Kaolinite and lizardite

Kaolinite and lizardite are the Al-dioctahedral and Mg-trioctahedral end members, respectively, for TO phyllosilicates having the general SF of Si₂(R ³⁺_cR ²⁺_d)O₅(OH)₄. For the kaolinite dioctahedral end member, c and d are 2 and 0, respectively, and R ³⁺ is Al, while for the lizardite trioctahedral end member, c and d are 0 and 3, respectively, and R ²⁺ is Mg. No or limited octahedral substitutions (mainly Fe³⁺ for Al³⁺) occur in natural kaolinite. Using the synthesis method, the Fe³⁺ substitution amount can be increased slightly and other octahedral cations can be introduced into the structure (Table 3). Among the large set of published data available for pure natural Al end member kaolinite, the Keokuk kaolinite studied using Rietveld refinement (Bish &Von Dreele, Reference Bish and Von Dreele1989) was selected as representative for this study. According to the general SF above, lizardite sensu stricto does not have tetrahedral substitutions. Consequently, in this study, lizardite with >0.1 ^IVAl was considered in the Al-serpentine series rather than in the lizardite series.

Table 3. Data used for TO phyllosilicates.

b is a crystallographic parameter (Å).

R = mean ionic radius of octahedral cations (Å; see text for details).

^a Sample reference in the paper.

^b Brindley (Reference Brindley1982).

^c Brindley et al. (Reference Brindley, Dunham, Eyles and Taylor1951).

^d Calculated from chemical analyses in Brindley et al. (Reference Brindley, Dunham, Eyles and Taylor1951).

^e Crystal structure refinement.

^f Average value.

^g Caryopilite.

As shown in Fig. 5a, the b vs R plots for all TO samples display a relatively scattered pattern. Two different regressions (i.e. the kaolinite–lizardite (K–L) and greenalite–caryopilite (G–C) lines) can be distinguished, however, with a wide cloud of dots at their intersection (Fig. 5a).

Figure 5. b vs mean ionic radius of octahedral cations R for TO phyllosilicates (Table 3). (a) Circles represent natural samples and triangles represent synthetic samples: dark blue = kaolinite; yellow = lizardite; black = antigorite; light green = Al-serpentine, with black border = brindleyite, open circle = kellyite; red = Fe³⁺-serpentine, full circles = cronstedtite, with black border = pecoraite, open circles = guidottite; dark green = greenalite; brown = caryopilite; violet = R ²⁺-chrysotile series; pink = Co-lizardite. (K–L) and (G–C) correspond to kaolinite–lizardite and greenalite–caryopilite regression lines, respectively. (b) Focus on the synthetic kaolinite–lizardite series: dark blue triangles = Fe³⁺-kaolinite series, open triangle = theoretical end member; light blue triangle = Ga³⁺-substituted kaolinite; red triangles = R ³⁺-kaolinite series; yellow triangles = Ni–Mg lizardite series; pink triangles = Co-lizardite; open violet triangles = R ²⁺-chrysotile; light green triangles = Mg–Al serpentine series (Chernosky, Reference Chernosky1975), open light green triangles = other Mg–Al serpentines; brown triangles = R ²⁺–Al serpentine series; green triangle = greenalite. (c) Focus on natural Al-serpentines (circles) and Fe³⁺-serpentines (triangles). Polytype (partly) and tetrahedral Al or Fe³⁺ pfu are indicated: light blue circles = amesite; orange circles = berthierine, orange open circle = Ti-berthierine; green open circle = brindleyite; pink circles = odinite; dark blue circle = kellyite; green circles = other; red triangles = cronstedtite (2H ₁, 2H ₂, 3T, 1T, 6T ₂ and 3T + 1M polytypes); blue triangle = pecoraite; green triangles = guidottite.

Natural kaolinite, the synthetic Al–Fe³⁺ kaolinite series and the synthetic Ni–Mg lizardite series appear quasi-aligned ((K–L) line in Fig. 5a,b). The (K–L) line was first calculated with the synthetic series of Fe³⁺-kaolinites (Petit et al., Reference Petit1990; Iriarte et al., Reference Iriarte, Petit, Huertas, Fiore, Grauby, Decarreau and Linares2005) and Ni–Mg lizardites (Baron et al., Reference Baron, Pushparaj, Fontaine, Sivaiah, Decarreau and Petit2016b; Fig. 5a,b). Including natural kaolinite in these two synthetic series increases the correlation coefficient slightly (0.9987 instead of 0.9985) without modifying the regression significantly (b = 1.5092R + 8.1371 instead of b = 1.5097R + 8.1368). The K–L regression including the natural kaolinite was kept in the following analyses. Because aluminium is the octahedral cation with the smallest ionic radius (0.535 Å; Table 1), the b of the pure Al end member exhibits the smallest value observed for TO phyllosilicates when forming a TO clay structure. Accordingly, the natural Keokuk pure kaolinite is located at the origin of the regression line with an R value of 0.535 Å and a b value of 8.945 Å according to Bish & Von Dreele (Reference Bish and Von Dreele1989). Few b values for synthetic Fe³⁺- and Ga³⁺-substituted kaolinites of Bentabol et al. (Reference Bentabol, Ruiz Cruz and Huertas2009) are lower than 8.945 Å (Fig. 5b & Table 3), suggesting an underestimation of these b values. The data for the kaolinite synthesized with the greatest Cr³⁺ content also deviate slightly from the correlation lines (Fig. 5b). Except for the samples described in Bentabol et al. (Reference Bentabol, Ruiz Cruz and Huertas2009), the dataset for other synthetic diversely substituted kaolinites is located on or close to the regression line (Fig. 5b).

Up to ~0.1 octahedral Fe³⁺ per formula unit (pfu) is observed in natural kaolinites, whereas up to 0.6 substituted Fe³⁺ pfu can be measured in synthetic kaolinites (Table 3). For the theoretical Fe³⁺-kaolinite end member (Si₂Fe³⁺₂O₅(OH)₄), b extrapolated using the experimental data from Iriarte et al. (Reference Iriarte, Petit, Huertas, Fiore, Grauby, Decarreau and Linares2005) is located close to the K–L regression line, supporting the suitability of the dataset for a wide range of compositions (Fig. 5b). Moreover, as concluded previously by some authors (Petit et al., Reference Petit, Decarreau, Eymery and Thomassin1988; Petit & Decarreau, Reference Petit and Decarreau1990; Iriarte et al., Reference Iriarte, Petit, Huertas, Fiore, Grauby, Decarreau and Linares2005), the Al–Fe³⁺ kaolinite synthetic series behaves like a solid solution within the compositional range explored, and no evidence exists to date to suggest that the maximum value obtained experimentally (0.6 pfu) corresponds to a steric limit of Fe³⁺ substitution in kaolinite.

