Structural Aspects of “Memory Effect” for MgGa LDHs: New Data Obtained by Simulation of XRD Patterns for 1D Disordered Crystals

Abstract

Simulation of diffraction patterns for 1D disordered crystals was used to investigate the structure of the initial CO₃²⁻ containing MgGa LDHs with a different Mg²⁺/(Mg²⁺ + Ga³⁺) ratio equal to 0.67, 0.75, and 0.80; mixed oxides obtained by calcination of LDHs at a temperature of 550 °C; and the hydroxide obtained by hydration of MgGa oxide with the Mg²⁺ content of 0.80. The initial LDHs contain lamellar inclusions of manasseite structure (polytype 2H₁) in the hydrotalcite structure (3R₁). A loss of water at 200 °C leads to the formation of a metastable dehydrated phase where layers are packed, as in polytypes 3R₂ and 1H, with turbostratic disorder. The structure of mixed oxides is also layered and consists of periclase-like octahedral layers and spinel-like octahedral-tetrahedral layers. Hydration of the oxides results in restoring the initial layered hydrotalcite structure (polytype 3R₁) for Mg²⁺ mole fractions 0.67 and 0.75. For the Mg²⁺ content of 0.80, the phase composition is represented by the hydroxide with hydrotalcite structure and the layered mixed hydroxide with the alternation of hydrotalcite and brucite lamellar domains, which was also revealed by calculation of diffraction patterns using models of 1D disordered crystals.

1. Introduction

In recent years, many works on the synthesis, investigation, and application of layered double hydroxides (LDHs) with different cationic and anionic composition have appeared [1,2,3]. Generally, LDHs have the formula ${\left[{\mathrm{M}}^{2+}{}_{1-\mathrm{x}}{\mathrm{M}}^{3+}{}_{\mathrm{x}}{\left(\mathrm{OH}\right)}_2\right]}^{\mathrm{x}+}{\left[{\mathrm{A}}^{\mathrm{n}-}\right]}_{\mathrm{x}/\mathrm{n}}\times {\mathrm{yH}}_2\mathrm{O}$, where M²⁺ and M³⁺ are the di- and trivalent cations of metals, and Aⁿ⁻ is the interlayer anion. Layered double hydroxides possess unique properties; for example, at a certain cationic composition, they exhibit the “memory effect”: the oxide obtained after calcination of LDHs at 500 ÷ 700 °C is able to restore the layered hydroxide structure upon contact with water [4,5]. This property makes it possible to use LDHs for the removal of various toxic anions from water, such as SO₄²⁻, Cl⁻, Br⁻, NO₃⁻, and others [6,7,8], dyes [9] for intercalation of large anions, such as oxometalates and anionic complexes of transition metals [10], and also for intercalation of metal complexes [11] intended for different applications. LDHs are applied in biomedicine and pharmaceutics [12,13,14,15,16]. They are used as adsorbents, functional materials, and nanocomposites [17,18,19,20]. LDHs are also quite promising for catalytic applications because they have high specific surface areas, improved basic properties, and thermal stability of the particles obtained upon reduction. These materials are used in the oxidation and reforming of methane to syngas with preliminary deposition of metal complexes of noble metals [21], in hydrogenation and dehydrogenation of light alkanes [22,23], and processing of biomass [24], as photocatalysts for degradation of pollutants, photocatalytic H₂ generation, and photocatalytic CO₂ conversion [25,26]. LDHs are promising materials for electrochemistry [27,28,29,30].

