Effects of the cation ordering in Mg:Al and Zn:Al layered double hydroxides on crystallographic and spectroscopical properties by means of first principles calculations

Applied Clay Science 223 (2022) 106496 Available online 11 April 2022 0169-1317/© 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/bync-nd/4.0/). Research paper Effects of the cation ordering in Mg:Al and Zn:Al layered double hydroxides on crystallographic and spectroscopical properties by means of first principles calculations Carlos Pimentel a , 1 , Alexander P´ erez de la Luz a , b , Alfonso Hern´ andez-Laguna a , C. Ignacio SainzDíaz a , * a Instituto Andaluz de Ciencias de la Tierra, Consejo Superior de Investigaciones Científicas-Universidad de Granada, Av. de las Palmeras, 4, 18100 Armilla, Granada, Spain b Departamento de química, Universidad Aut´ onoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco, 186, col. Vicentina, 09340 Ciudad de M´ exico, Mexico ARTICLE INFO Keywords: DFT Quantum Espresso CASTEP Cation ordering LDH Vibrational properties ABSTRACT Layered double hydroxides (LDH) are interesting materials due to their high absorption and catalytic properties. Their applications in environment, agriculture and pharmaceutical fields are becoming widely important. The interlayer and intralayer cation ordering on layered double hydroxides of Mg:Al 2:1 and Zn:Al 2:1 are studied by means of different ordering models at Density Functional Theory level. The cation ordering in LDH is interesting for monitoring the synthesis of these solids and for the applications of LDH, however it is difficult to determine experimentally. We have explored several ordering arrangements of the cation distribution in Mg:Al 2:1 and Zn: Al 2:1 LDH and the effect of these cation arrangements on some crystallographic and spectroscopic properties. 1. Introduction The layered double hydroxides (LDH) are metal hydroxides forming lamelar structures. LDH are structurally related with brucite, Mg(OH) 2 , where Mg cations are substituted by different relative proportions of other cations and vacancies. LDHs can be generally described using the following chemistry formula (Krivovichev et al., 2010; Andre et al., 2015): [M2+ (1−x)M3+ x(OH)2]x+[An− x/n⋅z H2O]x− where M 2+ =Mg 2+ , Zn 2+ , Fe 2+ …; M 3+ =Al 3+ , Fe 3+ , Cr 3+ …; A nis a charge balance anion (e.g., Cl − , CO 32− , SO 2− ), x is the cationic layer charge and z is the amount of water molecules in the interlayer. The layers are positively charged and anions are intercalated in the interlayer space for neutralizing the layered charge excess. These anions can be exchanged by other inorganic and organic anions (Miyata, 1983; Cavani et al., 1991). This property provides important adsorption capacity to these minerals, acting as an inorganic membrane. This behaviour and the small particle size are some characteristics because of they are considered within the clay minerals group (Forano et al., 2006), although LDH are not silicate compounds. These minerals provide confined spaces in the interlayer zones, which along with the selective membrane behaviour and the energy provided by the electrostatic interactions from the charge gradient offer a scenario for the first prebiotic reactions, which could be critical for the origin of life (Greenwell and Coveney, 2006; Duval et al., 2019). LDHs are easily synthesized in the laboratory and their description can be found in numerous papers (Forano et al., 2006; Figueiredo et al., 2018). However, it is difficult to determine experimentally how the cations are distributed in the crystal structure due to their small crystal domains and stacking disorder (Krivovichev et al., 2010; Zhitova et al., 2010). The knowledge of the cation ordering can be useful for monitoring the synthesis process of these solids, and also for evaluating their catalytic activity regarding to the distribution and segregation of the active sites. Cation ordering in minerals is interesting for crystallographic analysis, for crystal growth, crystal stability and for industrial applications. The formation of synthetic minerals is produced in reaction rates much faster than the formation of natural minerals. Some synthetic minerals * Corresponding author. E-mail address: [email protected] (C.I. Sainz-Díaz). 