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1.
The nucleation kinetics of binary solid solutions, with general formula BxC1−xA, crystallising from aqueous solution can be described using a generalised expression for the nucleation rate: the function, J(x), in which supersaturation, interfacial free energy and other parameters of the classical nucleation rate equation are considered as functions of the solid composition. As an example, we studied the behaviour of such J(x) functions for the case of the (Ba,Sr)SO4 and (Ba,Sr)CO3 solid solutions. J(x) functions are very sensitive to slight changes in the composition of the aqueous solution, which result in strong modifications of the nucleation kinetics. The implications of the relationship between supersaturation and nucleation rate functions for the general nucleation behaviour in solid solution-aqueous solution (SS-AS) systems are discussed. Finally, we present a method for constructing non-equilibrium Roozeboom diagrams based on the nucleation kinetics in SS-AS systems. Our Roozeboom diagrams calculated for different departures from equilibrium conditions are consistent with previous experimental work and they can be used to predict actual distribution coefficients.  相似文献   

2.
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.  相似文献   

3.
Coprecipitation of barite with trace constituents was simulated with consideration of aqueous speciation and complexation, mixing properties for the binary solid solutions (Zhu, this issue), precipitation and dissolution kinetics, and advective-dispersive transport. Speciation-solubility modeling was used to reproduce BaSO4-RaSO4 coprecipitation experimental results, and to calculate CrO42− aqueous concentrations in equilibrium with a Ba(SO4,CrO4) solid solution. Kinetic reaction path modeling was used to simulate the coprecipitation of barite with RaSO4 to form an onion-like chemically zoned solid upon the cooling of oil field brine.A one-dimensional coupled reactive mass transport model shows a strikingly different transport pattern for the tracer Ra2+, when the dominant attenuation reaction is with solid solution (Ba, Ra) SO4 as compared to the case when it is controlled by pure RaSO4 and barite solids under local equilibrium conditions. A self-enrichment of Ra2+ in the groundwater and aquifer solid matrix—higher concentrations of Ra2+ downstream from the reaction front—results from the coprecipitation reaction and advective-dispersive transport. This self-enrichment process generates a secondary tracer source, which has tracer concentrations higher than that of the original source. On the other hand, coprecipitation reactions can reduce Ra2+ concentrations in groundwater to a much lower level (below ppb) than that of pure RaSO4(c) solubility (near ppm), which has been used to establish the Ra2+ concentration limits in groundwater, soil, and nuclear waste repositories.  相似文献   

4.
A hypothesis is presented that the dissolution of albite includes the exchange of sodium for hydrogen ion in a surface layer of the mineral and the structural collapse of the residual anionic lattice of the layer. The ion exchange is described by the first law of diffusion (D25°C = 3 × 10?22 and 1.5 × 10?20 cm2sec?1 at PCO2 = 0 and 26.2 atm, respectively). The surface residual layer reaches a steady-state thickness ranging from n × 10?8 to n × 10?5 cm according to the temperature and PCO2. The increase in aqueous sodium with time in a continuous ground-water system is described by a simple exponential equation. The equation is used to estimate the percolation time of ground water from the data on the chemical composition of a water sample. The probable times range from 14 to 3840 days for various ground-water systems and are compared to the times of percolation calculated from the geothermal and hydraulic data. Both estimates are found to be in general agreement. The concentrations of Al and Si in cold water from granitic rocks are shown to be controlled by the chemical equilibrium with respect to an aged aluminosilicate. The aluminosilicate precipitates from ground water as an amorphous isoelectric solid. Its chemical composition is represented by a simplified stoichiometric formula [Al(OH)3](1?x)[SiO2]x and varies linearly with pH of the solution. The atoms of Al, O and H tend to occupy a fixed position in the solid given by the gibbsite structure upon aging in the field. The solubility product of the solid is estimated from the published data on experimental and field research into the dissolution of feldspars: logK = (1 ? x) × log [Al3+] + xlog [H4SiO4] ? (3 ? 3x) log [H+] = 8.56 ? 11.26x, where x is the molar fraction of silica in the aluminosilicate.  相似文献   