In contrast to kaolinite, various end members of lizardite are encountered, and Mg cations are commonly replaced at least partially by other divalent cations (Table 3). As shown in Fig. 5b, the synthetic Mg–Ni lizardites are well aligned on the (K–L) line, The Co-lizardite does not fit the regression well. The two different b values were measured in the same sample, as Bayliss (Reference Bayliss1981) calculated a significantly greater b than that measured by Dalmon & Martin (Reference Dalmon and Martin1968; Fig. 5b). The deviation from the (K–L) regression line and the b fluctuations probably suggest there being a problem with these data. In a review of serpentine group minerals, Bayliss et al. (Reference Bayliss, Berry, Mrose and Smith1980) observed some significant fluctuations in reported b values with apparently the same chemistry, suggesting different methods had been employed to measure this parameter or inaccuracies had occurred during these measurements. Fluctuations are noticed for synthetic Mg end members, with b ranging from 9.204 to 9.241 Å (Table 3). Fluctuations are also observed for natural lizardites whose single-crystal XRD refinement of two different crystals from a same sample with an assumed homogeneous chemical composition resulted in two different b values, as illustrated by the Gew-graze lizardite-1T (Mellini et al., Reference Mellini, Cressey, Wicks and Cressey2010) and the Monte Fico lizardite-1T (Mellini & Viti, Reference Mellini and Viti1994; Table 3). More consistent with the results observed here, Mellini & Zanazzi (Reference Mellini and Zanazzi1987) measured a slight variation in b coupled with a slight variation in the chemical composition between two polytypes of the Coli lizardite sampled within the same vein (Table 3). These examples illustrate how the established correlation lines can help us to identify whether deviation originated from structural features or difficulties in accurately measuring b.

Lizardite, chrysotile and antigorite are three polymorphs with flat, curved and corrugated wavy layer structures, respectively. Antigorite corresponds to a polysomatic series, with regularly inversed T sheets in polysomes (Fig. 4). A more correct general formula for antigorite would then be (Mg)_3m–3Si_2mO_5m(OH)_4m−6, where m represents the number of tetrahedra within a full wavelength, and m = 17 has been proposed as the most common value (Capitani & Mellini, Reference Capitani and Mellini2004). The dataset does not allow for the identification of possible differences between the polymorphs. As far as synthetic Mg- and Ni-lizardites (Baron et al., Reference Baron, Pushparaj, Fontaine, Sivaiah, Decarreau and Petit2016b) and chrysotiles (Jasmund et al., Reference Jasmund, Sylla, Freund and Bailey1976) are concerned, b values measured for chrysotiles appear slightly lower than those measured for lizardites (Table 3). Because the two sets of samples were measured using various techniques, we cannot conclude with certainty that b values for chrysotiles are lower than for lizardites.

Al- and Fe³⁺-serpentines

Al- and Fe³⁺-serpentines whose general SFs are (Si_2–xAl_x)(Mg_3–xAl_x)O₅(OH)₄ and (Si_2–xFe³⁺_x)(Fe³⁺_xFe²⁺_3–x)O₅(OH)₄, respectively, most often exhibit great tetrahedral substitution contents (up to 1 Al or Fe³⁺ per O₅(OH)₄) to neutralize the positive octahedral layer charge generated by the heterovalent octahedral substitutions of divalent cations (mainly Mg and Fe²⁺) by trivalent cations (mainly Fe³⁺ and Al). The dataset for Al- and Fe³⁺-serpentines are scattered significantly (Fig. 5a), and this scattering is more pronounced for natural samples than for synthetic Al-serpentines, which lie close to the (K–L) regression line (Fig. 5b). The natural Al- and Fe³⁺-serpentines exhibit a wide range of tetrahedral substitutions and several polytypes, but no specific trend can be observed between these two characteristics and b (Fig. 5c).

Greenalite and caryopilite

Greenalite and caryopilite are, respectively, Fe²⁺- and Mn-rich TO phyllosilicates with corrugated structures and with the following general SF: Si₂(M)_(2.5–3)O₅(OH)₄, with M = Fe, Mn, Mg and Al as the main octahedral cations. Partial oxidation of octahedral Fe and Mn often occurs, and some octahedral sites may be vacant. The regression parameters for the (G–C) line (Fig. 5a) and the structural interpretation are discussed in detail below. The slope of the (G–C) regression line is ~4.5 times greater than that of the (K–L) line. Jasmund et al. (Reference Jasmund, Sylla, Freund and Bailey1976) reported that the greenalite synthesized with the Fe²⁺ end member was structurally non-equivalent to the Ni-, Mg- and Co-lizardites. The observed scattering of samples around the (G–C) line (Fig. 5a) can be tentatively assigned to uncertainties in the data and/or to the various modulated local substructures. Greenalite and caryopilite exhibit domed island-like structures due to tilting of the tetrahedra with periodic inversions of three- and four-fold rings (Guggenheim & Eggleton, Reference Guggenheim and Eggleton1998). This structural adjustment is a way to enlarge the T sheet dimensions to allow congruence with the large O sheet dimensions due to the occurrence of significant amounts of octahedral cations with large ionic radii, such as Mn²⁺ and Fe²⁺ (Table 1).

Influence of tetrahedral composition

Whereas no relation can be observed between tetrahedral content and b as shown above (Fig. 5c), it is clear, however, from a simple comparison between, for example, Mn-rich serpentines (i.e. kellyite; ^IVAl-serpentine, guidottite (^IVFe³⁺-serpentine) and caryopilite (negligible tetrahedral substitution and corrugated structure), that the tetrahedral composition plays a role in the dimensional misfit between T and O sheets. All of these Mn-rich serpentines have great R (from ~0.73 to ~0.80 Å) and b values (from ~9.4 to ~9.8 Å) due to their great Mn content. The tetrahedral substitutions in kellyite and guidottite allow the lateral dimension of the T sheet to increase, making the fit between T and O sheets possible without corrugation of the layer.

The b/b _tet. values were calculated for all TO phyllosilicates and plotted as a function of R (Fig. 6a). Three general trends are observed. The (K–L)’ correlation line (Fig. 6a) corresponds to the (K–L) line (Fig. 5a), and the regression was calculated using the same data. These samples have no tetrahedral substitutions and thus the correction with the b _tet. value does not influence the data alignment (Fig. 6a). Note that the synthetic R ²⁺–Al serpentine samples (Bentabol & Ruiz Cruz, Reference Bentabol and Ruiz Cruz2013) that were above the (K–L) line (Fig. 5a,b) are now closer to the (K–L)’ line (Fig. 6a). The odinite data deviate systematically from the trend (Figs 5a & 6a), and possible impurities and redox variation make their SF unsure. Compared to the b vs R plot (Fig. 5a), the cloud of dots associated with the Al-serpentine disappeared in Fig. 6a. Less predictable is that the corrugated Fe²⁺–Mn serpentines approximately follow the same high-slope (G–C)’ line as most of the Al-serpentines (Fig. 6a). For this (G–C)’ line, the regression was calculated using antigorites, greenalites, caryopilites and Al-serpentines that are on (or close to) the (G–C)’ line. Furthermore, the Fe³⁺-serpentines, except the pecoraite sample, which lies on the (G–C)’ line, follow fairly well the different linear trend of (Fe³⁺–Serp)’ with the same slope as the (G–C)’ line (Fig. 6a).

