Dehydration of dioctahedral aluminous phyllosilicates: thermodynamic modelling and implications for thermobarometric estimates

Abstract

We propose a solid-solution model for dioctahedral aluminous phyllosilicates accounting for the main compositional variations, including hydration, observed in natural smectites, interlayered illite/smectite, illites, and phengites from diagenetic to high-grade metamorphic conditions. The suggested formalism involves dehydrated micas and hydrated pyrophyllite-like thermodynamic end-members. With these end-members, the equilibrium conditions of quartz + water + K-bearing mica-like phyllosilicates of fixed 2:1 composition are represented by a line in P–T space along which the interlayer water content varies. The relevant thermodynamic properties required for the calculation of equilibrium conditions were derived using a set of 250 natural data of known maximal temperature and pressure conditions, which covers a range between 25°C and few MPa to 800°C and 5 GPa. The temperatures calculated at fixed pressure with our model are in fair agreement with those reported in the literature for the 250 natural data. At low temperature and pressure, the amount of interlayer water in K-deficient phengite and illite is predicted to reach 100% of the apparent vacancies, which is consistent with previous values reported in the literature. Although the amount of interlayer water is predicted to decrease with pressure and temperature, it is calculated to be significant in K-deficient phengite from LT–HP pelites metamorphosed at about 350°C, 10 kbar. The presence of molecular water in the interlayer site of such phengites has been confirmed by FTIR mapping. Its implications for P–T estimates are discussed.

Appendix

The possibility of having more than (1 − IC) mol H₂O in the interlayer of smectite requires the definition of new interlayer sites compared to illite and mica. Four interlayer sites (A1–A4) that are progressively filled by water when hydration increases are necessary to account for the 0w to 3w states:

• For smect0w and illite with H₂O ≤ (1 − IC), water is incorporated into the site A1, which corresponds to the cation-free interlayer site of micas with IC < 1 and pyrophyllite.

• For smectite with a basal distance >10A (smect.1w to 3w) and H₂O > (1 − IC), water is also incorporated on the sites A2, A3 and A4. It is assumed that the ratio of H₂O/IC is constant over all these sites. Water is first incorporated on A1 until (H₂O + IC)_A1 = 1, then on A2 until (H₂O + IC)A2 = 1, on A3 until (H₂O + IC)A3 = 2 and finally on A4.

Table 6 presents the repartition of elements in end-members and on crystallographic sites for phengites, illites and smectites on the traditional tetrahedral, octahedral and first interlayer sites. Table 7 focuses on the distribution of water and cations on smectites interlayer sites A2, A3 and A4.

Table 6 Element site repartition in end-members and algorithm of repartition of elements in phengites, illites and smectites (excluding A2, A3 and A4 presented in Table 7)

Table 7 Element site repartition in the interlayer sheet for Prl end-members and algorithm of repartition specific to smectites

With this formalism, the ideal part of the activities of the Prl·mH₂O _nw end-members is calculated with the following general formula:

$$ a_{\text{ideal}} (\Pr l \cdot m{\text{H}}_{ 2} {\text{O}}_{{n{\text{w}}}} ) = (X{\text{Si}}_{\text{T1}} )^{2} (X{\text{Si}}_{\text{T2}} )^{2} (X{\text{Al}}_{\text{M2M3}} )^{2} (Xv_{\text{M1}} )\prod\limits_{0}^{n} {(X{\text{H}}_{ 2} {\text{O)}}_{\text{An}} Xv_{{{\text{A}}n + 1}} } $$

(A1)

For all interactions and/or ternary interactions summed on each site with c cations, non-ideal activity coefficient γ _m is calculated as (Berman 1991; Parra et al. 2002):

$$ {{n_{s}\,RT\,{ \ln }\,\gamma_{m} = \sum\limits_{j = 1}^{nc - 1} {\sum\limits_{k = j}^{nc} {\sum\limits_{\begin{subarray}{l} l = j \\ l \ne k \end{subarray} }^{nc} {{\text{WG}}_{jkl} X_{j} X_{k} X_{l} \left( {{\frac{{Q_{m} }}{{X_{m} }}} - 2} \right)} } } }} $$

