The unit-cell parameters of lizardite-1T (S.G. P31m) (a=b= 5.37 Å, c = 7.36 Å) compare well with previous values obtained at the same theoretical level (e.g., Prencipe et al., 2009; Hossain et al., 2001; Adebayo et al., 2011; Tunega et al., 2012; Ghaderi et al., 2015). As usually observed in DFT modeling performed at the GGA level, they are overestimated with respect to their experimental counterparts (e.g., a=b= 5.3267 Å, c= 7.2539 Å; Gregorkiewitz et al., 1996). Each layer of the structure contains a pseudo-hexagonal silica sheet of corner-shared SiO4 units linked to a trioctahedral sheet of edge-sharing MgO2(OH)4 octahedra. Selected theoretical lengths of cation oxygen bonds (Table 1) are in good agreement with the experimental findings and consistent with previous theoretical calculations (Balan et al., 2002; Prencipe et al., 2009). The Mg–O(Si) distance is the longest Mg–O distance, and the apical Si–O bonds are shorter than the equatorial ones. The interlayer-OH bonds is longer than the inner-OH bond by 0.004 Å. The theoretical magnitude of the ditrigonal distortion (α=-4.1∘) is slightly overestimated with respect to the experimental value of -2.6∘ (Gregorkiewitz et al., 1996).

Vibrational properties of lizardite (Table 2) are consistent with those previously determined (Balan et al., 2002; Prencipe et al., 2009). Note however that the theoretical frequencies slightly differ from those of Balan et al. (2002) due to the full relaxation of the unit cell in the present study and use of different pseudo-potentials. The inner-OH stretching mode leads to a weak absorption band at 3783 cm-1 (Fig. 1). The transverse optical (TO) frequency of the in-phase stretching mode (A1 symmetry) of interlayer-OH groups is calculated at 3721 cm-1 (Table 2) and leads to an absorption band at 3740 cm-1 in the spectrum computed for a (001) platy particle shape (Fig. 1). For a mode polarization along the [001] direction, this higher frequency coincides with the longitudinal optical (LO) frequency of the mode (Balan et al., 2005), indicating a LO–TO splitting of 19 cm-1. This value compares well with those previously determined (21 cm-1, Balan et al., 2002; 14 cm-1, Prencipe et al., 2009). The degenerate out-of-phase stretching mode (E symmetry) of interlayer-OH groups is calculated at 3704 cm-1 (Table 1).

At lower frequency (Fig. 2), the stretching modes involving apical or equatorial Si–O bonds correspond to absorption bands at 1062 and 880 cm-1, respectively, with the former being calculated at the LO frequency because of the platy morphology of the particle (Balan et al., 2002). The bands at 643, 607 and 590 cm-1 correspond to the libration of interlayer-OH groups, the libration of inner-OH group and the hindered translation in the [001] direction of interlayer-OH groups, respectively. The bands at 422 and 401 cm-1 correspond to more complex displacement patterns involving the interlayer-OH groups and contributions of Mg and Si cations. Finally, the band at 274 cm-1 involves a collective atomic motion corresponding to an internal shearing of the layers parallel to the (001) plane.

Cationic substitution at the octahedral site reduces the 3m symmetry of the system to a mirror symmetry. The average Fe2+ oxygen bond length increases from 2.09 to 2.13 Å due to the slightly larger ionic radius of Fe2+ (0.78 Å) compared to that of Mg2+ (0.72 Å) (Shannon, 1976). The length of inner-OH (OH4) and interlayer-OH (OH3) groups increases by 0.001 to 0.002 Å with respect to those in pure lizardite (Table 1). The three interlayer-OH groups linked to the substituting cation are not equivalent. The interlayer-OH group located on the mirror plane (noted OHm) can be distinguished from the two other OH groups (noted OHe), which are symmetrically equivalent by mirror operation. In the Fe2+-bearing system, the OHm is 0.001 Å shorter than the two OHe groups.

These local structural changes affect the vibrational properties. The presence of a Fe2+ cation in the coordination sphere of the inner-OH group shifts its vibrational frequency from 3783 to 3761 cm-1 (Table 2). The Born effective charge tensor of hydrogen is also affected, and the IR absorption coefficient of the corresponding OH stretching band increases by 33 % with respect to that in pure lizardite. The stretching modes related to the interlayer-OH groups are also shifted at lower frequency with respect to the interlayer stretching modes of pure lizardite (Table 2). Due to the symmetry reduction, the mode at 3686 cm-1 is dominantly related to the shorter OHm bond, whereas the mode at 3676 cm-1 involves the out-of-phase stretching of the two other OHe groups. The intermediate mode at 3678 cm-1 combines the in-phase stretching of the OHe groups with an out-of-phase motion of the OHm group. Compared with the splitting of interlayer-OH stretching modes of A1 and E symmetry in pure lizardite (∼ 20 cm-1), the frequency splitting of the OH modes associated with the substitutional defect is reduced to less than 10 cm-1.

