Electron wind force

Migration and coalescence of voids as weU as their interactions with grain boundaries (GBs) in the presence of the electric wind force is crucial for understanding the failure mechanism. The first fundamental theory of void migration was developed by Krivoglaz [34] for an isolated spherical void and was later modified by Ho [35] for voids in the vicinity of an external surface. At that, the theory of electron wind force [36, 37] was used to demonstrate a (l/R)-size dependence of void velocity. However, the interaction of a void with GBs during electromigration (EM) was not considered. 

These surface voids migrate under the electron wind force (Figure 7.29). Migration velocity depends on the void size and on the presence of defects (in particular, GBs). 

An initially hemispherical shaped void, under the influence of an electric current, at the surface of a thin-fihn confined dielectric is considered. Its planar boundary is a dielectric and the spherical surface is copper. The evolution of the void in the absence of bulk diffusion is governed by two forces (a) the electron wind force that pushes and eventually redistributes the surface atoms, trying simultaneously to shift the void and change its shape and (b) the surface tension of the void that tries to minimize the void surface energy. Thus, the atomic flux density along the moving surface of the void consists of two terms [39]... 

Equation 7.151 has a very simple form, but represents a challenging formulation for calculation, since, to find the local current density (and, thus, the electron wind force), one has to solve the Laplace equation for the electric potential in the whole sample at each new time moment (as the void moves and changes the shape). At that, as shown in Figure 7.30a, the ratio of maximum and minimum current densities near the void can reach 2 orders of magnitude. A schematic representation of shape evolution is shown in Figure 7.30b. Since the current... 

If under the influence of the electron wind force, the void shifts by a distance of... 

Z can be called the effective charge, Z d is attributed to momentum exchange between the electron current and the moving atom and Zg/ is related to the direct electrostatic force on the moving atom. Z d, also called the electron wind, is the dominant factor, thus the atoms drift in the same directions as the electrons. The steady state solution of Eq. 3 occurs when the driving force due to generated stress equals that of electromigration, like in Eq. 5. n is the atomic volume and a the stress. 

In metals the high flux of electrons may transfer momentum to mobile defects, forcing them to move in the same direction as the electrons. This so-called electron wind is not present in MIECs, which usually exhibit lower electronic conductivities typical of semiconductors or insulators. 

Tension Control Roil These type rolls provide the important function of material tension control. There is a proportional relationship between winding tension and lay-on-roll forces (eliminating areas were bumps, valleys, unwanted stretch, etc. develop). There are various tension control techniques available. The proper selection involves decisions on how to produce the tension, how to sense the tension, and how to control the tension. For instance, if the material has a very low tension requirement and if exact control is required, then perhaps, using a magnetic particle brake with an electrical transducer roll with appropriate electronic control is best. However, if the material is on large diameter rolls and moves at slow speed, then a roll follower system can be used effectively. 

Titanium dioxide is used in paints because of its pure white color. When the sun is out, the titanium oxide particles can absorb the solar radiation and use this energy to promote its electrons to an excited, more reactive state. These electrons then act like tiny electron sources on diminutive batteries to break down organic pollutants, molecule by molecule. So as in the Aesop tale—the quarrel between the sun and the wind as to which was the stronger—that which resists force can often be conquered by gentle persuasion. The warm, welcome light of the sun. 

Mercury s weak magnetic field is strong enough to force charged particles in the solar wind to flow around the planet. The cavity that consequently exists about the planet is called a magnetosphere, and its existence prevents solar wind material (mainly protons and electrons) impacting directly on the planet s surface. 

Linear induction accelerators (induction linacs) Linear accelerators that operate by inducing an electromotive force in a cavity through a rapid change in the magnetic field strength. In effect, the electron beam acts as the analog of the secondary winding in a transformer. 

An electronically adjusted braid dofHng winds up the compressed braid, making it possible to control the ratio of horn gear speed and take-up speed. It provides the capability of presetting the braiding angle every time it is needed so that the fiber direction and the direction of force in the fiher-reinforced material correspond to each other. 

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