G.H. Nancollas

Kink densities along a crystal surface step at low temperatures and under nonequilibrium conditions

The kink density along a (01) step on the (001) face of a Kossel crystal is derived from a kinetic steady state approach by considering the elementary events at the step. When the thermal energy kT is small compared with the kink formation energy ϵ, the kink density, ϱ, is found to be a function of the saturation ratio, S. For S>1, ϱ = 2a-1S12 exp(-ϵ/kT), whil S <1, ϱ = 2a-1 exp(-ϵ/kT)/(2-S)12. At S = 1, both equations reduce to the expression obtained by statistical thermodynam arguments. The limiting rate laws for growth and dissolution of a vicinal surface with steps originating from a screw dislocation are also obtained. The current finding may provide a theoretical background for interpreting the observed growth and dissolution kinetics for many sparingly soluble salts in aqueous solutions.

Influence of calcium/sulfate molar ratio on the growth rate of calcium sulfate dihydrate at constant supersaturation

The growth kinetics of calcium sulfate dihydrate (CSD) has been investigated using the constant composition method over a range of calcium/sulfate molar ratios, r, in supersaturated solutions (0.17<r<5.0, at ionic strength, I=0.500m with potassium chloride as the supporting electrolyte and 0.08<r<10.0 at I=1.00m in sodium chloride medium). In spite of constancy of ion activity product, the rate increases with decreasing Ca/SO4 molar ratio, indicating that the rate of crystal growth is not merely a function of the thermodynamic driving forces but also depends upon the relative concentrations and characteristics of individual lattice ions.

Dual constant composition method and its application to studies of phase transformation and crystallization of mixed phases

Abstract In a novel approach, a dual constant composition (DCC) technique has been developed for the investigation of concurrent dissolution and growth processes such as crystalline phase transformation, as well as growth of mixed crystalline phases. DCC utilizes two potentiostats and electrode sets to control simultaneous reactions in the same medium. The kinetics of concurrent dissolution or growth of dicalcium phosphate dihydrate (DCPD) and the growth of octacalcium phosphate (OCP) were studied.

Dissolution deceleration of calcium phosphate crystals at constant undersaturation

The dissolution of dicalcium phosphate dihydrate (CaHPO4·2H2O) and octacalcium phosphate (Ca8H2(PO4)6·5H2O) has been followed as a function of time at constant undersaturations. The rate, after correction for changes in crystal surface area, decreases with time in spite of the sustained driving force, suggesting a decrease in the density of active sites on the crystal surface. This deceleration becomes more pronounced as the undersaturation decreases, leading to an increase in the effective dissolution order. The results of experiments in both Ultrapure and Reagent grade electrolyte solutions suggest that gradual contamination of the crystal surface is unlikely to account for the rate deceleration which may be interpreted by a decrease in the dislocation density during dissolution.

Intergrowth of calcium phosphates: an interfacial energy approach

A factor which is usually ignored in discussions of the induced crystallization of one phase by the surface of another is the surface free energy of the nucleus/substratum interface. Interfacial energies of hydroxyapatite (HAP), octacalcium phosphate (OCP) and fluorapatite (FAP) microcrystals against aqueous solutions, measured using a thin-layer wicking technique, were 9.0, 4.3 and 18.5 mJ m−2, respectively. The calculated low interfacial energy, 0.93 mJ m−2, between OCP and HAP provides strong support for the suggestion that OCP is the first forming phase that induces HAP crystallization in calcium phosphate precipitation reactions. Using the constant composition kinetics method, the nucleation and growth of OCP on titanium oxide surfaces were investigated. The interfacial energy calculated from the nucleation and growth data compared favorably with that obtained by thin layer wicking. Extending the interfacial energy approach to polymeric substrata such as poly(methyl methacrylate) (PMMA), and the radiofrequency glow discharge treated PMMA demonstrates, in predicting the ability of surfaces to induce mineral nucleation, the importance of the Lewis base parameter.

The growth of dicalcium phosphate dihydrate on octacalcium phosphate at 25°C

The crystallization of calcium phosphate phases from metastable supersaturated solutions following seeding with well characterized octacalcium phosphate [OCP) has been studied at 25°C, using a constant composition method. At pH 6.00, and at low supersaturation (σ<1.02), OCP is grown, whereas at higher supersaturation, dicalcium phosphate dihydrate (DCPD) nucleates and grows on the OCP seed, after well-defined induction periods. The linear dependencies of the logarithm of the induction periods upon (log supersaturation)−2, is indicative of a surface nucleation process for DCPD with an effective surface energy of 7±1 mJ m−2.