The effect of the substituting Fe2+ cation on the stretching frequency of the bands related to the other more distant OH groups, which are only linked to Mg cations, does not exceed 1 cm-1 (Fig. 1). The presence of Fe2+ has a weak effect on the other vibrational modes of the system (Fig. 2), which is consistent with the limited structural distortion of the octahedral sheet induced by the impurity, also previously reported by Scholtzová and Smrčok (2005). A 3 cm-1 splitting of the band related to the basal Si–O stretching mode leads to a shoulder at 877 cm-1 (not visible on Fig. 2). A more significant change affects the collective mode at 274 cm-1, which is split and downshifted to 264 cm-1. This suggests that the opposite shift reported by Baron and Petit (2016) as a function of Ni concentration in the lizardite-népouite series is predominantly due to the decrease in the system molar volume. This effect is not accounted for by the present modeling approach, which aims at determining the properties of defective systems in the high dilution limit. Weak additional bands related to a modification of the OH libration modes are observed in the 630–670 cm-1 range.

The experimental FTIR spectra of lizardite display the signals previously interpreted in the light of the theoretical modeling of pure lizardite (Balan et al., 2002; Prencipe et al., 2009). They are ascribed to the inner-OH stretching at 3703 cm-1 and to the in-phase (A1 symmetry) and out-of-phase (E symmetry) stretching of interlayer-OH groups at 3684 and 3645 cm-1, respectively (Fig. 4). Note that the frequency of the stronger in-phase stretching band of the interlayer-OH groups can display some variability depending on the sample microstructure and experimental geometry. These variations are related to long-range macroscopic electrostatic interactions affecting the vibrational spectra of polar crystals and are commonly observed in the powder spectra of hydrous phyllosilicates (Farmer, 1998, 2000; Balan et al., 2001, 2002, 2005) and layered hydroxides (Balan et al., 2008). In the case of powder spectra recorded on samples with arbitrary particle shapes, the intense band can be observed at a frequency intermediate between the corresponding TO and LO mode frequencies, with a width similar to the LO–TO splitting. For more specific shapes, such as blocky or cubic particles, the spectra can display asymmetric bands with components close to the LO and TO frequencies that can manifest as shoulders or inflection points (Fuchs, 1975). In the case of lizardite, the main band observed in the infrared spectrum of a thin film has been decomposed in two components at 3669 and 3688 cm-1, accounting for its asymmetry (Trittschack et al., 2012). Similarly, a component is observed at ∼ 3664 cm-1 as a shoulder on the low-frequency side of the main band at 3684 cm-1 in the FTIR powder spectrum of the Monte Fico lizardite (Fig. 4). Manifestations of long-range electrostatic effects are also observed in the Raman spectra recorded on oriented single crystals (Farmer, 2000). As discussed by Farmer (2000) for the Raman spectrum of dickite, when the spectrum is recorded on a (001) section in a backscattering geometry, the exchanged wave vector is parallel to the [001] polarization of the in-phase stretching mode of interlayer-OH groups, which enhances the signal at the higher LO frequency. In the case of lizardite, Compagnioni et al. (2021) reports a shift of the main band from 3688.5 cm-1 in the micro-Raman spectrum recorded on an isotropic lizardite section parallel to the (001) plane to ∼ 3678 cm-1 for measurements made on the perpendicular section. In this latter case, the main band appears asymmetric with a component at ∼ 3668–3670 cm-1 (average 3669 cm-1). Accordingly, the LO frequency of the in-phase stretching of interlayer-OH groups should be close to ∼ 3688 cm-1, whereas the component systematically observed at ∼ 3669 cm-1 would correspond to its TO counterpart. The related splitting is consistent with the theoretical LO–TO splitting, which is predicted to be in the 14–21 cm-1 range.

These interpretations enable a comparison of the experimental frequencies with their theoretical counterparts (Fig. 5). The comparison reveals an overestimation of the theoretical stretching frequencies of interlayer-OH groups amounting to 50 cm-1, which is consistent with the observations made on antigorite (∼ 57 cm-1, Balan et al., 2021b). It is also in the range expected from previous investigations on hydrous defects in oxides and silicates (Balan et al., 2020; Balan, 2020). The difference between theoretical and experimental frequencies results from the partial cancellation of two types of errors, one being due to the use of an approximate exchange-correlation functional, which tends to underestimate the vibrational frequencies, and the other to the use of the harmonic approximation, which artificially increases the OH stretching frequencies with respect to their anharmonic values (Balan et al., 2007). The theoretical correlation between bond length and OH frequencies (Tables 1 and 2) for the series of investigated models (Fig. 6) is also consistent with those previously determined at the same theoretical level on a series of hydroxylated defects in diopside and corundum (Balan et al., 2020; Balan, 2020). This relation between the vibrational frequency and a geometrical parameter rules out a contribution of the mass of the surrounding cations to the stretching dynamic of the OH groups, which is decoupled from the motion of other atoms.