1 Current address: Universit´ e Grenoble Alpes, CNRS, ISTerre, 38000 Grenoble, France. Contents lists available at ScienceDirect Applied Clay Science journal homepage: www.elsevier.com/locate/clay https://doi.org/10.1016/j.clay.2022.106496 Received 23 November 2021; Received in revised form 12 March 2022; Accepted 22 March 2022 Applied Clay Science 223 (2022) 106496 2 had not enough time for equilibrating into a minimal energy state. This fact affects some properties of the minerals especially the cation ordering, and their properties derived. Then, the cation ordering has great interest for thermodynamic models of mineral formation and as petrogenetic indicators. In last decades, many efforts have been made in cation ordering of clay minerals (Cuadros et al., 1999; Sainz-Díaz et al., 2000; Plançon, 2001; Botella et al., 2004; Palin et al., 2004; Mercier et al., 2005; Ortega-Castro et al., 2009), other silicates (Warren et al., 2001) and other minerals, such as carbonates (Hammouda et al., 2011; Pimentel et al., 2021) and also LDHs (Braterman and Cygan, 2006; Costa et al., 2010, 2011; Zhitova et al., 2010; Cadars et al., 2011; Liu et al., 2020). Cation and anion ordering on LDH structures has been previously experimentally studied finding discrepancies between different studies (Hofmeister and Platen, 1992; Evans and Slade, 2006; Krivovichev et al., 2010). Krivovichev et al. (2010) found ordered cation structure in natural Mg 2 Al(CO 3 ) LDH samples, whereas Zhitova et al. (2010) found similar natural LDH with disordered cation distribution probably by a higher temperature formation. For instance, Kruissink et al. (1981) and Vucelic et al. (1997) reported a random cation distribution in LDH structures, whereas Sideris et al. (2008) found by Nuclear Magnetic Resonance (NMR) studies that in LDH cations are not randomly distributed. However, Vucelic et al. (1997) and Sideris et al. (2008) reported experimentally a common result, M 3+ cations avoid close contacts, indicating that LDH could have local order, even if no longrange cation order is identified as other authors (Cadars et al., 2011; Figueiredo et al., 2021). In addition, Richardson and Braterman (2007) reported that LDH can be synthesized without cation ordering, although, due to an aging process, these structures can end up having cation ordering. In order to try to shed light on this problem, some theoretical studies have been carried out on the LDH structures. However, in some of these works, the effect of the different cation arrangements, i.e. orderdisorder, was not studied and the structures were considered to have the cations arranged only following the avoiding close contact principle (Wang et al., 2001, 2003; Lombardo et al., 2005, 2008; Costa et al., 2010, 2011; Jayanthi et al., 2017). Costa et al. (2010) calculated at DFT level the formation energy of carbonate-LDH from the pristine oxides, hydroxides and metal salts and water considering only the ordered cation distribution. On the other hand, Costa et al. (2011) studied by DFT calculations the hydration and dehydration process in Zn 2 AlCl LDH with an ordered cation configuration. Molecular dynamics simulations based on empirical force fields of Zn 2 AlCl LDH were used for determining the d(003) and d(006) spacings in X-Ray diffraction (XRD) patterns (Pisson et al., 2008). These authors compared two cation distributions, one 2D ordered and one disordered, finding that the cation ordering affects the structural and dynamical properties of the intercalated anions and water species. DFT calculations have been applied for studying the polytypism of LDH (Moraes et al., 2019). However, to the best of our knowledge, a theoretical study considering both 2-D and 3-D cation arrangements between the intralayer and interlayer cation ordering would be interesting. Taking into account the discrepancies on cation order in the literature and the importance of cation order for the industrial applications of LDHs, this work aims to shed light on the cationic ordering by means of modelling at first principles level. Therefore, it has been determined which orderings are energetically more favourable. In addition, new methods are provided for helping the experimental identification of the ordering degree of cations by obtaining theoretical diffractograms and vibrational-spectra. 2. Models The LDH models were taken from previous experimental crystallographic data of hydrotalcite, Mg 6 Al 2 (CO 3 )(OH) 16 ⋅4H 2 O (Allmann and Jepsen, 1969). This experimental formula has been changed according to the following features: i) the Mg 2+ :Al 3+ ratio was changed from 3:1 to 2:1; ii) carbonate groups were removed and substituted by Cl anions, one anion per aluminium cation in the structure, in order to maintain the electroneutrality of the structure in the interlayer space of the three layers; iii) some models were considered anhydrous, i.e., where water molecules were also removed from the structure; and iv) in order to study the Zn-LDH, Mg 2+ cations were substituted by Zn 2+ cations. So, the model formula is either Mg 4 Al 2 (Cl 2 )(OH) 12 or Zn 4 Al 2 (Cl 2 )(OH) 12 . A LDH 2x3x1 supercell was constructed for both Mg-LDH and ZnLDH. The Al 3+ cations substitutions were firstly placed tending a maximal dispersion along each octahedral sheet. Taking into account that the unit cell comprises 3 layers, different ordering of Al 3+ cations models were considered (Fig. 1). The substitution of Al 3+ cations in the LDH layers were followed by the introduction of Cl − anions between the interlayers. The minimum and maximum number of Cl − anions considered in the interlayers was 0 and 4 per interlayer, respectively. The hydrated models were generated placing a minimal water content in the interlayer space, such as, three molecules in each interlayer space per supercell. Initially, each water molecule was placed in the centre of the interlayer space, in a parallel orientation with respect to the ab plane, i.e. (001), and maximally dispersed along the supercell with the H atoms oriented towards the chloride anions and the O atoms close to the H atoms of the hydroxyl groups of the mineral surface. A Mg-LDH 4x6x1 supercell was also constructed to study the effect of Cl Cl OH OH OH MMAl MAlM OH OH OH Cl Cl OH OH OH Al M M MAlM OH OH OH Cl Cl OH OH OH MAlM MMAl OH OH OH 2-2-2 2-3-1 1-4-1 3-0-3 Cl Cl OH OH OH MMM MAlM OH OH OH Cl Cl OH OH OH Al M Al MAlM OH OH OH Cl Cl OH OH OH MAlM MMAl OH OH OH Cl OH OH OH MMAl MMM OH OH OH Cl Cl Cl OH OH OH Al Al M MAlAl OH OH OH Cl Cl OH OH OH MAlM MMM OH OH OH Cl Cl Cl OH OH OH Al M Al MAlM OH OH OH Cl OH OH OH MMM MMM OH OH OH Cl Cl OH OH OH MAlM Al M Al OH OH OH Fig. 1. Scheme of several cation distributions of 2x3x1 LDH structure considered in this study: 2-2-2 (homogeneous distribution of Al cations), 2-3-1, 1-4-1 and 3-0-3, being each digit the number of Al 3+ in each layer. M denotes both Magnesium and Zinc atoms for Mg-LDH and Zn-LDH, respectively. Al denotes aluminium atoms, Cl denotes chlorine atoms and OH denotes the OH layers both above and below the cationic layers. C. Pimentel et al. Applied Clay Science 223 (2022) 106496 3 the intralayer cationic order. In this case, three different arrangement of Al 3+ cations were considered in the second cationic layer (Fig. 2): i) maximum dispersion (MaxD); ii) all cations segregated (minimum dispersion) (MinD); and iii) all cations in line (L). 3. Methodology Preliminary calculations were performed exploring different force fields (FF). However, in the optimization at variable cell the cations lose the coplanarity that could alter our studies of cation ordering (see Fig. S1 in Supplementary Support). Such alterations of the octahedral sheets had been also observed in previous theoretical studies conducted using molecular dynamics with FF (Wang et al., 2001; Lombardo et al., 2008; P´ erez-S´ anchez et al., 2018). In these cases, however, the deformations can even lead to bending the octahedral layers, due to the rearrangement of chlorine ions and water molecules in the interlayer (Lombardo et al., 2008; P´ erez-S´ anchez et al., 2018). To overcome this alteration, quantum mechanical calculations based on Density Functional Theory (DFT) were used, applying 3-D periodical boundary conditions based on plane wave conditions, by using CASTEP (Clark et al., 2005), included in Materials Studio package (Biovia, 2018), and Quantum-Espresso (Giannozzi et al., 2009, 2017) codes with the generalized gradient approximation (GGA), and the Perdew-BurkeErnzerhof functional (PBE) for the exchange-correlation potential (Perdew et al., 1996). The graphical analysis of crystal systems have been performed by using the VESTA (Momma and Izumi, 2011) and XCRYSDEN (Kokalj, 1999) software. In the CASTEP calculations, on-the-fly generated (OTFG) ultrasoft pseudopotentials were used including Koelling-Harmon relativistic treatment (Vanderbilt, 1990). This computational approach was previously useful for study LDH (Liu et al., 2020; Li et al., 2021), and other minerals (Sainz-Díaz et al., 2004a, 2004b). Preliminary total energy calculations were performed at different values of energy cut-off in order to optimize the calculation parameters and to find the optimal value of energy cut-off for our mineral. We observed that the total energy decreases with the increase of energy cut-off until reaching a planar profile where the variation of total energy with respect to the energy cut-off is not significant (see Fig. S2a in Supplementary Support). This preliminary study allowed optimization of the calculation parameters in order to obtain the maximum precision and reliability of the simulation with the minimum computational cost. This cut-off was 571.4 eV and we considered this value for the rest of calculations in