5.
《Chemical Geology》2006,225(3-4):189-212
The dual-thermodynamic (DualTh) approach is shown to provide a useful alternative to other methods in: (i) forward modelling of equilibrium speciation, activities, and element partitioning in a heterogeneous system involving several variable-composition phases, such as the aqueous–solid solution system; (ii) estimation of interaction parameters of a non-ideal mixing model from known bulk compositions of coexisting aqueous and solid-solution phases; and (iii) retrieval of unknown stoichiometries and apparent standard chemical potentials of trace solid-solution end-members. Inverse-modelling tasks (ii) and (iii) can be performed when the solid solution of interest is shown experimentally to co-exist with the aqueous phase either in the equilibrium or at the minimum stoichiometric saturation state.DualTh calculations exploit the ability of Gibbs energy minimisation (GEM) algorithms to find simultaneously two numerical solutions of the isobaric–isothermal chemical equilibrium speciation problem: (1) primal solution x — a vector of amounts of components (species) in phases; and (2) dual solution u — a vector of chemical potentials of stoichiometry units (usually chemical elements and charge). Conversely, the chemical potential of a phase component can be found in two complementary ways: (i) primal via its standard-state potential, concentration and activity coefficient (the latter two are functions of the x vector); and (ii) dual through its formula stoichiometry multiplied by the u vector. The DualTh methods compare primal and dual values of the chemical potential in simple and straightforward equations that can be easily computed in a spreadsheet, or implemented in GEM geochemical modelling codes.  相似文献   

6.
The iron titanium oxide phases ulvite, ilmenite and ferropseudobrookite were synthesized in equilibrium with metallic iron at 1000 ° C, 1130 ° C and 1300 ° C in CO2/H2 gas mixtures.The composition of the phases were determined by wet chemical and electron microprobe analyses and by direct oxygen determination.The chemical composition of the Fe-Ti oxide phases in equilibrium with metallic iron is sensitively influenced by temperature and by bulk composition.Ulvite in equilibrium with wüstite does not contrivalent titanium in the whole temperature range up to the eutectic temperature at 1312 °C.Ulvite+ilmenite phase assemblages contain trivalent titanium only at temperatures above 1200 ° C.A ferropseudobrookite phase is stable under the given conditions at temperatures above 1068 °C (Ender and Woermann, 1977).Ferropseudobrookite in equilibrium with metallic iron always contains trivalent titanium.Deviations from stoichiometric compositions of the solid solution phases are generally small. Thus recalculation of microprobe data to stoichiometric solid solutions does not involve a major error.From: Bruno Simons, Diplomarbeit Aachen, October 1974  相似文献   

7.
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 (CaxMg2 − 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.  相似文献   

8.
Thermodynamic modeling of equilibria in the system water–rock–organic acids was used to study the influence of organic acids on Ca and Mg redistribution between a solution and a solid phase in connection with the use of calcites of variable composition CaxMg1–xCO3 as indicators of paleoclimatic environments. In the thermodynamic model, high-molecular humic substances (fulvic + humic acids) were represented by a set of independent metal-binding centers. Therefore, their number was preset based on the given density of proton- or metal-binding sites. The numerical implementation of several geochemical situations involving the dissolution/deposition of calcites with different Mg contents showed that the main effect of fulvic and humic acids is the acidification of solutions and the reduction of carbonate stability. Although humic substances can play an important role in fixing Ca and Mg and removing them from solution, their actual concentrations in natural media (<<1 g/L) do not cause significant changes in the composition of CaxMg1–xCO3 phases. On the other hand, there is quantitative evidence that variations in the Mg/Ca ratio in a solution and a solid phase are significantly influenced by the evaporative concentration of Mg-oversaturated solutions, alkalization/acidification during their evolution, or CO2 content variations owing to changes in climate and lake activity.  相似文献   

