Effect of solution saturation state and temperature on diopside dissolution
- Suvasis Dixit^{1} and
- Susan A Carroll^{1}Email author
https://doi.org/10.1186/1467-4866-8-3
© Dixit and Carroll; licensee BioMed Central Ltd. 2007
Received: 14 November 2006
Accepted: 26 March 2007
Published: 26 March 2007
Abstract
Steady-state dissolution rates of diopside are measured as a function of solution saturation state using a titanium flow-through reactor at pH 7.5 and temperature ranging from 125 to 175°C. Diopside dissolved stoichiometrically under all experimental conditions and rates were not dependent on sample history. At each temperature, rates continuously decreased by two orders of magnitude as equilibrium was approached and did not exhibit a dissolution plateau of constant rates at high degrees of undersaturation. The variation of diopside dissolution rates with solution saturation can be described equally well with a ion exchange model based on transition state theory or pit nucleation model based on crystal growth/dissolution theory from 125 to 175°C. At 175°C, both models over predict dissolution rates by two orders of magnitude indicating that a secondary phase precipitated in the experiments.
The ion exchange model assumes the formation of a Si-rich, Mg-deficient precursor complex. Lack of dependence of rates on steady-state aqueous calcium concentration supports the formation of such a complex, which is formed by exchange of protons for magnesium ions at the surface. Fit to the experimental data yields
$Rate\phantom{\rule{0.5em}{0ex}}(moldiopsidec{m}^{-2}{s}^{-1})=k\times {\text{10}}^{-{E}_{a}/2.303RT}{\left(\frac{{a}_{{H}^{+}}^{2}}{{a}_{M{g}^{2+}}}\right)}^{n}$
where the Mg-H exchange coefficient, n = 1.39, the apparent activation energy, E_{ a }= 332 kJ mol^{-1}, and the apparent rate constant, k = 10^{41.2} mol diopside cm^{-2} s^{-1}.
Fits to the data with the pit nucleation model suggest that diopside dissolution proceeds through retreat of steps developed by nucleation of pits created homogeneously at the mineral surface or at defect sites, where homogeneous nucleation occurs at lower degrees of saturation than defect-assisted nucleation. Rate expressions for each mechanism (i) were fit to
${R}_{i}=c{b}_{i}\mathrm{exp}\phantom{\rule{0.5em}{0ex}}\left(\frac{-{E}_{b,i}}{kT}\right){K}_{T,eq}\mathrm{exp}\phantom{\rule{0.5em}{0ex}}\left(\frac{\pi {\alpha}_{T,i}^{2}\omega h}{3{(kT)}^{2}}\left|\frac{1}{\mathrm{ln}\phantom{\rule{0.5em}{0ex}}\Omega}\right|\right)$
where the step edge energy (α) for homogeneously nucleated pits were higher (275 to 65 mJ m^{-2}) than the pits nucleated at defects (39 to 65 mJ m^{-2}) and the activation energy associated with the temperature dependence of site density and the kinetic coefficient for homogeneously nucleated pits (E_{b-homogeneous} = 2.59 × 10^{-16} mJ K^{-1}) were lower than the pits nucleated at defects (E_{b-defect assisted} = 8.44 × 10^{-16} mJ K^{-1}).
1. Background
Chemical weathering of minerals play an important control on a variety of process in the Earth's near surface environment. As a consequence, a large number of studies have been devoted to quantifying dissolution rate of minerals both in the laboratory and in the field. Laboratory studies have been conducted to understand the mechanism of dissolution and also to quantify the effect of various physico-chemical conditions on dissolution rates. Despite these efforts in the last two decades, dissolution rates predicted from laboratory studies are two to several orders of magnitude higher than those measured in the field [1]. One of the causes of this discrepancy is attributed to the fact dissolution rates measured in the laboratory are mostly obtained at far-from equilibrium conditions and are extrapolated to close to equilibrium field conditions assuming a simple function of dissolution rate with respect to solution saturation. However the few studies that have been conducted in the last decade show a much more complex relation between dissolution rate and Gibbs free energy (ΔG_{r}) [2–20]. The macroscopic rates have either been fit with a complex functional dependence on ΔG_{r} [2–5] or fit with inferred dissolution mechanisms; such as the ion exchange model [18] or pit nucleation model [6, 7].
The objectives of this study are to investigate the effect of solution saturation state and temperature on diopside dissolution and in the process develop a database against which some of the mechanistic dissolution models can be evaluated. We chose to study diopside, (CaMgSi_{2}O_{6}), a clinopyroxene mineral, because of its widespread occurrence in nature and also because Ca and Mg containing minerals have been targeted for geological sequestration of CO_{2}. In this study we measured steady-state dissolution rates of diopside as a function of solution saturation state using a titanium flow-through reactor at pH 7.5 and temperature ranging from 125 to 175°C. Additionally, we tested the hypothesis that sample dissolution history impacts the measured dissolution rates in stacked experiments [8].
2. Materials and methods
Chemical composition of diopside.
Oxide | Wt% |
---|---|
SiO_{2} | 54.25 |
CaO | 21.58 |
MgO | 16.03 |
Fe_{2}O_{3} | 3.01 |
Al_{2}O_{3} | 0.61 |
All dissolution experiments were carried out in a titanium mixed flow-through reactor from Parr Instruments (see [20] for detailed description). A series of stacked experiments were performed by simply changing the input solution composition and/or the flow rate on the same mineral specimens to study mineral dissolution and precipitation kinetics as a function of solution composition without disturbing the mineral phase. The net dissolution rates normalized to their specific surface area (A) are calculated using the following expression
$Rat{e}_{net}=\frac{\Delta [i]FR}{A{\upsilon}_{i}}\phantom{\rule{0.5em}{0ex}}\left(1\right)$
where [i] is the difference between the effluent and influent concentration of a solute, FR is the flow rate, and υ_{i} is the stoichiometric coefficient of the element i in the mineral formula. The experiments were conducted at an in situ pH of 7.5 and temperatures ranging from 125 to 175°C. The inlet solution was continuously purged with nitrogen to remove CO_{2} from the solution to avoid precipitation of carbonate minerals. About 2.5 grams of ground diopside were used in stacked experiments in 0.1 M NaCl solutions buffered using 20 mM sodium borate and HCl. Most of the stacked experiments approached equilibrium from high degrees of undersaturation by changing the flow rate from about 4 to 0.01 ml hr^{-1}.
Experiments were also conducted to test the hypothesis that sample history can impact measured dissolution rates in stacked experiments. In one set of experiments equilibrium was approached from high degrees of undersaturation by decreasing the flow rate. In a second set of experiments, far from equilibrium conditions were approached from near equilibrium by decreasing the Ca concentration of the input solutions from 500 μM and then increasing the flow rate to obtain higher degrees of undersaturation. Solutions were analyzed for Ca, Mg, and Si by ICP-AES. Solution pH was measured at room temperature. The solution matrix of the standards was the same as the input solutions.