The basic layered structure of LDHs is based on that of brucite, Mg(OH)₂, with edgesharing hydroxyl octahedra occupied by M²⁺ cations. These edge-sharing octahedral unites form infinite layers with the OH ions sitting perpendicular to the plane of the layers. Part of the divalent cations is isomorphically substituted by trivalent cations such that layers acquire a positive charge, which was balanced by intercalation of anions between the layers. Crystallization water molecules were also found in the interlayer space. Brucite-like octahedral layers can have different packing, which gives rise to various possible structural polytypes [31,32]. Nevertheless, for carbonate-containing LDHs, only two polytypes exist in nature: three-layer rhombohedral 3R₁ (AC = CB = BA = …) and double-layer hexagonal 2H₁ (AC = CA = …) polytypes, which correspond to hydrotalcite and manasseite, respectively. Here, A, B, and C are the positions of anions. It should be noted that the interlayers in these two polytypes are shaped as a trigonal prism (denoted as “=”) because oxygen atoms in OH groups of the adjacent layers are located in similar positions, which is determined by the geometry and position of CO₃ groups (a regular triangle that is parallel to layers in the middle of the interlayer). Materials belonging to the family of layered double hydroxides have various composition because it is possible to change the nature and ratio of di- and trivalent cations as well as the interlayer anions during synthesis. The most studied are MgAl LDHs [33]; however, there are also the synthesized LDHs containing other cations in the brucite-like layers, both divalent: M²⁺ = Mg²⁺, Be²⁺, Ca²⁺, Cu²⁺, Ni²⁺, Zn²⁺, Co²⁺, Mn²⁺, Fe²⁺ Cd²⁺, etc., and trivalent: M³⁺ = Al³⁺, Fe³⁺, Ga³⁺, Cr³⁺, Ni³⁺, Mn³⁺, V³⁺, Ti³⁺, In³⁺, Co³⁺, etc. [34,35]. LDHs with hydrotalcite-like structure can form in the range of 0.20 < x < 0.33, where x = M³⁺/(M³⁺ + M²⁺), i.e., in the range of M²⁺/M³⁺ ratios from two to four.

The cationic composition determines many properties of LDHs, particularly the “memory effect”. It is known that the ability to restore the layered structure is exhibited by the oxide obtained by calcination of MgAl LDH in the temperature range of 450–600 °C [36,37], whereas the oxides based on NiAl LDH can restore the structure only partially and only at elevated temperatures and pressures [38,39]. Studies on the “memory effect” of MgGa LDH are quite scarce. Thus, in refs. [40,41] it was observed that in a K₂CO₃ solution, the layered hydroxide structure is completely restored from the oxide obtained by calcination of MgGa LDH (Mg:Ga = 2.89) at 600 °C. The restoration of the initial layered structure of the hydroxide containing OH⁻ groups in the interlayer was observed in decarbonized water for 1 h [4]. A study on the “memory effect” of the MgGa LDH calcined at 500 °C [42] showed that its layered structure is restored by 96% upon hydration of MgGa oxide with water vapor during 18 h. In [41], it was found that a relative humidity of 80% at 70 °C leads to the sorption of water vapor and to complete restoration of the layered structure.

When the crystal structure of LDHs is examined by XRD, some problems with correct interpretation of data emerge because LDHs contain stacking faults due to the variety of possible polytypes. In addition, layered crystals have such imperfections as the turbostratic disorder and mixed layers. The indicated features affect the shape and position of peaks in X-ray diffraction patterns. So, the structure of LDHs cannot be described within the three-dimensionally ordered model, which is implied in the Rietveld method conventionally used for the analysis of structure [43]. A promising method for investigation of such systems is the simulation of X-ray diffraction patterns using statistical models of 1D disordered crystals [44,45]. A model of the crystal is a set of individual layers, the statistical sequence of which along the normal to the layers is specified by a set of probabilities. The indicated approach makes it possible to create different models of the layered structures and calculate the corresponding diffraction patterns, comparing them with the experimental ones.

Thus, the analysis of the literature data demonstrated that hydration of the mixed oxide obtained by calcination of MgGa LDH in the temperature range of 450–600 °C leads to complete or partial restoration of the layered hydroxide structure. However, the “memory effect” of the calcined MgGa LDH exposed to water has been poorly studied in terms of structure. This may be caused by the defect structure of the initial, calcined, and rehydrated LDHs and the related difficulties with interpreting the X-ray diffraction patterns. Therefore, this work aimed to investigate the phase and structural transformations, which occur upon calcination of MgGa LDHs with different ratio of cations in the brucite layers and subsequent hydration of MgGa oxides, by simulation of diffraction patterns for 1D disordered crystals.