this work, although some further calculations were also carried out at a cut-off of 630 eV. All calculations were performed in the Γ point of the irreducible Brillouin zone of the crystal lattice. Besides, the effect of dispersion corrections from Grimme (2006) and Tkatchenko (Tkatchenko and Scheffler, 2009) methods were compared fully optimizing the crystal structure including the atomic positions and the cell parameters. All structures of LDH with different cation ordering were optimized using the same calculation conditions and 2x3x1 supercell, except for the intralayer order simulations, which were performed using a 4x6x1 supercell with a cut-off of 489.8 eV. The powder X-ray diffraction patterns were simulated from the crystal structures using the REFLEX code (Biovia, 2018). Infrared and Raman vibration modes frequencies were calculated using CASTEP code (Clark et al., 2005). Prior to infrared and Raman calculations, the optimized structures were re-optimized with an energy cut-off of 630 eV, in order to avoid the presence of negative frequencies in the spectra. Subsequently, OTFG norm conserving pseudopotentials and an energy cut-off of 925.2 eV were used. In the Quantum Espresso calculations, PAW (Projector Augmented Wave) pseudopotentials (Bl¨ ochl, 1994) and USPP (ultrasoft pseudopotentials) (Vanderbilt, 1990) were tested and we chose the PAW pseudopotentials because they allowed a better description of the experimental values of the cell parameters of these systems than with the USPP pseudopotentials. A preliminary study was also performed to find the optimal parameters and obtain the best precision at minimum computational cost. Different energy cut-off values were tested for finding the optimal calculation conditions. So, preliminary total energy calculations were performed with different values of energy cut-off E cut (wfc) (40–140 Ry) (see Fig. S2b in Supplementary Support) and cut-off for the rho charge density (160–840 Ry) with different ratios of rho-cut-off/energy-cut-off (4–7) (Fig. S3). Initially the energy decreased drastically with the increase of energy cut-off, decreasing the slope of the profile until reaching a planar zone where the total energy becomes practically constant with the increase of energy cut-off. Then, the energy cut-off E cut (wfc) used for crystal structures calculations was 100 Ry and with a charge density cut-off of 400 Ry in this work. This level is a good compromise between calculation level and computational effort. In addition, several k point grid samplings for the optimization of the Brillouin zone (Monkhorst and Pack, 1976) were explored, finding the optimal calculations conditions (see Table S1 in Supplementary Support) with 3x2x1 k-points grid. In all calculations dispersion corrections were included according to the DFT-D3 scheme (Grimme et al., 2010). Finally, the frequencies of the vibration normal modes of the optimized crystals were obtained from calculations based on the Density Functional Perturbation Theory (DFPT) (Baroni et al., 1987, 2001). The spectroscopical vibration modes were analysed by using the Molden code (Schaftenaar and Noordik, 2000). 4. Results and discussion 4.1. Optimization of LDH structures The full optimization, atomic positions and lattice cell parameters, calculated with dispersion corrections yielded a crystal structure with closer cell parameter values to experimental data than without considering these corrections (Table 1). Therefore, the dispersion correction of Al Mg Mg Al Mg Mg Mg Al Mg Mg Al Mg Al Mg Mg Al Mg Mg Mg Al Mg Mg Al Mg Al Al Al Al Mg Mg Al Al Al Al Mg Mg Mg Mg Mg Mg Mg Mg Mg Mg Mg Mg Mg Mg Al Al Al Al Al Al Mg Mg Mg Mg Mg Al Mg Mg Mg Mg Mg Al Mg Mg Mg Mg Mg Mg MaxD MinD L Fig. 2. Scheme of the distributions of Mg and Al in the second cationic layer of the Mg-LDH: maximum dispersion (MaxD), minimum dispersion (MinD) and all cations in line (L). Table 1 Crystal structures of the 2x3x1 supercell of Mg-LDH (Mg:Al =2:1) calculated without and with dispersion correction with CASTEP, comparing with experimental values (distances in Å and angles in ◦). Parameters Without correction TS a Grimme b Exp c a 3.090 3.064 3.060 3.04 b 3.083 3.056 3.054 3.04 c 22.48 22.154 22.259 23.0 α 89.8 89.7 89.6 90 β 90.0 90.1 90.1 90 γ 120.4 120.4 120.4 120 a Tkatchenko dispersion correction. b Grimme dispersion correction. c Experimental values from Figueiredo et al. (2021). C. Pimentel et al. Applied Clay Science 223 (2022) 106496 4 Grimme was included in all calculations of this work. Once determined the best theoretical approach to study the LDH structures, both Mg-LDH and Zn-LDH structures with an equal distribution and maximum dispersion of