Figure 6. (a) b/b _tet. ratio vs mean ionic radius of octahedral cations R for TO phyllosilicates (Table 3), with the same symbols and colours as in Fig. 5a. (K–L)’ and (G–C)’ correspond to kaolinite–lizardite and greenalite– caryopilite regression lines, respectively. (b) Evolution of the percentage of octahedral enlargement compared to hydroxides (Equation 6; see text for details) vs R: blue squares = kaolinites and lizardites; green squares = natural Al-serpentines; green triangles = synthetic Al-serpentines (focus on the Chernosky's (Reference Chernosky1975) series); red squares = Fe³⁺-serpentines; black squares = antigorite; brown squares = caryopilites and greenalites; blue dotted line = regression for the kaolinite–lizardite series. (c) Evolution of the percentage of octahedral enlargement vs b _tet. for Al- and Fe³⁺-serpentines, with the same symbols and colours as in Fig. 5c for natural samples, except light green crosses = synthetic Al-serpentines.

For Al- and Fe³⁺-serpentines, a general relationship of b vs R, introducing the tetrahedral composition, can be formulated from each (K–L)’, (G–C)’ and (Fe³⁺–Serp)’ regression line (Fig. 6a) according to Equation 7:

(7)$$b = R( {aT + c} ) + dT + e$$

with T being the number of ^IVAl or ^IVFe³⁺ pfu.

For Al-serpentines following the (K–L)’ line (Fig. 6a):

$$b = R( {0.061T + 1.509} ) + 0.327T + 8.137$$

For Al-serpentines (and Fe³⁺-serpentine; i.e. pecoraite) following the (G–C)’ line (Fig. 6a):

$$b = R( {0.275T + 6.854} ) + 0.173T + 4.302$$

For Fe³⁺-serpentines following the (Fe³⁺–Serp)’ line (Fig. 6a):

$$b = R( {0.470T + 6.854} ) + 0.27T + 3.932$$

The intersect coordinates for the two (K–L)’ and (G–C)’ lines are R = 0.717 and b = 9.220 Å, approximately corresponding to the Mg-lizardite end member. The corresponding b/b _tet. value is 1.007, thus indicating a tetrahedral rotation angle α close to 0°. Accordingly, theoretical modelling using the distance least-squares method indicates that the O and T sheets fit together without any major distortions in the Mg-lizardite structure (Bish, Reference Bish1981; Wicks & Hawthorne, Reference Wicks and Hawthorne1986; Wicks & O'Hanley, Reference Wicks, O'Hanley and Bailey1991), and α measured using structure refinement is close to 0° (approximately –1.5(1)°) for the natural Mg end member lizardite (Guggenheim & Zhan, Reference Guggenheim and Zhan1998; Mellini et al., Reference Mellini, Cressey, Wicks and Cressey2010).

Based on all of the results above, three main distinct mechanisms of adjustment between O and T sheet lateral dimensions to compensate for the misfit of kaolinite–lizardite, Al- and Fe³⁺-serpentines and phyllosilicates with corrugated structure are proposed in the following subsections.

Focus on the structural adjustment mechanism for the kaolinite–lizardite family

Samples on the (K–L)’ line (Fig. 6a) are those for which b is driven by R according to the good regression observed for the (K–L) line (Fig. 5a). For pure kaolinite (Al end member that exhibits the lowest R), T sheets are relatively large compared to O sheets and have to reduce their lateral dimensions to adjust to the O sheets. Moving to lizardite, and thus increasing R, makes the dimensional misfit decrease. The (K–L)’ trend (Fig. 6a) gives evidence of a progressive decrease of the angle of tetrahedral rotation α with increasing R. Accordingly, the rotation of tetrahedra to ditrigonal symmetry (Fig. 1d) is the principal process for overcoming the misfit when b _oct. <  b _tet. in TO phyllosilicates by reducing the lateral dimension of the T sheet (e.g. Radoslovich, Reference Radoslovich1963; Bailey, Reference Bailey and Bailey1966; Wicks & Whittaker, Reference Wicks and Whittaker1975; Guggenheim & Eggleton, Reference Guggenheim and Eggleton1987). However, this process is not the only one to achieve congruency between the T and O sheet dimensions. Indeed, the O sheet enlargement (Equation 6) increases progressively with a decrease of R (Fig. 6b). The O sheet enlargement corresponds to a lateral expansion of the sheet by thinning (Bailey, Reference Bailey and Bailey1984b). The b _oct. value corresponding to an unconstrained O sheet was taken for hydroxides as determined above (b _oct. = 4.51R + 6.22; Fig. 3d). Consequently, positive % O enlargement corresponds to an O sheet flattening (or thinning) compared to hydroxides, whereas negative % O enlargement corresponds to a thickening of the O sheet compared to hydroxides, with a null value being obtained for R = 0.642. With the ionic radius of Fe³⁺ being 0.645 Å (Table 1), the theoretical Fe³⁺-kaolinite end member would have similar dimension to the corresponding hydroxide. The Fe(OH)₃ mineral bernalite exists but it has a pseudo-cubic structure of perovskite type (Birch et al., Reference Birch, Pring, Reller and Schmalle1993) that cannot be compared. Kaolinite exhibits the greatest enlargement: 3.6% as compared to hydroxides (10.1% as compared to undistorted O sheets), which agrees well with the value measured using structure refinement (10.1%; Bish & Von Dreele, Reference Bish and Von Dreele1989). Co-lizardite with the lowest octahedral enlargement (–3.7% and 2.3% compared to hydroxides and undistorted O sheets, respectively) and has the thickest O sheet of the family. The linear regression observed between kaolinite and lizardite (Fig. 6b & (K–L) line Fig. 5a) suggests an increase of the size of the vacant site with an increase of R for dioctahedral samples.

The few Al- and Fe³⁺-serpentines with a rather low rate of tetrahedral substitution that lie on (or close to) the (K–L)’ line (i.e. brindleyite, pecoraite and synthetic R ²⁺–Al serpentines; Fig. 6a) behave similarly to the kaolinite and lizardite family. These Al-serpentines exhibit a great number of octahedral vacant sites, possibly increasing the plasticity of the octahedral sheet compared to the other serpentines.

Focus on the Al- and Fe³⁺-serpentines family

The samples that are scattered between the (K–L) and (G–C) lines exhibit a high degree of misfit due to their relatively small O sheet lateral dimensions (small R) compared to their large T sheet lateral dimensions due to tetrahedral substitutions. The T sheet dimensions have to decrease significantly to adjust to the O sheet. As for kaolinite and lizardite, this reduction of T sheet dimensions with decreasing R is due to a progressive increase in the tetrahedral rotation angle α, as evidenced by the (G–C)’ and (Fe³⁺–Serp)’ regressions (Fig. 6a). However, contrary to the kaolinite–lizardite series, the O sheet enlargement does not vary linearly with R and is relatively more pronounced than for kaolinite–lizardite (Fig. 6b). This explains the greater b relative to R observed for Al- and Fe³⁺-serpentines compared to the kaolinite–lizardite series (Fig. 5a). In Al- and Fe³⁺-serpentines, the O sheet enlargement is linked directly to the tetrahedral substitutions, as shown by the plot of the O sheet enlargement vs b _tet. (Fig. 6c). Each of the two observed regressions (calculated using natural samples only) concerns mainly Al-serpentines or Fe³⁺-serpentines and corresponds to the (G–C)’ or (Fe³⁺–serp)’ lines, respectively (Fig. 6a). The two regressions intersect for b _tet. ≈ 9.13 Å and % O enlargement ≈ –2.7 (~3.4% compared to a free O sheet). This b _tet. value is close to the theoretical 9.15 Å value calculated for a free T sheet (e.g. Equation 3; Bailey, Reference Bailey, Brindley and Brown1981). The % O enlargement is negative or close to 0 for amesite, meaning that O sheets are always thicker/never thinner in Al- and Fe³⁺-serpentines than in their corresponding hydroxides (i.e. hydroxide with the same R). For amesite, the ~0% O enlargement compared to hydroxides means than the flattening of the O sheet is the same as for hydroxides: ~6.3% compared to the free O sheet, agreeing well with the structural refinement of amesite (Wiewiora et al., Reference Wiewiora, Raussel-Colomb and Garcia-Gonzales1991; Zheng & Bailey, Reference Zheng and Bailey1997a).

