# Does crystallographic anisotropy prevent the conventional treatment of aqueous mineral reactivity? A case study based on K-feldspar dissolution kinetics

Marion Pollet-Villard, Damien Daval, Philippe Ackerer, Giuseppe D. Saldi, Bastien Wild, Kevin G. Knauss, Bertrand Fritz

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## ► To cite this version:

Marion Pollet-Villard, Damien Daval, Philippe Ackerer, Giuseppe D. Saldi, Bastien Wild, et al. Does crystallographic anisotropy prevent the conventional treatment of aqueous mineral reactivity? A case study based on K-feldspar dissolution kinetics. Geochimica et Cosmochimica Acta, 2016, 190, pp.294-308. 10.1016/j.gca.2016.07.007. insu-03707896

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1 **Does crystallographic anisotropy prevent the conventional**

2 **treatment of aqueous mineral reactivity? A case study based on**

3 **K-feldspar dissolution kinetics – Revision 1**

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5 Marion Pollet-Villard¹*, Damien Daval¹,², Philippe Ackerer¹, Giuseppe D. Saldi², Bastien

6 Wild¹, Kevin G. Knauss² and Bertrand Fritz¹

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8 ¹Laboratoire d'Hydrologie et de Géochimie de Strasbourg, Université de Strasbourg/EOST,

9 CNRS, 67084, Strasbourg, France

10 ²Earth Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720,

11 USA

12 *Correspondence: Marion Pollet-Villard (polletvillard@unistra.fr), +33 (0)3 68 85 05 56,

13 Laboratoire d'Hydrologie et de Géochimie de Strasbourg, Université de Strasbourg/EOST,

14 CNRS, 67084, Strasbourg, France

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**Abstract**

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# 1. Introduction

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Chemical weathering spontaneously affects most solids including building and industrial materials (e.g. Nicoleau et al., 2013; King et al., 2014; Hellmann et al., 2015), biomaterials (e.g. Derry et al., 2005) or geomaterials (e.g. Lasaga and Lüttge, 2001). Accordingly, mineral dissolution drives a series of fundamental processes of industrial (e.g. CO₂ sequestration (Knauss et al., 2005; Saldi et al., 2015)), enhanced geothermal systems (Fritz et al., 2010)), biological (e.g. nutrient supply, see Lower et al., 2001) and geologic (e.g. carbon cycle (Maher and Chamberlain, 2014)) relevance. For most of these fields and in particular, in Earth sciences, two main approaches have been commonly applied to model the fate of chemical weathering at large space and time scales. The first category of models relies on a phenomenological, top-down strategy where empirical relations between mineral dissolution and effective external forcing parameters such as temperature or runoff are used (Berner, 1990). Since the early 90's, this approach has been gradually superseded by reactive transport models, where mineral reactivity is accounted for via kinetic rate laws derived from dissolution experiments carried out on powdered single-crystals. This strategy now fuels most simulations of fluid-mineral interactions (see e.g. Knauss et al., 2005; Fritz et al., 2010; Beaulieu et al., 2012; Maher and Chamberlain, 2014).

Compared to the top-down approach, the bottom-up strategy is often praised for its presumably greater reliability. Because experiments are conducted on powdered materials under well-defined conditions, it is often claimed that the resulting kinetic rate laws supposedly reflect the underlying elementary dissolution and precipitation mechanisms (Schott et al., 2009), rendering the corresponding fluid-mineral simulations more robust.

In addition to their technical simplicity, measurements of bulk dissolution rates became widespread and conventional because of the conceptual framework in which the corresponding kinetic rate laws have been developed. Application of the transition state
theory (TST) initially developed for elementary reactions in homogeneous media to overall dissolution processes in heterogeneous media was proposed in the early 80's (Aagaard and Helgeson, 1982), and subsequently coupled to surface complexation models (SCM), paving the way to the SCM/TST framework (Schott et al., 2009). A fundamental and appealing implication of applying this conceptual framework is that the complexity of heterogeneous chemical reactions is boiled down to the isotropic dissolution of a given solid, justifying the conventional measurement of bulk dissolution rates, and pushing to the background any potential crystallographic control on the reaction rate and rate law.

Arguably, the SCM/TST framework has succeeded in describing the dissolution of materials with simple chemistry and fairly high symmetry space-groups, such as simple metal oxides or hydroxides (e.g. Schott et al., 2009; Ohlin et al., 2010 and references therein). However, the detailed mechanisms and corresponding dissolution rate laws for more complex materials such as silicates are still a source of lively debate (e.g. Burch et al., 1993; Oelkers et al., 1994; Lasaga and Lüttge, 2001; Gautier et al., 1994; Hellmann and Tisserand, 2006; Beig and Lüttge, 2006; Hellmann et al., 2010; Gruber et al., 2014). More broadly, rate data collected via the conventional approach have long been shown to diverge from their field counterparts (White and Brantley, 2003), revealing inconsistencies of orders of magnitude for most minerals, even at the laboratory scale (Fischer et al., 2014), which questions the reliability of rate models developed on such datasets. As a matter of fact, aside from a limited number of studies which managed to reconcile experimental and field data at specific sites (e.g. Maher et al., 2009), upscaling laboratory results to the field without adjustments of several modeling parameters has essentially remained an elusive goal.

The source for the above-mentioned discrepancies remains an open question: aside from identified complicating factors including aqueous transport-limitations (Ruiz-Agudo et al., 2012; Laanait et al., 2015) or passivation by surface layers (Daval et al., 2011, 2013), a
handful of recent studies has pointed out that mineral surfaces do not homogeneously and isotropically react with aqueous fluids (Godinho et al., 2012; Daval et al., 2013; Godinho et al., 2014; Fischer et al., 2014; Laanait et al., 2015). Although crystallographic control of aqueous mineral reactivity has been suggested for decades (e.g. Gratz et al., 1991), the lack of quantitative data coupled to the potential problems inherent to the difficulties associated with modeling of anisotropic dissolution (such as tracking mineral texture over time in reactive transport codes), the heterogeneity and anisotropic nature of the dissolution process has long remained overlooked. In fact, the recognition that atomic ordering primarily impacts solid reactivity is relatively new, essentially resulting from the advent of microscopic, spectroscopic and computational methods allowing one to probe heterogeneous reactions at the molecular-level (e.g. Yanina and Rosso, 2008; Bandstra and Brantley, 2008; Kubicki et al., 2012; Daval et al., 2013; Lüttge et al., 2013; Kurganskaya and Lüttge, 2013; Fenter et al., 2014). Taken together, these recent observations motivated the present study, aimed at clarifying the validity and limitations of the conventional protocol commonly used to measure and upscale mineral dissolution rates.

Below, we provide measurements of K-feldspar (orthoclase, KAlSi₃O₈) dissolution, considered as a model mineral. Orthoclase was selected because of (1) its chemical composition and low-symmetry space-group, which substantially deviate from simple oxides/hydroxides for which the SCM/TST model putatively applies, (2) the fairly large dataset related to the bulk dissolution kinetics and dissolving surface structure of orthoclase (see Gautier et al., 1994; Fenter et al., 2014 and references therein) and feldspars as a whole (Beig and Lüttge, 2006; Hellmann and Tisserand, 2006; Hellmann et al., 2010) and (3) undoubtedly, the relevance of feldspar dissolution for major processes such as atmospheric CO₂ drawdown through continental weathering of silicates (Kampman et al., 2009). As opposed to previously applied methods (e.g. Gautier et al., 1994; Hellmann and Tisserand,
117 (2006) and following the pioneering measurements of Lüttge et al. (1999), our study benefited
118 from the use of vertical scanning interferometry (VSI) technique to monitor orthoclase
119 dissolution kinetics as a function of surface orientation and chemical affinity, which
120 represents the driving force for any chemical reaction and is consequently the most
121 fundamental parameter to be investigated.

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123 **2. Materials and methods**

124 **2.1 Sample characterization and preparation**

125 The starting material is a natural orthoclase single crystal from Afghanistan. No minor
126 phases were detected with X-ray diffraction or scanning electron microscopy (SEM).
127 Monolithic orthoclase samples (tens to several mm on a side) were cut with a diamond blade
128 saw and polished through a multi-step abrasive sequence using diamond suspensions of
129 decreasing grain sizes and soft polishing cloths, with an ultimate polishing step in a colloidal
130 silica suspension. Although such treatments were previously shown to potentially increase the
131 density of shallow (< 100 nm-deep) damage, they were also shown to negligibly affect the
132 defect density of the inner mineral volume (e.g. Lucca et al., 2006). The crystallographic
133 orientation of each sample was determined using an electron backscatter diffraction (EBSD)
134 detector attached to the SEM (TESCAN® Vega 2). The initial roughness of each surface was
135 measured at different scales with vertical scanning interferometer (ZYGO® NewView 7300).
136 For each sample, the initial average arithmetic roughness (Ra), defined as the arithmetic
137 average of the absolute values of the roughness profile, ranged between 5 nm and 20 nm, and
138 Rq (the roughness calculated with the root-mean-square of the vertical distance between the
139 surface elevation and the mean surface line) ranged between 7 nm and 28 nm. These initial
140 roughness parameters were measured on 270 × 360 µm² VSI images.
141 2.2 Aqueous dissolution experiments

142 Oriented samples were mounted in a titanium support as designed by Daval et al., 2013
143 (Fig. 1a), where a Viton® disk held with a screw creates a non-wetted reference area. Partially
144 masked samples were reacted in a synthetic alkaline solution in Parr® mixed-flow reactor at
145 180°C and 50 bars for durations ranging from one to three weeks to check for the linearity of
146 the surface retreat as a function of time. In this set-up, the pressure is kept constant through
147 the use of a back pressure regulator (Grove Mity Mite® S91XW), and the aqueous solution
148 was continuously stirred thanks to a magnetic stirrer rotating at a constant speed of 125 RPM.
149 Such rotation speeds are usually sufficient to ensure dissolution rates that are not transport-
150 controlled for the range of mineral reactivity which is considered (see e.g. Saldi et al., 2013).
151 Inlet solutions were made with ultrapure deionized water (18.2 MΩ.cm⁻¹) and analytical grade
152 NaOH, KCl, AlCl₃ and Na₂SiO₃. The pH was adjusted with the concentration of NaOH in the
153 solution (pHₜ in situ-180°C = 9.1 ± 0.3). No pH buffer was used in solution because, as it has been
154 generally observed, buffers can influence the dissolution rate of silicates (e.g. Golubev and
155 Pokrovsky, 2006). Investigating the dissolution of K-feldspar in alkaline solutions ensures
156 that the dissolution process is not influenced by the formation of amorphous silica-rich
157 surface layers (Hellmann et al., 1997) which could ultimately control the dissolution rate of
158 the silicate mineral (e.g. Daval et al., 2013; Maher et al., 2016). The Al concentration was
159 kept constant ([Al] = 3.8 +/- 0.5 ppm) for each experiment to get rid of any potential
160 inhibitory effect that Al may play on the dissolution rate, as suggested in several studies
161 (Gautier et al., 1994). The concentration of the others chemical species was varied to
162 investigate different values of the Gibbs free energy of orthoclase dissolution (ΔG). During
163 experiments, the outlet fluid was sampled every day. Compositions of the inlet and the outlet
164 solutions were measured by ICP-AES (THERMO ICAP 6000 Series). Aqueous
165 concentrations at steady-state conditions are listed in Table 1. The CHESS code (van der Lee
and De Windt, 2002) was used to determine the *in situ* pH and saturation indices with respect to orthoclase and secondary phases. It was verified that all solutions were undersaturated with respect to any secondary phase.

