Structural relaxations computational model

Intercalation of cations into a framework of titanium dioxide is a process of wide interest. This is due to the electrochromic properties associated with the process (a clear blue coloration results from the intercalation) and to the system s charge storage capabilities (facilitated by the reversibility of the process) and thus the potential application in rocking-chair batteries. We have studied alkali-metal intercalation and ion diffusion in the Ti02 anatase and spinel crystals by theoretical methods ranging from condensed-phase ab initio to semiempirical computations [65, 66]. Structure relaxation, electron-density distribution, electron transfer, diffusion paths and activation energies of the ion intercalation process were modeled. 

Notably stronger structural relaxation should accompany the formation of sites on the MgO(OOl) surface that are characterized by a reduced coordination number of ions, such as point (vacancy) or extended (step, edge, comer, etc.) defects [87]. This new situation is adequately reproduced by DF cluster models. For instance, for the edge formed by the intersection of (001) and (100) surfaces of MgO, a notable inward (into the substrate) displacement of Mg and O ions from the bulk-terminated position was computed in the [101] direction, by 15 and 12 pm, respectively [95]. Comer three-coordinated Mgsc cations are predicted to move even further, 32 pm, along the [111] direction, "down" to the three O anion neighbors [60], Opposite displacements of the Mg and O ions, to partly restore the bulk-terminated geometry, take place when an adsorbate effectively repairs the reduction of coordination numbers at these defects on clean MgO surface, e.g. Refs. 60 and 95. 

There are three distinctly different ways to terminate a (0001) surface in alumina a single layer of Al ions, a double layer of Al " ions, or only ions. This basal-plane surface of alumina has a lower energy than the rhombohedral-plane surface because the single outer layer of AF ions can relax by moving in toward the bulk. We know this from computer modeling. It is very difficult to observe structure experimentally. 

These data show that the inclusion of structural relaxation has a dramatic effect The stability order is almost completely reversed, and the surface formation energy spans a much more narrow range of values with respect to the unrelaxed data. Relaxation is then important. For example, the (0001) surface, which is the most unstable unrelaxed face, becomes the most stable when relaxation is taken into account. It is worth noting that slab models with more than 20 atomic layers are required to reach full convergence on stability order. The computed trend for the unrelaxed surfaces is close to that obtained from classical simulations within a fully ionic model by Tasker " and Mackrodt, whereas the three sets differ after relaxation ... 

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