9.
Reaction-based modeling of quinone-mediated bacterial iron(III) reduction   总被引：1，自引：0，他引：1  
This paper presents and validates a new paradigm for modeling complex biogeochemical systems using a diagonalized reaction-based approach. The bioreduction kinetics of hematite (α-Fe2O3) by the dissimilatory metal-reducing bacterium (DMRB) Shewanella putrefaciens strain CN32 in the presence of the soluble electron shuttling compound anthraquinone-2,6-disulfonate (AQDS) is used for presentation/validation purposes. Experiments were conducted under nongrowth conditions with H2 as the electron donor. In the presence of AQDS, both direct biological reduction and indirect chemical reduction of hematite by bioreduced anthrahydroquinone-2,6-disulfonate (AH2DS) can produce Fe(II). Separate experiments were performed to describe the bioreduction of hematite, bioreduction of AQDS, chemical reduction of hematite by AH2DS, Fe(II) sorption to hematite, and Fe(II) biosorption to DMRB. The independently determined rate parameters and equilibrium constants were then used to simulate the parallel kinetic reactions of Fe(II) production in the hematite-with-AQDS experiments. Previously determined rate formulations/parameters for the bioreduction of hematite and Fe(II) sorption to hematite were systematically tested by conducting experiments with different initial conditions. As a result, the rate formulation/parameter for hematite bioreduction was not modified, but the rate parameters for Fe(II) sorption to hematite were modified slightly. The hematite bioreduction rate formulation was first-order with respect to hematite ”free“ surface sites and zero-order with respect to DMRB based on experiments conducted with variable concentrations of hematite and DMRB. The AQDS bioreduction rate formulation was first-order with respect to AQDS and first-order with respect to DMRB based on experiments conducted with variable concentrations of AQDS and DMRB. The chemical reduction of hematite by AH2DS was fast and considered to be an equilibrium reaction. The simulations of hematite-with-AQDS experiments were very sensitive to the equilibrium constant for the hematite-AH2DS reaction. The model simulated the hematite-with-AQDS experiments well if it was assumed that the ferric oxide “surface” phase was more disordered than pure hematite. This is the first reported study where a diagonalized reaction-based model was used to simulate parallel kinetic reactions based on rate formulations/parameters independently obtained from segregated experiments.  相似文献   

10.
We present a new formulation to describe the thermodynamics of liquids in the system O-S-Fe. The model is based on an associated regular solution formulation. According to this model, liquids in the O-S-Fe ternary are made up of an equilibrium solution of the six melt species S, Fe, FeO, FeO1.5, FeS and FeOS. The model presented here represents oxygen and sulfur fugacities as well as phase equilibria with stoichiometric solid phases better than models from the literature on O-Fe and S-Fe binaries. Furthermore, this model represents a substantial improvement on the model of Kress (1997), which is the only other thermodynamic model available in the ternary system. Asymmetric regular solution parameters are required along the FeO join in order to reproduce experimental data with the chosen list of species. Symmetric regular solution parameters are required along the Fe-S binary. Mixing between any of the species considered and FeOS close to ideal. The associated solution model presented here will serve as a more solid foundation for future models in O-S-Fe- Ni-Cu liquids. Efficient and robust strategies for calculating equilibrium speciation and estimating model parameters are presented. Received: 15 June 1999 / Accepted: 5 February 2000  相似文献   

11.
The equations relating element distribution and pH are derived for systems containing an ideal solid solution in equilibrium with an ideal aqueous solution, assuming no polymeric complexes form in the aqueous solution and the solid solution does not contain molecular units with multiple atoms of the substituting elements. These expressions demonstrate that the ratio of the partition coefficients describing element distribution for a system containing a multi-component solid solution is inversely proportional to the solubilities of the end member components at any given pH raised to the power equal to the ratio of the sum of the stoichiometric coefficients of the end-member salt to the stoichiometric coefficient of the substituting radical. The coefficient describing distribution between the aqueous phase and a two-component solid solution is equal to the inverse of the ratio of the end member solubilities raised to the above power. Element distribution between the two phases will be homogenous at any pH resulting in identical solubilities for the two end-member components, and a reversal in relative solubilities will result in a corresponding reversal in the element preferentially incorporated into the solid solution. Because of the dependence of element distribution on pH, a crystal could develop both zoning and reverse zoning as a result of changes in pH. The distribution coefficient could provide information regarding the pH of the aqueous solution at the time of mineral formation if independent evidence establishes the ratio of end-member components in the aqueous phase. The equations describing element distribution may be expressed in terms of the solubility products of the end-member components and the ionization constants of the substituting radicals. Based on the relative values of the ionization constants, pH intervals can be established in which only the concentration of a single complex for each substituting radical need be considered. Within such an interval, the curve of the log of the distribution coefficient vs. pH is linear with a slope equal to the difference in the charges of the two complexes. This approach to the examination of element distribution is developed in some detail for the geologically important case of a two component solid solution having composition (A2+, B2+) X2?.  相似文献   