Aqueous speciation, ion activity, pH, and the Gibbs free energy of the reaction at elevated temperature were calculated using Geochemist's Workbench [21] by conducting a speciation calculation at 25°C based on room temperature measurements followed by a speciation calculation at the experiment temperature. Dissolution of diopside can be described by
CaMgSi_{2}O_{6} + 4H^{+} + 2H_{2}O ⇔ Ca^{2+} + Mg^{2+} + 2H_{4}SiO_{4}. (2)
The Gibbs free energy for the above dissolution reaction is calculated from
$\Delta {G}_{r}=RT\mathrm{ln}\phantom{\rule{0.5em}{0ex}}\left(\frac{{a}_{C{a}^{2+}}{a}_{M{g}^{2+}}{a}_{{H}_{4}Si{O}_{4}}^{2}}{{K}_{eq}{a}_{{H}^{+}}^{4}}\right)\phantom{\rule{0.5em}{0ex}}\left(3\right)$
where, K_{ eq }is the equilibrium constant and a_{ i }represents the activity of the aqueous species. The equilibrium constants at 125, 150, 160, and 175°C are 10^{14.48}, 10^{13.27}, 10^{12.82}, 10^{12.19}, respectively [22]. No attempt was made to experimentally determine the equilibrium constant of the diopside in the study.
3. Results and Discussion
3.1. Steady-state concentration and stoichiometry of dissolution
Results of diopside dissolution in flow-through experiments^{1,2}.
Temp-ID | Si (μM) | Ca (μM) | Mg (μM) | pH(T) | Flow rate ml min^{-1} | log Rate mol diospside cm^{-2} s^{-1} | ΔG_{r} kJ mol^{-1} | $\mathrm{log}\phantom{\rule{0.5em}{0ex}}\left(\frac{{a}_{{H}^{+}}^{2}}{{a}_{M{g}^{2+}}}\right)$ |
---|---|---|---|---|---|---|---|---|
175-1 | 26.8 ± 2.2 | 10.4 ± 1.2 | 8.5 ± 0.4 | 7.508 | 4.00 | -12.20 ± 0.03 | -22.78 ± 0.07 | -9.35 ± 0.05 |
175-2 | 29.6 ± 1.0 | 16.6 ± 0.9 | 11.8 ± 0.9 | 7.513 | 2.00 | -12.46 ± 0.02 | -18.89 ± 0.05 | -9.50 ± 0.02 |
175-3 | 43.6 ± 1.4 | 22.3 ± 1.9 | 14.6 ± 0.7 | 7.517 | 1.00 | -12.59 ± 0.1 | -14.01 ± 0.05 | -9.60 ± 0.04 |
175-4 | 51.3 ± 1.6 | 25.6 ± 1.0 | 16.4 ± 0.6 | 7.520 | 0.50 | -12.82 ± 0.1 | -11.75 ± 0.03 | -9.66 ± 0.02 |
175-5 | 54.8 ± 2.2 | 28.5 ± 1.3 | 19.3 ± 1.1 | 7.523 | 0.25 | -13.10 ± 0.2 | -10.15 ± 0.04 | -9.73 ± 0.02 |
175-6 | 67.7 ± 1.5 | 31.1 ± 0.7 | 18.6 ± 1.6 | 7.523 | 0.10 | -13.40 ± 0.1 | -8.40 ± 0.04 | -9.72 ± 0.01 |
160-1 | 19.0 ± 0.6 | 13.1 ± 1.8 | 7.9 ± 0.5 | 7.511 | 4.50 | -12.30 ± 0.01 | -28.48 ± 0.07 | -9.36 ± 0.06 |
160-2 | 27.1 ± 2.2 | 17.0 ± 2.1 | 11.5 ± 0.5 | 7.515 | 2.00 | -12.50 ± 0.04 | -23.50 ± 0.08 | -9.53 ± 0.05 |
160-3 | 35.8 ± 2.4 | 20.2 ± 1.2 | 16.2 ± 0.7 | 7.519 | 1.00 | -12.68 ± 0.03 | -19.50 ± 0.05 | -9.69 ± 0.03 |
160-4 | 41.1 ± 2.3 | 22.8 ± 1.7 | 17.2 ± 0.6 | 7.520 | 0.75 | -12.74 ± 0.02 | -17.85 ± 0.05 | -9.72 ± 0.03 |
160-5 | 45.4 ± 1.6 | 24.4 ± 0.7 | 19.8 ± 1.6 | 7.522 | 0.50 | -12.88 ± 0.02 | -16.30 ± 0.04 | -9.78 ± 0.01 |
160-6 | 59.4 ± 3.4 | 32.2 ± 1.8 | 28.2 ± 1.2 | 7.53 | 0.25 | -13.06 ± 0.02 | -11.85 ± 0.05 | -9.95 ± 0.02 |
160-7 | 75.6 ± 3.9 | 36.5 ± 2.3 | 30.2 ± 1.4 | 7.533 | 0.10 | -13.35 ± 0.02 | -9.32 ± 0.05 | -9.99 ± 0.03 |
160-8 | 88.6 ± 4.5 | 38.2 ± 2.5 | 34.9 ± 0.6 | 7.536 | 0.05 | -13.59 ± 0.02 | -7.41 ± 0.04 | -10.06 ± 0.03 |
150-A-1 | 16.8 ± 1.1 | 4.6 ± 0.4 | 5.6 ± 0.2 | 7.505 | 3.23 | -12.50 ± 0.03 | -37.00 ± 0.06 | -9.23 ± 0.04 |
150-A-2 | 18.4 ± 0.8 | 5.1 ± 0.4 | 6.1 ± 0.2 | 7.506 | 2.37 | -12.59 ± 0.02 | -35.66 ± 0.05 | -9.27 ± 0.04 |
150-A-3 | 20.9 ± 1.4 | 6.7 ± 0.6 | 8.0 ± 0.3 | 7.508 | 1.50 | -12.74 ± 0.03 | -32.79 ± 0.06 | -9.39 ± 0.04 |
150-A-4 | 24.4 ± 1.7 | 10.3 ± 1.2 | 9.8 ± 0.4 | 7.511 | 1.00 | -12.85 ± 0.03 | -29.38 ± 0.07 | -9.48 ± 0.05 |
150-A-5 | 27.3 ± 1.1 | 9.9 ± 1.0 | 11.3 ± 0.3 | 7.511 | 0.76 | -12.92 ± 0.02 | -28.23 ± 0.05 | -9.54 ± 0.04 |
150-A-6 | 30.6 ± 1.3 | 11.9 ± 0.4 | 13.2 ± 0.7 | 7.513 | 0.51 | -13.04 ± 0.02 | -26.17 ± 0.04 | -9.61 ± 0.01 |
150-A-7 | 35.4 ± 1.3 | 13.7 ± 0.3 | 15.4 ± 0.7 | 7.515 | 0.36 | -13.13 ± 0.02 | -24.04 ± 0.03 | -9.69 ± 0.01 |
150-A-8 | 42.0 ± 1.0 | 17.9 ± 0.5 | 18.8 ± 0.4 | 7.519 | 0.22 | -13.27 ± 0.01 | -21.08 ± 0.02 | -9.78 ± 0.01 |
