Supersaturation functions in binary solid solution-aqueous solution systems

In this paper, we present a brief review of the thermodynamic equilibrium of binary solid solution-aqueous solution (SS-AS) systems and derive an expression that allows us to evaluate the supersaturation or undersaturation of a given aqueous solution with respect to the whole range of solid compositions: the δ(x) function. Such an expression is based on the two conditions that define the SS-AS thermodynamic equilibrium. The derivation of the new supersaturation function, δ(x), was made by considering in detail the compositional relationships between solid and aqueous phases. To represent the new formulation on Lippmann diagrams, we have defined a new thermodynamic concept: the “actual activity.” In addition, we show how our supersaturation function behaves for both ideal and subregular solid solutions. The behaviour and applicability of both the δ(x) function and a previous supersaturation function, β(x), defined by Prieto et al. (1993), is discussed.     

Simulation of the nucleation and growth of binary solid solutions in aqueous solutions

We present a model which, for the first time, accounts for nucleation, growth and/or resorption of particles of variable composition in aqueous solutions (AS). Devised for describing the precipitation of binary solid solutions, it yields the time evolution of all ion activities in the AS, together with the particle population characteristics: number, size and composition profile of particles as a function of time and of their time of nucleation. We apply this numerical approach to the prototypical case of (Ba,Sr)CO₃ solid solution precipitation. We demonstrate the great sensitivity of the composition profiles and particle sizes to the initial conditions under which the AS is prepared, and thus illustrate the possibility of engineering the particle characteristics into a chosen state. Finally, by comparing the precipitation of two solid solutions (Ba,Sr)CO₃ and (Ba,Sr)SO₄, we evidence the sensitivity of the particle composition profiles to the ratio of the end-member solubility products, which leads to the formation of core-shell particles in the case of (Ba,Sr)SO₄.     

Structural and compositional characterization of synthetic (Ca,Sr)-tremolite and (Ca,Sr)-diopside solid solutions

Tremolite (Ca_xSr_1–x)₂Mg₅[Si₈O₂₂/(OH)₂] and diopside (Ca_xSr_1–x)Mg[Si₂O₆] solid solutions have been synthesized hydrothermally in equilibrium with a 1 molar (Ca,Sr)Cl₂ aqueous solution at 750°C and 200 MPa. The solid run products have been investigated by optical, electron scanning and high resolution transmission electron microscopy, electron microprobe, X-ray-powder diffraction and Fourier-transform infrared spectroscopy. The synthesized (Ca,Sr)-tremolites are up to 2000 µm long and 30 µm wide, the (Ca,Sr)-diopsides are up to 150 µm long and 20 µm wide. In most runs the tremolites and diopsides are well ordered and chain multiplicity faults are rare. Nearly pure Sr-tremolite (tr_0.02Sr-tr_0.98) and Sr-diopside (di_0.01Sr-di_0.99) have been synthesized. A continuous solid solution series, i.e. complete substitution of Sr²⁺ for Ca²⁺ on M₄-sites exists for (Ca,Sr)-tremolite. Total substitution of Sr²⁺ for Ca²⁺ on M₂-sites can be assumed for (Ca,Sr)-diopsides. For (Ca,Sr)-tremolites the lattice parameters a, b and β are linear functions of composition and increase with Sr-content whereas c is constant. For the diopside series all 4 lattice parameters are a linear function of composition; a, b, c increase and β decreases with rising Sr-content. The unit cell volume for tremolite increases 3.47% from 906.68 ų for tremolite to 938.21 ų for Sr-tremolite. For diopside the unit cell volume increases 4.87 % from 439.91 ų for diopside to 461.30 ų for Sr-diopside. The observed splitting of the OH stretching band in tremolite is caused by different configurations of the next nearest neighbors (multi mode behavior). Resolved single bands can be attributed to the following configurations on the M₄-sites: SrSr, SrCa, CaCa and CaMg. The peak positions of these 4 absorption bands are a linear function of composition. They are shifted to lower wavenumbers with increasing Sr-content. No absorption band due to the SrMg configuration on the M₄-site is observed. This indicates a very low or negligible cummingtonite component in Sr-rich tremolites, which is also supported by electron microprobe analysis.     

