Obtuse Steps Research Articles

Computer simulation of calcite growth inhibition: A study of monophosphonate interaction with calcite

We have performed atomistic surface simulations of the interaction of monophosphonate growth inhibitor ions with the planar and obtuse stepped { 10 1 ¥ 4 } surfaces of calcium carbonate. We show that phosphonate inhibitor ions have a smaller adsorption energy on the planar { 10 1 ¥ 4 } surface compared to the obtuse stepped { 10 1 ¥ 4 } surface in accordance with experiment; and that the binding energy of the inhibitor with the surface is dominated by electrostatic forces. We find that replacement processes which simulate the irreversible incorporation of monophosphonate ions at terrace and step sites are energetically more favourable than those calculated for the diphosphonate ion. The inhibition mechanism proposed to operate for the deprotonated monophosphonate/calcite system is via the binding or incorporation of monophosphonate ions to the calcite obtuse step sites and kink sites thus slowing step flow and thereby destroying and/or delaying the formation of potential kink sites and step assembly.

Surface structures, stabilities, and growth of magnesian calcites: A computational investigation from the perspective of dolomite formation

Atomistic computer modeling methods are used to investigate the surface structures and stabilities of magnesite MgCO 3 and dolomite MgCa(CO 3 ) 2 in comparison with calcite, CaCO 3 . The surfaces are generally more stable than magnesite, but less so than calcite. Upon hydration, the magnesite {101̅4} surface becomes more stable than either calcite or dolomite, due to the less favorable interactions between dolomite surface ions and adsorbing water molecules. The high affinity of the surface magnesium ions for adsorbing water molecules, shown by the large average hydration energy over all surfaces for magnesite (134 kJ/mol), is negated in the case of dolomite by the inaccessibility of the surface magnesium ions, due to surface relaxations and rotation of the carbonate groups. In addition, the larger lattice spacing of dolomite compared to magnesite disrupts the extensive network of hydrogen bonding between the adsorbed water molecules that are present on the latter, leading to similar average hydration energies for calcite, dolomite, and magnesian calcite surfaces (80-101 kJ/mol). Not only are the dolomite planes under aqueous conditions less stable than their calcite counterparts, dolomite-like surfaces of disordered magnesian calcites are calculated to be more stable than either pure calcite or dolomite surfaces. Extensive molecular dynamics simulations of the growth of CaCO 3 and MgCO 3 at two experimentally observed calcite steps show that, on thermodynamic grounds, Mg is easily incorporated into a growing calcite crystal, but will then inhibit incorporation of further Ca. Furthermore, although the calculations suggest a small energetic advantage (~10 kJ/mol) to ordering of the Ca and Mg ions on the obtuse growth step, a disordered arrangement is favored at the acute growth step and incorporation of Mg is always energetically more favorable than Ca, in accord with the occurrence of highly magnesian calcites in nature.

Molecular Dynamics Simulations of the Growth Inhibiting Effect of Fe2+, Mg2+, Cd2+, and Sr2+ on Calcite Crystal Growth

Molecular dynamics simulations were employed to investigate the initial stages of growth of calcium, magnesium, iron, cadmium, and strontium carbonates at two experimentally observed calcite steps. The calculated energies suggest that in a solution containing all five cations MgCO3, FeCO3, and SrCO3 grow onto the steps in preference to CdCO3 and especially CaCO3. Initial incorporation of all impurity ions is more exothermic at the more open, obtuse step than at the acute step edge (by 44−86 kJ mol-1), although growth next to an existing CaCO3 unit occurs preferentially at the acute step. Growth of full rows of impurity carbonates is highly exothermic for the first row at −25 to −155 kJ mol-1 per MCO3 depending on M (M = Mg, Fe, Cd, Sr), but is much less so for a subsequent row (−5 to −80 kJ mol-1 per MCO3), due to increasing mismatch between the rows of MCO3 at the surface and the underlying calcite lattice, especially for the large strontium ion. Calcite growth, which is a slightly endothermic process in its pure form (on average +1.8 to +35 kJ mol-1 per CaCO3), is severely hindered by the presence of impurity ions at the step edges, when the average enthalpies of the CaCO3 growth process increase to +15 to +75 kJ mol-1 per CaCO3, depending on the type of cation decorating the step. The results of these molecular dynamics simulations therefore suggest that growth of impurity carbonates at the calcite steps is initially an energetically very favorable process, hence competing effectively with growth of pure calcite. Subsequent incorporation of impurities, however, becomes more and more endothermic, until finally the presence of steps decorated with rows of impurities inhibits further crystal growth, in agreement with experimental evidence, which shows for example that the presence of magnesium and iron ions inhibits calcite growth.