12.
Equilibrium reactions involving Cu(II) and As(V) have been studied with respect to formation of complexes in aqueous solutions as well as formation of solid phases. Potentiometric titrations performed at 25 °C (I = 0.1 M Na(Cl)) and at different Cu to As ratios gave no evidence for the existence of Cu(II) arsenate complexes in solution below the pH of the precipitation boundaries (pH ≈ 4), irrespective of the Cu to As ratio and pH. Mixing of solutions of Cu(II) and As(V) at different proportions and adjusting pH to values ranging from 4 to 9 resulted in precipitation of five different solid phases. The elemental composition of the solids was determined using X-ray Photoelectron Spectroscopy, and Environmental Scanning Microscopy-Field Emission Gun equipped with an energy dispersive spectroscopy detector. The average Cu/As ratio was determined by dissolving the solids. Total soluble concentrations of the components Cu(II) and As(V), as well as the basicity of the solid phases were determined by analysis of aqueous solutions. Based upon these experimental data the stoichiometric composition of the solid phases and their stability were determined. The resulting equilibrium model includes the solid phases Cu3(AsO4)2, Cu3(AsO4)(OH)3, Cu2(AsO4)(OH), Cu5Na(HAsO4)(AsO4)3 and Cu5Na2AsO4)4, where Cu5Na(HAsO4)(AsO4)3 and Cu5Na2(AsO4)4 have not been reported previously. In 0.1 M Na(Cl), Na+ was found to be a significant component in two of the solid phases. The Cu5Na2(AsO4)4 was formed in weakly alkaline conditions with pNa < 2.5. Stability constants for all solid phases have been determined. Distribution diagrams as well as predominance area (pNa-pH) diagrams are presented to illustrate stability fields of the different solid phases.  相似文献   

13.
The structure and reactivity of the dolomite (104)-water interface was probed in situ with high resolution X-ray reflectivity and surface force microscopy at room temperature. Measurements in stoichiometric solutions alternating between saturated and supersaturated (log IAP/K = 2.3) conditions show that the dolomite surface termination readily changes in response to solution composition, but these changes are self-limiting and partially irreversible. The freshly cleaved dolomite (104) surface in contact with the saturated solution has a stoichiometric termination, a distinct surface hydration layer and small surface structural displacements, similar to those observed previously at the calcite-water interface. After reaction with supersaturated solutions dolomite is terminated by a two-layer thick Ca-rich film with substantial structural displacements of the cations. With subsequent exposure to a saturated solution this surface was transformed to an interfacial structure different from the freshly cleaved surface, having a reduced density of the outermost surface layer and a Ca-rich second layer. These results provide new insight into the lack of dolomite growth in modern carbonate environments (i.e., the “dolomite problem”), suggesting that this behavior is associated with a combination of thermodynamic and kinetic factors, including (1) growth of compositionally modified epitaxial CaXMg2−X(CO3)2 layers having thicknesses limited by lattice strain, (2) slow incorporation of Mg during layer growth, and (3) partial irreversibility of surface reactions.  相似文献   