Molecular-scale surface processes during the growth of calcite in the presence of manganese

This paper deals with the growth behaviour of the Mn-Ca-CO₃-H₂O solid solution-aqueous solution system on calcite {104} surfaces. This system represents a model example, which allows us to study the effect of a number of controlling factors on the crystallisation: (1) the supersaturation function, β(x), and nucleation rate function, J(x), for the Mn-Ca-CO₃-H₂O system, (2) the relationship of such functions to the molecular scale growth mechanisms operating on growing surfaces, and (3) the surface structure of the calcite {104} faces. In situ atomic force microscopy (AFM) growth experiments revealed a wide variety of surface phenomena, such as the transition between growth mechanisms, anisotropic changes in the step rates, and the influence of the Mn-bearing newly formed surface on subsequent growth (step stoppage followed by the formation of two-dimensional nuclei and the reproduction of the original calcite {104} surface microtopography). These phenomena result from the interplay between the controlling parameters and are explained in those terms.     

X-ray photoelectron spectroscopic studies of dolomite surfaces exposed to undersaturated and supersaturated aqueous solutions

Cleaved surfaces of dolomite were studied using ex-situ X-ray photoelectron spectroscopy (XPS) following exposure of the surfaces to various experimental conditions. Dolomite samples exposed to air, to a highly undersaturated solution (0.1 M NaCl, pH = 9), and to solution with a supersaturation (−Δμ/kT) of 5.5 (pH = 9) were investigated with semiquantitative methods of analysis to ascertain the degree of non-stoichiometry resulting at the dolomite surface from reactive conditions. It was found that the dolomite cleavage surface in undersaturated solution was not altered significantly from the stoichiometric surface termination. The composition of the cleaved surface after exposure to supersaturated solution, a surface known to have self-limiting growth characteristics under similar conditions, was found to be Ca²⁺ rich (Ca_xMg_2 − x(CO₃)₂, 1.7 > x > 1.3). The observations, while underscoring differences in hydration/dehydration kinetics of the two alkaline earth cations, suggest that achievement of equilibrium at dolomite-water interfaces may be subject to significant barriers from both undersaturated and supersaturated solutions.     

Modeling the kinetics of silica nanocolloid formation and precipitation in geologically relevant aqueous solutions

The kinetics of the formation and precipitation of nanocolloidal silica from geologically relevant aqueous solutions is investigated. Changes in monomeric (SiO_2(mono)), nanocolloidal (SiO_2(nano)) and precipitated silica (SiO_2(ppt)) concentrations in aqueous solutions from pH 3 to 7, ionic strengths (IS) of 0.01 and 0.24 molal, and initial SiO₂ concentrations of 20.8, 12.5 and 4.2 mmolal (reported in [Icopini, G.A., Brantley, S.L., Heaney, P.J., 2005. Kinetics of silica oligomerization and nanocolloid formation as a function of pH and ionic strength at 25 °C. Geochim. Cosmochim. Acta69(2), 293-303.]) were fit using two kinetic models. The first model, termed the concentration model, is taken from Icopini et al. (2005) and assumes that the rate of change of SiO_2(mono) as a function of time has a fourth-order dependence on the concentration of SiO_2(mono) in solution. The second model, termed the supersaturation model, incorporates the equilibrium concentration of amorphous silica and predicts that polymerization will be a function of the degree of silica supersaturation in solution with respect to amorphous silica. While both models generally predicted similar rate constants for a given set of experimental conditions, the supersaturation model described the long-term equilibrium behavior of the SiO_2(mono) fraction more accurately, resulting in significantly better fits of the monomeric data. No difference was seen between the model fits of the nanocolloidal silica fraction. At lower pH values (3-4), a metastable equilibrium was observed between SiO_2(mono) and SiO_2(nano). This equilibrium SiO_2(mono) concentration was found to be 6 mmolal, or three times the reported solubility of bulk amorphous silica under the experimental conditions studied and corresponds to the predicted solubility of amorphous silica colloids approximately 3 nm in diameter. Atomic force microscopy was used to determine the average size of the primary nanocolloidal particles to be ∼3 nm, which is in direct agreement with the solubility calculations. Larger aggregates of the primary nanocolloids were also observed to range in size from 30 to 40 nm. This work provides the first kinetic models describing the formation and evolution of nanocolloidal silica in environmentally relevant aqueous solutions. Results indicate that nanocolloidal silica is an important species at low pH and neutral pH at low ionic strengths and may play a more important role in geochemical cycles in natural aqueous systems than previously considered.     

Crystallization kinetics of strontianite from Sr(HCO3)2 solutions

The kinetics of crystallization of strontium carbonate (strontianite) from strontium bicarbonate solutions were examined. CO₂ was stripped from a slightly acidic solution of Sr(HCO₃)₂ by stirring resulting in critical supersaturation and precipitation of strontianite. The reduction of the Sr²⁺ concentration was recorded as a function of time by measuring the electrolytic conductivity and the pH value.

