Sr approached one. The XRD pattern of the experimental test revealed no obvious diffraction peak at 2θ = 6.8°. Therefore, we speculated that no mixed-crystal formation of Ca_1−xSr_xAl₂Si₂O₈ occurred.

As shown in Figure 10B, unlike SrAl₂Si₂O₈, obvious diffraction peaks were observed at 2θ = 11.38°, 16.12°, and 17.38° in the XRD patterns of Sr₂Al₂SiO₇ (experimental) and Ca_2−xSr_xAl₂SiO₇ (simulated). This finding suggested that a mixed-crystal structure of Ca_2−xSr_xAl₂SiO₇ formed in the sintered solidified product. The mechanical properties of the Ca_2−xSr_xAl₂SiO₇ mixed crystals that appeared in the experiment were calculated, and the elastic moduli are shown in Figure 11A. With increased Sr content, the bulk modulus, Young’s modulus, and shear modulus of the polycrystal showed a downward trend, indicating that adding Sr caused a deterioration in mechanical properties. According to the Pugh criterion, the ratio of B/G was generally 1.75 as the boundary ratio between ductility and brittleness. These results confirmed that the brittle crystal transformed into a ductile one with increased Sr content, as shown in Figure 11B.

3.5. Analysis of Electron Localization Function (ELF)

The degree of electron localization at different locations in a three-dimensional real space can be expressed by the ELF, with a value ranging from 0 to 1, which quantitatively characterizes the degree of electron localization. A closer ELF value to 1 corresponds to a stronger localization of electrons in this region and greater difficulty for electrons to escape. Issues, such as charge-transfer bonds, metallic bonds, and hydrogen bonds, have been extensively studied using ELF [41]. Figure 12 shows the three-dimensional ELF diagrams of SrAl₂Si₂O₈ obtained via VESTA as well as the two-dimensional ELF diagrams in sections of 3.24 and 9.72 Å away from the setting plane in the direction of the (0 1 0) crystal plane. The ELF values near the Sr and O atoms were relatively high, indicating that the localization of electrons near the two atoms was relatively strong.

Moreover, the Sr atoms were contracted at the side that was neighboring the O atoms, and the same contraction of ELF was also observed at the O atom in Figure 12B,C [42]. Thus, Sr and O were most likely to combine with each other in the form of ionic bonds. Figure 13A shows the three-dimensional ELF diagrams of Sr₂Al₂SiO₇, and the four Sr atoms in the crystal lattice are marked in Figure 13B–E. Similar to SrAl₂Si₂O₈, the localization of electrons around the Sr and O atoms was relatively high. Therefore, we inferred that Sr and O also combined with each other in the form of ionic bonds in the Sr₂Al₂SiO₇ crystal.

3.6. Comparison of Different Sr-Containing Ceramic Solidified Products

The selection of mineral substrates is currently the primary issue in the preparation and research of Sr-containing solidified products. In this study, three typical Sr-containing ceramic solidified products, Sr₀.₅Zr₂(PO₄)₃, SrTiO₃, and SrZrO₃, were selected, and the bond energy and mechanical properties of Sr in different mineral phases were calculated using VASP and compared with those of SrAl₂Si₂O₈ and Sr₂Al₂SiO₇. Then, the chemical stabilities and mechanical properties of the solidified products were evaluated. The Sr bond energies in the different mineral phases are shown in Figure 14, and the elastic moduli of the different mineral phases are shown in Figure 15A. The Sr bond energies of SrAl₂Si₂O₈ and Sr₂Al₂SiO₇ were higher than those of the other three mineral phases, i.e., 11.6 and 12.1 eV, respectively. This order of magnitude is higher than that of Sr₀.₅Zr₂(PO₄)₃ with apatite structures and SrZrO₃ with zirconium-based perovskite structures. This finding indicates good chemical stability in the solidified product containing Sr produced in this study.

The bulk modulus B, shear modulus G, and Young’s modulus E of several Sr-containing mineral phases all exhibited the following trend: SrTiO₃ > Sr₀.₅Zr₂(PO₄)₃ > Sr₂Al₂SiO₇ > SrAl₂Si₂O₈ > SrZrO₃. Among these mineral phases, SrTiO₃ exhibited the best mechanical properties, whereas SrZrO₃ exhibited the worst. The proportions of Sr₂Al₂SiO₇, SrAl₂Si₂O₈, and mullite in the solidified product changed continuously with increased Sr content. The formation of the mullite crystal phase can lead to enhanced hardness and modulus in the solidified product [28]. Therefore, a decrease in the mullite proportion may be the main reason for the decline in the mechanical properties of the solidified product. Therefore, to increase the mechanical properties of the solidified product, the content of allophane during the immobilization of Sr should be appropriately increased. The Pugh’s ratio in Figure 15B also shows that only SrTiO₃ had partial brittleness, and the other ceramic solidified products had a certain ductility.

4. Conclusions

The immobilization performance of the natural mineral allophane on the heat-generated nuclide strontium was investigated through ceramic solidification. Stable crystals called Sr₂Al₂SiO₇ and SrAl₂Si₂O₈ were formed in the solidified products after sintering at 1200 °C. These crystalline materials enabled the effective immobilization of strontium, and the immobilization ratio reached 100%. DFT simulations further revealed the structural characteristics and stabilities of the sintered products. The increased strontium content caused a transition from brittle to ductile crystal. From the ELF diagrams, we inferred that Sr and O are highly likely to be bonded to each other through ionic bonds in the two crystals mentioned above. Moreover, the Sr bond energies of SrAl₂Si₂O₈ and Sr₂Al₂SiO₇ were 11.6 and 12.1 eV, respectively, higher than those of the other three common mineral phases. These results indicate that the natural mineral allophane is promising for the final disposal of strontium.