2. Materials and Methods

2.1. Synthesis

Carbonate-containing MgGa (MgGa-CO₃) LDHs with different mole fractions of Mg²⁺ (Mg²⁺/(Mg²⁺ + Ga³⁺) = 0.67; 0.75; 0.80 were synthesized by co-precipitation from aqueous solutions of nitrates containing di- and trivalent cations of metals [46]. The total concentration of di- and trivalent cations in each solution was constant and equal to 3 mol/L. The obtained solutions were added dropwise under vigorous stirring to a Na₂CO₃ solution (1 mol/L). A constant value of pH 10 was maintained during the synthesis by adding a NaOH solution (1 mol/L). Temperature of the synthesis was 60 °C. Ageing of the precipitate was performed at 60 °C for 18 h. The resulting samples were washed with distilled water to a neutral pH of the wash water, filtered, and then dried for 16 h at 80 °C. The synthesized samples contained preferentially carbonate anions in the interlayer. The samples were calcined at 550 °C for 2 h (MgGa oxides), cooled in air, and hydrated in distilled water, with subsequent drying at 110 °C (MgGa-OH LDHs).

2.2. TG-DTG-DTA

The TG-DTG-DTA analysis was performed on an STA-449C Jupiter instrument connected by a heated capillary to a QMS-403C Aeolos quadrupole mass-spectrometer (NETZSCH-Gerätebau GmbH, Selb, Germany). Measurements were made in dynamic mode using an argon medium. Samples were heated at a rate of 10 °/min. The weight of the samples was 10–20 mg.

2.3. Powder X-ray Diffraction

X-ray diffraction studies were carried out on a powder X-ray diffractometer D8 Advance (Bruker AXS, Karlsruhe, Germany) using a Cuk_α source in the 2θ angular range 5 ÷ 80° with a 0.05° step and acquisition time 5 s at a point. Lattice parameters and average crystallite sizes were found, respectively, from positions and half-widths of 003, 006, and 110 peaks. Silicon was used as the internal standard. Diffraction patterns were calculated within the statistical model of defect crystals using the software described in [32,33]. The oxide structure was refined by the Rietveld method using the TOPAS 4.2 (Bruker) software.

2.4. In Situ XRD

In situ high-temperature XRD studies were carried out on a powder X-ray diffractometer D8 Advance, (Bruker AXS, Karlsruhe, Germany) using an XRK-900 (Anton Paar, Graz, Austria) reaction chamber. The heating rate was 12 °C/min. The temperature was increased from 150 to 400 °C with a step of 25 °C, and from 400 to 600 °C with a step of 100 °C. XRD patterns were recorded twice at each temperature in the 2θ range from 7 to 67° with a step of 0.05°, and 3 s at a point (60 min for a scan). Silicon was used as the internal standard.

3. Results and Discussion

3.1. Structure of the Synthesized MgGa-CO₃ LDHs

Experimental diffraction patterns of the initial MgGa-CO₃ LDHs with different mole fractions of the divalent cation (Mg²⁺/(Mg²⁺ + Ga³⁺) = 0.67; 0.75; 0.80) show (Figure 1a) that they do not correspond to the 3R₁ (AC = CB = BA = …) or 2H₁ (AC = CA = …) polytype. In distinction to the diffraction patterns of the 3R₁ and 2H₁ polytypes, asymmetric distortions of the peak shape in the region of medium diffraction angles 2θ = 35° ÷ 45° (012, 015 and 018 peaks) are observed in the experimental diffraction patterns.

In our earlier study [47], the simulation of diffraction patterns in approximation to 1D disordered crystal using the DIFFaX program revealed that such a distortion is caused by the stacking faults associated with the inclusion of the 2H₁ polytype fragments into the 3R₁ polytype. Details of simulation and coordinates of the atoms in layers used in the calculation are given in Supplementary Materials. The diffraction pattern calculated for such a model (Figure 1b) adequately describes the experimental curve using the model of crystallites comprising 60% of the 3R₁ polytype and 40% of the 2H₁ polytype. According to calculations, the fraction of stacking faults is similar irrespective of the content of the divalent cation. X-ray diffraction data were used to calculate the microstructural characteristics of the tested samples (

Table 1. Lattice constants a, c (hydrotalcite) and average crystallite sizes L_a, L_c of MgGa-CO₃ LDHs.