Homogeneous primary nucleation is dominant at high supersaturations, whereas heterogeneous primary nucleation prevails at low supersaturations. The crystal growth rate increases with increasing supersaturation. This effect is less pronounced at higher supersaturations. The growth rate is mostly transport-controlled at high supersaturation. At lower supersaturation the crystal growth is mainly determined by integration of ions into the crystal lattice. These results may be used to explain the deposition of strontianite in natural systems.     

Determination of Sr and Ba partition coefficients between apatite and water from 5°C to 60°C: a potential new thermometer for aquatic paleoenvironments

Apparent partition coefficients of Sr and Ba between calcium phosphate and water were measured experimentally for temperature ranging from 5°C to 60°C. Calcium phosphates were precipitated from an aqueous mixture of Na₂HPO₄ · 2H₂O (10⁻² M) and CaCl₂ · 2H₂O (10⁻² M). Spiked solutions of Sr or Ba were introduced into the CaCl₂ · 2H₂O solution at Sr/Ca and Ba/Ca ratios of 0.1. The experiment consisted in sampling the liquid and solid phases after 1, 6, 48, and 96 h of interaction. The amorphous calcium phosphate (ACP) precipitated early in the experiment was progressively replaced by hydroxylapatite (HAP), except at 5°C where brushite (di-calcium phosphate di-hydrate or DCPD) was formed. We observed that the crystallinity of the solid phase increased with time for a given temperature and increased with temperature for a given time of reaction. With the exception of the experiment at 5°C, yield (R%) and apparent partition coefficients (K_a-w^Sr/Ca and K_a-w^Ba/Ca) both decreased with increasing reaction time. After 96 h, R%, K_a-w^Sr/Ca and K_a-w^Ba/Ca were observed to be constant, suggesting that the solid phases were at steady-state with respect to the aqueous solutions. The thermodependence of Sr and Ba partitioning between apatite and water at low temperature could therefore be calculated:

     

Incorporating solid solutions in reactive transport equations using a kinetic discrete-composition approach

A new approach is proposed for incorporating solid solution reactions into mass conservation equations describing reaction paths in both closed and open systems. The method is applicable to problems involving advective, dispersive, and diffusive transport in a porous medium. By representing the continuously variable solid solution composition with a discrete set of stoichiometric solids that span composition space, combined with a kinetic formulation of their rates of reaction, a self-determining spatial and temporal evolution of the solid solution concentration and composition is obtained. It is demonstrated that equilibrium of an aqueous solution with a stoichiometric solid derived from a solid solution corresponds to equilibrium of the solid solution itself if and only if equilibrium of the stoichiometric solid is stable. One advantage of this approach is that it is unnecessary to introduce any additional compositional variables to represent the solid solution. Discretization may be over the entire range of composition space, or over some subset depending on the system. A major consequence of the kinetic discrete-composition solid solution representation is that modeling solid solutions is similar to modeling pure mineral phases with the exception of a weighting factor applied to reaction rates of stoichiometric solids corresponding to a common solid solution. With this approach, precipitation leads to a discrete zonation of the solid solution that approximates the continuous variation in composition expected for the actual solid solution. The approach is demonstrated for a hypothetical ideal and non-ideal binary solid solution A_xB_1−xC for a reaction path formulation and reactive transport involving advection and diffusion.     

The influence of impurities on the dissolution of Ca- and Sr-bearing barite at room temperature

1INTRODUCTION BARITE(BASO4)ISANEXTREMELYINSOLUBLESALT;THISAROUSESPROBLEMSINPETROLEUMINDUSTRYBECAUSE BASO4ISAPARTICULARLYINTRACTABLESCALINGAGENT.BARITE PRECIPITATIONINTHEWELLBOREENVIRONMENTGENERALLYRE QUIRESMECHANICALREMOVAL,WITHCONSIDERABLEASSOCIAT EDEXPE…     

Interaction between dissolved silica and calcium carbonate: 1. Spontaneous precipitation of calcium carbonate in the presence of dissolved silica