In serpentine, when Tschermak substitutions (coupled tetrahedral R ³⁺/Si⁴⁺ to octahedral R ³⁺/R ²⁺ substitutions) occur, there is a cumulative antagonistic effect of R ³⁺. Note, however, that in the case where Tschermak substitutions occur with coupled tetrahedral Al³⁺/Si⁴⁺ to ^VIM ³⁺/Mg²⁺ substitutions, with r(^VIM ³⁺) > r(^VIAl³⁺) such as for ^VIM ³⁺ = ^VIFe³⁺, the antagonistic effect can be neutralized. The antagonistic effect of Al is well illustrated with the synthetic series ((Si_2–xAl_x)(Mg_3–xAl_x)O₅(OH)₄, with 0 ≤ x ≤1) of Chernosky (Reference Chernosky1975; Table 3). For this series, b _tet. and b _oct. are anticorrelated, making the misfit increase dramatically when R decreases (Fig. 6a). The lateral dimensions of the O and T sheets are identical for b _tet. = b _oct. = 9.33 Å, corresponding to R = 0.690, x = 0.49 and b ≈ 9.2 Å. This x value has been discussed widely in the past, and an Al content corresponding to x ≈ 0.3 (corresponding to R ≈ 0.702) has been proposed (Bates, Reference Bates1959; Radoslovich, Reference Radoslovich1963; Chernosky, Reference Chernosky1975; Caruso & Chernosky, Reference Caruso and Chernosky1979). The difference between these two x values comes mainly from the values taken for M–O bond length calculations of b _tet. and b _oct..

Due to the antagonistic effect of Al, tetrahedral substitutions are not expected to release the misfit between T and O sheets in aluminous serpentines but to promote it further. Consequently, strong constraints are expected to occur for the Al-richest samples as a result of T and O sheet lateral dimension accommodation. Furthermore, for the Al-richest serpentine with an end member amesite-like composition, T sheets contract significantly (b/b _tet. = 0.961; Fig. 6a), all the more so as O sheet enlargement is relatively limited (Fig. 6b). This contraction corresponds to an angle of tetrahedral rotation α ≈ 16°, a value that agrees well with α ≈ 14–15° measured using structure refinement of natural amesite (Bailey, Reference Bailey and Bailey1991c; Wiewiora et al., Reference Wiewiora, Raussel-Colomb and Garcia-Gonzales1991; Zheng & Bailey, Reference Zheng and Bailey1997a). With increasing heterovalent substitutions, an increasing linkage by H bonding from layer to layer occurs, and the interlayer thickness decreases when the ditrigonalization of the T sheet increases (Mellini & Viti, Reference Mellini and Viti1994). Structural refinement of natural amesites also indicates various cation ordering patterns. This cation ordering and the electrostatic attraction between layers due to substantial tetrahedral substitutions are believed to have positive effects on the regularity of the stacking of layers in amesite (Bailey, Reference Bailey and Bailey1991c). This may explain its platy morphology even though a curled morphology might be expected due to misfit constraints. This may also explain the existence of multilayer polytypes in serpentine with significant amounts of trivalent cations. Accordingly, Chernosky (Reference Chernosky1975) observed a one-layer ortho-cell structure for 0.05 ≤ x ≤ 0.375 and a six-1ayer ortho-cell structure for x > 0.375.

Focus on the phyllosilicates with corrugated structure

These samples follow the (G–C) and (G–C)’ lines (Figs 5a & 6a), and the high degree of misfit is due to O sheet lateral dimensions being greater than T sheet lateral dimensions. In greenalite and caryopilite, high b _oct. values are due to large octahedral cations such as Fe²⁺ and Mn²⁺, whereas b _tet. values are relatively low compared to Al- and Fe³⁺-serpentines due to negligible tetrahedral substitutions. The stretching of the T sheet attains its limits, constraining the O sheet to curl and the T sheet to be discontinuous, forming modulated layers. It is worth noting that for these TO phyllosilicates the % O enlargement is similar to those of equivalent hydroxides (Fig. 6b). Detailed descriptions of the various n-ring arrangements to accommodate misfit in modulated 1:1 layer silicates can be found in the literature (Guggenheim & Eggleton, Reference Guggenheim and Eggleton1987, Reference Guggenheim, Eggleton and Bailey1988, Reference Guggenheim and Eggleton1998) and will not be discussed here.

Impact of misfit on layer curling and morphology

Layer curling arises because of the complex interplay between chemical compositions and the structural adjustments required to achieve articulation between the O and T sheets. From the above results, it is hypothesized that samples close to the b/b _tet. = 1 line correspond mostly to samples with a flat morphology. The misfit between the O and T sheets dimensions is accommodated mainly by tetrahedra rotation to reduce T sheet dimensions. The existence of vacant sites also probably increases the plasticity of O sheets, facilitating their lateral dimension increase. Exceptions must be made for chrysotiles (Fig. 6a), which exhibit a non-flat morphology (cylindrical morphology; Fig. 4b). Only three data points were available, and these samples are synthetic and may not be representative. However, the curling observed in chrysotile is not due to misfit between T and O sheet dimensions, but rather to reaction kinetics, with chrysotile occurring as a metastable form of a serpentine (Evans, Reference Evans1976, Reference Evans2004; Andréani et al., Reference Andreani, Grauby, Barronnet and Munoz2008). Accordingly, Jasmund & Sylla (Reference Jasmund and Sylla1971) observed that tubes of synthetic Mg- and Ni-chrysotiles transformed into platy Mg- and Ni-antigorites with increasing reaction time. An analogy, previously highlighted by Bates (Reference Bates1959), can be made with halloysite (which is not represented in this study, its b and R values being similar to those of kaolinite). Halloysite probably curls for the same reason as chrysotile. The morphology of halloysite, which can be tubular, spheroidal, onion-like, crumpled lamellar and so on, but also platy, is related to crystallization conditions and geological occurrences (Joussein et al., Reference Joussein, Petit, Chruchman, Theng, Righi and Delvaux2005). Notably, synthetic kaolinites can also exhibit spherical metastable particles precipitating from solution with a high degree of supersaturation (e.g. Fiore et al., Reference Fiore, Huertas, Huertas and Linares1995).

