Surface formation energy

Within the slab model approach, the surface formation energy is computed as... 

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 ... 

Periodic DFT methods are well suited to the calculation of bulk and surface properties. The periodic simulation method requires that a slab of some finite thickness be simulated the slab will have two surfaces of area, A iab, exposed to the vacuum and a number of atoms A siab- The consequences of this simulation method are that the surface formation energy can be written as... 

The area term has a prefactor of 2, indicating that within the simulation two surfaces have been formed. Adsorption of oxygen to the surface in some arrangement, X, from some oxygen source of chemical potential jA-o results in a new surface formation energy that can be written as the sum of the clean slab and the changes due to adsorption ... 

Writing the surface formation energy of the oxygen containing surface this way is convenient because it makes explicit that surface phase stability can be studied by examining... 

Tasker s classification of surfaces allows some qualitative conclusions to be made about the surface stability. The quantitative calculations of the surface formation energy in slab models are considered in the next sections. 

The cleaning process proceeds by one of three primary mechanisms solubilization, emulsification, and roll-up [229]. In solubilization the oily phase partitions into surfactant micelles that desorb from the solid surface and diffuse into the bulk. As mentioned above, there is a body of theoretical work on solubilization [146, 147] and numerous experimental studies by a variety of spectroscopic techniques [143-145,230]. Emulsification involves the formation and removal of an emulsion at the oil-water interface the removal step may involve hydrodynamic as well as surface chemical forces. Emulsion formation is covered in Chapter XIV. In roll-up the surfactant reduces the contact angle of the liquid soil or the surface free energy of a solid particle aiding its detachment and subsequent removal by hydrodynamic forces. Adam and Stevenson s beautiful photographs illustrate roll-up of lanoline on wood fibers [231]. In order to achieve roll-up, one requires the surface free energies for soil detachment illustrated in Fig. XIII-14 to obey... 

F1 NMR of chemisorbed hydrogen can also be used for the study of alloys. For example, in mixed Pt-Pd nanoparticles in NaY zeolite comparaison of the results of hydrogen chemisorption and F1 NMR with the formation energy of the alloy indicates that the alloy with platinum concentration of 40% has the most stable metal-metal bonds. The highest stability of the particles and a lowest reactivity of the metal surface are due to a strong alloying effect. 

Crystals have spatially preferred directions relative to their internal lattice structure with consequences for orientation-dependent physico-chemical properties i.e., they are anisotropic. This anisotropy is the reason for the typical formation of flat facetted faces. For the configuration of the facets the so-called Wullf theorem [20] was formulated as in a crystal in equihbrium the distances of the facets from the centre of the crystal are proportional to their surface free energies. ... 

Here A Gx is the free energy of chain break and formation of new bonds Gm is the free energy of chain surface bond formation Gs is the free energy of the surface formation Gex.s is the excessive combinatorial free energy stipulated by different disposition of chain molecules on the surface ziGcom.s is the combinatorial free energy stipulated by different disposition of intermolecular chain surface bonds on chain molecule. The rest of the G terms possess the abovementioned physical sense. Index ( ) relates to the end state of the system. 

In section 3.6.3 we mentioned that in growth on a curved face the strain surface free energy os takes the role the lateral surface free energy tr played in the flat surface case, namely that of a barrier to the formation of the first stem. This analogy cannot be made since, in contrast to surface free energy is associated with the deposition of any stem. Therefore and because of its physical origin (the volume strain) it is closely linked with the free energy of fusion. This is... 

After examining the film breakdown process, we have another question Once broken, how is the film reformed To answer this question, it is necessary to calculate the formation energy for a passive-film nucleus on the film-free surface. The contribution of chemical energy is newly added to the electrocapillary energy. The total energy is thus given by... 

In Equation (1) we assume particles are spherical with radius r. The chemical potentials are and for the particle and the solvated atoms or molecules, respectively, n is the number of moles per unit volume and a is the surface energy (or tension). Since the particle has formed, we can take the bulk term as negative with Ap = p — Ps<0 hence favorable, but formation of the surface costs energy so is positive and unfavorable. These two functionalities yield a maximum in AG. Differentiation of Equation (1) finds this maximum to be at a critical size Vc given by... 

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