The kinetics of spontaneous precipitation of CaCO₃ from aqueous solution in the presence of dissolved silica was investigated by recording pH as a function of time. The presence of dissolved silica, at concentrations below saturation with respect to the amorphous phase, decreases induction time for CaCO₃ nucleation, but does not affect CaCO₃ polymorphism. For a “pure” system without silica, the surface free energy, σ, determined from classical nucleation theory is 42 mJ m⁻². This agrees well with values reported in the literature for vaterite and indicates some degree of heterogeneous nucleation, which can occur because of the relatively low degree of supersaturation used for the experiments. In the presence of 1 and 2 mM silica, σ is 37 and 34 mJ m⁻², indicating an increasing degree of heterogeneous nucleation as the amount of polymeric silica increases. The ratio of Ca²⁺ to CO₃²⁻ activity was a governing parameter for determining which CaCO₃ polymorph precipitated. At high Ca²⁺ to CO₃²⁻ activity ratios, almost all initial solid was vaterite, whereas at low ratios, a mixture of vaterite and calcite was observed. In solutions with low Ca²⁺ to CO₃²⁻ activity ratios, the presence of silica at concentrations above saturation with respect to amorphous silica led to formation of only calcite and strongly influenced the crystalline structure and morphology of the precipitates. At high Ca²⁺ to CO₃²⁻ ratios, system behaviour did not differ from that without silica.     

The effect of cation:anion ratio in solution on the mechanism of barite growth at constant supersaturation: Role of the desolvation process on the growth kinetics

The mechanism of barite growth has been investigated in a fluid cell of an Atomic Force Microscope by passing solutions of constant supersaturation (Ω) but variable ion activity ratio (r=a_Ba/a_SO4) over a barite substrate.The observed dependence of step-spreading velocity on solution stoichiometry can be explained by considering non-equivalent attachment frequency factors for the cation and anion. We show that the potential for two-dimensional nucleation changes under a constant thermodynamic driving force due to the kinetics of barium integration into the surface, and that the growth mode changes from preexisting step advancement to island spreading as the cation/anion activity ratio increases. Scanning electron microscopy studies of crystals grown in bulk solutions support our findings that matching the ion ratio in the fluid to that of the crystal lattice does not result in maximum growth and nucleation rates. Significantly more rapid rates correspond to solution stoichiometries where [Ba²⁺] is in excess with respect to [].Experiments performed in dilute aqueous solutions of methanol show that even 0.02 molar fraction of organic cosolvent in the growth solution significantly accelerates step growth velocity and nucleation rates (while keeping Ω the same as in the reference solution in water). Our observations suggest that the effect of methanol on barite growth results first of all from reduction of the barrier that prevents the Ba²⁺ from reaching the surface and corroborate the hypothesis that desolvation of the cation and of the surface is the rate limiting kinetic process for two-dimensional nucleation and for crystal growth.     

Kinetics of crystal nucleation in ionic solutions: Electrostatics and hydration forces

The heat of precipitation, the mean crystal size and the broadness of crystal size distribution of barium sulfate precipitating in aqueous solutions of different background electrolytes (KCl, NaCl, LiCl, NaBr or NaF), was shown to vary at constant thermodynamic driving force (supersaturation) and constant ionic strength depending on the salt present in solution. The relative inversion in the effect of respective background ions on the characteristics of barite precipitate was observed between two studied supersaturation (Ω) and ionic strength (IS) conditions. The crystal size variance (β²) increased in the presence of background electrolytes in the order LiCl < NaCl < KCl at Ω = 10^3.33 and IS = 0.03 M and KCl < NaCl < LiCl at Ω = 10^3.77 and IS = 0.09 M. At a given Ω and IS the respective size of barite crystals decreased with increasing β² in chloride salts of different cations and remained constant in sodium salts of different anions.We suggest that ionic salts affect the kinetics of barite nucleation and growth due to their influence on water of solvation and bulk solvent structure. This idea is consistent with the hypothesis that the kinetic barrier for barium sulfate nucleation depends on the frequency of water exchange around respective building units that can be modified by additives present in solution. In electrolyte solution the relative switchover between long range electrostatic interactions and short range hydration forces, which influence the dynamics of solvent exchange between an ion solvation shell and bulk fluid, results in the observed inversion in the effect of differently hydrated salts on nucleation rates and the resulting precipitate characteristics.     