## 2.3 Vertical scanning interferometry (VSI) surface topography measurements

After dissolution experiments, sample surfaces were analyzed with VSI in stitching mode (magnification: ×5) to estimate the average change in height between the unreacted reference surface and the reacted mineral surface (Fig. 1b). For each oriented sample, dissolution rates were calculated according to the following equation (see e.g. Arvidson et al., 2004):

$$r^{(hkl)} = \frac{\Delta h}{\Delta t} \nu^{-1} \quad (1)$$

where $r^{(hkl)}$ (mol.m⁻².s⁻¹) is the dissolution rate of the (hkl) face, $\Delta h$ is the surface retreat, $\Delta t$ is the alteration duration and $\nu$ (m³.mol⁻¹) is the molar volume of orthoclase.

Surface imaging at higher magnification (×10 to ×100) was also achieved in order to quantify the etch pit density. The images were subsequently processed by color thresholding using the ImageJ software (Abramoff et al., 2004; Schneider et al., 2012). Measurements were performed after equal time durations on faces (001), (010), (110), (130) and (111) over the entire range of ΔG conditions that was investigated. The statistical analysis of pits covering the (101) face was not possible because of the complex surface features of this face, possibly resulting from the extensive coalescence of etch pits which prevented the above-described image processing.

# 3. Results
186 3.1 Face-specific dissolution rate of K-feldspar

187 The surface retreat measurements and associated dissolution rates of 6 natural faces of
188 orthoclase were calculated and are listed in Tables 2 and 3, respectively. Because the
189 application of Eq. (1) requires that the overall surface retreat is a linear function of time, the
190 temporal evolution of the surface retreat was monitored on several selected experimental
191 conditions for durations of up to 3 weeks (Fig. 1c and Table 2). These specific experiments
192 verified that the surface retreat increases linearly with time.

193 The rate data are reported as a function of ΔG in Fig. 2. To get rid of any contribution to
194 the measured dissolution rates of the slight variations in pH from one experiment to the other,
195 the measured experimental K-feldspar dissolution rates (blue triangles) were corrected and
196 recalculated for an exact pH of 9.0, based on the pH-dependence of K-feldspar dissolution
197 given by Palandri and Kharaka, 2004 (black squares) (see Daval et al., 2010 for previous
198 similar treatment). Of note, this correction assumes that the pH-dependence is the same for all
199 faces. To the best of our knowledge, whether or not the pH-dependence of K-feldspar
200 dissolution varies with crystallographic orientation is unknown. However, for most cases, the
201 pH variations were very modest, resulting in limited variations of the adjusted rate values.
202 The solid black lines (Fig. 2) represent non-linear least-squares curve fittings (Levenberg-
203 Marquardt method) using the phenomenological relation of Hellmann and Tisserand, 2006.
204 The fitting parameters are listed in Table 4 – note that the actual values of the fitted
205 parameters are not meant to be related to any specific molecular mechanism at that stage. In
206 fact, our main concern was to propose an *ad hoc* curve which could adequately fit our
207 experimental datasets to ultimately provide overall r-ΔG relations for the arbitrary crystal
208 morphologies reported in Fig. 4. Solid red lines are rate-curves based on the transition state
209 theory.
The relation between $r^{(hkl)}$ and $\Delta G$ is apparently specific to the crystallographic orientation which is considered, since the dissolution rate plateau value observed at far-from-equilibrium conditions is different for each face (Fig. 2). The face-specific dissolution rates $r^{(hkl)}$ observe the following trend: $r^{(001)} \approx r^{(010)} \approx r^{(\overline{1}10)} \lesssim r^{(\overline{1}30)} \ll r^{(\overline{1}01)} \approx r^{(\overline{1}11)}$. A tenfold factor is measured between the rate plateau value of the slowest dissolving face (001) and the fastest dissolving face (111). In addition, the shape of the $r-\Delta G$ relations also depends on the crystallographic orientation. Whereas the (001), (010) and (110) faces exhibit a relatively well-defined switch from rapid to slower dissolution rate, the dissolution rate of the (101), (111) and (130) faces decreases more gradually as $\Delta G$ increases. Finally, one can notice that the $r-\Delta G$ relations are systematically at odds with the TST-based relation implemented in most reactive transport codes.

## 3.2 Face-specific microstructural aspects of K-feldspar surfaces

The time-resolved growth and coalescence of etch pits was monitored on selected experiments, and when possible, the etch pit density was systematically measured after equal time durations for all experiments. These measurements evidenced that the anisotropic reactivity of K-feldspar is also reflected in the microstructural features of the different surfaces (Fig. 3). Regarding the (001), (010) and (110) faces, abundant µm-deep 3D etch pits can be observed at far-from-equilibrium conditions. For $-45 < \Delta G < -20$ kJ.mol$^{-1}$, the etch pit surface density dramatically drops, and much scarcer 2-D flat bottom pits likely originating from point defects is observed. On the other hand, for (111) and (130) faces, the 3D etch pits surface density remains relatively constant over the entire range of Gibbs free energies that was considered.

Overall, these results suggest that the dissolution rate of K-feldspar is tightly related to its surface microstructure, which critically depends on the crystallographic structure of K-feldspar.
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feldspar. In the next section, we further expand the rationale which could justify such an
assumption, and provide a critical analysis of the consequences of these findings.

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# 4. Discussion

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## 4.1 Far-from-equilibrium dissolution rate as a function of surface orientation

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Consistent with previous work (e.g. Zhang and Lüttge, 2009), the (010) and (001) surfaces are part of the less reactive faces of K-feldspar. As opposed to other classes of silicate minerals such as inosilicates (Daval et al., 2013) or phyllosilicates (Turpault and Trotignon, 1994) for which the anisotropic reactivity could be easily inferred from the connectedness of Si tetrahedrons in the crystallographic structure of the minerals, explaining the anisotropic reactivity of K-feldspar is more complex because feldspars belong to the category of tectosilicates, which have a three-dimensional framework of Si tetrahedra. As such, a suitable strategy consists in analyzing the data in the framework of the periodic bond chain (PBC) theory (Hartman and Perdok, 1955). The PBC theory states that crystal faces can be sorted out according to the number of uninterrupted chains of energetically strong bonds (PBC) they contain. Faces containing respectively ≥2, 1 and no PBC are commonly termed F-(for flat), S-(for stepped) and K-(for kinked) faces. The structure of K-feldspar was studied by Woensdregt, 1982 according to the PBC theory, who suggested to further subdivide the F category between F1 and F2 subcategories, which either contain only the strongest PBCs of the structure (with only Al-O or Si-O bonds) (F1), or also contain weaker K-O PBC (F2). Interestingly, Woensdregt, 1982 proposed that faces (110), (001) and (010) belong to the F1 subcategory, as opposed to faces (101), (111) and (130), which belong to the F2 category. Therefore, with the exception of face (130) (cf. section 3.1; see also section 4.2 for further

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257 discussion), our measurements verify that face reactivity is correlated with the strength of the
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## 4.2 Face-specific dissolution rates as a function of ΔG

260 The anisotropic nature of the dissolution process is further confirmed when the whole
261 range of chemical affinities is considered (Fig. 2). According to our results, F1 faces exhibit a
262 relatively well-defined switch from rapid to slower dissolution rate, whereas dissolution rate
263 decreases more gradually as ΔG increases in the case of F2 faces (Figs. 2 and 4).

264 The divergence between the reactivity of F1 and F2 faces is also reflected by the
265 microstructural aspects of the different surfaces (Fig. 3). As stated above, the etch pit density
266 drastically decreases when approaching equilibrium for F1 faces; in contrast, F2 faces are
267 characterized by a relatively constant density of µm-deep 3D etch pits typically originating
268 from outcropping dislocations (e.g. Gratz et al., 1991), regardless of ΔG.

269 These observations can be interpreted in the framework of the stepwave model (Lasaga
270 and Lüttge, 2001), which states that etch pit nucleation is a major driver of crystal dissolution.
271 Following this model, a critical free energy (ΔG<sup>crit</sup>) value is required to open up etch pit at
272 line defects spontaneously, the pit walls representing a continuous source of steps which
273 travel throughout the crystal surface, eventually leading to its overall retreat. Conversely, if
274 this energetic threshold is exceeded, etch pit nucleation at dislocation outcrops is no longer
275 spontaneous, and the dissolution is essentially driven by point defects and dissolution on pre-
276 existing corners and edges at a much slower rate.

