Semiquantitative and quantitative XRD analysis

The compounds studied were characterized and identified using XRD, as reported in previous studies (Reference LeoniLeoni, 2008; Reference Scardi and LeoniScardi & Leoni, 2002; Reference Scardi, Leoni and BeyerleinScardi et al., 2011). Two associated analysis concepts were utilized to achieve this. The first was the ‘semi-quantitative XRD analysis,’ which involved determining the structure of the compounds by calculating the d ₀₀₁ basal intercalated value, the full width at half maximum (FWHM), the crystallite size (solved using the Scherrer equation), and the rationality parameter (ξ). The expression for ξ is as follows (Reference BaileyBailey, 1980; Ben Reference Ben Brahim, Besson and TchoubarBrahim et al., 1984):

(2) $\xi \left(\mathring{A}\right)=\sum _{n=1}^N\left(\frac{d_{001}-lx{d}_{00l}}{n}\right)$

The second was ‘quantitative XRD analysis,’ which involved determining the structural parameters (SP) at the nanoscale and provided a detailed overview of the interlamellar space (IS) contents, the arrangement of hydrated CC (M ²⁺ + H₂O molecules), the average number of layers per stacking $\overline{M}$ , the layer stacking mode (LSM), the homogeneity, and/or heterogeneity of the crystallites, crystallite defects, and more. This approach was implemented using an indirect modeling technique that involved comparing experimental profiles with theoretically predicted ones. This highlights the importance of conducting a quantitative investigation and the limitations of semiquantitative analysis in understanding the lamellar structure.

XRD profile modeling: Theoretical diffracted intensity and modeling strategy

Modeling diffractograms enables the quantification of mixed-layer structures (MLS) (Reference LansonLanson, 2005), identification of the hydration state (0W → 3W), determination of structural heterogeneities, CEC variations, crystallite size D, optimal IS configuration, and average number of layers per crystallite. This indirect method follows a well determined mathematical formalism (Reference Drits and TchoubarDrits & Tchoubar, 1990), and the expression of the diffracted intensity for the space following the reciprocal z-axis is given by:

(3) $I_{00l}\left({}^{\circ },2,\theta \right)=L_p{S}_{\mathrm{pur}}\mathrm{Re}\left(\varphi \right)\left(W\right)\left(\left(I\right),+,2,\sum _n^{\overline{M}-1},\left(\frac{\overline{M}-n}{n}\right),{\left(Q\right)}^n\right)$

In the above equation, Re represents the real part of the final matrix, S_pur is the sum of the diagonal terms of the real matrix, L_p is the Lorentz polarization factor, $\overline{M}$ is the number of layers per stack, and n ranges from 1 to (1– $\overline{M}$ –1). [Ф] is the matrix of structure factors, [I] is the identity matrix, [W] is the diagonal matrix of the proportions of the different types of layers, and [Q] is the matrix representing the interference phenomena between adjacent layers.

This indirect method allows for the determination of the abundance of different types of layers (W_i), the layer types of LSM, and the average number, $\overline{M}$ , for the distributions of layers per coherent scattering domain (CSD) (Reference Oueslati, Rhaiem and AmaraOueslati et al., 2012). Within a CSD, the stacking of layers is described by a set of junction probabilities (P_ij). The relationship between probabilities and the abundance W_i of two different layer types (i and j) can be described as follows: (1) segregation tendency is given by W_i < P_ii and W_j < P_jj; (2) total demixing is obtained for P_ii = P_jj = 1; (3) regular tendency is obtained if W_i < P_ji < 1 and W_j < P_ij < 1; and (4) the boundary between the last distribution labeled chaotic or random is obtained when Wi = P_ji = P_ii, W_j = P_ij = P_jj with ΣW_i = 1 and ΣP_ij = 1 (Reference Drits and TchoubarDrits & Tchoubar, 1990; Reference Sakharov and LansonSakharov & Lanson, 2013).