(A2)

where Q _m is the number of j, k and l subscripts that are equal to m and WG _jkl  = (WH − T × WS + (P − 1) × WV) _jkl . In this expression, ternary interaction parameters (j ≠ k ≠ l) are exclusively functions of the binary interaction parameters:

$$ {{\text{W}}_{jkl} = ( {\text{W}}_{jjk} + {\text{W}}_{jkk} + {\text{W}}_{jjl} + {\text{W}}_{jll} + {\text{W}}_{kkl} + {\text{W}}_{kll} )/ 2} $$

(A3)

In the case of the Prl·mH₂O _nw end-members, the non-ideal part of the Prl·mH₂O _nw end-members is calculated with the following formula:

$$ {{RT\,{ \ln }\,\gamma_{{{\text{Prl}} \cdot m{\text{H}}_{ 2} {\text{O}}n{\text{w}}}} = \sum\limits_{\text{TOT}} {\left( {\sum\limits_{j = 1}^{nc - 1} {\sum\limits_{k = j}^{nc} {\sum\limits_{\begin{subarray}{l} l = j \\ l \ne k \end{subarray} }^{nc} {{\text{WG}}_{jkl} X_{j} X_{k} X_{l} \left( {{\frac{{Q_{m} }}{{X_{m} }}} - 2} \right)} } } } \right)} + \sum\limits_{\text{A1}}^{{{\text{A}}n}} {\left( {\sum\limits_{j = 1}^{nc - 1} {\sum\limits_{k = j}^{nc} {\sum\limits_{\begin{subarray}{l} l = j \\ l \ne k \end{subarray} }^{nc} {{\text{WG}}_{jkl} X_{j} X_{k} X_{l} \left( {{\frac{{Q_{m} }}{{X_{m} }}} - 2} \right)} } } } \right)} }} $$

(A4)

In equations (A1) and (A4), the contribution of the 2:1 sites to the activity of the Prl·mH₂O _nw end-members is the same, so that equilibrium constant K _R3, K _R4, K _R5 and K _R6 do not depend on the 2:1 layers composition, as illustrated below for K _R3:

$$ K_{R3} = {\frac{{a\Pr{\text{l}} \cdot 0{\text{H}}_{2} {\text{O}}}}{{a\Pr{\text{l}} \cdot 1{\text{H}}_{2} {\text{O}}_{0{\text{w}}} }}} = {\frac{{X \nu_{{\text{A}}1} \cdot \gamma (\Pr{\text{l}} \cdot 0{\text{H}}_{2} {\text{O}})}}{{X{\text{H}}_{2} {\text{O}}_{{\text{A}}1} \cdot \gamma (\Pr{\text{l}} \cdot 1{\text{H}}_{2} {\text{O}}_{0{\text{w}}} )}}} = {\frac{{X \nu_{{\text{A}}1} \cdot \exp \left( {RT\left( {\sum\nolimits_{{\text{TOT}}} + \sum\nolimits_{{\text{A}}1}^{V} } \right)} \right)}}{{X{\text{H}}_{2} {\text{O}}_{{\text{A}}1} \cdot \exp \left( {RT\left( {\sum\nolimits_{{\text{TOT}}} + \sum\nolimits_{{\text{A}}1}^{{\text{H}}} } \right)} \right)}}} \\ = {\frac{{X \nu_{{\text{A}}1} \cdot \exp \left( {RT\sum\nolimits_{{\text{A}}1}^{V} } \right)}}{{X{\text{H}}_{2} O_{{\text{A}}1} \cdot \exp \left( {RT\sum\nolimits_{{\text{A}}1}^{H} } \right)}}} $$

(A5)

where $\sum\nolimits_{\text{TOT}} {}$stands for the first term of equation (A4), and $\sum\nolimits_{\text{A1}}^{V} {}$and$\sum\nolimits_{\text{A1}}^{H} {}$represent all the non-ideal interactions involving vacancies and H₂O on A1.