277 Lasaga and Blum, 1986 showed that a basic expression for calculating the numerical
278 value of ΔG<sup>crit</sup> at screw dislocations can be written as follows:

$$ \Delta G^{\text{crit}} = \frac{-2\pi^2 \sigma^2 V}{\mu b^2} \qquad (2) $$
where $\sigma$ is the surface free energy, $\nu$ is the molar volume, $\mu$ is the bulk shear modulus, and $b$ is the Burgers vector of the dislocation. As anticipated by Lasaga and Blum, 1986 and confirmed in our study, this expression illustrates that several values of $\Delta G^{crit}$ may exist for a given mineral, depending on the surface energy of the specific face which is considered, and the length of the Burgers vectors outcropping at the crystal surface. Combining this expression with the classification of K-feldspar faces proposed by Woensdregt, 1982 further indicate that the differences in $\Delta G^{crit}$ revealed in our study (-45 < $\Delta G$ < -20 kJ.mol$^{-1}$ for F1 faces; $\Delta G$ > -10 kJ.mol$^{-1}$ (if any) for F2 faces) may stem from the surface energy differences between F1 and F2 faces, since the PBC theory predicts that the surface energy of F1 faces deviates from that of F2 faces.

Overall, these results nicely illustrate that the differences in terms of microstructural features revealed at the µm-scale, which are directly inherited from the anisotropic distribution of atomic positions in the K-feldspar cell unit at the Å-scale, can have a major impact at the macro-scale and result in specific kinetic hallmarks, such as the observed discrepancies between the $r^{(F1)}$-$\Delta G$ and $r^{(F2)}$-$\Delta G$ trends. Consistent with our results, supposing that K-feldspar dissolution can be interpreted in the combined framework of the PBC and stepwave models leads to the following additional comments:

(i) The proposed intimate link between the macroscopic $r$-$\Delta G$ relations and corresponding microstructural aspects of the dissolving surface is in close agreement with recent published work. For instance, Arvidson and Lüttge, 2010 demonstrated that a steep kinetic drop is observed for albite crystal surfaces (001) when the starting etch pit density is dramatically decreased. Conversely, $r$-$\Delta G$ relations such as those observed for F2 faces where the decrease of the dissolution rate is a gradual function of the chemical affinity is typical of pit-dominated dissolution regardless of the free energy which is considered, as previously shown by Beig and Lüttge, 2006.
(ii) It may seem intriguing that the surface retreat is a linear function of time, in spite of the growing density of etch pits that nucleate on the various surfaces of K-feldspar. For instance, it has been recently proposed that the development of pit walls with lower surface energy was responsible for increasing the proportion of weakly reactive surface area, ultimately leading to an intrinsic decrease of the long-term dissolution rate of the considered surface (e.g. Godinho et al., 2012; Smith et al., 2013). As a matter of fact, this mechanism should have a great impact on the dissolution of surfaces with high initial reactive site densities, such as K- or S-faces, which were not investigated in the present study. If one states that K-feldspar reactivity complies with the PBC theory, then the pit walls developed on the F-faces cannot be less reactive than the F-faces themselves, which probably explain why the dissolution rate of the faces that were considered in the present study does not decline with time. Conversely, following simple geometric considerations, one could claim that the dissolution rate of a given surface should increase as a function of time, because of the additional surface area that is exposed to the solution due to the nucleation of etch pits. While this question will be addressed in detail in an upcoming companion study, as a preliminary piece of evidence, we roughly estimated the increase in surface area resulting from the development of pit walls on the (001) surface. Such an increase never exceeded 20% for all experiments, which is on the same order of magnitude as the spatial variability of the measured surface retreat (see Table 2), and any intrinsic temporal increase of the face-specific dissolution rate should be considered as speculative at that stage.

(iii) Finally, although our rate data are consistent with the PBC theory for 5 out of the 6 investigated crystallographic orientations, the use of the PBC theory cannot easily account for the anomalously slow reactivity of the (11̄0) face. A tentative explanation may rely on the anisotropic distribution of dislocations in the K-feldspar structure: as described in several studies (see Tullis, 1983 for a review), the occurrence of dislocations in feldspars chiefly
depends on two parameters: (1) the length of the Burgers vector of the dislocation and (2) the deformation history of the minerals. From an energetic standpoint, Burgers vectors with the shortest length should be favored (i.e., for K-feldspar: [001]). In fact, dislocations oriented following the [001] direction are very common in naturally and experimentally deformed feldspars, although other Burgers vectors can also be observed, depending on the orientation of the stress applied on the crystals (Tullis, 1983). Of note, the (130) face is parallel to the [001] direction, such that screw dislocations with [001] Burgers vectors do not outcrop at the surface of the (130) face. As mentioned above, screw dislocations are often considered as important drivers for the dissolution process. Therefore, the dissolution rate of the (130) face may be slower than that of the other F2 faces ((111) and (101)) because of the smaller number of screw dislocations outcropping at the surface of the (130) face. Although further work would be necessary to confirm this suggestion, it is noteworthy that the etch pit surface density is smaller for this face than for any other faces (Fig. 3), which may be considered as an indirect evidence which supports the mechanism that we propose.

### 4.3 On the limitations of the conventional treatment of aqueous mineral reactivity

Overall, our results demonstrate the strong anisotropic nature of aqueous mineral reactivity. The expression of such an anisotropy stems from differences in absolute face-specific dissolution rates and the non-uniqueness of $r^{(hkl)}$- $\Delta G$ relations. This anisotropic reactivity is intimately related to the anisotropic distribution of atomic crystallographic sites in the mineral structure, and its recognition has the far-reaching conceptual and methodological consequences listed below:

(i) First, defining a unique dissolution rate constant for a given mineral is intrinsically misleading, as the bulk dissolution rate of a crystal critically depends on its morphology (i.e. relative proportions of different faces exposed to the aqueous solution). Although with
different arguments, the present study concurs with the conclusions reached in recent papers (e.g. Lüttge et al., 2013; Fischer et al., 2014) that using the commonplace ‘bulk surface normalization approach’ to provide rate constants is not appropriate to quantify the reactivity of crystalline materials that are not controlled by aqueous transport limitation or passivation. Acknowledging the anisotropic nature of aqueous mineral dissolution invalidates the use of isotropic rate laws to mechanistically account for mineral reactivity. Accordingly, deriving a single isotropic dissolution rate law for a mineral is not simply a simplification of the dissolution process, it is conceptually improper, since an overall isotropic rate law cannot capture the sensitivity of the individual faces to a given parameter.

(ii) Similarly, the conventional determination of reaction mechanisms based on measurements of bulk powder dissolution rates may be misleading. Even in the unlikely case where powders are made of grains with monodispersed morphologies, the resulting macroscopic dissolution rates remain a combination of the underlying reaction mechanisms dictated by the grain morphology: as an example, the lively debate regarding the exact shape of overall r-ΔG relations (sigmoidal or linear, see e.g. Burch et al., 1993; Oelkers et al., 1994; Gautier et al., 1994; Lasaga, 1995; Taylor et al., 2000; Hellmann and Tisserand, 2006; Hellmann et al., 2010; Beig and Lüttge, 2006) may simply vanish if one considers that the original experiments were run with powders containing different dominant morphologies (Fig. 4). Aside from offering an interpretative framework for the disparities between rate data reported in different studies as pointed out by e.g. Fischer et al., 2014, an important conclusion of this work is that when dealing with powders, the impact of a macroscopic parameter as fundamental as ΔG will not lead to an unique dissolution rate, which greatly complicates the prediction of crystalline materials reactivity, even under well-defined environmental conditions.
(iii) As a final important comment, one can expect that the anisotropic aqueous mineral reactivity of crystalline materials may lead to a continuous modification of the dissolution rate of a single crystal as a function of the reaction progress, because of the gradual development of fast dissolving faces at the expense of the slower ones. This assertion was verified by monitoring numerically the dissolution features of single crystals with various morphologies.

In brief, the numerical model is based on the description of a crystal by $N_x \times N_y \times N_z$ elementary cells (ECs) where $N_x$ (respectively $N_y$ and $N_z$) represents the number of ECs following $x$ (respectively $y$ and $z$) directions. The ECs have a hexahedral shape. For each EC, the model lists the number and the orientation of faces which contact the fluid. With these data, each EC is listed as belonging to a face orientation at the macroscopic scale. The ECs which have only one face in contact with the fluid belong to the macroscopic (100), (010) or (001) face (e.g. an EC which has only one face belonging to the (xOy) plane in contact with the fluid belongs to the (001) surface). In contrast, the ECs which have two non-parallel faces exposed to the solution are either assigned as (110), or (101) or (011), depending on the faces of the ECs which are exposed to the solution (e.g. the ECs whose faces exposed to the fluid are parallel to the (yOz) and (xOz) are assigned as (110). The (111) face is composed by ECs which have the three faces parallel to (xOy), (xOz), and (yOz) in contact with the fluid. For each face category, a linear retreat with time was defined, consistent with the experimental results. A constant “period” $\overline{k}$ is defined by the number of iterations required to dissolve an EC which contacts the fluid. The values of $\overline{k}$ used in simulations are listed in table 5.

As observed experimentally, some faces such as the (101) and (111) faces dissolve ten times faster than others (e.g. (001), (010), (110)). For the (100) or (011) faces which may enter in simulations but which were not experimentally measured, we chose an arbitrary value of 10 (Fig. 5a). Importantly, we made sure that choosing other arbitrary values for such faces do not modify the main trends which are reported below – see another set of simulations with
$\overline{k^{(100)}} = \overline{k^{(011)}} = 1$ in Fig. 5b. At each time step, the model counts the number of existing ECs, the number of faces in contact with the fluid and the face orientation. These data are subsequently used to calculate the dissolved volume, the mineral surface area and, in turn, the dissolution rate per unit of area and per iteration. Simulation results for different crystal habits are presented in Fig. 5.

In spite of its simplicity (in particular, the orientation of the faces which are developed as a function of time is limited to the existing faces defined at the beginning of the simulation, and the stabilization of faces with new orientations is precluded), the first-order results show that dissolution anisotropy induces a complex evolution of the overall crystal dissolution rate as a function of the reaction progress. Both the onset of the overall dissolution rate and its evolution as a function of the reaction progress are primarily inherited from the starting morphology of the dissolving grains, precluding the attainment of a unique crystal habit. Similar conclusions were previously reached in the kinetic modeling study conducted by Zhang and Lüttge, 2009 on albite feldspar. Regarding K-feldspar, we anticipate that such trends would be even more dramatic if K- or S- faces were implemented in the model, since their dissolution rate is expected to greatly exceed that of F2-faces. More generally, the difference between the isotropic and anisotropic scenarios can drastically increase if the rate factor between rapid and slow faces is even greater. This scenario may be encountered for very anisotropic structures such as inosilicates or phyllosilicates, where the dissolution rate of the fastest faces can be up to two orders of magnitude greater than that of the slowest faces (e.g. Daval et al., 2013), strengthening the crucial attention which should be paid to the anisotropic reactivity of dissolving minerals.