The fitting strategy is an approach used to determine the structural parameters of materials from experimental XRD data (Reference Oueslati, Mejri and AmaraOueslati et al., 2022a). It involves comparing the experimental diffractogram model with a theoretical model that is created using a principal interstratified structure. This theoretical model can be adjusted by introducing extra contributions, such as a mixed-layer structure, to account for any discrepancies between the experimental and theoretical models. The aim of this fitting process is to achieve an improved agreement between the theoretical and experimental models, which allows for the determination of the structural parameters of the material being studied.

The presence of two MLS does not imply that two particle populations exist physically in the sample (Reference Ammar, Oueslati, Chorfi and RhaiemAmmar et al., 2014a, Reference Ammar, Oueslati, Rhaiem and Amara2014b, Reference Ammar, Oueslati, Ben Rhaiem and Ben Haj Amara2014c; Reference Ferrage, Lanson, Sakharov and DritsFerrage et al., 2005a, Reference Ferrage, Lanson, Malikova, Plançon, Sakharov and Drits2005b; Reference LansonLanson, 2005; Reference Oueslati and MeftahOueslati & Meftah, 2018). Therefore, layers with a similar HS appear in different MLS, contributing to the diffracted intensity, and are expected to have identical properties such as chemical composition, layer thickness, and z-coordinates of atoms. The XRD modeling method’s details are explained extensively in previous work (Reference Ammar, Oueslati, Chorfi and RhaiemAmmar et al., 2014a, Reference Ammar, Oueslati, Rhaiem and Amara2014b, Reference Ammar, Oueslati, Ben Rhaiem and Ben Haj Amara2014c; Reference Ferrage, Lanson, Sakharov and DritsFerrage et al., 2005a, Reference Ferrage, Lanson, Malikova, Plançon, Sakharov and Drits2005b; Reference Manohar, Krishnan and AnirudhanManohar et al., 2002; Reference Oueslati and MeftahOueslati & Meftah, 2018; Reference Oueslati, Rhaiem and AmaraOueslati et al., 2012).

The z-coordinates in the T–O–T layer of the IS content (exchangeable cation, molecules, etc.) are optimized during the modeling process to reduce the disagreement between the theoretical and experimental findings (Table 2). This is controlled using an R_WP unweighted factor, expressed by Reference LansonLanson (2011) and Reference Laverov, Yudintsev, Kochkin and MalkovskyLaverov et al. (2016) as:

Table 2 The types of atoms, their number, and their z-positioning along the c* axis for the case of a TOT phyllosilicate

(4) $R_{\mathrm{WP}}=\sqrt{\frac{\sum {\left({I\left({{}^{\circ }2\theta }_i\right)}_{\exp },-,{I\left({}^{\circ },{2\theta }_i\right)}_{\mathrm{calc}}\right)}^2}{\sum {\left({I\left({{}^{\circ }2\theta }_i\right)}_{\exp }\right)}^2}}\times 100\%$

To achieve optimal quantitative structural characterization of a given sample, it is necessary to search for agreement between the calculated profiles and the experimental profiles (Reference Bérend, Cases, François, Uriot, Michot, Masion and ThomasBérend et al., 1995; Reference Cases, Bérend, François, Uriot, Michot and ThomasCases et al., 1997; Reference Oueslati and MeftahOueslati & Meftah, 2018), regardless of the type of hydration state of the layers or the position of the exchangeable metal cations (located in the middle of the IS along the c* axis).