Fluorapatite growth kinetics and the influence of solution composition

Although the rates of dissolution and growth of crystals are usually expressed as a function of the thermodynamic driving forces, the actual stoichiometry of the solutions may be an important factor. The kinetics of fluorapatite (FAP) growth on FAP seed crystals has been investigated using the constant composition (CC) method in supersaturated solutions containing both stoichiometric and nonstoichiometric crystal lattice ion molar ratios. The rate of reaction varies with the ζ-potential of the crystal surfaces, decreasing as the latter approaches zero. Flocculation is also shown to be an important factor determining the reaction rates. Rate data as a function of supersaturation is interpreted in terms of the Burton-Cabrera-Frank model. Calculated interfacial free energies of the FAP crystals are compared to the values obtained by independent experiments.

The influence of magnesium ion on the kinetics of crystal growth and dissolution of strontium fluoride

Abstract The influence of magnesium ion on the growth and dissolution of strontium fluoride crystals has been studied over an ionic strength range, 0.071–0.150 mol dm −3 , in aqueous solutions at constant super- and under-saturation using a constant composition method. The rates of reaction, expressed in terms of the relative super- and under-saturations show an effective order, n , of 3.7±0.1 at relative super-saturations 0.95 to 1.86 and 1.1±0.1 at relative under-saturations of 0.06 to 0.2. However, under conditions close to equilibrium, both growth and dissolution approach a parabolic rate law probably reflecting surface controlled reactions. The addition of magnesium ions, even at relatively low concentration (10 −6 mol dm −3 ), reduced the rates of both growth and dissolution. Moreover, the effect was enhanced in the regions of parabolic kinetics. The influence of magnesium ions on the strontium fluoride reactions may be interpreted in terms of a Langmuir-type adsorption isotherm.

Constant composition kinetics studies of the simultaneous crystal growth of alkaline earth carbonates; the calcium/strontium system

Abstract The kinetics of crystal growth of strontium carbonate have been investigated over a range of supersaturation using the constant composition method. The rate is second order in relative supersaturation suggesting a surface controlled spiral growth mechanism and the reduction in rate in the presence of calcium ions can be interpreted in terms of a Langmuir adsorption isotherm with an affinity coefficient of (1.4±0.35)X10 4 L mol -1 . By using ion specific hydrogen and calcium ion electrodes to control titrants for strontium carbonate and calcium carbonate crystallization, respectively, a dual constant composition method has been developed for studying the simultaneous crystal growth of these phases in solutions supersaturated with respect to both salts. When strontium carbonate seed crystals alone are introduced into the mixed supersaturated solutions, calcium carbonate nucleates at the surface and both alkaline earth carbonates undergo crystal growth. Conversely, strontium carbonate crystal growth is induced at calcite surfaces immediately upon adding these seed crystals to the mixed supersaturated solutions. X-ray data suggest that the presence of strontium ion induces the formation of aragonite having some incorporated strontium ions in the crystal lattice. However, when strontium carbonate is induced at the surface of calcium carbonate seed crystals in the mixed supersaturated solutions, the only calcium carbonate X-ray peaks observed are those characteristic of calcite. The nucleation and subsequent growth reactions are also confirmed by Fourier transformation infrared (FTIR) spectroscopy and energy dispersive X-ray (EDX) analysis.

Crystal growth of strontium fluoride from aqueous solution

The kinetics of growth of strontium fluoride crystals has been studied in aqueous solution at 25 °C using a constant-composition method in which the supersaturation and ionic strength were maintained constant by the addition of titrants consisting of strontium nitrate and potassium fluoride solutions. The rate of crystallization is independent of ionic strength and, at low supersaturation, is best represented in terms of a spiral growth mechanism with a reaction order, n= 2, with respect to relative supersaturation. At higher supersaturations, a greater change in rate of growth with increasing concentration (n≈ 4.3) suggests a polynuclear mechanism. Inhibition of crystallization by the presence of phosphonates can be interpreted in terms of a Langmuir isotherm.