150-A-9 | 47.0 ± 1.3 | 20.3 ± 0.8 | 21.3 ± 0.5 | 7.522 | 0.16 | -13.36 ± 0.01 | -19.66 ± 0.03 | -9.80 ± 0.02 |
150-A-10 | 56.3 ± 1.3 | 23.0 ± 1.8 | 25.1 ± 0.7 | 7.525 | 0.10 | -13.48 ± 0.01 | -16.94 ± 0.04 | -9.92 ± 0.03 |
150-A-11 | 73.3 ± 2.6 | 32.4 ± 1.2 | 30.9 ± 0.5 | 7.533 | 0.05 | -13.67 ± 0.02 | -12.90 ± 0.03 | -10.02 ± 0.02 |
150-A-12 | 83.7 ± 2.6 | 38.1 ± 1.0 | 36.0 ± 0.8 | 7.538 | 0.03 | -13.91 ± 0.01 | -10.71 ± 0.02 | -10.10 ± 0.01 |
150-A-13 | 97.2 ± 3.2 | 49.0 ± 3.6 | 41.4 ± 0.3 | 7.546 | 0.01 | -14.25 ± 0.01 | -8.03 ± 0.04 | -10.18 ± 0.03 |
150-B-1 | 18.0 ± 1.4 | 4.6 ± 1.0 | 5.6 ± 1.2 | 7.505 | 4.00 | -12.38 ± 0.03 | -36.51 ± 0.14 | -9.23 ± 0.09 |
150-B-2 | 19.8 ± 1.3 | 9.3 ± 1.0 | 11.0 ± 0.6 | 7.511 | 2.00 | -12.64 ± 0.03 | -30.83 ± 0.07 | -9.53 ± 0.05 |
150-B-3 | 27.1 ± 1.7 | 17.1 ± 1.3 | 11.2 ± 0.8 | 7.515 | 1.00 | -12.80 ± 0.03 | -26.26 ± 0.06 | -9.55 ± 0.03 |
150-B-4 | 36.7 ± 1.9 | 18.5 ± 1.5 | 17.5 ± 1.3 | 7.519 | 0.50 | -12.97 ± 0.02 | -22.18 ± 0.06 | -9.75 ± 0.04 |
150-B-5 | 49.3 ± 1.4 | 19.9 ± 2.9 | 22.3 ± 1.3 | 7.522 | 0.10 | -13.54 ± 0.01 | -18.89 ± 0.07 | -9.86 ± 0.06 |
150-B-6 | 86.7 ± 1.6 | 51.4 ± 2.8 | 48.5 ± 1.5 | 7.551 | 0.01 | -14.30 ± 0.01 | -7.96 ± 0.03 | -10.26 ± 0.02 |
150-B-7 | 46.2 ± 3.2 | 23.7 ± 1.7 | 25.4 ± 1.0 | 7.526 | 0.10 | -13.57 ± 0.03 | -18.15 ± 0.06 | -9.92 ± 0.03 |
150-B-8 | 36.1 ± 1.8 | 21.7 ± 1.1 | 18.8 ± 1.0 | 7.521 | 0.50 | -12.98 ± 0.02 | -21.41 ± 0.04 | -9.78 ± 0.02 |
150-B-9 | 24.6 ± 0.7 | 17.0 ± 0.4 | 9.5 ± 1.0 | 7.514 | 1.00 | -12.84 ± 0.01 | -27.62 ± 0.05 | -9.47 ± 0.01 |
150-B-10 | 16.4 ± 1.1 | 9.0 ± 0.9 | 7.3 ± 0.8 | 7.509 | 2.00 | -12.72 ± 0.03 | -33.77 ± 0.08 | -9.35 ± 0.04 |
150-B-11 | 14.0 ± 2.1 | 6.4 ± 1.2 | 6.5 ± 0.8 | 7.507 | 4.00 | -12.48 ± 0.06 | -36.49 ± 0.13 | -9.30 ± 0.08 |
150-C-1 | 32.2 ± 1.8 | 473.4 ± 10.3 | 15.8 ± 1.0 | 7.721 | 0.10 | -13.73 ± 0.02 | -5.97 ± 0.04 | -10.11 ± 0.01 |
150-C-2 | 34.6 ± 1.0 | 283.6 ± 6.9 | 16.0 ± 1.0 | 7.646 | 0.10 | -13.69 ± 0.01 | -9.44 ± 0.04 | -9.96 ± 0.01 |
150-C-3 | 42.8 ± 2.5 | 140.9 ± 6.3 | 20.3 ± 1.5 | 7.583 | 0.10 | -13.60 ± 0.03 | -11.48 ± 0.05 | -9.94 ± 0.02 |
150-C-4 | 60.2 ± 3.7 | 54.7 ± 3.0 | 24.9 ± 2.5 | 7.541 | 0.10 | -13.45 ± 0.03 | -12.97 ± 0.06 | -9.95 ± 0.02 |
150-C-5 | 65.4 ± 4.9 | 32.5 ± 2.8 | 27.8 ± 2.4 | 7.531 | 0.10 | 13.42 ± 0.03 | -14.12 ± 0.07 | -9.97 ± 0.04 |
150-C-6 | 32.3 ± 3.1 | 15.8 ± 1.5 | 16.4 ± 1.5 | 7.517 | 0.50 | -13.03 ± 0.04 | -23.91 ± 0.08 | -9.72 ± 0.04 |
150-C-7 | 24.1 ± 2.6 | 15.1 ± 1.9 | 12.2 ± 1.1 | 7.515 | 1.00 | -12.85 ± 0.05 | -27.22 ± 0.10 | -9.59 ± 0.06 |
150-C-8 | 17.8 ± 1.4 | 9.3 ± 1.5 | 11.0 ± 1.1 | 7.511 | 2.00 | -12.68 ± 0.03 | -31.07 ± 0.09 | -9.59 ± 0.07 |
150-C-9 | 15.9 ± 1.6 | 6.1 ± 1.6 | 6.6 ± 0.7 | 7.507 | 4.00 | -12.43 ± 0.04 | -35.08 ± 0.14 | -9.30 ± 0.11 |
150-C-10 | 19.8 ± 1.1 | 8.8 ± 0.6 | 9.3 ± 0.9 | 7.510 | 2.00 | -12.64 ± 0.03 | -31.65 ± 0.06 | -9.46 ± 0.03 |
150-C-11 | 24.6 ± 2.9 | 13.0 ± 0.7 | 9.5 ± 1.0 | 7.512 | 1.00 | -12.84 ± 0.05 | -28.62 ± 0.09 | -9.47 ± 0.02 |
150-C-12 | 30.6 ± 3.8 | 14.0 ± 1.8 | 15.0 ± 1.6 | 7.515 | 0.50 | -13.05 ± 0.05 | -25.10 ± 0.10 | -9.67 ± 0.06 |
150-C-13 | 55.8 ± 5.2 | 25.1 ± 2.1 | 25.5 ± 3.0 | 7.526 | 0.10 | -13.49 ± 0.04 | -16.62 ± 0.08 | -9.93 ± 0.04 |
150-C-14 | 96.7 ± 6.7 | 44.4 ± 2.2 | 41.3 ± 2.8 | 7.544 | 0.01 | -14.25 ± 0.03 | -8.49 ± 0.06 | -10.17 ± 0.02 |
125-1 | 1.0 ± 0.1 | 0.4 ± 0.1 | 0.4 ± 0.1 | 7.500 | 4.50 | -13.6 ± 0.02 | -79.36 ± 0.06 | -8.08 ± 0.03 |
125-2 | 1.3 ± 0.0 | 0.5 ± 0.1 | 0.5 ± 0.1 | 7.500 | 2.00 | -13.8 ± 0.01 | -76.09 ± 0.03 | -8.21 ± 0.02 |
125-3 | 1.7 ± 0.1 | 0.7 ± 0.1 | 0.7 ± 0.1 | 7.501 | 1.00 | -14.0 ± 0.02 | -72.07 ± 0.05 | -8.34 ± 0.03 |
125-4 | 2.1 ± 0.1 | 0.9 ± 0.1 | 0.9 ± 0.1 | 7.501 | 0.50 | -14.2 ± 0.01 | -68.60 ± 0.07 | -8.47 ± 0.05 |
125-5 | 2.5 ± 0.1 | 1.2 ± 0.1 | 1.1 ± 0.1 | 7.501 | 0.25 | -14.4 ± 0.05 | -65.99 ± 0.08 | -8.54 ± 0.04 |