Case of the SWy-Ni samples

Based on the X-ray experimental results for the SWy-Ni samples, which were subjected to varying conditions of pH, temperature, and duration (pH = 2; T = 50°C; t = 5 h ⟶ pH = 4; T = 100°C; t = 15 h), an asymmetry was observed for the main 001 reflections at 5.8°2θ with d ₀₀₁ ≈ 15 Å, indicating the presence of 2W, filled by Ni²⁺ cations in the middle of IS and bounded between two sheets of water. A shoulder toward the wide angles around 7°2θ (d ₀₀₁ ≈ 12.6 Å) was also observed and was attributed to excess salt in the starting sample SWy-Na. The asymmetry of the 001 reflections was reflected in large values of FWHM and ξ, indicating the appearance of a set of hydration states in the mineral and an incomplete CEP. However, for samples with higher pH, temperature, and duration values (pH = 5; T = 125°C; t = 20 h / pH = 6; T = 150°C; t = 25 h), the absence of the shoulder toward the wide angles (linked to the sodium residue) was observed, and the symmetry of the 001 lines was probably due to a complete CEP (Table 5).

Table 5 Qualitative X-ray analysis of the samples SWy-Ni, SWy-Mg, and SWy-Zn

°2θ Bragg angle, d ₀₀₁ basal distance of the 1^st reflection, D average crystalline size, FWHM full width at half maximum, ξ rationality deviation parameters

Case of the SWy-Mg samples

The X-ray experimental models for SWy-Mg samples obtained at low values of pH, T, and t (pH = 2; T = 50°C; t = 5 h ⟶ pH = 4; T = 100°C; t = 15 h) showed 001 reflections (n = 1) localized at ~5.9°2θ (d ₀₀₁ ≈ 14.9 Å), indicating the appearance of two hydration states (1W and 2W) within the stacks accompanied by partial cation exchange (Reference Ammar, Oueslati and Ben Haj AmaraAmmar et al., 2018). The Mg²⁺ compensating cation could be distinguished from the starting sodium cation Na⁺ by XRD analysis at room conditions in this case (Table 5). For the other complexes (pH = 5; T = 125°C; t = 20 h / pH = 6; T = 150°C; t = 25 h), an increase in the FWHM value was observed, along with the creation of a stacking toward the wide angles (7.15°2θ ⟶ d ₀₀₁ = 12.35 Å), which was attributed to the sodium residue from the starting sample SWy-Na (Fig. 4).

Case of the SWy-Zn samples

The experimental X-ray diffractogram profiles of SWy-Zn samples (Fig. 5) revealed that, for most samples (pH = 2; T = 50°C; t = 5 h ⟶ pH = 5; T = 125°C; t = 20 h), the main 001-reflection was situated at ~ 5.8°2θ (d ₀₀₁ ≈ 15.2 Å), indicating a 2W hydration state. This probably reflects a complete CEP (Reference Oueslati, Rhaiem and AmaraOueslati et al., 2011). However, there was a slight deviation in the intensity of the 001-reflections toward the wide angles with an increase in the applied coupling constraint intensity. The profile of the last sample (pH = 6; T = 150°C; t = 25 h) was positioned at ~ 6°2θ (d ₀₀₁ ≈ 14.7 Å), which was interpreted as the appearance of two hydration states (1W and 2W – interstratified structure), estimated by partial cation exchange, knowing that the zinc (Zn²⁺) hydrate was bound to two layers of water 2W (~ 15 Å) (Table 5).

Case of the SWy-Ni samples

The quantitative XRD analysis of the SWy-Ni series indicated the appearance of two different hydration states as the amplitude of applied stresses increased (Fig. 3). The complexes with small values of pH, T, and t (pH = 2; T = 50°C; t = 5 h → pH = 4; T = 100°C; t = 15 h) indicated the emergence of two hydration states (i.e. 1W → d ₀₀₁ ≈ 12.2 Å and 2W → d ₀₀₁ ≈ 15.2 Å), with 2W being the dominant state. The CEC of the results obtained was satisfied partially by Na⁺ and Ni²⁺ cations. This was because, under ambient conditions, sodium hydrated to form a single water layer (1W) (Reference Oueslati and MeftahOueslati & Meftah, 2018), while nickel hydrated with two water layers (2W). When the applied stress strength was increased, the interstratification spacing (IS) expanded, with the d ₀₀₁ value changing from 15 to 15.4 Å for samples with pH = 5, T = 125°C, and t = 20 h and pH = 6, T = 150°C, and t = 25 h. This expansion occurred due to the transition from an interstratified 1W/2W phase to a harmonically stacked 2W phase, which was saturated by Ni²⁺ cations only. The widening of the IS was attributed to the prolonged contact time (t ≈ 20 to 25 h) of the soil solution (NiCl₂) with the sample (Table 6).