Dissolution Kinetics of Calcite in 0.1 M NaCl Solution at Room Temperature: An Atomic Force Microscopic (AFM) Study

Atomic force microscopy (AFM) was used to study the rates of migration of the (10¯1 4) plane of a single-crystal of calcite dissolving in 0.1 M NaCl aqueous solutions at room temperature. The solution pH and PCO 2 controlled in the ranges 4.4 < pH < 12.2 and 0 < PCO 2 10.8, only the velocity of the obtuse steps increased as pH increased, whereas that of acute steps gradually decreased. The dissolution rate of the mineral can be calculated from the measured step velocities and average slope, which is proportional to the concentration of exposed monomolecular steps on the surface. The average slope of the dissolving mineral, measured at pH 5.6 and 9.7, was 0.026 (±0.015). Using this slope, we calculate bulk dissolution rates for 5.3 < pH < 12.2 of 4.9(±3.0) × 10-11 to 1.8(±1.0) × 10-10 mol cm-2 s-1. The obtained dissolution rate can be expressed by the following empirical equation: Rdss = 10-4.66(±0.13)[H+] + 10-3.87(±0.06)[HCO3 -] + 10-7.99(plusmn; 0.08)[OH-] We propose that calcite dissolution in these solutions is controlled by elementary reactions that are similar to those that control the dissolution of other amphoteric solids, such as oxides. The mechanisms include the proton-enhanced hydration and detachment of calcium-carbonate ion pairs. The detachments are enhanced by the presence of adsorbed nucleophiles, such as hydroxyl and bicarbonate ions, and by protons adsorbed to key oxygens. A molecular model is proposed that illustrates these processes.

Molecular dynamics simulation of crystal dissolution from calcite steps

Molecular-dynamics simulations were used to model two stepped ${101\ifmmode\bar\else\textasciimacron\fi{}4}$ surfaces of the calcium carbonate polymorph calcite. The acute monatomic steps were found to be more stable than the obtuse monatomic steps. The initial stages of dissolution from the steps were considered in vacuo and in water. In vacuo ${\mathrm{CaCO}}_{3}$ was shown to dissolve preferentially from the obtuse step. In aqueous environment both stepped surfaces are stabilized by the presence of the water molecules although the relative stabilities remain similar. Using potential parameters that reproduce experimental enthalpies of the dissolution of calcite crystal, the formation of the double kinks on the obtuse step is shown to cost less energy than dissolution from the acute step, probably due to the lower stability of the obtuse surface. The simulations suggest that formation of the kink sites on the dissolving edge of the obtuse step of calcite is the rate determining step and this edge is predicted to dissolve preferentially, which is in agreement with experimental findings of calcite dissolution under aqueous conditions.

The structure and properties of the stepped surfaces of MgO and NiO

Abstract The static lattice computer simulation method has been used to study the structure and properties of high index faces of MgO and NiO. The (10n) series of faces can be considered as stepped (001) surfaces and have been studied for both materials. In addition, the (403) and (302) faces which can be considered as stepped (101) surfaces have been studied for NiO. The calculated energies for steps on the (001) face are 3.72×10−10 and 3.62×10−10 J m−1 for MgO and NiO respectively. The NiO energy also requires correction for the crystal field splitting. The energy of steps on the (101) surface is at least an order of magnitude lower. The interaction between the steps is repulsive but of short range. The large variation of surface energy with angle indicates that torque terms cannot be neglected in the analysis of thermal grooving experiments. The step structure is modified by substantial ionic displacements leading to an obtuse step angle. The structure is qualitatively similar for both NiO and MgO. The large distortions are likely to modify the step properties from those deduced by consideration of only the ideal geometry.

The structure and properties of the stepped surfaces of MgO and NiO

The static lattice computer simulation method has been used to study the structure and properties of high index faces of MgO and NiO. The (10 n ) series of faces can be considered as stepped (001) surfaces and have been studied for both materials. In addition, the (403) and (302) faces which can be considered as stepped (101) surfaces have been studied for NiO. The calculated energies for steps on the (001) face are 3.72×10 −10 and 3.62×10 −10 J m −1 for MgO and NiO respectively. The NiO energy also requires correction for the crystal field splitting. The energy of steps on the (101) surface is at least an order of magnitude lower. The interaction between the steps is repulsive but of short range. The large variation of surface energy with angle indicates that torque terms cannot be neglected in the analysis of thermal grooving experiments. The step structure is modified by substantial ionic displacements leading to an obtuse step angle. The structure is qualitatively similar for both NiO and MgO. The large distortions are likely to modify the step properties from those deduced by consideration of only the ideal geometry.

Complex Frank Loops and Fault Climb

The Burgers vectors of the dislocations bounding steps in the stacking fault in Frank dislocation loops in quenched silver and copper-aluminium alloys have been identified by comparison of experimental electron microscope images and images computed using the Head-Humble technique. The steps in the fault are generally acute, faulted, and bordered by t&lt;llO) stair-rod dislocations. However, obtuse unfaulted steps bordered by t&lt;1l2) Shockley dislocations have also been observed. A characteristic configuration for a stepped loop consists of a triangular region within the main loop with one edge, a dissociated Frank dislocation, forming an edge of the main loop, and the other two edges, acute fault bends bordered by t&lt;llO) dislocations, forming steps in the fault.