For samples with b/b _tet. < 1 (Fig. 6a), the T sheet is compressed, constraining the O sheet to increase its lateral dimensions by flattening the octahedra, as described above. If layers curl, the O sheets are always on the convex side of the layer. However, in Al- and Fe³⁺-serpentines, increasing heterovalent substitutions induce increased electrostatic attraction between layers and an ordering of cation distributions favouring a flat morphology.

It is tempting to further discuss the morphology of serpentines as a function of misfit, as has been examined previously by many authors (e.g. Pauling, Reference Pauling1930; Bates, Reference Bates1959; Radoslovich, Reference Radoslovich1963; Bailey, Reference Bailey and Bailey1966). However, the simple approach developed here cannot replace detailed structural studies for determining the actual structure and morphology of TO layer silicates. For example, some serpentines, such as polygonal serpentines, may appear as fibres, but are composed of 1:1 flat layers (Baronnet et al., Reference Baronnet, Mellini and Devouard1994; Mellini, Reference Mellini2013), and conversely, structural modulation can account for apparently plate-like particles (Guggenheim & Eggleton, Reference Guggenheim and Eggleton1987). Moreover, mixtures of several morphologies are often reported in synthetic series (Chernosky, Reference Chernosky1975; Bentabol & Ruiz Cruz, Reference Bentabol and Ruiz Cruz2013) as well as in natural samples (Capitani et al., Reference Capitani, Compagnoni, Cossio, Botta and Mellini2021).

Pyrophyllite–talc

Pyrophyllite and talc are TOT layer silicates composed of electro-neutral stacked 2:1 layers formed by two T sheets sandwiching one O sheet (Fig. 7a). These two minerals correspond to the Al-dioctahedral and Mg-trioctahedral end members, respectively, having the general SF of Si₄(R ³⁺, R ²⁺, □)₃O₁₀(OH,F)₂, with R ³⁺ being mainly Al, R ²⁺ being mainly Mg but also potentially being very different and □ being a vacant site. In the present study, kerolites were also included in this group because these clay minerals are considered hydrated (but disordered) talc-like minerals (Brindley et al., Reference Brindley, Bish and Wan1977). The available data found in the literature for this group of minerals cover only a small range of chemical variability (Table 4). For dioctahedral minerals, only pyrophyllite, with limited Fe³⁺ substitutions, and ferripyrophyllite are reported to occur, with ferripyrophyllite exhibiting the highest R and b values. For trioctahedral phyllosilicates, Ni-talc exhibits the lowest R and b values. Natural talcs with significant amounts of Fe and Ni are not rare. The Mg–Ni solid solution is complete in talc (talc–willemseite sequence) and kerolite (kerolite–pimelite sequence), whereas the Fe²⁺–Mg solid solution is limited to (Fe²⁺/(Fe²⁺ + Mg)) values near 0.4 for natural as well as synthetic minerals (Corona et al., Reference Corona, Jenkins and Dyar2015). Minnesotaite, a chemically Fe²⁺ talc-like end member, is reported here, but it displays a modulated structure (Guggenheim & Bailey, Reference Guggenheim and Bailey1982; Guggenheim & Eggleton, Reference Guggenheim and Eggleton1986, Reference Guggenheim and Eggleton1987). Synthetic talcs with other divalent octahedral cations, such as Co (complete solid solution), Zn and Cu (limited solid solution), can be synthesized (e.g. Wilkins & Ito, Reference Wilkins and Ito1967). Unfortunately, detailed XRD data are not available for these minerals.

Figure 7. Schematic representation of the structures of various TOT phyllosilicates: (a) neutral TOT (e.g. pyrophyllite and talc), (b) low-charge hydrated TOT (e.g. smectite) and (c) high-charge TOT (e.g. mica).

Table 4. Data used for TOT phyllosilicates with a neutral structure.

b is a crystallographic parameter (Å).

R = mean ionic radius of octahedral cations (Å; see text for details).

^a Sample reference in the paper.

^b Refined unit cell.

Except for minnesotaites and some natural kerolites, data for natural and synthetic samples appear quasi-aligned on a line joining dioctahedral (i.e. pyrophyllite) and trioctahedral (i.e. talc) end members on the b vs R plot (Fig. 8a). This agrees with the work of MacEwan (Reference MacEwan and Brown1961), who deduced a coefficient proportional to the ionic radius of Mg and Al from the pyrophyllite–talc pair, which can be used to calculate b by multiple regression. The b vs R regression for the pyrophyllite–talc (P–T) line, calculated using pyrophyllite and the three natural talc samples (Mg, Antwerp Fe²⁺-substituted talc and Ni²⁺-substituted talc (i.e. willemseite); Table 4) is excellent, and leads to the relation b = 1.1162R + 8.3691 (Fig. 8a).

Figure 8. (a) b vs mean ionic radius of octahedral cations R for electro-neutral TOT phyllosilicates (Table 4), with circles representing natural samples and triangles representing synthetic samples: dark blue circles = pyrophyllite; light blue circles = ferripyrophyllites; open circles = same sample; yellow circle = Mg-talc; red circle = Fe²⁺-talc; light green circles = willemseite; dark green circles = minnesotaites; brown circles = natural kerolites; light green triangles = synthetic Mg–Ni kerolite series; red triangles = Mg–Fe²⁺ synthetic talc series. (P–T) corresponds to the natural pyrophyllite–talc regression line. Grey dotted line = regression calculated with Mg–Fe²⁺ and Mg–Ni synthetic series. (b) b/b _tet. ratio vs the mean ionic radius of octahedral cations R for the same samples (and colour code) as (a). (c) Evolution of the percentage of octahedral enlargement (Equation 6; see text for details) vs R for the same samples (and colour code) as (a); dotted line = regression calculated excluding ferripyrophyllite, natural kerolite and minnesotaite samples.

Another regression was calculated using the synthetic Fe²⁺–Mg talc (Forbes, Reference Forbes1969) and Ni–Mg kerolite series (Baron et al., Reference Baron, Pushparaj, Fontaine, Sivaiah, Decarreau and Petit2016b) only, and the equation is similar to the former one (Fig. 8a), with the slight difference being possibly due to the lower crystallinity of these samples.

Ferripyrophyllites follow the general trend (Fig. 8a), but the data selected here appear prone to bias given that the three available SFs exhibit a deficit of layer charge, probably due to impurities (Table 4). Accordingly, Chukhrov et al. (Reference Chukhrov, Zvyagin, Drits, Gorshkov, Ermilova, Goilo, Rudnitskaia, Morland and Farmer1979a) identified ~5% smectite in their ferripyrophyllite sample, justifying the Ca presence in the SF to balance the layer charge. Coey et al. (Reference Coey, Chukhrov and Zvyagin1984) studied the same sample using Mössbauer spectroscopy and revisited its SF, attributing more Fe³⁺ to the T sheet (Table 4). However, in light of recent studies: (1) the partition coefficient of Al³⁺ and Fe³⁺ between tetrahedral sites in dioctahedral smectites indicated a strong preference of Al³⁺ to substitute for Si in the T sheet (Decarreau & Petit, Reference Decarreau and Petit2014); and (2) Mössbauer spectroscopy was shown to be inadequate for quantifying tetrahedral Fe³⁺ in smectite if its content was unknown (Baron et al., Reference Baron, Petit, Pentrack, Decarreau and Stucki2017). Consequently, it appears that the SF given by Chukhrov et al. (Reference Chukhrov, Zvyagin, Drits, Gorshkov, Ermilova, Goilo, Rudnitskaia, Morland and Farmer1979a) is probably more suitable than the SF revisited by Coey et al. (Reference Coey, Chukhrov and Zvyagin1984).

