Surface stress potential

Surface Stresses and Edge Energies. Some surface tension values, that is, values of the surface stress t, are included in Table VII-2. These are obtained by applying Eq. Vll-5 to the appropriate lattice sums. The calculation is very sensitive to the form of the lattice potential. Earlier calculations have given widely different results, including negative r [43, 51, 52]. 

Sco et al (1987) employed the piezoelectric surface stress technique to study the behaviour of gold on electrochemical cycling in aqueous sulphate solution. They obtained plots of u and vs. E at a range of pH from 0.3 to 14 and a typical example of these is shown in Figure 2.12 which shows the plots obtained at pH 3. It should be emphasised that the data in Figure 2.12 were obtained dynamically by simultaneously scanning the potential in the... 

In addition to examining the surface structure, the STM may also be used as a transducer to monitor deformation associated with potential dependence of the surface stress and associated electrocapillary phenomena at solid electrodes. In this instance, the high z-sensitivity of the STM is used to follow the minute displacements of a surface, which is supported in a cantilever geometry [54,55],... 

Recently, the change in the interfacial free energy and surface stress has been determined for Au(lll) electrodes in electrolytes containing nonspecrfically adsorbed F anions. This behavior was compared to that of specifically adsorbed S04 anions [43]. It was found that the surface stress is more sensitive to the changes in electrode potential than the interfacial free energy. 

A relation between the surface stress and the structural change within the Pb UPD layer on Au film electrode has been studied, applying a bending beam method [487]. A maximum in the surface stress versus potential dependence emerged at the onset of UPD, similarly as in electrocapillary curve. 

The gradient composition in FGMs not only results in a spatial variation in properties but will also generate residual stresses, which will affect the mechanical properties. One of the potential advantages of FG components is the positive influence of compressive residual surface stresses on the strength and wear resistance. A correct design of the gradient for an optimal distribution of the residual stresses is therefore important, as discussed in this chapter. 

Mathematically, this problem bears some resemblance to those considered above. The governing partial differential equation is still Eq. (6), and on the surfaces boundary conditions of constant potential, constant charge density or linear regulation [i.e., Eq. (45)] must be imposed. However, a further constraint arises from the need to satisfy mechanical equilibrium at the interface, and it is this new condition that provides the mathematical relation needed to calculate the interface shape. The equation is the normal component of the surface stress balance, and it is given by [12]... 

In most cases the variation in surface stress has been determined indirectly by measuring the potential dependence of the strain (i.e., electrode deformation) and then obtaining the variation in stress from the appropriate form of Hookes law (-> bending beam or cantilever beam method, bending plate methods e.g., the measurement of the deformation of the electrode with the help of a —r Kosters laser interferometer). 

Stockholm convention 60 stoichiometric number 42 stokes 112 strain 12 bulk 12 linear 12 shear 12 volume 12 stress 12, 72 Strouhal number 65 structural formula 45 structure factor 36 sublimation 51 substance concentration 5 substitution structure distance 24 sum over states 39 surface amount 63 surface charge density 14, 59 surface chemistry 63 surface concentration 42 surface coverage 63 surface density 12 surface electric potential 59 surface excess 63 surface excess concentration 63 surface pressure 63 surface properties 64 surface tension 12, 48, 63 susceptance 15 svedberg 111 symbols 5... 

A relation between the surface tension y and the surface stress T can be directly derived from the Gibbs-Duhem equation, Eq. (7). At constant temperature, chemical potentials, and electric potential we have... 

The surface stress of some solids in a liquid might be determined by measuring solubility changes of small particles [97,98]. As small liquid drops have an increased vapor pressure in gas, small crystals show a higher solubility than larger ones. The reason is that, due to the curvature of the particles surface, the Laplace pressure increases the chemical potential of the molecules inside the particle. This is described by the Kelvin equation, which can be written (Ref. 3, p. 380)... 

In a somewhat related experiment, surface stress changes due to an applied electric potential were determined by measuring the bending of a circular plate. This bending was measured interferometrically 1169-172] or with a STM 1173.174],... 

This idea was confirmed experimentally by Berschtein [29]. The solid surfaces contain potentially reactive interatomic bonds, therefore, generation and propagation of crystal fracture and under the action of stresses (applied and residual) in the presence of water proceed via mechanically induced hydrolysis. The experimental data obtained for loaded bonds in quartz in the presence or absence of water were treated according to equation... 

The meteorological input required in the Unified EMEP model are the 3D horizontal and vertical wind fields, specific humidity, potential temperature cloud cover, and precipitation. The transferred surface 2D fields for use in the chemical transport model are surface pressure, 2 m temperature, surface flux of momentum, sensible and latent heat, and surface stress. All variables are given in 3-h interval. Table 13.1 lists the variables and their main purposes in the EMEP model. Inside the model different boundary layer parameters like the stability, eddy diffusion, and mixing height are calculated based on MOST. 

A second consequence of the surface valence charge depletion relates to surface stress. It seems to now be rather well-established that clean unreconstructed elemental metal surfaces are in a state of tensile stress [60]. This means that the surface atoms would prefer to have a shorter interatomic spacing parallel to the surface. In some cases (such as Au(lll) and Au(lOO) surfaces) this effect can lead to a reconstruction of the surface layer to a (more) close-packed overlayer (e.g. [61]). However, in most metals the surface atoms that are under tensile stress are locked in the periodic potential of the underlying bulk. Substituting some fraction of the atoms in such a surface by... 

The cantilever deflection results from a change in the surface stress as the electrode potential is varied. The surface stress is related to the surface energy by the Shuttleworth equation ... 

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