424

425

426
427 Conclusions

428 Overall, this combined experimental and modeling study illustrates some limitations of
429 the conventional treatment of aqueous mineral reactivity. In particular, our results suggest that
430 the mechanistic basis for the bottom-up simulations of chemical weathering that rely on
431 overall kinetic rate laws may not be as robust as commonly expected. Although the current
432 reactive transport simulations cannot be simply abandoned, one has to keep in mind that most
433 of the so-called kinetic rate laws that can be retrieved in thorough database and review papers
434 may probably not reflect more than empirical relations, such that one has to remain careful
435 with respect to the predictive ability of the outputs of such simulations.

436 Alternative approaches are therefore necessary to improve the reliability of such
437 simulations. Although based on a simple parameterization, the model described above is
438 unlikely to be easily implemented into reactive transport codes "as is". In fact, the variations
439 of porosity, pore connectivity and resulting medium diffusivity as a function of the reaction
440 progress already represents a challenge in itself (Emmanuel et al., 2015; Noiriel, 2015; Steefel
441 et al., 2015), such that tracking the mineral and porosity textures of a mineralogical
442 assemblage over time adds a supplementary layer of complexity which may rule out any
443 further implementation in reactive transport codes. Alternatively, it may be tempting to
444 establish detailed texture evolutions and dissolution rate laws for a limited number of
445 equilibrium crystal habits predicted by the PBC theory, and to use the numerically-derived
446 textures and overall dissolution rates in the corresponding simulations of porous medium
447 weathering. However this treatment would probably be hopeless as well, because euhedral
448 crystals are only occasionally found in the field (Velbel, 2009), where grain morphology
449 results from the complex coupling between physical erosion and chemical weathering. Indeed,
450 statistical investigations of the intricate interplay between mechanical breakage of crystal
451 structures and chemical hydrolysis may represent a necessary step to isolate the dominant
reaction modes and continue promoting a bottom-up treatment of mineral reactivity, for which Kinetic Monte Carlo (KMC) simulations may represent the most promising strategy (see Lüttge et al., 2013; Kurganskaya and Lüttge, 2013). Of note, as opposed to the recent successful KMC attempts on nuclear glass corrosion (see e.g. Cailleteau et al., 2008), where the simulations essentially remained underconstrained because of the large number of bond-breaking probabilities to be adjusted, multiple measurements of mineral face-specific dissolution rates can be used to over-constrain the bond-breaking probabilities implemented in KMC models for a given mineral structure. In that respect, instead of being a detrimental complicating factor, the recognition of the anisotropy of crystalline materials reactivity offers an invaluable opportunity to refine our understanding of fluid-solid reactions at a molecular-scale, paving the way for a paradigm shift in experimental measurements of aqueous mineral reactivity.

464

465 Acknowledgements

This work has been funded through a grant attributed to D.D. for the project "Feldspar reactivity in the context of Soultz-sous-Forêts: From microstructural characterizations to numerical modeling" under the framework of the LABEX ANR-11-LABX-0050_G-EAU-THERMIE-PROFONDE which benefits from a funding from the state managed by the French National Research Agency as part of the French "Investissements d'avenir". M.P.-V. thanks the Région Alsace and LABEX "G-EAU-THERMIE PROFONDE" for funding her PhD contract. K.G.K. effort at LBL was supported by the Director, Office of Science, Office of Basic Energy Sciences, Chemical Sciences, Geosciences, and Biosciences Division, of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231.

We are indebted to G. Schäfer (Strasbourg, France) for ensuring the smooth progress of the work at LHyGeS. Thanks are due to R. Boutin, G. Morvan and A. Aubert for their help with
477 analyses and technical contributions at the LHyGeS (Strasbourg, France). We also thank G.

478 A. Waychunas (LBNL Berkeley, USA) for providing us the K-spar crystal used to carry out
479 this study and R. Hellmann (ISTerre, Grenoble, France) for providing additional equipment.

480 The insightful review of (AE) Carl Steefel and constructive and supportive comments by three
481 anonymous reviewers were much appreciated and helped improving an earlier version of the
482 manuscript.

483

484 References

485 Aagaard, P. and Helgeson, H.C. (1982). Thermodynamic and kinetic constraints on reaction-
486 rates among minerals and aqueous-solutions. 1. Theoretical considerations. *Am J Sci* **282**,
487 237-285.

488 Abramoff, M.D., Magalhaes, P.J. and Ram, S.J. (2004). Image Processing with ImageJ.
489 *Biophotonics International* **11**, 7, 36-42.

490 Arvidson, R.S., Beig, M.S. and Luttge, A. (2004). Single-crystal plagioclase feldspar
491 dissolution rates measured by vertical scanning interferometry. *Am. Mineral* **89**, 51-56.

492 Arvidson, R.S. and Luttge, A. (2010). Mineral dissolution kinetics as a function of distance
493 from equilibrium - New experimental results. *Chem. Geol.* **269**, 79-88.

494 Bandstra, J.Z. and Brantley, S.L. (2008). Surface evolution of dissolving minerals
495 investigated with a kinetic Ising model. *Geochim. Cosmochim. Ac.* **72**, 2587-2600.

496 Beaulieu, E., Godderis, Y., Donnadieu, Y., Labat, D. and Roelandt, C. (2012). High
497 sensitivity of the continental-weathering carbon dioxide sink to future climate change.
498 *Nat Clim Change* **2**, 346-349.

499 Beig, M.S. and Luttge, A. (2006). Albite dissolution kinetics as a function of distance from
500 equilibrium: Implications for natural feldspar weathering. *Geochim. Cosmochim. Ac.* **70**,
501 1402-1420.
502 Berner, R.A. (1990). Atmospheric Carbon Dioxide Levels Over Phanerozoic Time. *Science* **249**, 1382-1386.

503 Burch, T.E., Nagy, K.L. and Lasaga, A.C. (1993). Free energydependence of albite dissolution kinetics at 80°C and pH 8.8. *Chem. Geol.* **105**, 137-162.

506 Cailleteau, C., Angeli, F., Devreux, F., Gin, S., Jestin, J., Jollivet, P. and Spalla, O. (2008). Insight into silicate-glass corrosion mechanisms. *Nature Materials* **7**, 978-983.

508 Daval, D., Hellmann, R., Corvisier, J., Tisserand, D., Martinez, I. and Guyot, F. (2010). Dissolution kinetics of diopside as a function of solution saturation state: Macroscopic measurements and implications for modeling of geological storage of CO2. *Geochim. Cosmochim. Ac.* **74**, 2615-2633.

512 Daval, D., Hellmann, R., Saldi, G.D., Wirth, R., Knauss, K.G. (2013). Linking nm-scale measurements of the anisotropy of silicate surface reactivity to macroscopic dissolution rate laws: New insights based on diopside. *Geochim. Cosmochim. Ac.* **107**, 121-134.

515 Daval, D., Sissmann, O., Menguy, N., Saldi, G.D., Guyot, F., Martinez, I., Corvisier, J., Garcia, B., Machouk, I., Knauss, K.G. and Hellmann, R. (2011). Influence of amorphous silica layer formation on the dissolution rate of olivine at 90°C and elevated pCO₂. *Chem. Geol.* **284**, 193-209.

519 Derry, L.A., Kurtz, A.C., Ziegler, K. and Chadwick, O.A. (2005). Biological control of terrestrial silica cycling and export fluxes to watersheds. *Nature* **433**, 728-731.

521 Emmanuel, S., Anovitz, L. M. and Day-Stirrat, R. J. (2015). Effects of coupled Chemo-Mechanical Process on the Evolution of Pore-Size Distributions in Geological Media *Reviews in Mineralogy and Geochemistry*, **80**, 45-60.

524 Fenter, P., Zapol, P., He, H. and Sturchio, N.C. (2014). On the variation of dissolution rates at the orthoclase (0 0 1) surface with pH and temperature. *Geochim. Cosmochim. Ac.* **141**, 598-611.
527 Fischer, C., Kurganskaya, I., Schäfer, T. and Lüttge, A. (2014). Variability of crystal surface reactivity: What do we know? *Appl. Geochem.* **43**, 132-157.

529 Fritz, B., Jacquot, E., Jacquemont, B., Baldeyrou-Bailly, A., Rosener, M. and Vidal, O. (2010). Geochemical modelling of fluid-rock interactions in the context of the Soultz-sous-Forets geothermal system. *Cr. Geosci.* **342**, 653-667.

532 Gautier, J.M., Oelkers, E.H. and Schott, J. (1994). Experimentale study of K-feldspar dissolution rates as a function of chemical affinity at 150°C and pH 9. *Geochim. Cosmochim.* Ac. **58**, 4549-4560.

535 Godinho, J.R.A., Piazolo, S. and Balic-Zunic, T. (2014). Importance of surface structure on dissolution of fluorite: Implications for surface dynamics and dissolution rates. *Geochim. Cosmochim.* Ac. **126**, 398-410.

538 Godinho, J.R.A., Piazolo, S. and Evins, L.Z. (2012). Effect of surface orientation on dissolution rates and topography of CaF₂. *Geochim. Cosmochim.* Ac. **86**, 392-403.

540 Golubev, S.V. and Pokrovsky, O.S. (2006). Experimental study of the effect of organic ligands on diopside dissolution kinetics. *Chem. Geol.* **235**, 377-389.

542 Gratz, A.J., Manne, S. and Hansma, P.K. (1991). Atomic Force Microscopy of Atomic-Scale Ledges and Etch Pits Formed During Dissolution of Quartz. *Science* **251**, 1343-1346.

544 Gruber, C., Zhu, C., Bastian Georg, R., Zakon, Y. and Ganor, J. (2014) Resolving the gap between laboratory and field rates of feldspar weathering. *Geochimica et Cosmochimica Acta*, **147**, 90-106.

547 Hartman, P. and Perdok, W.G. (1955). On the relations between structure and morphology of crystals. I. *Acta Crystallographica* **8**, 49-52.