Some natural kerolites deviate from the general trend (Fig. 8a). As mentioned above, kerolites differs from talcs by their water content, possibly due to a small charge occurrence from octahedral vacant sites, resulting in some swelling properties. Some natural kerolite samples were also characterized as talc–stevensite mixed-layer minerals (Maksimovic, Reference Maksimovic and Heller1966; Brindley et al., Reference Brindley, Bish and Wan1977; Eberl et al., Reference Eberl, Jones and Khoury1982; Pozo & Casas, Reference Pozo and Casas1999). Their deviation from the pyrophyllite–talc regression line could reflect the degree of their ‘smectitic’ character. Accordingly, the P-7 kerolite (Eberl et al., Reference Eberl, Jones and Khoury1982; Table 4), possessing the greatest charge of the kerolite group in this study and in which Eberl et al. identified 30% expandable layers, is the farthest above the (P–T) line. These results suggest that the occurrence of a negative octahedral charge in trioctahedral TOT clay minerals tends to induce a decrease in b.

Minnesotaites are dramatically out of trend and exhibit greater b values than expected from R (Fig. 8a). This can be seen as reminiscent of the roles played by structure and morphology on crystal parameters, similarly to TO phyllosilicates with corrugated structures (see below).

Calculated with the same data than for the (P–T) line, the regression for the (P–T)’ line is b/b _tet. = 0.122R + 0.9144 (Fig. 8b). The similarity between Fig. 8a and Fig. 8b is related to the negligible amounts of tetrahedral substitutions for the pyrophyllite–talc family. The lower b/b _tet. is 0.984 for pyrophyllite. The calculated tetrahedral rotation angle α ≈ 11.6°, which is in agreement with that determined using structure refinement (α ≈ 10°; Evans & Guggenheim, Reference Evans, Guggenheim and Bailey1991), allows the lateral dimensions of T sheets to be reduced to adjust to the smaller O sheets. When R increases, b/b _tet. increases linearly to a value slightly greater than 1, thus indicating that the mismatch between the T and O sheet lateral dimensions decreases progressively, as discussed above for TO phyllosilicates. Accordingly, the angle of tetrahedral rotation α is low, being ~3.6° in talc (Perdikatsis & Burzlaff, Reference Perdikatsis and Burzlaff1981). The synthetic Fe²⁺-richest talc (with octahedral composition: Mg_2.4Fe²⁺_0.6) exhibits the greatest b/b _tet. (1.008). Note that the natural Antwerp talc contains a similar Fe²⁺ amount, but the presence of octahedral Al and Fe³⁺ tends to lower R (Table 4). The continuous increase in b/b _tet. with R implies a progressive decrease in tetrahedral rotation angle approaching 0° with T sheets stretched maximally for the greatest R (i.e. Fe²⁺-rich talc). Although a miscibility gap between Fe²⁺-rich talc and minnesotaite, if one exists, has not been determined between the limit R values of ~0.74 (Fe²⁺-rich talc) and ~0.76 (minnesotaite), the misfit between the T and O sheets is too high (high b/b _tet.; Fig. 8b) and the constraints are released by structural modulations, inducing the development of a superlattice for minnesotaite (Guggenheim & Eggleton, Reference Guggenheim and Eggleton1986). Minnesotaite has a continuous O sheet with adjacent Si tetrahedra on each side. Tetrahedral strip widths are narrow, being three and four tetrahedra wide compared to the seven tetrahedra found across the island in greenalite (Guggenheim & Eggleton, Reference Guggenheim and Eggleton1986). This is consistent with the smaller b/b _tet. measured for minnesotaite (~1.03) compared to greenalite TO phyllosilicate (~1.05).

Thexcelent linear relation, according to the (P–T) line, observed between O sheet enlargement (Equation 6) with R for all samples except minnesotaites and the out-of-trend kerolite P-7 (Fig. 8c), indicates that O sheet thinning (and thickening compared to hydroxides) acts together with the tetrahedral rotation angle to attain congruency between T and O sheet dimensions, as observed for the kaolinite–lizardite family (Fig. 6b). The O sheet enlargement increases progressively with decreasing of R from –3.6% to 3.8% compared to hydroxides (2.5% and 10.3% compared to an ideal unconstrained O sheet, respectively; Fig. 8c), with a null value being obtained for R = 0.635, corresponding well to ferripyrophyllite. According to the results above, the crystal structure refinement of a Mg-talc indicates that the O sheet was thinner than the ideal dimensions and that O sheet flattening occurs before the T sheet is stretched maximally (α ≈ 3.6°; Perdikatsis & Burzlaff, Reference Perdikatsis and Burzlaff1981).

Two compositional gaps are observed between the pyrophyllite and talc end members for R from ~0.54 to ~0.65 and from ~0.65 to ~0.69 (Fig. 8a–c). For the former range, all values of R could be obtained by varying the Al³⁺:Fe³⁺ ratio, suggesting that the pyrophyllite–ferripyrophyllite solid solution is limited due to the respective contrasting geological occurrences of the two end members: mainly low-grade, Al-rich metamorphic rocks for pyrophyllite (Deer et al., Reference Deer, Howie, Zussman, Deer, Howie and Zussman2009) and precipitation from low-temperature, Fe-rich hydrothermal fluids for ferripyrophyllite (Chukhrov et al., Reference Chukhrov, Zvyagin, Drits, Gorshkov, Ermilova, Goilo and Rudnitskaia1979b; Badaut et al., Reference Badaut, Decarreau and Besson1992).

The second range of R values corresponds to the ‘di-trioctahedral region’, with the greatest value for the dioctahedral end member being R =  0.645 (for r(^VIFe³⁺)) and the lowest value for trioctahedral end members being 0.69 (r(Ni²⁺); Table 1). Neutral di-trioctahedral structures would then require Tschermak substitutions and/or extra octahedral vacant sites to neutralize the charge due to heterovalent substitutions. Tschermak substitution would create stress within the structure due to the antagonistic effect of the trivalent cations on the misfit, as discussed above for TO phyllosilicates. However, in contrast to TO structures, excessive out-of-plane tilting of tetrahedra in TOT phyllosilicates cannot occur because the identical sheets on opposite sides of a neighbouring O sheet hold it flat under tension (Guggenheim & Eggleton, Reference Guggenheim and Eggleton1986). To our knowledge, no neutral di-trioctahedral TOT layer silicates have been reported to occur to date.