Fraction of Mg2+	Phase Composition	a, Å	c, Å	La, nm	Lc, nm
0.67	LDH	3.087	22.88	37.1	56.5
0.75	LDH	3.093	23.33	51.5	91.3
0.80	LDH	3.104	23.81	26.6	24.1

).

An increase in the mole fraction of the divalent cation in all the studied samples increases the lattice parameter a, which is related to a greater ionic radius of Mg²⁺ (0.072 nm) as compared to Ga³⁺ (0.062 nm), and parameter c, which is caused by weakening of electrostatic interaction between positively charged brucite-like layers and negatively charged interlayers due to a decrease in the charge of the layers. An increase in the mole fraction of the divalent cation up to 0.75 leads to a growth of the crystallite sizes L_c and L_a, whereas its further increase facilitates a decrease in their values. The results obtained agree well with the literature data [48,49,50].

3.2. Thermal Decomposition of MgGa-CO₃ LDHs

3.2.1. TG/DTG/DTA analysis

Thermal decomposition of MgGa-CO₃ LDHs (Figure 2) resembles that of the carbonate-containing MgAl LDHs. The process can be divided into four steps: (1) removal of physisorbed water, (2) removal of interlayer water, (3) dehydroxylation of brucite-like layers, and (4) decarbonization of interlayers [51]. Dehydroxylation and decarbonization temperatures as well as the thermal decomposition rate depend on the mole fraction of the divalent cation. The higher is the content of the divalent cation, the earlier is the onset of the dehydration of interlayers. For a sample with the mole fraction of Mg = 0.67, one can see on the DTG curve that the decomposition rate is quite high in the first weight loss step and exceeds the decomposition rate in the second step (Figure 2a). For a sample with Mg = 0.75, a virtually similar decomposition rate is observed in both weight loss steps on the DTG curve (Figure 2b). For MgGa-CO₃ DTG with the mole fractions of Mg²⁺ = 0.67 and 0.75, dehydroxylation and decarbonization steps start at different temperatures. An intense endothermic peak on the DTA curve at 220–420 °C corresponds to the onset of dehydroxylation of the brucite-like layers. At the same time, an increase in the Mg²⁺ fraction to 0.80 leads to a decrease in the decomposition rate in the first weight loss step (Figure 2c). The observed weight losses are accompanied by the appearance of three endothermic peaks on DTA curves. It means that two processes occur jointly in the second weight loss region. The first endothermic peak at 210–250 °C is associated with the dehydration of interlayers. As the mole fraction of Mg²⁺ increases to 0.80, this peak broadens and grows in intensity. The dehydration temperature maximum shifts toward lower temperatures with an increase in the mole fraction of Mg²⁺. The second endothermic peak at 330–350 °C corresponds to the partial dehydroxylation of brucite layers. When the mole fraction of Mg²⁺ increases, this peak shifts toward higher temperatures: at Mg²⁺ = 0.80, its superposition with the third peak becomes visible. The third endothermic peak with the maximum at 410–425 °C is associated with complete decomposition of the layered structure, leading to the formation of the oxide phase.

3.2.2. In Situ XRD Analysis

For a sample with the mole fraction of Mg²⁺ = 0.67, in situ high-temperature X-ray diffraction (HTXRD) was performed in the range from 25 to 600 °C (Figure 3). It was found that an increase in the temperature up to 150 °C produces virtually no changes in the diffraction pattern. At 175 °C, peaks of the initial hydroxide (purple lines) decrease in intensity, and there appear the peaks of another phase with a decreased interlayer distance, which is equal to d₀₀₃ in hydrotalcite (3R₁ polytype). The interlayer distance decreases from 7.58 Å to 6.54 Å, and the interplanar distance d₀₀₆ = d₀₀₃/2 decreases from 3.85 Å to 3.41 Å. In the medium angular range, 013, 015, and 018 peaks decrease in intensity and a narrow peak with the interplanar distance d = 2.67 Å and a broad peak with d = 2.42 Å appear. At 200 °C there remain only the peaks corresponding to the new phase (olive lines). In the range of high angles, one asymmetric peak with d = 1.54 Å remains instead of hydrotalcite peaks 110 and 113. According to thermal analysis data, approximately at this temperature the dehydration of interlayers is observed. This is why the new metastable phase is commonly called the dehydrated LDH phase [52]. A further heating to 300 °C decreases the intensity of the peak corresponding to d = 6.54 Å. Low-intensity peaks of the dehydrated phase (hereinafter denoted as MgGa-dehydrat) can be observed up to a temperature of ca. 350 °C, at which peaks of the oxide phase with interplanar distances d = 2.12 and 1.50 Å become the main ones (pink lines).