14.
Speciation of aqueous calcium chloride and the solubility of wollastonite represented by the reaction wollastonite + 2HCl° → CaCl2° + quartz + H2O were experimentally investigated at 1 and 2 kbar in the range 425–600°C using rapid-quench hydrothermal techniques and a modified Ag + AgCl buffer technique (Frantz and Popp, 1979). Variation in the measured concentration in HCl° as a function of total dissolved calcium was used to identify associated aqueous CaCl2° as the predominant calcium species in the fluid at temperatures above 500°C at 2 kbar. The data were used to calculate the equilibrium constant for the above reaction as a function of temperature and pressure, from which the difference in Gibbs free energy of formation between CaCl2° and HCl° at 1 and 2 kbar, 450°–600°C was calculated. Solubility constants for minerals in the system MgO-CaO-SiO2-H2O-HCl-CO2 were calculated using the data from this study and from Frantz and Popp (1979). Calculated mineral solubilities were used to calculate the solution compositions and solid alteration products resulting from interactions of a Ca-Mg silicate mineral (diopside) with hydrothermal solutions containing a range of different total chloride concentrations. High total chloride (2.0 m) in the solution results in Si-Mg enrichment in the solids and Ca enrichment in the fluid, whereas low total chloride (0.008 m) results in Mg enrichment in the solids and Ca-Si enrichment in the fluid.  相似文献   

15.
Tremolite (CaxSr1–x)2Mg5[Si8O22/(OH)2] and diopside (CaxSr1–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 (tr0.02Sr-tr0.98) and Sr-diopside (di0.01Sr-di0.99) 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 Å3 for tremolite to 938.21 Å3 for Sr-tremolite. For diopside the unit cell volume increases 4.87 % from 439.91 Å3 for diopside to 461.30 Å3 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.  相似文献   

16.
Phase relations in the system TiO2–ZrO2 were examined in the pressure range of 3.5–12?GPa at 1,800?°C, using multianvil apparatus. At 1,800?°C, TiO2 rutile transforms to αPbO2 structure at 10?GPa, and the αPbO2-type solid solution is stable in compositional range between TiO2 and about (Ti0.6, Zr0.4)O2 at 3.5–12?GPa. Combination of the present results with the published data at 0–3?GPa demonstrates that continuous solid solution with the αPbO2-type structure is stable between TiO2 and (Ti1?x , Zr x )O2 (x?≈?0.6) at 0–12?GPa. This indicates that both the αPbO2-type TiO2 and srilankite Ti2ZrO6 with the same structure belong to the continuous solid solution system though the two phases have been regarded as different minerals. With increasing ZrO2 content, lattice parameters of a- and c-axes of the αPbO2-type solid solution increase, but b-axis is almost constant or slightly decreases. At higher pressure, the αPbO2-type solid solution dissociates into two phases, αPbO2-type phase and tetragonal zirconia. Srilankite with more TiO2-rich composition than Ti2ZrO6 might be found in natural rocks derived from the deep upper mantle.  相似文献   

17.
Equilibrium constants at stoichiometric saturation with respect to various magnesian calcite compositions were measured using free-drift dissolution rate data and inverse time plots to estimate equilibrium pH. The equilibrium constants determined for two ultrasonically cleaned and annealed biogenic magnesian calcites (12 and 18 mole % MgCO3) in CaCl2 + MgCl2 media at two Mg:Ca molar ratios (1:5 and 5:1) are about three times smaller than those previously reported by Plummer and Mackenzie (1974). These equilibrium constants are not affected by changes in initial pH value, solid:solution ratio, or solution Mg:Ca molar ratio when the ion activity product is expressed in the fractional exponent form. Other models for expression of the equilibrium ion activity product fail to yield consistent values in solutions of different Mg:Ca molar ratios.Experiments performed using crushed samples not ultrasonically cleaned and annealed yield equilibrium constants which vary with solid:solution ratio. Those performed at high solid:solution ratios yield values which approach those previously reported. Submicron size particles and crystal strain induced by crushing the biogenic carbonates may cause more rapid dissolution rates and, hence, overestimation of the solubility of samples not prepared so as to minimize these effects. Thus, the large range in reported solubilities of magnesium calcites may be a result of differences in sample preparation procedure.The results of these measurements shift the thermodynamic equivalence point of aragonite and magnesian calcite from 7.5 mole % MgCO3 up to 12 mole % MgCO3 and prompt a reassessment of models for carbonate diagenetic reactions in natural environments.  相似文献   

18.