125-6 | 4.1 ± 0.1 | 2.0 ± 0.1 | 1.6 ± 0.1 | 7.502 | 0.10 | -14.6 ± 0.04 | -59.72 ± 0.07 | -8.72 ± 0.02 |
125-7 | 5.4 ± 0.1 | 2.3 ± 0.1 | 2.0 ± 0.1 | 7.502 | 0.05 | -14.8 ± 0.03 | -56.63 ± 0.07 | -8.83 ± 0.04 |
125-8 | 6.2 ± 0.1 | 2.7 ± 0.1 | 2.4 ± 0.1 | 7.503 | 0.025 | -15.0 ± 0.03 | -54.78 ± 0.06 | -8.90 ± 0.03 |
125-9 | 8.8 ± 0.1 | 3.2 ± 0.1 | 3.3 ± 0.1 | 7.504 | 0.01 | -15.3 ± 0.05 | -50.61 ± 0.09 | -9.04 ± 0.03 |
3.2. Hysteresis in dissolution rates as a function of saturation state
A chief advantage of using mixed flow-through reactors to study mineral dissolution and precipitation kinetics is that it allows the rate at which minerals dissolve and precipitate to be evaluated as a function of solution composition without disturbing the mineral phase. As a result, experiments are typically performed in series of stacked experiments by simply changing the input solution composition and/or the flow rate on the same mineral specimens. Beig and Luttge [8] raised the concern that stacked experiments started from high or low degree of undersaturation can have a major impact on the observed rate dependency on solution saturation state, and hence the mechanisms invoked to explain the dissolution behavior. Beig and Luttge [8]compared dissolution rates for albite (NaAlSi_{3}O_{8}) initially treated at 185°C and pH 9 with an output solution composition that was far from equilibrium (ΔG_{r} < 35 kJ/mol) with dissolution rates of untreated albite surfaces. When the treated and untreated specimens were subsequently reacted at the same conditions, they found that the treated albite dissolution rates were 0.6 to 2 orders of magnitude faster than the untreated samples depending on the solution composition; the difference in rates were higher closer to equilibrium. The authors showed that the faster dissolution rates of the treated samples occurred on pre-existing etch pits from the initial treatment and at step edges, while the slower dissolution rates of untreated samples occurred mostly at step edges.
3.3. Dissolution rate as a function of ΔG_{r}
A generalized rate law for overall mineral dissolution can be written as
R_{diss} = k_{+} f(ΔG_{r}), (4)
where ΔG_{r} = RT lnΩ = RT ln(Q/K_{eq}), Ω is the saturation state, Q and K_{eq} are the ion activity quotient and equilibrium constant of the dissolution reaction, respectively, and k_{+} is the apparent rate constant for the forward reaction at a given temperature which may include the effect of pH, presence of other solutes which might inhibit or enhance dissolution, and reactive surface area. The functional dependence of the rate on the Gibbs free energy of reaction (ΔG_{r}) has been derived from transition state theory and, in its simplest form, is given by [24].
$f(\Delta {G}_{r})=1-\mathrm{exp}\phantom{\rule{0.5em}{0ex}}\left(\frac{\Delta {G}_{r}}{\sigma RT}\right)\phantom{\rule{0.5em}{0ex}}\left(5\right)$
An extension of transition state theory where a rate limiting ion exchange reaction controls dissolution [15–18] and an extension of crystal growth theory to dissolution dominated by 2D nucleation of etch pits or by detachment of ions at dislocation sites [7] have been used to explain similar continuous decreases in dissolution rates with approach to equilibrium. We generally refer to these models as the ion exchange and pit nucleation models. Below we use diopside dissolution rates that span over three orders of magnitude, a wide range of ΔG_{r} and temperature to evaluate these two models which propose distinct dissolution mechanisms. We also derive corresponding rate expressions, because an important strength of both of these models is that rates are linked to solution saturation allowing complex description of geochemical processes when kinetic and thermodynamic data bases are coupled with flow and transport.