3.2.3. The Structure of Dehydrated MgGa LDH

The structure of the dehydrated phase formed at 200 °C was revealed by simulating the structure of 1D disordered crystals and calculating the diffraction patterns using Defect software [45]. Broadening and asymmetry of peaks on the diffraction pattern of the dehydrated phase (Figure 4) may indicate the presence of stacking faults and turbostratic disorder. In our earlier study [53], the structure of the dehydrated phase formed at 200 °C was established for MgAl and NiAl LDHs; it was shown that the structure does not depend on the nature and ratio of di- and trivalent cations in the brucite layer. A model was proposed for the structure comprising predominantly the 3R₂ (AC~BA~CB~…) and 1H (AC~AC) layered fragments without prismatic interlayers, as in the initial LDHs. In the dehydrated phase, the oxygen atoms in OH groups of adjacent layers occupy different positions, forming octahedral interlayers (such an interlayer is denoted as “~”), which may be caused by a change of anion orientation after a loss of crystallization water and the appearance of tetrahedrally coordinated cations in the interlayers. Along with changes in polytypes, the structure of the dehydrated phase is characterized by the presence of turbostratic disorder, which implies random displacements or turns of the layers. In the Defect software [45], such type of structural disturbance is introduced under the assumption that layers randomly deviate from ideal positions in a polytype, and these deviations are distributed according to the Gaussian function with the mean-square deviation σ. The diffraction pattern of the dehydrated MgGa phase is similar to those of MgAl and NiAl dehydrated phases; therefore, calculations were made using the model that was earlier suggested for these systems. The calculations showed (Figure 4) that in the MgGa-dehydrat structure, the predominant type of layer stacking is similar to that in 3R₂ (AC~BA~CB~…) and 1H (AC~AC) polytypes with a small inclusion of 3R₁ (3R₁:1H:3R₂ = 0.1:0.5:0.4) polytype. In addition, the turbostratic disorder (σ = 0.15) is present in the structure.

3.2.4. Structure of Calcined MgGa LDHs

The diffraction patterns of MgGa LDH samples calcined at 550 °C with different Mg²⁺ content are quite similar and differ only in the width of the peaks of periclase-like oxide (Figure 5), which is related to an increase in the average crystallite sizes with increasing the mole fraction of Mg²⁺ from 4.4 nm (mole fraction Mg²⁺ = 0.67) to 5.4 nm (mole fraction Mg²⁺ = 0.80).

The observed difference in crystallite sizes may be caused by the difference in temperatures at which the layered hydroxide structure starts to break down, leading to the formation of the oxide, which depends on the fraction of the divalent cation. All the diffraction patterns also contain a broad peak at 2θ~35° (d = 2.56 Å), the origin of which is unknown. The strongest 311 peak of the MgGa₂O₄ spinel located at 2θ~36° (d = 2.49 Å) is far enough.

It should be noted that the structure of MgGa oxides obtained by calcination of MgGa-CO₃ LDHs at 550–600 °C has not been completely understood; for simplicity, it is considered as the periclase-like one (periclase, MgO, structural type NaCl) [54,55]. The calculated values of the lattice parameters a are higher than its value for pure periclase (MgO, a = 4.211 Å) and depend virtually linearly on the Ga³⁺ content: the smaller is the mole fraction of Ga³⁺, the higher is the value of parameter a. This indicates that the oxide contains Ga³⁺ ions. However, the ionic radius of Ga³⁺ (r = 0.62 Å) is smaller than the ionic radius of Mg²⁺ (r = 0.72 Å), and isomorphic substitution of Mg²⁺ ions by Ga₃₊ should decrease the lattice parameter of the periclase structure.