The 21 cm-1 downshift of the inner-OH stretching frequency induced by the presence of Fe2+ in its coordination sphere is similar to that determined at the same theoretical level for a Ni2+ for Mg2+ substitution in talc (23 cm-1, Blanchard et al., 2018). As in talc, the theoretical value however slightly overestimates the experimental observation. Based on the analysis of overtone bands in the near-infrared range (Balan et al., 2021a; Fritsch et al., 2021), the shift between Mg3–OH and Mg2Fe–OH in lizardite (16 cm-1) is close to that determined in talc (14 cm-1, Petit et al., 2004). Accordingly, the inner-OH stretching band corresponding to a Mg2Fe2+ environment should occur at ∼ 3687 cm-1, overlapping with the strong band related to the in-phase interlayer-OH stretching band of lizardite.

The signal of interlayer-OH groups in a Mg2Fe2+ environment is theoretically determined at a frequency ∼ 20 cm-1 lower than that of the out-of-phase stretching of interlayer OH in a Mg3 environment (Fig. 1). However, its contribution is not resolved in the experimental FTIR spectra (Fig. 4) and should mostly contribute to the broadening of the out-of-phase (E symmetry) stretching band identified at 3645 cm-1. Interestingly, the micro-Raman spectrum of lizardite reported by Compagnoni et al. (2021) reveals the occurrence of two components with different polarization properties at ∼ 3653 and ∼ 3642 cm-1. The relative intensity of the component at ∼ 3653 cm-1 is enhanced in the spectrum recorded on an isotropic section parallel to the (001) plane. Based on the comparison with the theoretical frequencies, this component could correspond to the out-of-phase stretching band of pure lizardite, whereas that determined at ∼ 3642 cm-1 could be ascribed to the stretching of interlayer-OH groups in a Mg2Fe2+ environment (Fig. 5). It is noteworthy that the splitting of the bands associated with the substituted site is relatively weak (8 cm-1, Fig. 1), potentially leading to the experimental observation of a single band at the average frequency. However, a contribution of trivalent cations (mostly octahedrally coordinated Al3+ in the Monte Fico sample) cannot be excluded as they lead to theoretical absorption signals at similar frequencies (Fig. 1).

Assuming that a difference between experimental and theoretical frequencies close to 50 cm-1 is also valid for the interlayer-OH groups in Al3+- and Fe3+-bearing models, the bands respectively observed at 3584 and 3568 cm-1 in the Monte Fico and Lz1 samples (Fig. 4) are most likely associated with the occurrence of trivalent cations. Consistently, this type of signal is lacking in the laboratory-grown pure lizardite sample. The shift of the band observed between the Monte Fico and Lz1 samples is also consistent with the respective predominance of octahedrally coordinated Al3+ and Fe3+ in these samples (Fig. 5).

It is however challenging to discriminate the occurrence of octahedral or tetrahedral Al3+. Despite a difference in the associated stretching frequencies amounting to 27 cm-1, both could contribute to the broad signal centered at 3584 cm-1 (half width at half maximum of ∼ 35 cm-1). The contribution related to tetrahedral Fe3+ is expected at a frequency 75 cm-1 lower than that associated with octahedral Fe3+, corresponding to an expected experimental frequency of ∼ 3490 cm-1. The absence of such a signal suggests that the concentration of tetrahedral Fe3+ is too low to be detected in the samples. Additional features can also complicate the identification of bands related to trivalent cations at tetrahedral sites. The expected signal likely overlaps with the broad absorption by water molecules adsorbed at the surface of the particles, which is centered at 3405 cm-1 in the pure and finely divided synthetic lizardite sample (Fig. 4). Moreover, the frequency of the interlayer-OH stretching bands appears to be controlled by the perturbation of the silicate sheet geometry, which affects the H-bonding pattern. Recalling that the present theoretical models correspond to a perfectly ordered cationic distribution because of the periodic boundary conditions, they are expected to only provide a local description of the changes induced by the presence of the impurity. The more random cationic ordering occurring in experimental samples likely induces a distribution of the tetrahedra rotation angles and of the related H-bond lengths, causing a broadening of the OH stretching signal.

To this respect, the occurrence of tetrahedral trivalent cations should efficiently contribute to the broadening of the whole vibrational properties of lizardite, not only affecting the stretching modes of interlayer-OH groups but also the other vibrational modes observed in the mid-IR range. In comparison, low concentration of cations at octahedral sites should have a more local effect and weaker broadening efficiency. It is however noteworthy that higher substitution levels of divalent or trivalent cations can also lead to a significant broadening due to the combined effect of the induced structural strain and increasing variability of cationic configurations, which include the electrostatically favored coupled substitution of trivalent cations at both M and T sites (e.g. Yariv and Heller-Kallai, 1973; Serna et al., 1979; Velde, 1980; Baron and Petit, 2016).