4. Ion Exchange Model
Oelkers [18] expanded equation 4 to explicitly account for the dependence of multi-oxide silicate mineral dissolution rates on solution composition by the formation of rate-limiting Si-rich surface complexes formed by metal-proton exchange reactions. The hydrolysis of the Si-O-Si bonds ultimately results in the dissolution of the mineral. These authors also note that for some framework silicate minerals the mineral is dissolved only through metal-proton exchange reactions. This model has been used to describe the dependence of alumino-silicate minerals on dissolved aluminum concentrations and the dependence of magnesio-silicate minerals and glass on dissolved magnesium concentrations. For alumino-silicate minerals, alkali and alkaline earth metals are exchanged fast and the Si-rich surface precursor complexes are formed from Al-H exchange reactions [11, 15, 16, 20]. For mafic silicates, Oelkers (2001) predicts that the Ca-H exchange reaction will precede Mg-H exchange reaction and that rate-limiting Si-rich surface precursor complexes are formed by Mg-H exchange [13, 15]. The concentration of the surface complexes would be therefore dependent on the dissolved Mg and pH according to the following reaction:
>nMgSiO + 2nH^{+} = >SiOH_{2n}+ nMg^{2+}, (6)
where, n is the stoichiometric exchange coefficient for H^{+} and Mg^{2+}, >nMgSiO and >SiOH_{2n}are the Mg-filled and the Si-rich mineral surface sites. Using transition state theory and assuming that the forward rate of the dissolution of minerals is proportional to the concentration of the Si-rich surface complex, and that there is a fixed number of mineral surface sites, the net dissolution rate of diopside is then given by
${R}_{net}={k}_{+}\lfloor \frac{{\left(\frac{{a}_{{H}^{+}}^{2}}{{a}_{M{g}^{2+}}}\right)}^{n}K}{1+K{\left(\frac{{a}_{{H}^{+}}^{2}}{{a}_{M{g}^{2+}}}\right)}^{n}}\rfloor \left[1-\mathrm{exp}\phantom{\rule{0.5em}{0ex}}\left(\frac{\Delta {G}_{r}}{\sigma RT}\right)\right]\phantom{\rule{0.5em}{0ex}}\left(7\right)$
where k_{+} is the apparent forward dissolution rate constant and K is the equilibrium constant for the formation of the Si-rich surface complex (Equation 6). When relatively low concentrations of the surface precursor complex are present such that $K{\left(\frac{{a}_{{H}^{+}}^{2}}{{a}_{M{g}^{2+}}}\right)}^{n}$ is substantially less than 1, then dissolution rates are dependent on the activity of H^{+} and Mg^{2+} and equation 7 reduces to
${R}_{net}=k{\left(\frac{{a}_{{H}^{+}}^{2}}{{a}_{M{g}^{2+}}}\right)}^{n}\phantom{\rule{0.5em}{0ex}}\left(8\right)$
where k = k_{+}K. Under these conditions, the relation between log R_{net} and $\mathrm{log}\phantom{\rule{0.5em}{0ex}}\left(\frac{{a}_{{H}^{+}}^{2}}{{a}_{M{g}^{2+}}}\right)$ is linear and n is represented by the slope and log k is given as the y-intercept.
We do not fit the data at 175°C, because diopside dissolution rates are of similar magnitude at 175 and 160°C indicating secondary mineral precipitation at 175°C. It seems unlikely that the fall off in rates represents a leveling off of the activation energy at higher temperatures, because E_{ a }typically increases with temperature for mineral systems [28]. Nor is it likely that the fall off in rates represents a change in mechanism due to a more alkaline pH at higher temperature. The solution OH^{-} concentrations are similar based on a minimal decrease in pK_{w} of only 0.1 log units between 160 and 175°C [22]. The best fit to the data was obtained with n = 1.39, E_{ a }= 332 (kJ mol^{-1}) and k = 10^{41.2} (mol diopside cm^{-2} s^{-1}). A comparison between the experimental data and the fitted values, with an extrapolation to 175°C, are shown in Figure 8. The ion exchange model adequately describes diopside dissolution to within 0.5 log units from 125 to 160°C. Extrapolation of this model to 175°C suggests that the net measured rate is offset by precipitation of a secondary phase that is about 1.5 to 2.0 log units higher the net measured dissolution rate. It appears that the secondary precipitate is a Ca-Mg-silicate rather than a Mg-silicate, because the difference of rates calculated from dissolve Ca (which is nominally undersaturated with mineral phases) and dissolved Mg and Si concentrations do not account for difference between observation and model. Fits did not improve when ΔG_{r}, K and an associated enthalpy term were included to describe the full form of the ion exchange model.
The apparent activation energy obtained in this study is much higher than those reported previously, which varied from about 40 to 150 kJ mol^{-1} [29–32]. It is possible that the much higher activation energy reported may be due to differences in rate models and the temperature range studied. Previous studies did not explicitly account for the effect of solution saturation as was done here with the ion exchange model. The net result would be a lower activation energy derived from averaged rate constants. The previous studies were also conducted at temperatures below 100°C, where the activation energy may be lower.
5. Pit Nucleation Model
Dissolution mechanisms and rates have been explained recently using theories developed previously for crystal growth [33, 34]. Extension of crystal growth theory to mineral dissolution calls for dissolution through retreat of steps, whose velocity (ν) is dependent on the solution saturation state (Ω) by the following expression
ν = ωβK_{eq}(Ω-1) (10)
where β is the step kinetic co-efficient, ω is the molar volume of a molecule in the crystal, and K_{eq} is the equilibrium constant of the dissolution reaction. These steps originate from dislocations within the mineral crystal as pre-existing features or develop by nucleation of two-dimensional pits in an otherwise perfect surface once the energy barrier to their formation is overcome. Dissolution rates depend on the step source and density. In this paper we focus on dissolution controlled by homogeneous and defect-assisted nucleation, because they appear to be the dominant mechanisms for diopside over step retreat at dislocations [7]. The dissolution by nucleation of two-dimensional pits can be initiated in an otherwise perfect surface only if the free energy barrier to the formation of a pit is overcome. The resulting free energy is given by
$\Delta {G}_{crit}=-\frac{\pi {a}^{2}\omega h}{kTln\Omega}\phantom{\rule{0.5em}{0ex}}\left(11\right)$
where α is the step edge free energy, h is the step height, k the Boltzmann constant. As equation 11 predicts, the free energy barrier is dependent on temperature, degree of undersaturation, and by factors that affect the step edge free energy. According to this model, dissolution rates would then decrease continuously as equilibrium is approached because the number of pits decreases with decreasing reaction affinity. Additionally, homogeneous nucleation of pits should transition to defect-assisted nucleation of pits at conditions closer to equilibrium. The dependence of dissolution rates originating from nucleation of pits on the degree of undersaturation is then given by
R = h(υ^{2}J)^{1/3} (12)
where h is the step height and J is the nucleation rate. The steady-state nucleation rate is derived from nucleation theory and is given by
$J={\left|\frac{1}{\mathrm{ln}\phantom{\rule{0.5em}{0ex}}\Omega}\right|}^{1/2}{n}_{S}ah{K}_{T,eq}\beta \mathrm{exp}\phantom{\rule{0.5em}{0ex}}\left(-\frac{\pi {\alpha}_{T,i}^{2}\omega h}{3{(kT)}^{2}}\left|\frac{1}{\mathrm{ln}\phantom{\rule{0.5em}{0ex}}\Omega}\right|\right)\phantom{\rule{0.5em}{0ex}}\left(13\right)$
where a is the lattice spacing and n_{ s }is the nucleation site density.