549 Hellmann, R., Cotte, S., Cadel, E., Malladi, S., Karlsson, L.S., Lozano-Perez, S., Cabié, M. and Seyeux, A. (2015). Nanometre-scale evidence for interfacial dissolution–reprecipitation control of silicate glass corrosion. *Nat. Mater.* **14**, 307-311.
Hellmann, R., Daval, D. and Tisserand, D. (2010). The dependence of albite feldspar dissolution kinetics on fluid saturation state at acid and basic pH: Progress towards a universal relation. *Cr. Geosci.* **342**, 676-684.

Hellmann, R., Dran, J.C. and DellaMea, G. (1997). The albite-water system. Characterization of leached and hydrogen-enriched layers formed at 300°C using MeV ion beam techniques. *Geochim Cosmochim Ac* **61**, 1575-1594.

Hellmann, R. and Tisserand, D. (2006). Dissolution kinetics as a function of the Gibbs free energy of reaction: An experimental study based on albite feldspar. *Geochim. Cosmochim. Ac.* **70**, 364-383.

Kampman, N., Bickle, M., Becker, J., Assayag, N. and Chapman, H. (2009). Feldspar dissolution kinetics and Gibbs free energy dependence in a CO₂-enriched groundwater system, Green River, Utah. *Earth Planet Sc. Lett.* **284**, 473-488.

King, H.E., Satoh, H., Tsukamoto, K. and Putnis, A. (2014). Surface-specific measurements of olivine dissolution by phase-shift interferometry. *Am. Mineral.* **99**, 377-386.

Knauss, K.G., Johnson, J.W. and Steefel, C.I. (2005). Evaluation of the impact of CO₂, co-contaminant gas, aqueous fluid and reservoir rock interactions on the geologic sequestration of CO₂. *Chem. Geol.* **217**, 339-350.

Kubicki, J.D., Sofo, J.O., Skelton, A.A. and Bandura, A.V. (2012). A New Hypothesis for the Dissolution Mechanism of Silicates. *The Journal of Physical Chemistry C* **116**, 17479-17491.

Kurganskaya, I. and Luttge, A. (2013). A comprehensive stochastic model of phyllosilicate dissolution: Structure and kinematics of etch pits formed on muscovite basal face. *Geochim. Cosmochim. Ac.* **120**, 545-560.

Laanait, N., Callagon, E.B.R., Zhang, Z., Sturchio, N.C., Lee, S.S. and Fenter, P. (2015). X-ray-driven reaction front dynamics at calcite-water interfaces. *Science* **349**, 1330-1334.
577 Lasaga, A.C. (1995). Fundamental approaches in describing mineral dissolution and precipitation rates., in: White, A.F., Brantley, S.L. (Eds.), Chemical Weathering Rates of Silicate Minerals. *Mineralogical Society of America*, pp. 23-86.

580 Lasaga, A.C. and Blum, A.E. (1986). Surface chemistry, etch pits and mineral-water reactions. *Geochim. Cosmochim. Ac.* **50**, 2363-2379.

582 Lasaga, A.C. and Luttge, A. (2001). Variation of Crystal Dissolution Rate Based on a Dissolution Stepwave Model. *Science* **291**, 2400-2404.

584 Lower, S.K., Hochella, M.F., Beveridge and T.J. (2001). Bacterial Recognition of Mineral Surfaces: Nanoscale Interactions Between Shewanella and α-FeOOH. *Science* **292**, 1360-1363.

587 Lucca, D. A., Shao, L., Wetteland, C. J., Misra, A., Klopfstein, M. J. and Nastasi, M. (2006). Subsurface damage in (100) ZnSe introduced by mechanical polishing. *Nuclear Instruments & Methods in Physics Research, section B*, **249**, 907-910.

590 Lüttge, A., Bolt, E. W. and Lasaga, A. C. (1999). An interferometric study of the dissolution kinetics of anorthite; the role of reactive surface area. *American Journal of Science*, **299**, 652-678.

593 Lüttge, A., Arvidson, R.S. and Fischer, C. (2013). A Stochastic Treatment of Crystal Dissolution Kinetics. *Elements* **9**, 183-188.

595 Maher, K., Steefel, C. I., White, A. F. and Stonestrom, D. A. (2009). The role of reaction affinity and secondary minerals in regulating chemical weathering rates at the Santa Cruz Soil Chronosequence, California. *Geochimica et Cosmochimica Acta*, **73**, 2804-2831.

598 Maher, K. and Chamberlain, C.P. (2014). Hydrologic Regulation of Chemical Weathering and the Geologic Carbon Cycle. *Science* **343**, 1502-1504.
600 Maher, K., Johnson, N.C., Jackson, A., Lammers, L.N., Torchinsky, A.B., Weaver, K.L.,
601 Bird, D.K. and Brown Jr, G.E. (2016). A spatially resolved surface kinetic model for
602 forsterite dissolution. *Geochim. Cosmochim. Ac.* **174**, 313-334.

603 Nicoleau, L., Nonat, A. and Perrey, D. (2013). The di- and tricalcium silicate dissolutions.
604 *Cement and Concrete Research* **47**, 14-30.

605 Noiriel, C. (2015). Resolving Time-dependent Evolution of Pore-Scale Structure,
606 Permeability and Reactivity using X-ray Microtomography. *Reviews in Mineralogy and
607 Geochemistry*, **80**, 247-285.

608 Oelkers, E.H., Schott, J. and Devidal, J.-L. (1994). The effect of aluminum, pH, and chemical
609 affinity on the rates of aluminosilicate dissolution reactions. *Geochim. Cosmochim. Ac.*
610 **58**, 2011-2024.

611 Ohlin, C.A., Villa, E.M., Rustad, J.R. and Casey, W.H. (2010). Dissolution of insulating
612 oxide materials at the molecular scale. *Nature Materials* **9**, 11-19.

613 Palandri, J.L. and Kharaka, Y.K. (2004). A compilation of rate parameters of water-mineral
614 interaction kinetics for application to geochemical modeling, in: *U.S. Geological Survey*,
615 O.F.R. (Ed.), p. 70.

616 Ruiz-Agudo, E., Putnis, C.V., Rodriguez-Navarro and C., Putnis, A. (2012). Mechanism of
617 leached layer formation during chemical weathering of silicate minerals. *Geology* **40**,
618 947-950.

619 Saldi, G.D., Daval, D., Guo, H., Guyot, F., Bernard, S., Le Guillou, C., Davis, J.A. and
620 Knauss, K.G. (2015). Mineralogical evolution of Fe–Si-rich layers at the olivine-water
621 interface during carbonation reactions. *Am. Mineral.* **100**, 2655-2669.

622 Saldi, G. D., Daval, D., Morvan, G. and Knauss, K. G. (2013). The role of Fe and redox
623 conditions in olivine carbonation rates: An experimental study of the rate limiting
624 reactions at 90 and 150°C in open and closed systems. *Geochimica et Cosmochimica Acta*, **118**, 157 – 183.

626 Schneider, C.A., Rasband, W.S. and Eliceiri, K.W. (2012). NIH Image to ImageJ: 25 years of image analysis. *Nature Methods* **9**, 671-675.

628 Schott, J., Pokrovsky, O.S. and Oelkers, E.H. (2009). The Link Between Mineral Dissolution/Precipitation Kinetics and Solution Chemistry. *Rev. Mineral. Geochem.* **70**, 207-258.

631 Smith, M.E., Knauss, K.G. and Higgins, S.R. (2013). Effects of crystal orientation on the dissolution of calcite by chemical and microscopic analysis. *Chem. Geol.* 360–361, 10-21.

634 Steefel, C. I., Beckingham, L. E. and Landrot, G. (2015). Micro-Continuum Approaches for Modeling Pore-Scale Geochemical Processes. *Reviews in Mineralogy and Geochemistry*, **80**, 217-246.

637 Taylor, A.S., Blum, J.D. and Lasaga, A.C. (2000). The dependence of labradorite dissolution and Sr isotope release rates on solution saturation state. *Geochim. Cosmochim. Ac.* **64**, 2389-2400.

640 Tullis, J. (1983) Deformation of feldspars. In: Ribbe, P. H. (Ed.), Feldspar Mineralogy. *Reviews in Mineralogy*, **2**, 297-323.

642 Turpault, M.P. and Trotignon, L. (1994). The Dissolution of Biotite Single-Crystals in Dilute HNO₃ at 24°C - Evidence of an Anisotropic Corrosion Process of Micas in Acidic Solutions. *Geochim. Cosmochim. Ac.* **58**, 2761-2775.

645 van der Lee, J. and De Windt, L. (2002). CHESS Tutorial and Cookbook. Updated for version 3.0., Paris.

647 Velbel, M.A. (2009). Dissolution of olivine during natural weathering. *Geochim. Cosmochim. Ac.* **73**, 6098-6113.
649 White, A.F. and Brantley, S.L. (2003). The effect of time on the weathering of silicate
650 minerals: why do weathering rates differ in the laboratory and field? *Chem. Geol.* **202**,
651 479-506.

652 Woensdregt, C.F. (1982). Crystal morphology of monoclinic potassium feldspar: a qualitative
653 approach with special emphasis on the Periodic Bond Chain Theory of Hartman and
654 Perdrok. *Zeitschrift für Kristallographie* **161**, 15-33.

655 Yanina, S.V. and Rosso, K.M. (2008). Linked Reactivity at Mineral-Water Interfaces
656 Through Bulk Crystal Conduction. *Science* **320**, 218-222.

657 Zhang, L. and Lüttge, A. (2009). Morphological evolution of dissolving feldspar particles
658 with anisotropic surface kinetics and implications for dissolution rate normalization and
659 grain size dependence: A kinetic modeling study. *Geochim. Cosmochim. Ac.* **73**, 6757-
660 6770.