Smectites

Smectites are TOT clay minerals with a negative layer charge generally ranging between 0.2 and 0.6 pfu due to isomorphous octahedral and/or tetrahedral heterovalent substitutions. This charge is balanced by the presence of cations located in the interlayer space, whereas hydration of the cations leads to the intercalation of between 0 and several water sheets (Fig. 7b; e.g. Ferrage, Reference Ferrage2016). The general SF takes the form of (Si_4–xR ³⁺_x)(R ³⁺_aR ²⁺_bR ⁺_c□_d)O₁₀(OH)₂M_y, where a + b + c + d = 3 and y = x – 3a – 2b – c + 6 if the interlayer cation M is monovalent. Smectites present great variability in their chemical composition, density and location of layer charge, giving rise to numerous end members with a dedicated terminology (e.g. Brigatti et al., Reference Brigatti, Galán, Theng, Bergaya and Lagaly2013).

The dataset used is representative of the large compositional range encountered for both natural and synthetic smectites (Table 5). Vermiculite, although generally composed of macroscopic particles (e.g. de la Calle & Suquet, Reference de la Calle, Suquet and Bailey1991), was added to this category because it has the same SF as smectite at y > 0.6 and cannot be distinguished from high-charge saponite in its swelling properties (Suquet et al., Reference Suquet, Ijyama, Kodama and Pezerat1977).

Table 5. Data used for smectites.

b is a crystallographic parameter (Å).

R = mean ionic radius of octahedral cations (Å; see text for details).

^a Sample reference in the paper.

Especially for smectites, which are typically finely divided clay minerals, b and R are probably less reliable in terms of assessing value than for the other phyllosilicates. No single-crystal structural refinements have been carried out on smectites, and b has most often been measured using direct measurement of the (06ℓ;33ℓ) band. Using a Rietveld simulation of XRD traces of smectites synthesized by Andrieux et al. (Reference Andrieux and Petit2010), Heuser et al. (Reference Heuser, Andrieux, Petit and Stanjek2013) found b to be significantly greater than values obtained from the (06ℓ;33ℓ) band (Table 5; Petit et al., Reference Petit, Decarreau, Gates, Andrieux and Grauby2015). The nature of the interlayer cation and the hydration state were also shown to induce variation in b up to 0.03 Å (Suquet et al., Reference Suquet, Malard, Copin and Pézerat1981). The SF must also be viewed with caution due to:

1. (1) The difficulty in obtaining pure smectite, with admixtures affecting its chemical composition.

2. (2) The chemical heterogeneity within a given sample. Several populations of smectites may occur in the same sample, and the resulting R and b values measured thus represent mean values. For example, Ferrage et al. (Reference Ferrage, Lanson, Sakharov, Geoffroy, Jacquot and Drits2007) identified two populations of beidellites in a dioctahedral smectite, while the Ölberg iron-rich smectite first studied by Köster et al. (Reference Köster, Ehrlicher, Gilg, Jordan, Murad and Onnich1999) was shown to be heterogeneous, being constituted by Fe³⁺-montmorillonite and smectite with some tetrahedral charge and with less Mg and more Al than Fe³⁺-montmorillonite (Petit et al., Reference Petit, Caillaud, Righi, Madejová, Elsass and Köster2002).

3. (3) The chemical heterogeneity between samples from a given site. As an illustration, the SF of the Manito nontronite revealed 0.21^VIAl and 0.1^VIFe²⁺ in Köster et al. (Reference Köster, Ehrlicher, Gilg, Jordan, Murad and Onnich1999), while no ^VIFe²⁺ and only 0.03^VIAl were proposed by Radoslovich (Reference Radoslovich1962), both leading to different but coherent values (0.642 and 0.644 for R and 9.125 and 9.155 for b, respectively; Table 5). Similar observations can be made for some other smectites (Otay montmorillonite, Black Jack mine beidellite, Garfield nontronite, Unterrupsroth beidellite (Nadeau et al., Reference Nadeau, Farmer, Mc Hardy and Bain1985)).

4. (4) The difficulty in evaluating the actual rate of tetrahedral substitutions.

5. (5) The redox state.

Despite these limitations, the b vs R plot reveals that the samples generally follow the pyrophyllite–talc (P–T) trend (Fig. 9a). The scattering of data may be related mostly to the layer charge occurrence in smectite. For example, for the synthetic Fe³⁺-nontronite series (Si_4–xFe³⁺_x)Fe³⁺₂O₁₀(OH)₂Na_x (with 0.43 ≤ x ≤ 1.54), where tetrahedral iron was the only variable parameter, R is constant, while b increases with tetrahedral iron content (Fig. 10a), leading to vertical dot alignment on the b vs R plot (green triangles in Fig. 9a). A similar observation is made for natural and synthetic saponites (light green squares and triangles in Fig. 9a, respectively). For the synthetic saponite series with the general SF (Si_4–xAl_x)(Mg_(3–y)Al_y)Na_{x –y} (with 0.33 ≤ x ≤ 1 and y = 0 and 0.2, giving R of 0.720 and 0.708, respectively), Suquet et al. (Reference Suquet, Malard, Copin and Pézerat1981) established the following relationship: b = 9.174 + 0.079^IVAl – 0.07^VIAl. Tetrahedral Al increases b, while octahedral Al decreases b. For y = 0, x corresponds to the layer charge and to the ^IVAl content, and b increases linearly with it (Fig. 10b). For y = 0.2, the variation appears to be non-rigorously linear (Fig. 10b). Unfortunately, without having strong confidence in the accurate ^IVAl and ^VIAl contents (Suquet et al., Reference Suquet, Ijyama, Kodama and Pezerat1977), we cannot discuss this matter further.

Figure 9. (A) b vs mean ionic radius of octahedral cations R for smectites (Table 5). (P–T) corresponds to the pyrophyllite–talc regression line (Fig. 8a). Triangles = synthetic smectites: red = (SiAl)₄(Fe³⁺_(2–x)Al_x); light blue = (SiGa)₄(Fe³⁺_(2–x)Ga_x); green = (Si_4–xFe³⁺_x)Fe³⁺₂; brown = (SiFe³⁺)₄(Fe³⁺Mg)_y; pink = Fe²⁺-saponite series; light green = (Si_4–xAl_x)(Mg_(3–y)Al_y); yellow = Zn-stevensite; dark blue = stevensite series; dark blue open symbol = hectorite; black open symbol = hectorite and Zn-hectorite. Other symbols = natural samples. Squares = samples from Radoslovich (Reference Radoslovich1962): blue = beidellites; red = montmorillonites; green = nontronites; light green = saponites; yellow = sauconites; dark green = griffithite; black = hectorites; orange = stevensites; black = volkonskoites. Pink circles = samples from Brigatti (Reference Brigatti1983): open circles = nontronites; full circles = Al- and Fe³⁺-montmorillonites. Green circles = dioctahedral smectites (Russell & Clark, Reference Russell and Clark1978); red open circles = dioctahedral smectites (Tsipursky & Drits, Reference Tsipursky and Drits1984); blue circles = beidellites (Post et al., Reference Post, Cupp and Madsen1997); brown circles = intermediary smectites (Gaudin et al., Reference Gaudin, Petit, Rose, Martin, Decarreau, Noack and Borschneck2004). Red diamonds = dioctahedral smectites (Heuser et al., Reference Heuser, Andrieux, Petit and Stanjek2013); green diamonds = dioctahedral smectites (Köster et al., Reference Köster, Ehrlicher, Gilg, Jordan, Murad and Onnich1999); open green diamonds = other nontronites; brown diamonds = other intermediary smectites; blue diamonds = vermiculites. (b) b/b _tet. ratio vs the mean ionic radius of octahedral cations R for the same samples (and colour code) as (a). (P–T)’ corresponds to the pyrophyllite–talc regression line derived from Fig. 8b.