We fit our data from 125 to 160°C to an expanded form of equation 12 (after substitution of equation 13) to describe diopside dissolution as a function of temperature as well as solution composition [7]:
${R}_{i}=|\mathrm{ln}\phantom{\rule{0.5em}{0ex}}\Omega {|}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$6$}\right.}{(\Omega -1)}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}\left(h{\beta}_{i}{K}_{T,eq}{\left(h{\omega}^{2}{n}_{S,i}a\right)}^{1/3}\right)\mathrm{exp}\phantom{\rule{0.5em}{0ex}}\left(\frac{-{E}_{b,i}}{kT}\right)\mathrm{exp}\phantom{\rule{0.5em}{0ex}}\left(-\frac{\pi {\alpha}_{T,i}^{2}\omega h}{3{(kT)}^{2}}\left|\frac{1}{\mathrm{ln}\phantom{\rule{0.5em}{0ex}}\Omega}\right|\right)\phantom{\rule{0.5em}{0ex}}\left(14\right)$
where i indicates dissolution due to homogeneous or defect-assisted nucleation of pits on the surface. For ease of discussion, we simplify equation 14 to
where
$c={\left|\mathrm{ln}\phantom{\rule{0.5em}{0ex}}\Omega \right|}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$6$}\right.}{(\Omega -1)}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}\phantom{\rule{0.5em}{0ex}}\left(16\right)$
and
b_{ i }= hβ_{ i }(hω^{2}n_{s, i}a)^{1/3} (17)
The total dissolution rate is simply the summation of dissolution due to both mechanisms:
R_{ net }= R_{ homogeneous }+ R_{ defect-assisted } (18)
At a fixed temperature, b_{ i }and α_{ i }can be derived from a linear form of equation 15 by normalizing R_{ i }to solution saturation (c defined by equation 16) and applying the natural log:
$\mathrm{ln}\phantom{\rule{0.5em}{0ex}}\left(\frac{{R}_{i}}{c}\right)=\mathrm{ln}\phantom{\rule{0.5em}{0ex}}\left({b}_{T,i}{K}_{T,eq}\right)-\frac{\pi {\alpha}_{T,i}^{2}\omega h}{3{(kT)}^{2}}\left|\frac{1}{\mathrm{ln}\phantom{\rule{0.5em}{0ex}}\Omega}\right|\phantom{\rule{0.5em}{0ex}}\left(19\right)$
Changes in mineral dissolution as a function of temperature are accounted for by β_{ i }and n_{s,i}in the y-intercept and in α_{ i }in the slope in addition to the saturation terms (Ω, K_{T,eq}) and T in equation 19. The temperature dependence of β_{ i }and n_{s,i}can be estimated collectively from the Arrhenius equation:
$\frac{\partial \mathrm{ln}\phantom{\rule{0.5em}{0ex}}b}{\partial \frac{1}{T}}=\frac{{E}_{b}}{k},\phantom{\rule{0.5em}{0ex}}\left(20\right)$
where E_{ b }is the kinetic barrier. It is not possible to resolve the temperature dependence of β_{ i }and n_{s,i}separately with our data set. The temperature dependence of α_{ i }can be estimated from a variation of the Gibbs-Hemholtz equation:
$\frac{\partial \alpha}{\partial \frac{1}{T}}=\Delta H,\phantom{\rule{0.5em}{0ex}}\left(21\right)$
where ΔH is the enthalpy associated with the step edge energy for pit nucleation.
Pit Nucleation Model. Fitted parameters for equations 20 and 21 needed to describe diopside dissolution as a function of temperature.
ΔH_{α-homogeneous} = 749,700 mJ m^{-2} | |||||
ΔH_{α-defect assisted} = -91,644 mJ m^{-2} | |||||
E_{b-homogeneous} = 2.59 × 10^{-16} mJ K^{-1}, ln b_{homogeneous} = -11.57 mol cm^{-2} s^{-1} | |||||
E_{b-defect assisted} = 8.44 × 10^{-16} mJ K^{-1}, ln b_{defect assisted} = 83.34 mol cm^{-2} s^{-1} | |||||
ω = 1.1 × 10^{-28} m^{3}, h = 5.25 × 10^{-10} m | |||||
T°C | ^{ 1 } K _{ eq } | α_{ homogenous } mJ m^{-2} | ^{ 2 } y-intercept _{ homogeneous } | α_{ defect assited } mJ m^{-2} | ^{ 2 } y-intercept _{ defect-assisted } |
125 | 10^{14.48} | 275.9 | -25.5 | 39.4 | -36.9 |
150 | 10^{13.27} | 164.6 | -25.5 | 53.0 | -30.6 |
160 | 10^{12.82} | 123.7 | -25.5 | 58 | -28.3 |
175 | 10^{12.19} | ^{3}65.8 | ^{3}-25.5 | ^{3}65.1 | ^{3}-25.0 |
Final fits to the data indicate that dissolution is promoted predominately by homogenous nucleation at 125°C over the narrow range of solution saturation (1/lnΩ < 0.07) studied here. At 150 and 160°C dissolution is promoted by both homogeneous and defect-assisted nucleation of pits such that homogeneous nucleation is negligible at 1/lnΩ > 0.25 where it contributes less than 2% to the total dissolution rate. Extrapolation of the model to 175°C indicates that steady-state dissolution rates can be attributed to homogeneous and defect-assisted nucleation mechanisms in roughly equal proportions over the limited saturation range in this study. There is significant mismatch between the model prediction and diopside dissolution at 175°C. The most likely explanation for the mismatch is that the measured rates represent both dissolution of diopside and the precipitation of a secondary phase. Mineral precipitation was also indicated with the ion exchange model (see section 4).
Our results show that step edge energy for homogeneous nucleation is generally higher than step edge energy for defect-assisted nucleation, consistent with the observations for quartz, feldspar, and kaolinite [7]. However the difference between α_{homogenous} and α_{defect-assited} decreases at higher temperature, because estimated step edge energies for homogeneous and defect-assisted nucleation have different temperature dependencies. A decrease in step edge energy for homogeneous nucleation of pits at the diopside surface from about 275 to 65 mJ m^{-2} from 125 to 175°C suggests that the step edge energy required to form pits on an otherwise perfect crystal surface is lower at higher temperatures. There appears to be little dependence of the homogeneous pit site density or the kinetic coefficient on temperature as is illustrated by near constant y-intercept for the contribution of homogeneous nucleation of pits to diopside dissolution (Table 3). In contrast to homogeneous nucleation of dissolution pits, the temperature dependence of defect-assisted nucleation of dissolution pits on the diopside surface increases slightly with increasing temperature from about 39 to 65 mJ m^{-2} from 125 to 175°C. This increase suggests that defect-assisted pits form more readily at lower temperature than at higher temperature. Ostensibly higher step edge energy for defect-assisted nucleation at higher temperature appears to be compensated by an increase in the combined kinetic coefficient and site density for defect-assisted nucleation. Thus as the step edge energy rises with temperature, the kinetic barrier is lowered by increasing the number of defects that are accessible at higher temperature. The net result is higher dissolution rates at higher temperature at conditions closer to equilibrium where defect-assisted nucleation of dissolution pits are expected to dominate.