661

662 **Figure Legends**

663 Fig. 1: Surface retreat measurements after face-specific dissolution experiments. a, After
664 initial surface roughness measurements by AFM and VSI, K-feldspar sample was mounted on
665 a passivated titanium jig. A Viton disk held with a screw creates a non-wetted reference
666 surface. The crystal is subsequently altered in a flow-through reactor at 180°C in a synthetic
667 alkaline solution. b, Illustrative 3D-view of face (111) realized by VSI after one week of
668 alteration, evidencing a typical surface retreat between the non-wetted reference area and the
669 dissolved area. c, Surface retreat measurements carried out on faces (101), (111) and (001)
670 as a function of time (see tables 1-3 for details regarding the corresponding MRGT2
671 experiment). The surface retreat is linear with time (i.e., the dissolution rate is constant) but
672 depends on the crystallographic orientation: a tenfold factor is observed between the slowest
673 face (001) and the others.
674

Fig. 2: r-ΔG relations for the six crystallographic orientations investigated in the present study: (001), (010), (11̄0), (1̄30), (1̄11) and (1̄01). Dissolution experiments were carried

676
study: (001), (010), (11̄0), (1̄30), (1̄11) and (1̄01). Dissolution experiments were carried

677
out at 180°C and pH<sub>in situ</sub> = 9.1 ± 0.3. To remove any contribution of the slight variations in

678
pH from one experiment to the other, the measured experimental K-feldspar dissolution rates

(blue triangles) were corrected and recalculated for an exact pH of 9.0, based on the pH

680
dependence of K-feldspar given by Palandri and Kharaka, 2004 (black squares). As can be

681
seen, for most cases, such a treatment results in very modest variations of the adjusted rate

682
values. The solid black lines represent non-linear least-squares curve fittings (Levenberg-

Marquardt method) using the phenomenological relation of Hellmann and Tisserand, 2006.

684
The fitting parameters are listed in Table 4 – note that the actual values of the fitted

parameters are not meant to be related to any specific molecular mechanism. In fact, our main

686
concern was to propose an *ad hoc* curve which could adequately fit our experimental datasets

687
to ultimately provide overall r-ΔG relations for the arbitrary crystal morphologies reported in

688
Fig. 4. Solid red lines are rate-curves based on the transition state theory, for which the rate

plateau has been adjusted to the mean far-from-equilibrium dissolution rate of the considered

690
face.

691

692
Fig. 3: Proportion of etch pits (%) covering the surface of (001), (010), (1̄10), (1̄30) and

(1̄11̄) faces as a function of ΔG. A drop in the proportion of etch pits is observed for the

694
(001), (010) and (1̄10) faces (F1 faces) for -45 kJ.mol⁻¹ ≤ ΔG ≤ -20 kJ.mol⁻¹ (shaded area).

695
For the (1̄30) and (1̄11̄) faces, which belong to the F2 category, no obvious modification of

696
etch pit density can be seen for ΔG < ~ -10 kJ.mol⁻¹. These results illustrate that the TST

framework fails to predict the *r*-Δ*G* relations and emphasizes the control exerted by the

698
crystallographic structure on the reaction rate and rate law. In addition, these observations are
699

consistent with the existence of a critical value of $\Delta G$ ($\Delta G^{crit}$) as predicted by the stepwave

700

model (Lasaga and Lüttge, 2001), where a kinetic switch is observed depending on the

701

dominant mechanism (stepwaves originating from etch pits or dissolution at point defects and

702

pre-existing edges and corners).

703

704

Fig. 4: Reconstruction of the $r-\Delta G$ relations for three different ideal morphologies. The curves

705

were calculated according to the proportion of each face for three crystal habits (one

706

composed with only F1 faces, one composed with only F2 faces, and a final one composed

707

with all of the six faces investigated in the present study). This figure illustrates the crucial

708

dependence of the $r-\Delta G$ relation on the expressed faces in the K-feldspar crystal morphology.

709

710

Fig. 5: Numerical results of the evolution of the dissolution rate of various arbitrary crystal

711

morphologies over time. This figure shows the complex evolution of a crystal dissolution rate

712

over time because of the modification of its morphology with the reaction progress.

713

Importantly, the starting dissolution rate and its evolution depend on the initial crystal form.

714

For the anisotropic scenarios and consistent with our experimental results for minerals such as

715

K-feldspars, a tenfold factor between the dissolution rate of (101) and (111) faces and the

716

others was implemented. The dissolution rate of face (100) (not measured in the present

717

studied) was arbitrarily set to that of (a) typical F1 faces and (b) typical F2 faces. Considering

718

K and S faces or structures more anisotropic such as that of pyroxenes (see e.g. Daval et al.,

719

2013) would result in even more dramatic discrepancies between the various morphologies.

720

Details of simulation parameters are listed in table 5 and corresponding movies are available

721

online.
722 Tables

Table 1: Summary of experimental and calculated aqueous data of face-specific K-feldspar dissolution experiments. Columns 1-4 indicate: the name of experiment, the total time duration of experiment (days), the flow-rate v of the pump (mL/min) and the pH<sub>in situ</sub> calculated with the CHESS code. The *in situ* solution compositions (in ppm) are listed in the five next columns. Fluid concentration measurements, excepted for [Cl], were carried out with ICP-AES. The two last columns present the ionic strength (mol.L<sup>-1</sup>) of the solution and the ΔG<sub>r</sub> (kJ.mol<sup>-1</sup>) value with respect to K-feldspar dissolution calculated using CHESS.

<table><thead><tr><th rowspan="2">Expt.</th><th rowspan="2">t (days)</th><th rowspan="2">v (mL/min)</th><th rowspan="2">pH<sub>in situ</sub> 180°C</th><th colspan="5">Concentrations out (ppm)</th><th rowspan="2">Ionic strength (mol.L<sup>-1</sup>)</th><th rowspan="2">ΔG (kJ/mol)</th></tr><tr><th>[Si]</th><th>[Al]</th><th>[K]</th><th>[Na]</th><th>[Cl]</th></tr></thead><tbody><tr><td>MRG1</td><td>6.8</td><td>0.07</td><td>8.9</td><td>3.20</td><td>4.29</td><td>1.18</td><td>92.54</td><td>22.61</td><td>4.04E-03</td><td>-49</td></tr><tr><td>MRG2</td><td>7.0</td><td>0.07</td><td>8.9</td><td>3.23</td><td>4.32</td><td>1.46</td><td>92.34</td><td>13.77</td><td>4.04E-03</td><td>-48</td></tr><tr><td>MRG3</td><td>6.9</td><td>0.10</td><td>9.5</td><td>87.63</td><td>3.53</td><td>43.40</td><td>252.89</td><td>52.73</td><td>1.18E-02</td><td>-6</td></tr><tr><td>MRG4</td><td>7.0</td><td>0.10</td><td>9.5</td><td>85.66</td><td>3.29</td><td>42.62</td><td>252.89</td><td>52.08</td><td>1.18E-02</td><td>-7</td></tr><tr><td>MRG5</td><td>6.9</td><td>0.10</td><td>9.0</td><td>8.23</td><td>4.10</td><td>3.52</td><td>114.99</td><td>17.16</td><td>5.06E-03</td><td>-36</td></tr><tr><td>MRG6</td><td>7.0</td><td>0.10</td><td>9.0</td><td>8.51</td><td>4.26</td><td>3.72</td><td>115.04</td><td>17.10</td><td>5.07E-03</td><td>-35</td></tr><tr><td>MRG7</td><td>6.9</td><td>0.34</td><td>9.2</td><td>0.64</td><td>3.64</td><td>0.22</td><td>183.94</td><td>13.72</td><td>7.96E-03</td><td>-81</td></tr><tr><td>MRG8</td><td>6.9</td><td>0.35</td><td>9.2</td><td>0.65</td><td>3.61</td><td>0.20</td><td>183.94</td><td>13.46</td><td>7.96E-03</td><td>-81</td></tr><tr><td>MRG9</td><td>7.0</td><td>0.10</td><td>9.2</td><td>41.33</td><td>3.62</td><td>17.06</td><td>184.13</td><td>27.43</td><td>8.31E-03</td><td>-16</td></tr><tr><td>MRG10</td><td>6.8</td><td>0.10</td><td>9.2</td><td>43.66</td><td>3.63</td><td>22.74</td><td>184.18</td><td>31.97</td><td>8.46E-03</td><td>-14</td></tr><tr><td>MRG11</td><td>6.9</td><td>0.10</td><td>9.5</td><td>62.34</td><td>3.40</td><td>29.98</td><td>391.83</td><td>32.99</td><td>1.73E-02</td><td>-18</td></tr><tr><td>MRG12</td><td>6.9</td><td>0.10</td><td>9.5</td><td>64.07</td><td>3.67</td><td>28.69</td><td>390.83</td><td>41.14</td><td>1.73E-02</td><td>-17</td></tr><tr><td>MRG13</td><td>6.9</td><td>0.10</td><td>9.5</td><td>85.06</td><td>3.55</td><td>39.00</td><td>391.21</td><td>45.74</td><td>1.74E-02</td><td>-13</td></tr><tr><td>MRG14</td><td>7.0</td><td>0.10</td><td>9.5</td><td>86.41</td><td>3.69</td><td>37.27</td><td>390.83</td><td>48.09</td><td>1.74E-02</td><td>-12</td></tr><tr><td>MRG15</td><td>6.9</td><td>0.26</td><td>8.9</td><td>0.58</td><td>3.78</td><td>0.24</td><td>91.98</td><td>14.43</td><td>3.99E-03</td><td>-75</td></tr><tr><td>MRG16</td><td>6.9</td><td>0.26</td><td>8.9</td><td>0.78</td><td>3.81</td><td>0.30</td><td>91.99</td><td>14.36</td><td>4.00E-03</td><td>-71</td></tr><tr><td>MRG17</td><td>6.9</td><td>0.38</td><td>8.9</td><td>0.39</td><td>3.74</td><td>0.15</td><td>91.98</td><td>14.41</td><td>3.99E-03</td><td>-81</td></tr><tr><td>MRG18</td><td>6.8</td><td>0.38</td><td>9.2</td><td>0.91</td><td>3.81</td><td>0.38</td><td>160.97</td><td>14.00</td><td>6.97E-03</td><td>-77</td></tr><tr><td>MRG19</td><td>6.8</td><td>0.10</td><td>9.1</td><td>22.25</td><td>3.64</td><td>10.57</td><td>161.01</td><td>22.04</td><td>7.19E-03</td><td>-24</td></tr><tr><td>MRG20</td><td>6.8</td><td>0.10</td><td>9.1</td><td>23.10</td><td>4.05</td><td>10.21</td><td>160.97</td><td>22.75</td><td>7.18E-03</td><td>-23</td></tr><tr><td>MRGP1</td><td>6.9</td><td>0.23</td><td>9.2</td><td>3.03</td><td>3.55</td><td>1.24</td><td>161.06</td><td>9.04</td><td>7.00E-03</td><td>-55</td></tr><tr><td>MRGP2</td><td>7.7</td><td>0.24</td><td>9.3</td><td>4.24</td><td>3.58</td><td>1.62</td><td>195.58</td><td>0.00</td><td>8.49E-03</td><td>-53</td></tr><tr><td>MRGT1</td><td>4.8</td><td>0.20</td><td>9.0</td><td>0.25</td><td>3.99</td><td>0.12</td><td>114.96</td><td>12.82</td><td>4.99E-03</td><td>-89</td></tr><tr><td>MRGT2</td><td>20.5</td><td>0.20</td><td>8.9</td><td>1.45</td><td>3.78</td><td>1.11</td><td>97.09</td><td>13.58</td><td>4.23E-03</td><td>-59</td></tr></tbody></table>
<table><tr><td>MRGT3</td><td>3.5</td><td>0.20</td><td>8.9</td><td>2.19</td><td>3.71</td><td>1.32</td><td>101.29</td><td>13.83</td><td>4.43E-03</td><td>-54</td></tr></table>
Table 2: Surface retreat measurements. The first two columns indicate the name of experiment and the time duration. The surface retreats measured by VSI in stitching mode with 5x-magnification are listed in the next three columns (µm). The left part of the table present results for (010), (111) and (130) faces and on the right are results for (001), (101), (110) faces.