Fig. 3 Modeling of the experimental XRD patterns for SWy-Ni samples. (*) Halite, NaCl

Table 6 Extraction of all structural parameters of the SWy-Ni, SWy-Mg, and SWy-Zn samples, via the modeling approach

MLS Mixed Layer Structure, xW-echa.cat Layer type and associated exchangeable cation, d ₀₀₁ interlamellar distance (Å); nH₂O number of water molecules per half-cell, W_A abundance of layer type A, P_AA relative probabilities of succession law between two-layers type A, R* Reichweite factor R₀ and R₁ describe the MLS with random interstratifications, or with partial segregation/order respectively, $\overline{M}$ average number of sheets per stack, ${\overline{M}}_{\mathrm{tot}}$ total average number of sheets per stack, C Character: H Homogeneous, I Interstratified, R_WP Confidence factor

Case of the SWy-Mg samples

Theoretical models obtained through modeling (Fig. 4) confirmed the heterogeneous character of the samples by establishing a correlation between two types of hydration phases, namely 1W/2W (intermediate phase), regardless of the intensity of the applied external stress. Specifically, the minor contribution of the 1W phase increased from 20 to 45% as the intensity of the applied external stress rose (pH = 2; T = 50°C; t = 5 h ⟶ pH = 6; T = 150°C; t = 25 h). This increase was attributed primarily to the presence of sodium residue in the SWy-Na starting sample. On the other hand, the major hydration state observed in the calculated profile was the 2W phase, which was associated with the layer fragment saturated with the bivalent cation Mg²⁺. This fluctuation in weighting suggests an incomplete (partial) CEP (d ₀₀₁ ≈ 14.8 Å < 15 Å), which aligned with the qualitative analysis. Additionally, the slight shrinkage of the IS (d ₀₀₁ ≈ 14.92 Å ⟶ d ₀₀₁ ≈ 14.84 Å) was due probably to the temperature increase during the CEP (Table 6).

Fig. 4 Modeling of the experimental XRD patterns for SWy-Mg samples. (*) Halite, NaCl

Case of the SWy-Zn samples

The refinement of the experimental model (Fig. 5) uncovered the presence of two types of layers with a similar stacking mode (R₁), as determined by the modeling. This mixed-layer system (MLS) consists of two hydration states (Reference LansonLanson, 2005), namely: (1) 1W with d ₀₀₁ = 12.2 Å, and (2) 2W with d ₀₀₁ = 15.4 Å. Throughout the entire series of experiments (ranging from pH = 2; T = 50°C; t = 5 h to pH = 6; T = 150°C; t = 25 h) a heterogeneous character was observed, characterized by a minor presence of the ubiquitous 1W HS (~20–35% abundance). This 1W state was saturated with the Na⁺ cation, as reported by SWy-M (Reference Oueslati and MeftahOueslati & Meftah, 2018). Conversely, the major phase observed was the 2W phase (80–65% abundance), associated with the elemental part where the CEC was due probably to the temperature increase during the CEP (Table 6) saturated with the Zn²⁺ divalent cation (Reference Tan, Zhang, Zhang, Xie and LiuTan et al., 2008; Reference Oueslati, Mefath, Rhaiem and AmaraOueslati et al., 2009; Shi et al., 2010). This indicated an incomplete CEP. During the CEP, the increase in temperature (T ≈ 50°C ⟶ 150°C) along with the variation in the pH of the SS (pH ≈ 2 ⟶ 6) and the duration of contact (t ≈ 5 h ⟶ 25 h) resulted in the closure (shrinkage) of the IS. This closure was evident from the decrease in the value of d ₀₀₁ (Table 6). It is important to note that, for all the samples examined in the current study, the Debye–Waller temperature factor (the mean square displacement of an atom from the ideal position in the structure) exhibited a variation ranging from 2.3 to 10.9 Ų (Reference Ferrage, Lanson, Sakharov and DritsFerrage et al., 2005a, Reference Ferrage, Lanson, Malikova, Plançon, Sakharov and Drits2005b, Reference FerrageFerrage, 2016).