Background

The interaction between Ca-HAP and Pb2+ solution can result in the formation of a hydroxyapatite–hydroxypyromorphite solid solution [(PbxCa1?x)5(PO4)3(OH)], which can greatly affect the transport and distribution of toxic Pb in water, rock and soil. Therefore, it’s necessary to know the physicochemical properties of (PbxCa1?x)5(PO4)3(OH), predominantly its thermodynamic solubility and stability in aqueous solution. Nevertheless, no experiment on the dissolution and related thermodynamic data has been reported.

Results

Dissolution of the hydroxypyromorphite–hydroxyapatite solid solution [(PbxCa1?x)5(PO4)3(OH)] in aqueous solution at 25 °C was experimentally studied. The aqueous concentrations were greatly affected by the Pb/(Pb + Ca) molar ratios (XPb) of the solids. For the solids with high XPb [(Pb0.89Ca0.11)5(PO4)3OH], the aqueous Pb2+ concentrations increased rapidly with time and reached a peak value after 240–720 h dissolution, and then decreased gradually and reached a stable state after 5040 h dissolution. For the solids with low XPb (0.00–0.80), the aqueous Pb2+ concentrations increased quickly with time and reached a peak value after 1–12 h dissolution, and then decreased gradually and attained a stable state after 720–2160 h dissolution.

Conclusions

The dissolution process of the solids with high XPb (0.89–1.00) was different from that of the solids with low XPb (0.00–0.80). The average K sp values were estimated to be 10?80.77±0.20 (10?80.57–10?80.96) for hydroxypyromorphite [Pb5(PO4)3OH] and 10?58.38±0.07 (10?58.31–10?58.46) for calcium hydroxyapatite [Ca5(PO4)3OH]. The Gibbs free energies of formation (ΔG f o ) were determined to be ?3796.71 and ?6314.63 kJ/mol, respectively. The solubility decreased with the increasing Pb/(Pb + Ca) molar ratios (XPb) of (PbxCa1?x)5(PO4)3(OH). For the dissolution at 25 °C with an initial pH of 2.00, the experimental data plotted on the Lippmann diagram showed that the solid solution (PbxCa1?x)5(PO4)3(OH) dissolved stoichiometrically at the early stage of dissolution and moved gradually up to the Lippmann solutus curve and the saturation curve for Pb5(PO4)3OH, and then the data points moved along the Lippmann solutus curve from right to left. The Pb-rich (PbxCa1?x)5(PO4)3(OH) was in equilibrium with the Ca-rich aqueous solution.
Graphical abstractLippmann diagrams for dissolution of the hydroxypyromorphite–hydroxyapatite solid solution [(PbxCa1?x)5(PO4)3OH] at 25??C and an initial pH of 2.00.
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19.
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20.
An experimental study using piston-cylinder, Bridgman anvil and diamond anvil cell techniques was undertaken to study the effect of pressure on the composition of Fe x O in equilibrium with Fe. At constant temperature the value of x first increases and then decreases with increasing pressure. The rate of change of x is a function of temperature. We have theoretically calculated the variation of the composition of wüstite with pressure and temperature. The initial increase of x with pressure for P<10 GPa occurs because the partial molar volume of FeO in Fe x O is smaller than the molar volume of Fe, favouring an increase in stoichiometry of Fe x O. To reproduce the experimentally observed decrease in x above 10GPA, the bulk modulus of Fe x O must vary strongly with x for x?0.96, causing a rapid increase in the partial molar volume of Fe in Fe x O. Continuation of a strong sensitivity of K to x in Fe x O for x?0.96, however, leads to absurdly low molar volumes of Fe x O at high pressure and no equilibrium between Fe and Fe x O exists. Observations therefore require a reduced sensitivity of K with x for x<0.96, achieved by a negligible variation of K 0 with x for x<0.96, or a strong variation of dK/dP with x, or perhaps both.  相似文献   

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