Figure 10. b vs tetrahedral substitution rate for selected smectites (Table 5). (a) Data for synthetic dioctahedral smectites series: red = (SiAl)₄(Fe³⁺_(2–x)Al_x; Petit et al., Reference Petit, Decarreau, Gates, Andrieux and Grauby2015); light blue = (SiGa)₄(Fe³⁺_(2–x)Ga_x; Petit et al., Reference Petit, Baron, Grauby and Decarreau2016); green = (Si_4–xFe³⁺_x)Fe³⁺₂ (Baron et al., Reference Baron, Pushparaj, Fontaine, Sivaiah, Decarreau and Petit2016b). (b) Data for synthetic saponites (Suquet et al., Reference Suquet, Ijyama, Kodama and Pezerat1977), with blue circles representing the y = 0 series and red circles representing the y = 0.2 series (see text for details). (c) Data for natural beidellites (Post et al., Reference Post, Cupp and Madsen1997).

The vertical dot alignments are also observed on the b/b _tet. vs R plot (Fig. 9b). Most of the samples lie below the (P–T)’ line. Those that are the most above the line are synthetic samples that display b/b _tet. > 1 and are suspected to be erroneous. A small underestimation of the tetrahedral charge may induce a deviation from the (P–T)’ line. For example, modifying the ^IVAl content from 0.46 to ~0.62 for sample A of Chemtob et al. (Reference Chemtob, Nickerson, Morris, Agresti and Catalano2015), which exhibits the greatest deviation, would place it on the (P–T)’ line.

The specific influence of the tetrahedral composition when R varies, even in a simple system, is difficult to measure. For the synthetic Al–Fe³⁺ smectitic series (SiAl)₄(Fe³⁺_(2–x)Al_x), with 0–1.66 Al and 0.34–2 Fe³⁺ (Table 5; Petit et al., Reference Petit, Baron and Decarreau2017), b increases with R (i.e. with increasing octahedral Fe³⁺), with a greater slope compared to the (P–T) line (Fig. 9a). For this series, Petit et al. (Reference Petit, Baron and Decarreau2017) observed that tetrahedral substitutions were dominated by Al except when total Fe exceeded 1.8 pfu, and tetrahedral and octahedral Fe³⁺ had similar (and inseparable) effects on b. The specific role of tetrahedral Al could not be measured quantitatively (see the review of Petit et al., Reference Petit, Baron and Decarreau2017). A similar observation can be made for the Ga–Fe³⁺ smectitic series (Table 5), whose dots are also aligned on a slope greater than that of the regression (P–T) line (Fig. 9a) and whose b values were correlated with total Fe³⁺ (Petit et al. Reference Petit, Baron, Grauby and Decarreau2016). For these Ga–Fe³⁺ smectites, the great b/b _tet. slope (Fig. 9b) is due to the combined effect of the increase in b _oct. due to the relative increase in octahedral Fe³⁺ and the decrease in b _tet. due to the decrease in tetrahedral Ga³⁺. Various relations linking b with iron content are available in the literature for iron-rich natural smectites (e.g. Heuser et al., Reference Heuser, Andrieux, Petit and Stanjek2013) and generally work well, at least when Fe³⁺ is the dominant cation. Brigatti (Reference Brigatti1983) observed a linear correlation between total iron and b but for Fe³⁺ > 0.5 pfu only.

For the natural beidellite sample series from Post et al. (Reference Post, Cupp and Madsen1997), b does not follow the general (P–T) trend. Indeed, b decreases as R increases (dark blue circles in Fig. 9a), related to the fact that the R and Al contents of beidellites vary inversely. b increases linearly with increasing tetrahedral Al (Fig. 10c), resulting in b/b _tet. values that are exactly the same for the four samples (0.9716 ± 0.0001; Fig. 9b). Such a b/b _tet. value corresponds to an angle of tetrahedra rotation α ≈ 13.7°, which is within the range of that measured in aluminous dioctahedral TOT phyllosilicates (pyrophyllite and micas).

By analogy with the aforementioned other phyllosilicate structures, it is hypothesized that T sheets adjust their lateral dimensions via tetrahedral rotation to match those of the O sheet, and all the more so as they are further below the (P–T)’ line (Fig. 9b).

The % O enlargement vs R plot reveals an excellent alignment of samples along the line determined for neutral TOT structures (Fig. 11), indicating that smectite samples follow closely the same trend as for P–T. However, it can be observed that samples that are above the line mainly have dominant tetrahedral charge (e.g. beidellites, nontronites, saponites, sauconites, vermiculites; Table 5). These samples are those located above the (P–T) line (Fig. 9a; i.e. with b values greater than they should be with regard to R). The thinning of O sheets via octahedral flattening is greater than in neutral phyllosilicates to facilitate dimensional congruency between the T and O sheets, with b _tet. having greater values due to tetrahedral substitutions.

Figure 11. Evolution of the percentage of octahedral enlargement (Equation 6; see text for details) vs R for the same smectite samples (and colour code) as Fig. 9. (P–T)° corresponds to the pyrophyllite–talc regression (Fig. 8c).

In a less pronounced manner, smectites with dominant octahedral layer charge (e.g. montmorillonites, stevensites, hectorites) are either below or on the (P–T) line (Fig. 11), similarly to the intermediary Fe³⁺–Mg natural smectitic series (Gaudin et al., Reference Gaudin, Petit, Rose, Martin, Decarreau, Noack and Borschneck2004) and the Fe³⁺–Mg synthetic series (Grauby et al., Reference Grauby, Petit, Decarreau and Baronnet1994) that possess an almost constant layer charge from an octahedral origin. For samples located below the (P–T) line (Fig. 9a), b values are lower than they should be with regard to R, and it can be hypothesized that the flattening of octahedra is reduced compared to neutral TOT phyllosilicates.

When considering the whole series of samples, R covers the entire compositional range from dioctahedral to trioctahedral smectites, and, contrary to neutral TOT phyllosilicates, no compositional gaps could be observed (Figs 9 & 11). The possibility of having various tetrahedral compositions and balancing the negative layer charge with interlayer cations allows for a very wide range of compositions, including di-trioctahedral smectites. The variability in the chemistry and type of layer charge compensation, associated with the difficulty of accounting for the wide range of tetrahedral charges through b/b _tet., make it inappropriate to propose a general regression correlating b to R for smectites. One may thus assume that the (P–T) correlation line can apply as a first-order relation, but with a greater degree of uncertainty compared to other mineral families. To go a step further, one could derive specific sub-correlations, as has been done for beidellites or saponites (Fig. 10b,c).