Fig. 5 Modeling of the experimental XRD patterns for SWy-Zn samples. (*) Halite, NaCl

In this study, the samples saturated with magnesium and zinc demonstrated similar hydration behavior under increasing imposed coupling constraint intensity, contrasting with the sample saturated with nickel. The interlayer space (IS) thickness decreased for SWy-Mg and SWy-Zn, resulting in a reduction of the 2W phase and an increase in the 1W phase. This indicated an incomplete cation exchange process (CEP). Conversely, for SWy-Ni, the IS thickness increased, suggesting a transition from an intermediate hydration state (1W/2W) to a homogeneous state (2W). This observation was confirmed by modeling and the absence and/or disappearance of the sodium residue.

In this work, two hypotheses were developed to explain the hydration behavior of the samples:

1. (1) The first hypothesis suggests that hydration behavior of the SWy-Mg and SWy-Zn series was primarily influenced by the remarkable increase in temperature, while the impact of modifying the pH value of the soil solution (SS), and the duration of contact can be ignored. Previous studies (Reference Chalghaf, Oueslati, Ammar, Rhaiem and AmaraChalghaf et al., 2013; Reference Cui, Zhang and HanCui et al., 2020; Reference Meftah, Oueslati and AmaraMeftah et al., 2010, Reference Meftah, Oueslati and Amara2011; Reference Momeni, Bayat and AjalloeianMomeni et al., 2022; Reference Tlemsani, Taleb, Piraúlt-Roy and TalebTlemsani et al., 2022) demonstrated that the addition of an acidic and/or basic additive (HCl/NaOH) induced significant change in the mineral structure within a pH range of ~ 8–11 (basic medium). However, in the present study, the pH of the SS varied from 2 to 6 and, thus, the impact of pH variation was considered negligible. Similarly, the duration of the CEP was also considered to be negligible. This conclusion was supported by the observation that, despite the relatively long contact time (~ 48 h) during the CEP, the d ₀₀₁ value of the reference sample SWy-Mg (Table 4) remained at ~14.65 Å, indicating partial cation exchange. The modeling further confirmed the presence of three hydration states 0W, 1W, and 2W with percentages of 6, 14, and 80%, respectively. This finding was consistent with the SWy-Mg sample (pH = 2; T = 50°C; t = 5 h) where the CEP lasted only 5 h (Tables 5 and 6) and resulted in an interlamellar distance of 14.9 Å, indicating incomplete cationic exchange. This condition was characterized by the appearance of two phases (1W ≈ 20% and 2W ≈ 80%). The similarity observed in these results challenges the assumption that the structure of the smectite (Sme) evolves with variations in the duration of the CE.