734

<table><thead><tr><th rowspan="2">Expt.</th><th rowspan="2">t (days)</th><th colspan="3">Surface retreat Δh (µm)</th><th rowspan="2">Expt.</th><th rowspan="2">t (days)</th><th colspan="3">Surface retreat Δh (µm)</th></tr><tr><th>(010)</th><th>(111)</th><th>(130)</th><th>(001)</th><th>(101)</th><th>(110)</th></tr></thead><tbody><tr><td>MRG1</td><td>6.8</td><td>1.1 ± 0.3</td><td>5.1 ± 0.2</td><td>1.4 ± 0.1</td><td>MRG2</td><td>7.0</td><td>1.2 ± 0.2</td><td>12.0 ± 0.2</td><td>2.6 ± 0.2</td></tr><tr><td>MRG3</td><td>6.9</td><td>0.11 ± 0.02</td><td>0.4 ± 0.1</td><td>0</td><td>MRG4</td><td>7.0</td><td>0</td><td>0</td><td>0</td></tr><tr><td>MRG5</td><td>6.9</td><td>2.4 ± 0.7</td><td>7 ± 2</td><td>1.2 ± 0.3</td><td>MRG6</td><td>7.0</td><td>0.39 ± 0.05</td><td>10.1 ± 0.1</td><td>1.1 ± 0.3</td></tr><tr><td>MRG7</td><td>6.9</td><td>1.6 ± 0.7</td><td>18 ± 2</td><td>2.8 ± 0.5</td><td>MRG8</td><td>6.9</td><td>2.3 ± 0.7</td><td>17.4 ± 0.3</td><td>2.7 ± 0.7</td></tr><tr><td>MRG9</td><td>7.0</td><td>0.5 ± 0.2</td><td>2 ± 0.5</td><td>0.3 ± 0.1</td><td>MRG10</td><td>6.8</td><td>0.2 ± 0.1</td><td>3.6 ± 0.1</td><td>0.32 ± 0.02</td></tr><tr><td>MRG11</td><td>6.9</td><td>0.05 ± 0.03</td><td>0.8 ± 0.5</td><td>0.6 ± 0.3</td><td>MRG12</td><td>6.9</td><td>0.14 ± 0.05</td><td>2.3 ± 0.1</td><td>0.6 ± 0.3</td></tr><tr><td>MRG13</td><td>6.9</td><td>0.19 ± 0.04</td><td>0.4 ± 0.1</td><td>0.1 ± 0.05</td><td>MRG14</td><td>7.0</td><td>0.1 ± 0.05</td><td>0.76 ± 0.03</td><td>0.14 ± 0.05</td></tr><tr><td>MRG15</td><td>6.9</td><td>2.4 ± 0.5</td><td>10.8 ± 0.3</td><td>2.3 ± 0.4</td><td>MRG16</td><td>6.9</td><td>1.6 ± 0.2</td><td>10.85 ± 0.05</td><td>1.6 ± 0.3</td></tr><tr><td>MRG17</td><td>6.9</td><td>1.8 ± 0.5</td><td>9.3 ± 0.5</td><td>1.7 ± 0.3</td><td>MRG18</td><td>6.8</td><td>2.1 ± 0.2</td><td></td><td>2.7 ± 0.2</td></tr><tr><td>MRG19</td><td>6.8</td><td>0.5 ± 0.2</td><td>5.4 ± 0.1</td><td>1.4 ± 0.2</td><td>MRG20_01</td><td>6.8</td><td>0.28 ± 0.05</td><td>9.3 ± 0.3</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td>MRG20_02</td><td>6.8</td><td>0.4 ± 0.2</td><td></td><td></td></tr><tr><td>MRGT1</td><td></td><td></td><td></td><td></td><td>MRGT1</td><td></td><td></td><td></td><td></td></tr><tr><td>t<sub>1</sub></td><td>1.6</td><td>0.13 ± 0.02</td><td></td><td></td><td>t<sub>1</sub></td><td>1.6</td><td>0.24 ± 0.05</td><td></td><td></td></tr><tr><td>t<sub>2</sub></td><td>2.2</td><td>0.20 ± 0.05</td><td></td><td></td><td>t<sub>2</sub></td><td>2.2</td><td>0.32 ± 0.05</td><td></td><td></td></tr><tr><td>t<sub>3</sub></td><td>4.8</td><td>0.7 ± 0.2</td><td></td><td></td><td>t<sub>3</sub></td><td>4.8</td><td>0.9 ± 0.1</td><td></td><td></td></tr><tr><td>MRGT2</td><td></td><td></td><td></td><td></td><td>MRGT2</td><td></td><td></td><td></td><td></td></tr><tr><td>t<sub>1</sub></td><td>6.8</td><td></td><td>12 ± 2</td><td></td><td>t<sub>1</sub></td><td>6.8</td><td>1.1 ± 0.1</td><td>15.0 ± 0.2</td><td></td></tr><tr><td>t<sub>2</sub></td><td>13.6</td><td></td><td>32 ± 2</td><td></td><td>t<sub>2</sub></td><td>13.6</td><td>2.2 ± 0.1</td><td>34.1 ± 0.2</td><td></td></tr><tr><td>t<sub>3</sub></td><td>20.5</td><td></td><td>52 ± 5</td><td></td><td>t<sub>3</sub></td><td>20.5</td><td>4.3 ± 0.1</td><td>52 ± 3</td><td></td></tr><tr><td>MRGT3</td><td></td><td></td><td></td><td></td><td>MRGT3</td><td></td><td></td><td></td><td></td></tr><tr><td>t<sub>1</sub></td><td>1.79</td><td>1.8 ± 0.5</td><td>4.2 ± 0.5</td><td>1.0 ± 0.2</td><td>t<sub>1</sub></td><td>1.79</td><td>0.5 ± 0.2</td><td></td><td></td></tr><tr><td>t<sub>2</sub></td><td>3.5</td><td>2.5 ± 0.5</td><td>8.0 ± 0.5</td><td>1.5 ± 0.5</td><td>t<sub>2</sub></td><td>3.5</td><td>1.0 ± 0.2</td><td></td><td></td></tr></tbody></table>