Modulations in incommensurate (Ca1–xSrx)2MgSi2O7 single crystals

Single crystals of (Ca_1–xSr_x)₂MgSi₂O₇ slightly doped with 1000 ppm Mn²⁺ and with x ranging from 0.04 to 0.32 were grown from the melt in a mirror furnace applying the Czochalski technique. Transmission electron microscopy (TEM) revealed incommensurately modulated structures at room-temperature for all compositions in accordance with earlier studies by electron paramagnetic resonance (EPR). Electron diffraction patterns clearly show satellite reflections typical for two-dimensional modulation, and their successive destabilization with increasing Sr content. The modulation is of tartan-like appearance. Beyond a Sr/(Sr+Ca) ratio of about 0.32 the synthesis of stable solid solution åkermanite type crystals was proved not to be feasible, indicating the existence of a miscibility gap in the Sr åkermanite system. As presumed from the diffuse scattering around the satellite reflections, and suggested more conclusively by crystallographic processing of high resolution EM images the Sr ions incorporated into the incommensurate crystal phase are distributed in an ordered fashion and are partly adapted to the displacive modulation of the pure åkermanite. This means, occupational modulation even makes a contribution to the overall modulation characteristics in (Ca_1–xSr_x)₂ MgSi₂O₇.     

Radium uptake during barite recrystallization at 23 ± 2 °C as a function of solution composition: An experimental Ba and Ra tracer study

High-purity synthetic barite powder was added to pure water or aqueous solutions of soluble salts (BaCl₂, Na₂SO₄, NaCl and NaHCO₃) at 23 ± 2 °C and atmospheric pressure. After a short pre-equilibration time (4 h) the suspensions were spiked either with ¹³³Ba or ²²⁶Ra and reacted under constant agitation during 120-406 days. The pH values ranged from 4 to 8 and solid to liquid (S/L) ratios varied from 0.01 to 5 g/l. The uptake of the radiotracers by barite was monitored through repeated sampling of the aqueous solutions and radiometric analysis. For both ¹³³Ba and ²²⁶Ra, our data consistently showed a continuous, slow decrease of radioactivity in the aqueous phase.Mass balance calculations indicated that the removal of ¹³³Ba activity from aqueous solution cannot be explained by surface adsorption only, as it largely exceeded the 100% monolayer coverage limit. This result was a strong argument in favor of recrystallization (driven by a dissolution-precipitation mechanism) as the main uptake mechanism. Because complete isotopic equilibration between aqueous solution and barite was approached or even reached in some experiments, we concluded that during the reaction all or substantial fractions of the initial solid had been replaced by newly formed barite.The ¹³³Ba data could be successfully fitted assuming constant recrystallization rates and homogeneous distribution of the tracer into the newly formed barite. An alternative model based on partial equilibrium of ¹³³Ba with the mineral surface (without internal isotopic equilibration of the solid) could not reproduce the measured activity data, unless multistage recrystallization kinetics was assumed. Calculated recrystallization rates in the salt solutions ranged from 2.8 × 10⁻¹¹ to 1.9 × 10⁻¹⁰ mol m⁻² s⁻¹ (2.4-16 μmol m⁻² d⁻¹), with no specific trend related to solution composition. For the suspensions prepared in pure water, significantly higher rates (∼5.7 × 10⁻¹⁰ mol m⁻² s⁻¹ or ∼49 μmol m⁻² d⁻¹) were determined.Radium uptake by barite was determined by monitoring the decrease of ²²⁶Ra activity in the aqueous solution with alpha spectrometry, after filtration of the suspensions and sintering. The evaluation of the Ra uptake experiments, in conjunction with the recrystallization data, consistently indicated formation of non-ideal solid solutions, with moderately high Margules parameters (W_AB = 3720-6200 J/mol, a₀ = 1.5-2.5). These parameters are significantly larger than an estimated value from the literature (W_AB = 1240 J/mol, a₀ = 0.5).In conclusion, our results confirm that radium forms solid solutions with barite at fast kinetic rates and in complete thermodynamic equilibrium with the aqueous solutions. Moreover, this study provides quantitative thermodynamic data that can be used for the calculation of radium concentration limits in environmentally relevant systems, such as radioactive waste repositories and uranium mill tailings.     