2. (2) The second hypothesis based on the present study considers the relationship between the ionic potential (I_P) and electronegativity (E_N) of different samples. SWy-Mg and SWy-Zn, which have the lowest I_P values of 2.78 and 2.70 eV, respectively (Reference ShannonShannon, 1976), display a similar hydration behavior (d ₀₀₁ ↘) as the imposed constraint strength increased. E_N also followed the same trend, with SWy-Mg having an E_N of 1.31 and SWy-Zn an E_N of 1.65 (Fig. 6). In contrast, for SWy-Ni, increasing the coupling constraint intensity resulted in the expansion of the interlayer spacing (IS) (d ₀₀₁ ↗), which was attributed to its high I_P value. For larger values, the I_P indicated a greater affinity of the cation for water, and as water migrates in the IS, the compensating cations M²⁺ also migrate, leading to IS swelling. It was noteworthy that the I_P value for Ni-saturated Mnt was 2.90 eV (I_{P – SWy-Ni} > > I_{P – SWy-Mg} > I_{P – SWy-Zn}), and E_N = 1.91 (E_{N – SWy-Ni} > > E_{N – SWy-Zn} > E_{N – SWy-Mg}). This hypothesis aligned with a similar study by Reference Mejri, Oueslati, Haj and AmaraMejri et al., (2022a, Reference Mejri, Oueslati and Amara2022b), which investigated the influence of coupling first-order constraints (SS pH variation and thermal gradient) on three different metal cations (Co²⁺, Cu²⁺, and Ba²⁺). The study demonstrated that Mnt samples saturated with compensating cations (SWy-Co and SWy-Cu) possessing larger I_P and E_N values (I_{P – SWy-Co} = 3.08 eV > I_{P – SWy-Cu} = 2.74 eV > > I_{P – SWy-Ba} = 1.48 eV et E_{N – SWy-Co} = 1.88 ≈ E_{N – SWy-Cu} = 1.90 > > E_{N – SWy-Ba} = 0.89) exhibited a specific hydrous behavior, characterized by the expansion of IS (Fig. 7).

Fig. 6 Summary of the water behavior of SWy-Ni, SWy-Mg, and SWy-Zn samples under the effect of second-order coupling stress applied as a function of I_P and E_N, via an XRD modeling approach (Reference ShannonShannon, 1976)

Fig. 7 Summary of the water behavior of SWy-Co, SWy-Cu, and SWy-Ba samples under the effect of first-order coupling stress applied as a function of I_P and E_N, via an XRD modeling approach (Mejri et al., 2022; Reference ShannonShannon, 1976)

The increase in the percentage of the 2W phase was attributed to bivalent cations hydrating at two water layers. This leads to the development of an electronegativity limit (Fig. 8) that describes the hydrous behavior of Mnt saturated with metal cations (SWy-M) when subjected to similar external pressures with varying intensities.

Fig. 8 Limit of the CEP as a function of the electronegativity of the compensating cations (Mejri et al., 2022; Reference ShannonShannon, 1976)

The electronegativity limit defines the point at which layers of Mnt saturated with metal cations (SWy-M) start to open or close based on specific EN values (layer opening > 1.88 and layer closing < 1.65). An area of ambiguity exists between the values of 1.65 and 1.88 where the hydration behavior is not well understood. Therefore, additional experiments using different cations with varying I_P and E_N values should be conducted to gain further insight into this range of ambiguity.

Despite the originality of the first hypothesis, the rest of the work adopted the second idea because it seemed more logical.

It is important to note that the saturation of the monohydrated interlayers (1W) can occur not only with sodium (Na⁺) but also with compensating cations such as Ni²⁺, Mg²⁺, or Zn²⁺, depending on variations in the relative humidity levels (Reference Ammar, Oueslati, Chorfi and RhaiemAmmar et al., 2014a, Reference Ammar, Oueslati, Rhaiem and Amara2014b, Reference Ammar, Oueslati, Ben Rhaiem and Ben Haj Amara2014c; Reference Ferrage, Lanson, Sakharov and DritsFerrage et al., 2005a, Reference Ferrage, Lanson, Malikova, Plançon, Sakharov and Drits2005b; Reference Oueslati, Karmous, Rhaiem, Lanson and AmaraOueslati et al., 2007, Reference Oueslati, Rhaiem and Amara2012). Because the RH was not taken into account during the acquisition of XRD data at the laboratory scale in this study, the 1W hydration phases were considered to be saturated exclusively with monovalent cations, while the 2W hydration phases were saturated exclusively with divalent cations. It is important to emphasize that these models are approximate, where everything is relative.