735

736
<table><caption>Table 3: Calculated dissolution rates based on surface retreat measurements. The first two columns provide the name of experiment and the Gibbs free energy of the reaction with respect to K-feldspar dissolution. The next four columns indicate the pH<sub>in situ</sub> of the experiment and the dissolution rate of the different crystallographic orientations (in mol.m<sup>-2</sup>.s<sup>-1</sup>). The dissolution rates recalculated for an exact pH of 9.0, adjusted from measured r and based on the pH-dependence of K-feldspar dissolution given by Palandri and Kharaka, 2004 are listed in the last three columns.</caption><thead><tr><th rowspan="2">Expt.</th><th rowspan="2">ΔG (kJ/mol)</th><th rowspan="2">pH</th><th colspan="3">r (x 10<sup>-9</sup> mol.m<sup>-2</sup>.s<sup>-1</sup>)</th><th colspan="3">r (x 10<sup>-9</sup> mol.m<sup>-2</sup>.s<sup>-1</sup>) pH 9</th></tr><tr><th>(010)</th><th>(111)</th><th>(130)</th><th>(010)</th><th>(111)</th><th>(130)</th></tr></thead><tbody><tr><td>MRG1</td><td>-49</td><td>8.9</td><td>18</td><td>82</td><td>23</td><td>21</td><td>100</td><td>27</td></tr><tr><td>MRG3</td><td>-6</td><td>9.5</td><td>1.7</td><td>6.3</td><td>0</td><td>0,7</td><td>2,5</td><td>0</td></tr><tr><td>MRG5</td><td>-36</td><td>9.0</td><td>38</td><td>111</td><td>19</td><td>39</td><td>113</td><td>19</td></tr><tr><td>MRG7</td><td>-81</td><td>9.2</td><td>25</td><td>284</td><td>44</td><td>17</td><td>186</td><td>29</td></tr><tr><td>MRG9</td><td>-16</td><td>9.2</td><td>7.8</td><td>31</td><td>4.7</td><td>5,8</td><td>23</td><td>3,5</td></tr><tr><td>MRG11</td><td>-18</td><td>9.5</td><td>0.8</td><td>13</td><td>9.5</td><td>0,3</td><td>4,9</td><td>3,7</td></tr><tr><td>MRG13</td><td>-13</td><td>9.5</td><td>3.0</td><td>6.4</td><td>1.6</td><td>1,2</td><td>2,6</td><td>0,6</td></tr><tr><td>MRG15</td><td>-75</td><td>8.9</td><td>38</td><td>172</td><td>37</td><td>46</td><td>208</td><td>44</td></tr><tr><td>MRG17</td><td>-81</td><td>8.9</td><td>29</td><td>148</td><td>27</td><td>35</td><td>179</td><td>33</td></tr><tr><td>MRG19</td><td>-24</td><td>9.1</td><td>8.0</td><td>86</td><td>22</td><td>6,3</td><td>68</td><td>18</td></tr><tr><td>MRGT1</td><td>-89</td><td>9.0</td><td>15</td><td></td><td></td><td>15</td><td></td><td></td></tr><tr><td>MRGT2</td><td>-59</td><td>8.9</td><td></td><td>271</td><td></td><td></td><td>310</td><td></td></tr><tr><td>MRGT3</td><td>-54</td><td>8.9</td><td>83</td><td>258</td><td>50</td><td>100</td><td>312</td><td>60</td></tr></tbody></table><table><thead><tr><th rowspan="2">Expt.</th><th rowspan="2">ΔG (kJ/mol)</th><th rowspan="2">pH</th><th colspan="3">r (x 10<sup>-9</sup> mol.m<sup>-2</sup>.s<sup>-1</sup>)</th><th colspan="3">r (x 10<sup>-9</sup> mol.m<sup>-2</sup>.s<sup>-1</sup>) pH 9</th></tr><tr><th>(001)</th><th>(101)</th><th>(110)</th><th>(001)</th><th>(101)</th><th>(110)</th></tr></thead><tbody><tr><td>MRG2</td><td>-48</td><td>8.9</td><td>19</td><td>188</td><td>41</td><td>23</td><td>228</td><td>49</td></tr><tr><td>MRG4</td><td>-7</td><td>9.5</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr><tr><td>MRG6</td><td>-35</td><td>9.0</td><td>6.1</td><td>157</td><td>17</td><td>6,2</td><td>160</td><td>17</td></tr><tr><td>MRG8</td><td>-81</td><td>9.2</td><td>37</td><td>277</td><td>43</td><td>24</td><td>181</td><td>28</td></tr><tr><td>MRG10</td><td>-14</td><td>9.2</td><td>3.2</td><td>58</td><td>5.1</td><td>2,4</td><td>43</td><td>3,8</td></tr><tr><td>MRG12</td><td>-17</td><td>9.5</td><td>2.2</td><td>36</td><td>9.5</td><td>0,9</td><td>14</td><td>3,7</td></tr><tr><td>MRG14</td><td>-12</td><td>9.5</td><td>1.6</td><td>12</td><td>2.2</td><td>0,6</td><td>4,9</td><td>0,9</td></tr><tr><td>MRG16</td><td>-71</td><td>8.9</td><td>25</td><td>172</td><td>25</td><td>31</td><td>208</td><td>31</td></tr><tr><td>MRG18</td><td>-77</td><td>9.2</td><td>34</td><td></td><td>43</td><td>25</td><td></td><td>32</td></tr><tr><td>MRG20_01</td><td>-23</td><td>9.1</td><td>4.5</td><td>149</td><td></td><td>3,6</td><td>118</td><td></td></tr><tr><td>MRG20_02</td><td>-23</td><td>9.1</td><td>6.4</td><td></td><td></td><td>5,1</td><td></td><td></td></tr><tr><td>MRGT1</td><td>-89</td><td>9.0</td><td>19</td><td></td><td></td><td>18</td><td></td><td></td></tr><tr><td>MRGT2</td><td>-59</td><td>8.9</td><td>21</td><td>280</td><td></td><td>24</td><td>320</td><td></td></tr><tr><td>MRGT3</td><td>-54</td><td>8.9</td><td>31</td><td></td><td></td><td>37</td><td></td><td></td></tr></tbody></table>
<table><caption>Table 4: Fitting parameters of r-ΔG relations based on an overall rate law adapted from {Hellmann 2006}: $r = k_0 [\alpha (1 - \exp(-ng^{m_1})) + (1 - \alpha)(1 - \exp(-g))^{m_2}]$, where $k_0$ is the rate plateau in mol.m⁻².s⁻¹, α is a dimensionless number that has been determined by regression, $g=|ΔG|/RT$ and n, $m_1$ and $m_2$ are adjustable fitted parameters found with a non linear least-squares curve fitting (Levenberg-Marquardt method).</caption><thead><tr><th>Face</th><th>k<sub>0</sub></th><th>α</th><th>n</th><th>m<sub>1</sub></th><th>m<sub>2</sub></th></tr></thead><tbody><tr><td>(001)</td><td>2.60E-08</td><td>0.8350</td><td>3.96E-12</td><td>10.57</td><td>57.47</td></tr><tr><td>(010)</td><td>3.90E-08</td><td>0.8454</td><td>2.96E-12</td><td>12.45</td><td>46.70</td></tr><tr><td>(110)</td><td>3.50E-08</td><td>0.8920</td><td>9.82E-11</td><td>10.03</td><td>16.71</td></tr><tr><td>(11&#773;0)</td><td>4.16E-08</td><td>0.9138</td><td>2.15E-04</td><td>3.59</td><td>23.11</td></tr><tr><td>(1&#773;11)</td><td>2.37E-07</td><td>0.9410</td><td>1.52E-04</td><td>3.59</td><td>17.49</td></tr><tr><td>(1&#773;01)</td><td>2.32E-07</td><td>0.8743</td><td>8.72E-04</td><td>3.24</td><td>15.16</td></tr></tbody></table>
754

Table 5: Input parameters for the simulation of the evolution of crystal habit as a function of the reaction progress. The name of the crystal habit is listed in the first column. The next seven columns present the starting proportion of surface area for each face and the kinetic values $\overline{K}$ used in the model. This value corresponds to the period (i.e. the number of iterations) after which a mesh contacting the solution in a given direction dissolves. As observed experimentally, for minerals such as feldspars, some faces can dissolve ten times faster than others (e.g., (101) and (111) faces, compared to (001), (010) and (110) faces). The dissolution period for (011) and (100) faces were arbitrarily set to 10 for simulations carried out on habit 1, 2 and 3 and to 1 for habits 1', 2' and 3' (see below). The last three columns are the initial number of ECs in the crystal, the initial mesh volume and the initial crystal surface (arbitrary unit).

<table><thead><tr><th>Habit</th><th>S (%)</th><th>(001)</th><th>(010)</th><th>(110)</th><th>(111)</th><th>(101)</th><th>(100)</th><th>(011)</th><th>n<sub>0</sub></th><th>V<sub>0</sub></th><th>S<sub>0</sub></th></tr></thead><tbody><tr><td>Habit 1<br>isotropic</td><td>S (%)</td><td>40.28<br>10</td><td>40.52<br>10</td><td>18.73<br>10</td><td>0.24<br>10</td><td>0.00<br>10</td><td>0.00<br>10</td><td>0.23<br>10</td><td>3.72E+08</td><td>3.72E+11</td><td>3.66E+08</td></tr><tr><td>Habit 1<br>anisotropic</td><td>S (%)</td><td>40.28<br>10</td><td>40.52<br>10</td><td>18.73<br>10</td><td>0.24<br>1</td><td>0.00<br>1</td><td>0.00<br>10</td><td>0.23<br>10</td><td>3.72E+08</td><td>3.72E+11</td><td>3.66E+08</td></tr><tr><td>Habit 2<br>anisotropic</td><td>S (%)</td><td>44.31<br>10</td><td>44.31<br>10</td><td>0.06<br>10</td><td>0.00<br>1</td><td>0.06<br>1</td><td>11.01<br>10</td><td>0.25<br>10</td><td>4.96E+08</td><td>4.96E+11</td><td>4.47E+08</td></tr><tr><td>Habit 3<br>anisotropic</td><td>S (%)</td><td>19.06<br>10</td><td>44.75<br>10</td><td>8.81<br>10</td><td>0.22<br>1</td><td>26.94<br>1</td><td>0.00<br>10</td><td>0.22<br>10</td><td>5.66E+07</td><td>5.66E+10</td><td>9.67E+07</td></tr><tr><td>Habit 1'<br>isotropic</td><td>S (%)</td><td>39.85<br>10</td><td>39.85<br>10</td><td>0.11<br>10</td><td>0.00<br>10</td><td>0.11<br>10</td><td>19.85<br>10</td><td>0.23<br>10</td><td>2.48E+08</td><td>2.48E+11</td><td>2.48E+08</td></tr><tr><td>Habit 1'<br>anisotropic</td><td>S (%)</td><td>39.85<br>10</td><td>39.85<br>10</td><td>0.11<br>10</td><td>0.00<br>1</td><td>0.11<br>1</td><td>19.85<br>1</td><td>0.23<br>1</td><td>2.48E+08</td><td>2.48E+11</td><td>2.48E+08</td></tr><tr><td>Habit 2'<br>anisotropic</td><td>S (%)</td><td>25.15<br>10</td><td>50.76<br>10</td><td>23.77<br>10</td><td>0.07<br>1</td><td>0.00<br>1</td><td>0.00<br>1</td><td>0.31<br>1</td><td>9.26E+07</td><td>9.26E+10</td><td>1.46E+08</td></tr><tr><td>Habit 3'<br>anisotropic</td><td>S (%)</td><td>29.23<br>10</td><td>29.17<br>10</td><td>0.00<br>10</td><td>0.10<br>1</td><td>41.23<br>1</td><td>0.00<br>1</td><td>0.18<br>1</td><td>1.24E+08</td><td>1.24E+11</td><td>1.69E+08</td></tr></tbody></table>

766

767
<figure><img src="image_3.png" /></figure>

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<figure><img src="image_15.png" /></figure>
<figure><img src="image_16.png" /></figure>
<figure><img src="image_17.png" /><figcaption>Habit 1</figcaption></figure>

<figure><img src="image_18.png" /><figcaption>Habit 2</figcaption></figure>

<figure><img src="image_19.png" /><figcaption>Habit 3</figcaption></figure>

<figure><img src="image_20.png" /><figcaption>(b)</figcaption></figure>

<figure><img src="image_21.png" /><figcaption>Habit 1'</figcaption></figure>

<figure><img src="image_22.png" /><figcaption>Habit 2'</figcaption></figure>

<figure><img src="image_23.png" /><figcaption>Habit 3'</figcaption></figure>

<figure><img src="image_24.png" /><figcaption>Dissolution rate (a.u.)</figcaption></figure>