The thermodynamic properties of radium

The enthalpy, Gibbs free energy, and entropies of aqueous radium species and radium solids have been evaluated from empirical data, or estimated when necessary for 25°C and 1 bar. Estimates were based on such approaches as extrapolation of the thermodynamic properties of Ca, Sr, and Ba complexes and solids plotted against cationic radii and charge to radius functions, and the use of the Fuoss or electrostatic mathematical models of ion pair formation (Langmuir, 1979). Resultant log K (assoc) and ΔH⁰ (assoc) (kcal/mol) values are: for RaOH⁺ 0.5 and 1.1; RaCl⁺ ?0.10 and 0.50; RaCO⁰₃ 2.5 and 1.07; and RaSO⁰₄ 2.75 and 1.3. Log Ksp and ΔH⁰ (dissoc) (kcal/mol) values for RaCO₃(c) and RaSO₄(c) are ?8.3 and ?2.8, and ?10.26 and ?9.4, respectively.Trace Ra solid solution in salts of Pb and of the lighter alkaline earths, has been appraised based on published distribution coefficient (D) data, where D ～- (mM²⁺)(N_RaX)/(mRa²⁺)(N_MX) (m and N are the aqueous molality and mole fraction of Ra and cation M in salt X, respectively. The empirical solid solution data have been used to derive both enthalpies and Gibbs free energies of solid solution of trace Ra in sulfate and carbonate minerals up to 100°C. Results show that in every case D values decrease with increasing temperature. Among the sulfate and carbonate minerals, D values decrease for the following minerals in the order: anhydrite > celestite > anglesite > barite > aragonite > strontianite > witherite > cerussite.     

Metastable phenomena on calcite {101̄4} surfaces growing from Sr2+–Ca2+–CO32− aqueous solutions

In situ atomic force microscopy (AFM) experiments, scanning electron microscopy (SEM) imaging and composition analysis, and X-ray diffraction have provided information about the growth, dissolution and transformation processes promoted by Sr²⁺–Ca²⁺–CO₃²⁻ aqueous solutions in contact with calcite {101̄4} surfaces. Experiments have shown a wide variety of surface phenomena, such as the influence of the Sr-bearing newly-formed surface on the subsequent growth (template effect), the growth and subsequent dissolution of surfaces and the nucleation of secondary three-dimensional nuclei on calcite surfaces. These phenomena reveal the metastability of the crystallisation system and are a consequence of the interplay between thermodynamics (the relative stability of the two calcite and aragonite structure solid solutions that can be formed), supersaturation of the aqueous solution with respect to the two possible solid solutions, and the crystallographic control of the surfaces on cation incorporation.     

Structure and stability of the Fe(II)–Fe(III) green rust “fougerite” mineral and its potential for reducing pollutants in soil solutions

Fe(II)–Fe(III) layered double hydroxysalt green rusts, GRs, are very reactive compounds with the general formula, [Fe^II_(1−x) Fe^III_x (OH)₂]^x+·[(x/n) Aⁿ⁻·(m/n) H₂O]^x−, where x is the ratio Fe^III/Fe_tot, and reflects the structure in which brucite-like layers alternate with interlayers of anions Aⁿ⁻ and water molecules. Two types of crystal structure for GRs, GR1 and GR2, represented by the hydroxychloride GR1(Cl⁻) and the hydroxysulphate GR2(SO₄²⁻) are distinguished by X-ray diffraction due to different stacking. By analogy with GR1(Cl⁻) the structure of the fougerite GR mineral, [Fe^II_(1−x) Fe^III_x (OH)₂]^x+·[x OH⁻·(1−x) H₂O]^x-  Fe(OH)_(2+x)·(1−x) H₂O, is proposed displaying interlayers made of OH⁻ ions and water molecules (in situ deprotonation of water molecules is necessary for explaining the flexibility of its composition). The space group of mineral GR1(OH⁻) would be R3̄m, with lattice parameters a≅0.32 and c≅2.25 nm. Stability conditions and the E_h-pH diagram of Fe(OH)_(2+x) (the water molecules are omitted) are determined from hydromorphic soil solution equilibria with GR mineral in Brittany (France). Computed Gibbs free energies of formation from soil solution/mineral equilibrium fit well with a regular solid solution model: μ°[Fe(OH)_(2+x)]=(1−x) μ°[Fe(OH)₂]+x μ°[Fe(OH)₃]+RT [(1−x) ln (1−x)+x ln x]+A₀ x (1−x), where μ°[Fe(OH)₂]=−492.5 kJ mol⁻¹, μ°[Fe(OH)₃]=−641 kJ mol⁻¹ and A₀=−243.9 kJ mol⁻¹ at the average temperature of 9±1°C. The upper limit of occurrence of GR mineral at x=2/3, i.e. Fe₃(OH)₈, is explained by its unstability vs. α-FeOOH and/or magnetite; Fe(OH)₃ is thus a hypothetical compound with a GR structure which cannot be observed. These thermodynamic data and E_h-pH diagrams of Fe(OH)_(2+x) can be used most importantly to predict the possibility that GR minerals reduce some anions in contaminated soils. The cases of NO₃⁻, Se(VI) or Cr(VI) are fully illustrated.