Al 3+ cations on the 3 hydroxide layers, i.e. 2 Al 3+ per layer, were optimized by relaxing atomic positions and crystal lattice (Fig. 3, Table 2). In both optimized LDH structures, i. e. Mg and Zn, the cell parameters agree with those reported for experimental LDH with the same M 2+ :Al 3+ ratio (Ennadi et al., 2000; Lombardo et al., 2008; Mahjoubi et al., 2017; Figueiredo et al., 2021), with previous theoretical calculations of LDH (Andre et al., 2015), and with previous calculations using CASTEP on a monolayer brucite model (Liu et al., 2020). Comparing the results using both theoretical approximations, CASTEP and QE, both can be considered similar. No improvement was observed increasing the cut-off energy from 571.4 eV to 630 eV in the CASTEP calculations. As in the case of the experimental LDH, theoretical a and b parameters are slightly higher for Zn-LDH than for Mg-LDH, due to the higher ionic radii of Zn 2+ compared to Mg 2+ (Shannon, 1976). Moreover, almost all the cell angles can be considered similar to the experimental ones. In both LDH structures, Mg-LDH and Zn-LDH, the H – O bonds have an average length of 0.981 and 0.982 Å for the 2-2-2 cation arrangement, respectively (see radial distribution function in Fig. S5). In general, the chloride anions are in the centre of the interlayer with an average d(Cl…HO) distances of 2.32 Å and 2.35 Å for Mg-LDH and Zn-LDH, respectively. Nevertheless, the main differences between the theoretical and experimental results are in the c parameter, which are higher in the experimental LDH (Table 2). This difference is due to the different hydration state of the LDH, which are anhydrous in our calculations and hydrated in the experimental results. Therefore, 9 water molecules (3 per interlayer) were added to the 3x2x1 supercell of Mg-LDH and ZnLDH, i.e. 1.5 water molecules per unit cell. After the optimization using both CASTEP and Quantum Espresso calculations (Fig. 4), c is higher in the hydrated phases (Table 3), while all other parameters remain close to the values of the anhydrous structure. These results are in good agreement with the experimental results previously reported (Miyata, 1983; Boclair et al., 1999; Ennadi et al., 2000; Lombardo et al., 2008; Mahjoubi et al., 2017; Figueiredo et al., 2021). However, there are still some differences in the c parameters between the theoretical and experimental structures, which are influenced by the total number of water molecules in the interlayers (Wang et al., 2001; Pisson et al., 2008). Moreover, as stated by Figueiredo et al., 2021, depending on the method used to calculate the hydrated structure, different amounts of water molecules will be needed to reach the c parameter measured on AB Fig. 3. Crystal structure of a 2x3x1 supercell of Mg-LDH (A) and Zn-LDH (B) optimized using CASTEP code. Two Al 3+ cations can be found in each layer with a maximum dispersion. All the figures of structural models have been constructed using VESTA software (Momma and Izumi, 2011). Table 2 Unit cell parameters of anhydrous Mg-LDH and Zn-LDH, with 2 Al 3+ cations per layer, calculated using CASTEP and Quantum Espresso and compared with experimental data. Parameters Mg-LDH Zn-LDH CASTEP QE Exp a CASTEP QE Exp a a 3.060 (3.061) 3.075 3.04 3.131 (3.125) 3.123 3.08 b 3.054 (3.054) 3.066 3.04 3.114 (3.107) 3.100 3.08 c 22.259 (22.117) 22.020 23.0 22.287 (22.000) 21.950 23.22 α 89.6 (89.3) 89.6 90 89.3 (89.4) 89.8 90 β 90.1 (90.1) 90.0 90 90.0 (90.0) 89.9 90 γ 120.4 (120.4) 120.4 120 120.8 (120.7) 120.7 120 d(003) 7.42 (7.35) 7.33 7.67 7.43 (7.33) 7.32 7.73 In CASTEP parameters at two different cut-off are given: 571.4 eV and 630 eV (in brackets). All the distances are in Å and angles in ◦. a Experimental values from Figueiredo et al. (2021). AB Fig. 4. Hydrated crystal structure of a 2x3x1 supercell of Mg-LDH (A) and ZnLDH (B) optimized using CASTEP code. Two Al 3+ cations and 3 water molecules can be found in each layer and interlayer, respectively. Table 3 Hydrated LDH structures calculated using CASTEP and QE with 1.5 water molecules per unit cell. Parameters Mg-LDH hyd Mg-LDH hyd Zn-LDH hyd Zn-LDH hyd CASTEP QE CASTEP QE a 3.081 (3.081) 3.086 3.140 (3.138) 3.120 b 3.070 (3.070) 3.079 3.121 (3.119) 3.103 c 23.630 (23.630) 23.241 23.267 (23.122) 23.110 α 92.2 (92.2) 90.3 91.0 (90.6) 90.8 β 88.4 (88.4) 90.0 89.3 (89.7) 89.8 γ 120.3 (120.7) 120.6 121.0 (120.9) 120.7 d(003) 7.87 (7.87) 7.75 7.75 (7.71) 7.70 In CASTEP two different cut-off were used: 571.4 eV and 630 eV (in brackets). All distances are in Å and angles in ◦. C. Pimentel et al. Applied Clay Science 223 (2022) 106496 5 the experimental LDH. In general, the water molecules remain close to