The Rietveld refinement (Figure 6a) performed for a sample with the mole fraction of Mg²⁺ = 0.67 in space group Fm3m with the statistical distribution of Mg²⁺ and Ga³⁺ between octahedral positions showed that the intensity ratio of diffraction peaks 200 and 220 does not correspond to the experimental ratio. Peaks 200 and 220 on the experimental X-ray diffraction pattern have approximately equal intensities, whereas the intensity of theoretical peak 200 exceeds that of peak 220 by nearly twofold. The broad peak at ca. 35° also cannot be described by such a structure. Accordingly, R factor is quite high (R_wp = 20%).

After that, we considered a model of the oxide with the distribution of Mg²⁺ cations between octahedral positions 16d and 16c, and Ga³⁺ between tetrahedral positions 8a in space group Fd3m. The periclase and spinel structures have different cationic sublattices and a similar anionic sublattice, in which oxygen ions form the cubic closest packing. In spinel, cations occupy 1/2 of the octahedral voids (positions 16d) and 1/8 of the tetrahedral voids (positions 8a). Filling of the additional octahedral positions 16c along with the spinel positions 16d allows simulating the periclase-like structure in the frame of Fd3m group. In the periclase structure, all octahedral voids are occupied by cations, whereas cations are absent in the tetrahedra. Thus, such a model has features of two structures: periclase and spinel.

The Rietveld refinement (Figure 6b) performed for the indicated model showed that the intensity ratio of diffraction peaks 200 and 220 is closer to the experimental ratio. One can see also that the broad peak at ca. 35° is described by this structure.

As seen from the refinement data (

Table 2. Refinement of occupancies of the spinel positions 16d and 8a and non-spinel positions 16c in MgGa oxide.

Fraction of Mg2+	Position	Cation	Occupancy	Rwp, %
0.67	8a	Ga3+	0.42	13
	16c	Mg2+	0.93
	16d	Mg2+	1.66
0.75	8a	Ga3+	0.33	13
	16c	Mg2+	0.91
	16d	Mg2+	1.55
0.80	8a	Ga3+	0.27	15
	16c	Mg2+	0.91
	16d	Mg2+	1.46

), occupancies of the octahedral positions 16d for three MgGa oxides have values above 1, which indicates that not only the Mg²⁺ cations are present in these positions, but also the heavier Ga³⁺ cations. Occupancies of positions 16c, on the contrary, have values much lower than 1. Filling of positions 8a is lower than 1, which testifies that either Mg²⁺ ions reside in these positions along with Ga³⁺ ions or these positions are not completely filled.

If the spinel structure is viewed along the main diagonal (the [111] direction), one can see two types of the alternating layers: octahedral and mixed octahedral–tetrahedral layers. In the octahedral layer of spinel, three cations are in positions 16d, and one octahedron in position 16c remains empty. In the mixed layer, one cation is in the octahedral position 16d, two cations are in the tetrahedral position 8a, and three octahedral positions 16c are not occupied. Presumably, the partial filling of position 16c occurs exactly in the octahedral layer of spinel, which means that all octahedra in the octahedral layer become filled, as in the periclase structure. Thus, it can be supposed that the MgGa oxide structure includes the periclase-like octahedral (O) layers filled with Mg²⁺ and Ga³⁺ ions, and the spinel octahedral-tetrahedral (OT) layers.

The model with alternating O and OT layers was tested, taking into account occupancies from the Rietveld refinement (Table 2). It was shown that the introduction of OT layers leads to the appearance of an additional reflection in the region of the left slope of peak 111, as on the experimental diffraction pattern; in addition, the intensity ratio of peaks 200 and 220 on the calculated diffraction pattern is consistent with the experiment (Figure 7).

3.3. “Memory Effect” of the Heating Residues

It is known that MgGa-CO₃ LDH has the “memory effect”, which means that the related oxide (T_cal = 450–600 °C) is able to restore the layered structure of the initial hydroxide upon contact with water [42]. The hydration of MgGa oxides is followed by the formation of the MgGa-OH LDH phase, the diffraction patterns of which resemble those of MgGa-CO₃ LDH, but have some distinctions (Figure 8).

The diffraction pattern of MgGa-OH LDH samples with the Mg²⁺ mole fractions 0.67 and 0.75 corresponds to the pure 3R₁ polytype because the pronounced asymmetry of peaks in the region of medium diffraction angles disappears. Noteworthy also is a decrease in the thickness (L_c) of MgGa-OH crystallites in comparison with MgGa-CO₃: from 56.5 to 13 nm (the mole fraction of Mg²⁺ = 0.67) and from 91.3 to 8.8 nm (the mole fraction of Mg²⁺ = 0.75).