6. Broad implications for developing predictive geochemical models
Diopside dissolution can be described equally well by both an ion exchange model based on transition state theory and a pit nucleation model based on crystal growth/dissolution theory from 125 to 160°C (Figure 11), and both models predict much higher dissolution rates at 175°C than those measured indicating secondary mineral precipitation in the experiments. Thus based on the fitted data, we cannot determine if diopside kinetics are controlled by reversible reactions at the mineral surface (transition state theory) or if they are controlled by combined homogeneous and defect-assisted nucleation of pits on the mineral surface (crystal growth/dissolution theory). It was not possible to isolate pits due to homogeneous nucleation and defect-assisted nucleation by imagining gem stone quality diopside surfaces reacted at 150°C at distinct saturations representative of the two mechanism, as was done for quartz [7], because similar dissolution features and surface roughness were observed in both regions (interferometry data not shown). It is not clear if dissolution features were artifacts of the gem polishing technique or represented combined contributions from homogeneous and defect-assisted nucleations pits as predicted by fitted results of the macroscopic data.
Calibration of the ion exchange model requires that mineral dissolution rates be measured over a range of solution saturation and temperature at a single pH (at a minimum). The precursor forming exchange reactants (i.e. Mg-H for magnesio-silicates and Al-H for alumino-silicates) can be predicted from the relative dissolution rates of single hydroxides [15] and is related to the leached layer composition of the dissolving mineral. The exchange co-efficient (n in equation 6) is the number of cations removed to form the precursor complex should be determined empirically. Previous studies on alumino-silicate minerals suggested that n can be predicted from the charge balance where three protons are exchanged for each alumina [18]. This was not the case for diopside and may not be the case for other minerals. The apparent rate constant (k in equation 8) must also be determined empirically as a function of temperature to derive the apparent activation energy. Ideally, the effect of pH can be determined from experiments conducted at a single value, because pH is accounted for in the exchange reaction to form the Si-rich precursor (as shown in equation 6 for diopside). For enstatite dissolution, a model constrained at pH 2 is able to describe dissolution rates from pH 2 to 10 [17]. Similarly, for basaltic glass dissolution, the same model parameters describe dissolution at pH 3 and 11 [13]. In contrast, model parameters obtained at acid pH for kaolinite and muscovite dissolution are different from those obtained at basic pH conditions [11, 15].
Compared to the ion exchange model based on transition state theory, much more experimental data are required for the development and validation of a model based on crystal growth/dissolution theory. Mineral dissolution rates based on crystal growth/dissolution theory are dependent on the dominant source of steps. The source of steps can be at existing dislocations, existing crystal edges, nucleated homogeneously throughout the mineral surface or nucleated at specific defect sites. In the absence of experimental data (either microscopic or macroscopic), the source of steps cannot be determined a priori and are dependent on temperature and the extent of saturation for a given source of steps. For example Dove et al [7] showed that kaolinite dissolution rates obtained at 80°C are best explained by retreat of steps originating at dislocations. In contrast, rates obtained at 150°C are best explained by the pit nucleation model. The effect of solution pH is explicitly accounted for in the saturation terms and has been validated for kaolinite dissolution data obtained at 150°C under acid and circum-neutral pH conditions. However, the solution saturation ranges for homogeneous and defect-assisted nucleation of pits cannot be determined a priori. Even when the dominant step type is determined from microscopic observations, experimental dissolution data obtained over a range of saturation and temperature are still needed to empirically derive the temperature dependence for the step edge energy, site density, and kinetic coefficient.
A final note is that the precipitation rate expressions are needed to fully describe many rock-water interactions in the near surface. This is clearly illustrated in our experiments where mineral precipitation is indicated by similar rates measured at 160 and 175°C and by the mismatch between model predictions and measured rates.
Declarations
Acknowledgements
We wish to thank Kevin Knauss for helping with the experimental set up and discussion during the entire course of the study, Ron Pletcher for preparing the mineral powder, and Carl Steefel for helping with the multiple linear regressions and helpful discussions. We also thank the comments of three reviewers, which improved the manuscript. This work was supported by Department of Energy, Office of Basic Energy Science. This work was performed under the auspices of the U.S. Department of Energy by University of California, Lawrence Livermore National Laboratory under contract No. W7405-Eng-48.
Authors’ Affiliations
References
- White AF, Brantley SL: The effect of time on the weathering of silicate minerals: Why do weathering rates differ in the laboratory and field?. Chemical Geology. 2003, 202 (3–4): 479-506. 10.1016/j.chemgeo.2003.03.001.View ArticleGoogle Scholar
- Nagy KL, Lasaga AC: Dissolution and precipitation kinetics of gibbsite at 80°C and pH 3 – The dependence on solution saturation state. Geochimica et Cosmochimica Acta. 1992, 56 (8): 3093-3111. 10.1016/0016-7037(92)90291-P.View ArticleGoogle Scholar
- Nagy KL, Blum AE, Lasaga AC: Dissolution and precipitation kinetics of kaolinite at 80°C and pH 3 – The dependence on solution saturation state. American Journal of Science. 1991, 291 (7): 649-686.View ArticleGoogle Scholar
- Burch TE, Nagy KL, Lasaga AC: Free-Energy dependence of albite dissolution kinetics at 80°C and pH 8.8. Chemical Geology. 1993, 105 (1–3): 137-162. 10.1016/0009-2541(93)90123-Z.View ArticleGoogle Scholar
- Lasaga AC, Luttge A: Variation of crystal dissolution rate based on a dissolution stepwave model. Science. 2001, 291 (5512): 2400-2404. 10.1126/science.1058173.View ArticleGoogle Scholar
- Lasaga AC, Luttge A: A model for crystal dissolution. European Journal of Mineralogy. 2003, 15 (4): 603-615. 10.1127/0935-1221/2003/0015-0603.View ArticleGoogle Scholar