the centre of the interlayer changing their positions from the initial one, being the distances between atoms in the interlayer of Mg-LDH and ZnLDH structures the followings: d(Cl…OH) distance of 3.06 Å and 3.03 Å; d(H 2 O…HOM) of 2.06 and 1.95 Å, and d(H 2 O…Cl) of 2.89 Å and 2.65 Å. Both anhydrous and hydrated LDH structures optimized using CASTEP and QE keep the coplanarity of the octahedral layers (Figs. 3 and 4), in contrast with the preliminary results obtained using FF of anhydrous LDH (Fig. S1). The aim of this work is to study the effect of the cation order in the LDH structures. It is therefore necessary that the layers and interlayers of the structures used are as unaltered as possible in order to be able to determine the real effect of the different cation arrangements, which, due to the lack of suitability of the FF methods, has led to the study of these phases using quantum mechanics calculations. Moreover, the obtained parameters and angles are close to those reported in the literature (for both theoretical and experimental LDH) and close to the hexagonal crystal system (i.e. α =β =90◦and γ =120◦), so, both calculation methods are validated to be used, since no symmetry constraints were imposed on these structures in both CASTEP and QE calculations. Then, the calculations of the different ordering of Al 3+ cations were carried out by using only CASTEP with a cut-off of 571.4 eV. 4.2. Cation ordering on LDH structures Once optimized the Mg-LDH and Zn-LDH structures with 2 Al 3+ cations per octahedral layer (i.e. 2-2-2), three new structures with different Al 3+ cation arrangements were created to study the effect of the cation order on LDH structures. Such structures were designed by moving the aluminium cations between the different layers, being as follows: 2-3-1, 1-4-1 and 3-0-3 (Fig. 1), each number indicates the number of Al 3+ cations in each octahedral layer. In all these structures with different Al 3+ cation arrangements were also optimized at variable volume, and the a and b parameters remain quite close to the values of the initial structure, while c parameter was increased in the disordered structures compared to the initial structures (Tables 4 and 5). The highest c values in disordered LDH structures were in the 1-4-1 one for both Mg-LDH (22.899 Å) and Zn-LDH (22.492 Å). However, these values cannot be compared to those obtained experimentally due to the different hydration states. Therefore, these values are a sign of the stresses to which the lattice is subjected with the various cation arrangements. Moreover, comparing the energies of the different structures, the initial ordered structure (i.e. 2-2-2) has the lowest energy and can be assumed to be the most probable cation arrangement to be found in LDH structures. On the contrary, 1-4-1 and 3-0-3 seems to be the less probable configurations to be found in LDH structures due to their highest energies because of the distortions produced on the octahedral layers (Fig. 5 and Fig. S4). The same phenomenon is found in both Table 4 Interlayer Al 3+ cation ordering in Mg-LDH. Cation pattern 2-2-2 2-3-1 1-4-1 3-0-3 Anion pattern A222 A222 A231 A231 A141 A222 A312 A303 a 3.060 3.064 3.070 3.055 3.058 3.057 3.075 3.080 b 3.054 3.050 3.051 3.046 3.050 3.052 3.049 3.029 c 22.259 22.642 22.542 22.899 23.175 23.039 22.613 19.298 α 89.6 90.0 88.6 91.9 90.6 88.5 89.5 89.6 β 90.1 90.0 90.4 91.8 91.4 90.5 90.0 92.6 γ 120.4 120.4 120.3 120.2 119.3 120.2 120.5 120.1 energy 0 0.317 0.513 0.727 1.034 1.059 0.937 0.641 d(003) 7.42 7.55 7.51 7.62 7.72 7.68 7.54 6.42 Numbers indicate the number of Al cations in each LDH layer. The 2-2-2 one is the original structure optimized. Energy is the energy difference (in eV) per unit cell with respect to the lowest energy configuration. Distances are in Å, and angles in ◦. Table 5 Interlayer Al 3+ cation order in the Zn-LDH structure. Cation pattern 2-2-2 2-3-1 1-4-1 3-0-3 Anion pattern A222 A222 A231 A231 A141 A312 A303 A222 a 3.131 3.130 3.139 3.095 3.107 3.147 3.147 3.106 b 3.114 3.098 3.100 3.106 3.131 3.101 3.093 3.113 c 22.287 22.472 22.620 22.492 22.970 22.402 21.576 22.554 α 89.3 90.0 88.0 89.1 85.8 92.1 88.3 90.2 β 90.0 90.1 91.0 90.9 90.3 92.2 91.8 89.3 γ 120.8 120.6 120.6 118.7 119.3 121.1 120.8 120.9 energy 0 0.314 0.490 0.674 1.012 0.908 1.313 0.976 d(003) 7.43 7.49 7.54 7.50 7.63 7.45 7.19 7.52 Numbers indicate the number of Al cations in each LDH layer. The 2-2-2 one is the original structure optimized. Energy is the energy difference (in eV) per unit cell with respect to the lowest energy arrangement. Distances are in Å, and angles in ◦. AB Fig. 5. Crystal structure of a 2x3x1 supercell of 1-4-1 of Mg-LDH (A) and