Behavior of the Chemical Potential in Calcite and Magnesite Crystals: A Damped Harmonic Oscillation

Abstract

The behavior of the chemical potential of the species CaCO 3 and MgCO 3 in proximity of the (10.4) crystal face of calcite and magnesite is determined at the quantum−mechanical level by adopting a recent calculation strategy conceived in our research laboratory. A very peculiar trend of this quantity from the (10.4) surface to the center of the calcite and magnesite crystals was observed. The highest value of the chemical potential is related to the surface layer, while the lowest one is in correspondence to the underlying layer. Interestingly, the chemical potential converges to the bulk value via a damped oscillatory behavior (DOB). We observed that such DOB is strongly related to the structural modification of the slab caused by the presence of the surface, which produces a damped oscillating behavior of the interplanar distances, d 10.4 , very similar to the one described for the chemical potential. The implications of this finding are discussed.

(10.4) Face of Ordered and Disordered Dolomite, MgCa(CO3)2: A Computational Study to Reveal the Growth Mechanism

“…It is obvious that the cations diffusion will be more effective at higher temperature (i.e., T > 200 • C), being the diffusion coefficient an exponential function of T. It is important to underline that the intra-crystalline diffusion should start only when the disordered layers are far away enough from the interface to be considered bulk layers, that is, when the influence of the interface is negligible and, as a consequence, the minimum of the energy is reached by imposing the ordered structure SC1. However, according to our ab initio calculations performed on calcite and magnesite (10.4) slabs [39], the number of layers influenced by the presence of a surface is approximately four. It is then predictable that the layers below these ones can be considered bulk layers and, as a consequence, they will be ordered to reproduce the structure SC1.…”

“…The surface energy of the (10.4) face of calcite (0.507 J/m 2 ) is slightly higher than that of magnesite (0.493 J/m 2 ). Previous surface energy calculations on the (10.4) face of calcite and magnesite were performed by our research group, always using the B3LYP Hamiltonian but considering a poorer basis sets: 0.508 and 0.501 J/m 2 for calcite and magnesite, respectively [39]. These small ∞) when increasing the thickness of the slab, hindering in this way the comparison with the others surface terminations.…”

“…In addition, it is noteworthy to highlight that our calculations were performed at 0 K, and the vibrational energy and entropy of the slabs were not evaluated. However, according to the ab initio calculations performed by Bruno et al [39], the surface energies at 298 K of the (10.4) face of calcite (0.459 J/m 2 ) and magnesite (0.452 J/m 2 ) are reduced by the same percentage (~10%) with respect to the values at 0 K. Then, we can suppose that the surface energies of the (10.4) faces of dolomite are also reduced by the same percentage, and that the temperature does not affect their ratio.…”

The Flotation Separation of Magnesite and Limonite Using an Amine Collector

“…When the pH value increased from 2.1 to 11, the electric potential of magnesite decreased from 15.05 mV to −13.91 mV. When the pH value was 6.0, the magnesite electrical potential is zero, con-sistent with references [24,25]. When the medium pH is greater than the zero point of magnesite (pH = 6:0), the surface of magnesite is negatively charged.…”