For a sample with the mole fraction of Mg²⁺ = 0.80, the appearance of additional diffuse peaks between 003 and 006 peaks (2θ ≈ 14° and 22°) on diffraction patterns is observed. A substantial change in the intensities of peaks occurs in the region of medium 2θ diffraction angles: 30 ÷ 50°. Our calculations of diffraction patterns using the models of 1D disordered crystals revealed that the additional non-identified reflections between 003 and 006 peaks belong to the interstratified phase (IS-phase) consisting of hydrotalcite-like and brucite-like lamellar domains. The brucite layers are much thinner than the hydrotalcite layers because interlayers in brucite are not filled with anions and water molecules, as in hydrotalcite, since layers in brucite have a neutral charge.

The diffraction patterns were calculated within the model of hydrotalcite structure (3R₁ polytype) with a gradual introduction of brucite layers (Figure 9a).

It is seen that 003 and 006 peaks are displaced toward each other, they become broadened, and their intensity ratio changes with a gradual increase in the thickness of lamellar domains of the brucite type in hydrotalcite structure. Changes are observed also in the diffraction pattern in the medium region of diffraction angles.

Simulation under the IS phase model was used to calculate the diffraction pattern, which described quite well the appearance of additional peaks on the X-ray diffraction pattern (Figure 9b). In this IS phase, the average thickness of the lamellar domains with hydrotalcite and brucite structure is ca. 1.2 nm and ca. 0.8 nm, respectively.

Table 3. Microstructural characteristics for MgGa-OH samples after hydration of oxides.

Initial Mole Fraction of Mg2+	Calculated Mole Fraction of Mg2+	Phase Composition	c, Å	Lc, nm	$\bar{a}$, Å	La, nm	Lh, nm	Lb, nm
0.67	0.69	LDH	23.17	13	3.088	16.3	-	-
0.75	0.74	LDH	23.56	8.8	3.094	19.3	-	-
0.80	0.84	LDH	23.63	9	3.108	14.5	-	-
		IS-phase	-	-			1.2	0.8

lists the calculated data on the mole fraction of Mg²⁺ in the hydrated samples. The Mg²⁺ content was calculated from parameter a. One can see that the initial synthesized and hydrated samples have virtually a similar content of magnesium, except a sample with the Mg²⁺ mole fraction of 0.80, where the appearance of peaks corresponding to the IS-phase, which is enriched with Mg²⁺ ions as compared to LDH, was observed.

4. Conclusions

The X-ray diffraction method with calculation of X-ray diffraction patterns within the models of 1D disordered crystals was used to demonstrate that thermal decomposition of Mg-Ga LDHs occurs topotactically. The octahedral layers present in the initial LDH are preserved in the dehydrated phase and mixed oxide. In the structure of initial carbonate-containing Mg-Ga LDHs, the layers are packed relative to each other with prismatic interlayers, as in the 3R₁ (AC = CB = BA = …) and 2H₁ (AC = CA = …) polytypes. At a temperature of ca. 200 °C, LDH loses water and forms a metastable dehydrated phase, in which changes occur in the relative positions of layers with the formation of octahedral interlayers, as in the 3R₂ (AC~BA~CB~…) and 1H (AC ~ AC …) polytypes. Calcination at T > 350 °C results in the transformation of the dehydrated phase into Mg-Ga mixed oxide, which comprises the periclase-like octahedral layers and the spinel-like layers made of octahedra and tetrahedra. The periclase-like layers inherit the structure of the LDH cationic layers; the spinel-like layers are formed in the interlayers of LDH due to diffusion of cations. The ability to restore the layered hydrotalcite structure is associated with the reversible migration of Ga³⁺ ions into the interlayer during thermal decomposition of hydrotalcite and hydration of the oxide. The restoration is complete for the mole fraction of Mg²⁺ equal to 0.67 and 0.75, and its increase to 0.80 results in the appearance of the additional mixed layered phase consisting of hydrotalcite and brucite layers.