- Dove PM, Han NZ, De Yoreo JJ: Mechanisms of classical crystal growth theory explain quartz and silicate dissolution behavior. Proceedings of the National Academy of Sciences of the United States of America. 2005, 102 (43): 15357-15362. 10.1073/pnas.0507777102.View ArticleGoogle Scholar
- Beig MS, Luttge A: Albite dissolution kinetics as a function of distance from equilibrium: Implications for natural feldspar weathering. Geochimica et Cosmochimica Acta. 2006, 70 (6): 1402-1420. 10.1016/j.gca.2005.10.035.View ArticleGoogle Scholar
- Berger G, Cadore E, Schott J, Dove PM: Dissolution rate of quartz in lead and sodium electrolyte solutions between 25°C and 300°C – Effect of the nature of surface complexes and reaction affinity. Geochimica et Cosmochimica Acta. 1994, 58 (2): 541-551. 10.1016/0016-7037(94)90487-1.View ArticleGoogle Scholar
- Cama J, Ganor J, Ayora C, Lasaga CA: Smectite dissolution kinetics at 80°C and pH 8.8. Geochimica et Cosmochimica Acta. 2000, 64 (15): 2701-2717. 10.1016/S0016-7037(00)00378-1.View ArticleGoogle Scholar
- Devidal JL, Schott J, Dandurand JL: An experimental study of kaolinite dissolution and precipitation kinetics as a function of chemical affinity and solution composition at 150°C, 40 bars, and pH 2, 6.8, and 7.8. Geochimica et Cosmochimica Acta. 1997, 61 (24): 5165-5186. 10.1016/S0016-7037(97)00352-9.View ArticleGoogle Scholar
- Gautier JM, Oelkers EH, Schott J: Experimental-study of K-Feldspar dissolution rates as a function of chemical affinity at 150°C and pH 9. Geochimica et Cosmochimica Acta. 1994, 58 (21): 4549-4560. 10.1016/0016-7037(94)90190-2.View ArticleGoogle Scholar
- Gislason SR, Oelkers EH: Mechanism, rates, and consequences of basaltic glass dissolution: II. An experimental study of the dissolution rates of basaltic glass as a function of pH and temperature. Geochimica et Cosmochimica Acta. 2003, 67 (20): 3817-3832. 10.1016/S0016-7037(03)00176-5.View ArticleGoogle Scholar
- Hellmann R, Tisserand D: Dissolution kinetics as a function of the Gibbs free energy of reaction: An experimental study based on albite feldspar. Geochimica et Cosmochimica Acta. 2006, 70 (2): 364-383. 10.1016/j.gca.2005.10.007.View ArticleGoogle Scholar
- Oelkers EH: General kinetic description of multioxide silicate mineral and glass dissolution. Geochimica et Cosmochimica Acta. 2001, 65 (21): 3703-3719. 10.1016/S0016-7037(01)00710-4.View ArticleGoogle Scholar
- Oelkers EH, Schott J: Experimental study of anorthite dissolution and the relative mechanism of feldspar hydrolysis. Geochimica et Cosmochimica Acta. 1995, 59 (24): 5039-5053. 10.1016/0016-7037(95)00326-6.View ArticleGoogle Scholar
- Oelkers EH, Schott J: An experimental study of enstatite dissolution rates as a function of pH, temperature, and aqueous Mg and Si concentration, and the mechanism of pyroxene/pyroxenoid dissolution. Geochimica et Cosmochimica Acta. 2001, 65 (8): 1219-1231. 10.1016/S0016-7037(00)00564-0.View ArticleGoogle Scholar
- Oelkers EH, Schott J, Devidal JL: The Effect of aluminum, pH, and chemical affinity on the rates of aluminosilicate dissolution reactions. Geochimica et Cosmochimica Acta. 1994, 58 (9): 2011-2024. 10.1016/0016-7037(94)90281-X.View ArticleGoogle Scholar
- Taylor AS, Blum JD, Lasaga AC, MacInnis IN: Kinetics of dissolution and Sr release during biotite and phlogopite weathering. Geochimica et Cosmochimica Acta. 2000, 64 (7): 1191-1208. 10.1016/S0016-7037(99)00369-5.View ArticleGoogle Scholar
- Carroll SA, Knauss KG: Dependence of labradorite dissolution kinetics on CO_{2}(aq), Al-(aq), and temperature. Chemical Geology. 2005, 217 (3–4): 213-225. 10.1016/j.chemgeo.2004.12.008.View ArticleGoogle Scholar
- Bethke CM: The Geochemist's Workbench. 1994, University of IllinoisGoogle Scholar
- Johnson JW, Oelkers EH, Helgeson HC: Supcrt92 – a software package for calculating the standard molal thermodynamic properties of minerals, gases, aqueous species, and reactions from 1-Bar to 5000-Bar and 0°C to 1000°C. Computers & Geosciences. 1992, 18 (7): 899-947. 10.1016/0098-3004(92)90029-Q.View ArticleGoogle Scholar
- White AF, Brantley SL: Chemical weathering rates of pyroxenes and amphiboles. Chemical Weathering Rates of Silicate Minerals. 1995, 31: 119-346.Google Scholar
- Aagaard P, Helgeson HC: Thermodynamic and kinetic constraints on reaction-rates among minerals and aqueous solutions. 1. Theoretical Considerations. American Journal of Science. 1982, 282 (3): 237-285.View ArticleGoogle Scholar
- Carroll S, Mroczek E, Alai M, Ebert M: Amorphous silica precipitation (60 to 120°C): Comparison of laboratory and field rates. Geochimica et Cosmochimica Acta. 1998, 62 (8): 1379-1396. 10.1016/S0016-7037(98)00052-0.View ArticleGoogle Scholar
- Renders PJN, Gammons CH, Barnes HL: Precipitation and dissolution rate constants for cristobalite from 150°C to 300°C. Geochimica et Cosmochimica Acta. 1995, 59 (1): 77-85. 10.1016/0016-7037(94)00232-B.View ArticleGoogle Scholar
- Rimstidt JD, Barnes HL: The kinetics of silica-water reactions. Geochimica et Cosmochimica Acta. 1980, 44 (11): 1683-1699. 10.1016/0016-7037(80)90220-3.View ArticleGoogle Scholar
- Lasaga AC: Kinetic Theory in the Earth Sciences. 1998, Princeton University PressView ArticleGoogle Scholar
- Brantley SL, Chen Y: Chemical weathering rates of pyroxenes and amphiboles. Chemical Weathering Rates of Silicate Minerals. 1995, 31: 119-172.Google Scholar
- Chen Y, Brantley SL: Diopside and anthophyllite dissolution at 25° and 90°C and acid pH. Chemical Geology. 1998, 147 (3–4): 233-248.View ArticleGoogle Scholar
- Knauss KG, Nguyen SN, Weed HC: Diopside dissolution kinetics as a function of pH, CO_{2}, temperature, and time. Geochimica et Cosmochimica Acta. 1993, 57 (2): 285-294. 10.1016/0016-7037(93)90431-U.View ArticleGoogle Scholar
- Schott J, Berner RA, Sjoberg EL: Mechanism of pyroxene and amphibole Weathering.1. Experimental studies of iron-free minerals. Geochimica et Cosmochimica Acta. 1981, 45 (11): 2123-2135. 10.1016/0016-7037(81)90065-X.View ArticleGoogle Scholar
- Chernov AA: Modern Crystallography III. 1984, SpringerView ArticleGoogle Scholar
- Malkin AI, Chernov AA, Alexeev IV: Growth of dipyramidal face of dislocation-dree Adp crystals – Free-energy of steps. Journal of Crystal Growth. 1989, 97 (3–4): 765-769. 10.1016/0022-0248(89)90580-0.View ArticleGoogle Scholar
- Golubev SV, Pokrovsky OS, Schott J: Experimental determination of the effect of dissolved CO_{2} on the dissolution kinetics of Mg and Ca silicates at 25°C. 2005Google Scholar
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