ZnLDH (B) optimized using CASTEP code. As can be seen in B, Zn-LDH shows a distorted octahedral layer in the sheet with 4 Al 3+ cations. C. Pimentel et al. Applied Clay Science 223 (2022) 106496 6 systems, Mg-LDH and Zn-LDH with similar energy differences between the interlayer cation ordering arrangements. On the other hand, within this interlayer cation ordering, we have to consider also the anion ordering, because of some changes in this ordering can alter the charge balance within the interlayer space. In the most stable cation arrangement, 2-2-2, the anion distribution is also ordered 2-2-2, that we can name A222 to distinguished from the cation ordering nomenclature. In the cation arrangement 2-3-1 the A222 anion distribution is also the most stable. Nevertheless, we calculated the A231 distribution and it was 0.195 eV/unit-cell less stable than A222. In the 14-1 model the A222 configuration is not the most stable one. The A231 is 0.337 eV/unit-cell more stable than A222, because in the …1-4-1-1-41… interlayer cation sequence more anions have to be closer to the layer with more Al cations for change compensation (Table 4). However, the A141 is less stable (0.307 eV/unit-cell) than A222 because it produces a deformation in the cationic layer due to the high negative charge in the interlayer. For the 3-0-3 model, the A312 has higher energy than A303 (0.296 eV/unit-cell). However, the A303 configuration seems to be the least probable, due to the high deformation observed in the structure. In the A303 configuration, the cationic layers above and below the chlorine-free interlayer are very close, resulting in the deformation of the OHs in the layer without aluminium cations (see Fig. S4). Similar behaviours have been observed in Zn-LDH structures (Table 5). Therefore, we can conclude that for cation distributions 2-2-2 and 2-3-1, the most stable anion configuration is the A222; while for cation distributions 1-4-1 and 3-0-3, the most stable anion configurations are those in which the anions are distributed according to balance the charges, without acquiring the arrangements of the cations, i.e. A231 and A312, respectively. Taking into account that the ordered 2-2-2 interlayer distributions are the energetically most favourable for Mg-LDH and Zn-LDH, the intralayer arrangement of the aluminium atoms within the cationic layers has been also studied in the central layer of both Mg-LDH and ZnLDH 2-2-2 structures. Three different intralayer arrangements of Al cations were considered in the second cationic layer (Fig. 2): MaxD¸ MinD, and L shape. After the optimization, all structures have almost the same lattice parameters as the original structure (Table 6). However, the energy of the structures is different, being the lowest energy the original ordered structure (i.e. 2-2-2 structure) with maximal intralayer Al dispersion and the one with highest energy is the structure with minimum dispersion of the Al 3+ cations. These energy differences of intralayer ordering are smaller than the above interlayer ordering. This indicates that the maximal dispersion of Al 3+ cations is the most probable ordering in both senses, interlayer and intralayer ordering. Nevertheless, the experimental synthetic preparation processes of samples are at room or higher temperatures in fast reactions where a certain proportion of some of the above energetically disfavoured cation arrangements can be formed in both systems. In contrast to synthetic LDH, Krivovichev et al. (2010) reported a crystallographic analysis of several natural LDH crystals considering both 2D (intralayer) and 3D (interlayer) ordering finding a natural tendency to form ordered 2D and 3D superstructures in the sulfates and carbonates LDH with M 2+ -M 3+ ratio of 2:1. Previous experimental studies have observed a cation ordering phenomenon during the aging of the Mg-LDH with Mg:Al 2:1 ratio by a dissolution-recrystallization process (Richardson and Braterman, 2007), confirming our discussion. Nevertheless, previous experimental studies of LDH with Mg:M 2:1 ratio have demonstrated that trivalent M 3+ cations are completely scattered, in the octahedral layers of Mg:Fe LDH by X-ray absorption (EXAFS) (Vucelic et al., 1997) and of Mg:Al LDH by Nuclear Magnetic Resonance (NMR) (Sideris et al., 2008; Cadars et al., 2011) studies. 4.3. Diffractograms After optimizing all structures with the different cation arrangements, diffractograms for each structure were simulated without imposing any symmetry restriction. Therefore, small diffraction peaks can appear due to changes in the crystal lattice. Nevertheless, some of these peaks of low intensity would not appear by imposing its original R3m crystal system, due to the limitation of our models where only short range ordering is studied. In all diffractograms, the main peaks appear in the region of 10–15◦ for (003) reflection, 20–25◦for (006), ~35◦(012), ~40◦for (015) and 45–50◦for (018) (Figs. 6–8), which are in good agreement with the experimental diffractograms previously reported (Cavani et al., 1991; Leroux et al., 2001; Forano et al., 2006; Pisson et al., 2008; Andre et al., 2015). In the case of structures with different numbers of Al 3+ cations per layer, a detailed analysis makes it possible to distinguish the different structures. Thus, in the case of Mg-LDH, the different positions and shapes of the peaks corresponding to (006), (015) and (018) reflections could allow to differentiate between the different cation arrangements (Figs. 6 and 7). The non-ordered arrangements produce an additional reflection at 8◦that is not observed in the 2-2-2 one (Fig. 6). This low angle reflexion comes from the higher space planes along the c axis as a consequence of the interlayer disorder, being as lower angle as the highest is the asymmetry coming from the interlayer disorder. This fact is interesting for interpreting experimental XRD analysis in these LDH. For instance, in the diffractogram reported by Andre et al. (2015), the author interpreted as an artefact one peak close to 8◦. However, we have discovered that it could not be an artefact and it can be the 002 reflection produced by the different non-ordered arrangement of the Al 3+ cations in the cationic layers. This peak has a certain intensity in the 3-0-3 configuration. It is interesting to note that this 002 peak has not been observed in other theoretical studies on LDH in which only one layer and one intralayer have been used (Costa et al., 2011), supporting the goodness of the results obtained in this work. On the other hand, the presence of multiple peaks at 35◦, 40◦and 47◦ zones in disordered arrangements, like 4-1-4 (Fig. 6c) is consistent with the broad peaks observed experimentally in these zones in LDH synthesized (Boclair et al., 2001; Frost et al., 2009). In the intralayer ordering configurations (Fig. 7A and B), only differences in relative intensity are observed. The MinD and L arrangements show reflections at <10◦that do not appear in MaxD. Probably they are related with the cation ordering. Nevertheless, their relative intensities are too small (<1%) to be considered. For Zn-LDH structures, the peaks that could allow to distinguish between the different cation arrangements are those belonging to (012), (015) and (018) reflections (Figs. 7C, D and 8). In addition, it could be also possible to identify a peak close to ~8◦in the 1-4-1 and 3-0-3-structures, and very small in the 2-3-1, which belongs to the (002) plane, and comes from the larger space due to the interlayer disorder. In this ZnLDH case, the effect of distortions coming from the interlayer disorder Table 6 Intralayer Al 3+ cation ordering in the 2-2-2 interlayer arrangement of 4x6x1 supercells of Mg-LDH and Zn-LDH optimized with CASTEP (E cut-off =489.8 eV). Parameters ordering Mg-LDH Zn-LDH MaxD MinD L MaxD MinD L a 3.058 3.056 3.055 3.128 3.127 3.126 b 3.048 3.045 3.043 3.106 3.100 3.093 c 22.472 22.530 22.490 22.431 22.464 22.441 α 89.6 90.0 90.0 89.4 89.8 89.8 β 90.0 90.1 89.9 90.0 89.9 90.1 γ 120.4 120.3 120.2 120.8 120.4 120.3 energy 0 0.132 0.094 0 0.087 0.081 MaxD is the original structure optimized and discussed in the previous section. MinD refers to the structure with all cations bound together and L refers to the structure with all cations in line. Energy is the difference per unit cell with respect to the lowest energy configuration. All the distances are in Å, angles in ◦ and energy in eV. C. Pimentel et al. Applied Clay Science 223 (2022) 106496 7 Fig. 6. XRD diffractograms of the interlayer cation arrangements of Mg-LDH, 2-2-2 (A), 2-3-1 (B), 1-4-1 (C), and 3-0-3 (D). All diffractograms have been truncated to allow better visualisation of the less intense peaks, being the peak (003), ~12 ◦the most intense one with 100%. This is extended to the rest of diffractograms below. C. Pimentel et al. Applied Clay Science 223 (2022) 106496 8 Fig. 7. XRD diffractograms of the intralayer cation arrangements of Mg-LDH and Zn-LDH. Mg-LDH diffractograms for the different cation arrangements are: MaxD (see Fig. 6A), MinD (A), and form L (B). For Zn-LDH the diffractograms correspond to MaxD (see Fig. 8a), MinD (C), and form L (D). C. Pimentel et al. Applied Clay Science 223 (2022) 106496 9 Fig. 8. XRD diffractograms of the interlayer cation arrangements of Zn-LDH, 2-2-2 (A), 2-3-1 (B), 1-4-1 (C), and 3-0-3 (D). C. Pimentel et al.