Displacement plating

Displacement damage function, 14 436 Displacement desorption, factors governing choice of method, l 614t Displacement plating, 24 141 Displacements per atom (dpa), 14 436 Displays... 

There are other kinds of geological events that proceed in zones of subduc-tion, but the result of these processes is the same the acceleration of the transformation of dispersed organic material to petroleum. The movement zones are two very important areas for petroleum formation phenomena formation of lenses traps and movement of organic material from the ocean into the trap by means of the displaced plates. 

Figure 4 shows the schematic principle for displacement plating. In this case, you don t need any external electron source to make the metal ions in the solution precipitate onto the work. Instead, the metal component of the work would dissolve to give the metal ions in the solution electrons. The chemical reactions can be written in the following way schematically. Eq. 1 is the cathode reaction for the precipitation and plating film formation, while Eq. 2 is the anode reaction to give the plating metal electrons. 

This type of plating is often called displacement plating and is a type of electroless plating. 

Electrolytic Environment Electroplating Electroless platings Displacement plating Electrophoretic deposition... 

In electroless or autocatalytic plating, no external voltage/current source is required. The voltage/current is supplied by the chemical reduction of an agent at the deposit surface. The reduction reaction is catalyzed by a material, which is often boron or phosphorous. Materials that are commonly deposited by electroless deposition are Ni, Cu, Au, Pd, Pt, Ag, Co, and Ni-Fe alloys. Displacement plating is the deposition of ions in solution on a surface and results from the difference in electronegativity of the surface and the ions. The relative... 

Electroless electrolytic cleaning relies on the difference in electromotive potentials to remove material from one surface and deposit it on another (i.e. displacement plating. Sec. 1.1.2). 

Displacement plating When an ion in a solution has a smaller negative electrochemical potential than the atom of the solid and spontaneously displaces the atom of the solid and deposits on the solid. Examples Au (+ 1.50volts) plating onto Cu (+0.52 volts) Pb (-0.126 volts) or Sn (—0.136 volts) (from solder) plating on A1 (—1.67 volts). Also called Immersion plating. See also Electrochemical series. 

Immersion or displacement plating is the deposition of a metallic coating (M) on a metallic substrate (S) from a solution that contains the metal being plated, and the metal on the substrate is displaced by a metal ion from solution that has a lower standard electrode potential than the displaced metal ion. The displaced substrate material enters the solution in ionic form (S" ) and the metal ion (M" ) deposits onto the substrate in its place. 

We call a plate the shallow shell when k =k2 = 0. This implies that the plate mid-surface coincides with the plane z = 0, and the plate is limited by the two parallel planes z = h, z = —h and a boundary contour. Let us redenote the horizontal and vertical displacements of the plate mid-surface by u = ui, u = U2, w. In this case, the plate horizontal and vertical displacements are not coupled. Indeed, it follows from (1.18), (1.19), that U = (ui,U2) is described by the following equilibrium equations ... 

Now we formulate the models for perfectly elastoplastic plates considered in Chapter 5. By the Hencky law (1.9), the vertical component w of the plate displacements satisfies the equations (Erkhov, 1978)... 

Let a punch shape be described by the equation z = ip(x), and xi,X2,z be the Descartes coordinate system, x = xi,X2). We assume that the mid-surface of a plate occupies the domain fl of the plane = 0 in its non-deformable state. Then the nonpenetration condition for the plate vertical displacements w is expressed by the inequalities... 

We formulate boundary conditions in the two-dimensional theory of plates and shells. Denote by u = U,w), U = ui,U2), horizontal and vertical displacements at the boundary T of the mid-surface fl c R. Then the horizontal displacements U may satisfy the Dirichlet-type conditions... 

In this chapter we analyse a wide class of equilibrium problems with cracks. It is well known that the classical approach to the crack problem is characterized by the equality type boundary conditions considered at the crack faces, in particular, the crack faces are considered to be stress-free (Cherepanov, 1979, 1983 Kachanov, 1974 Morozov, 1984). This means that displacements found as solutions of these boundary value problems do not satisfy nonpenetration conditions. There are practical examples showing that interpenetration of crack faces may occur in these cases. An essential feature of our consideration is that restrictions of Signorini type are considered at the crack faces which do not allow the opposite crack faces to penetrate each other. The restrictions can be written as inequalities for the displacement vector. As a result a complete set of boundary conditions at crack faces is written as a system of equations and inequalities. The presence of inequality type boundary conditions implies the boundary problems to be nonlinear, which requires the investigation of corresponding boundary value problems. In the chapter, plates and shells with cracks are considered. Properties of solutions are established existence of solutions, regularity up to the crack faces, convergence of solutions as parameters of a system are varying and so on. We analyse different constitutive laws elastic, viscoelastic. 

As we know the vertical displacements of the plate defined from (2.7), (2.8) can be found as a limit of solutions to the problem (2.9)-(2.11). Two questions arise in this case. The first one is the following. Is it possible to solve an optimal control problem like (2.19) when w = w/ is defined from (2.9)-(2.11) The second question concerns relationships between solutions of (2.19) and those of the regularized optimal control problem. Our goal in this subsection is to answer these questions. 

We continue the investigation of the contact problem for a plate under creep conditions. In this section the case of both normal and tangential displacements of the plate is considered. 

The model of the plate considered in this section actually corresponds to a shallow shell having zeroth curvatures. The gradient of the punch surface is assumed to be rather small, so that the nonpenetration condition imposed in the domain is the same as in the usual case for a plate. Meanwhile, the restriction imposed on the crack faces contains three components of the displacement vector. 

Denote next by % = (IT, w) a displacement vector of the mid-surface points of the plate, where W = is horizontal displacements and w is... 

We consider the Kirchhoff-Love model of the plate for which both vertical and horizontal displacements of the mid-surface points are to be found. 

The Kirchhoff-Love model of the plate is characterized by the linear dependence of the horizontal displacements on the distance from the mid-surface, that is... 

The above formula for H(x) contains three different terms which correspond to the bending energy of the plate, to the deformation energy of the midsurface, and to the work of the exterior force /, respectively. Also, we introduce the set of admissible displacements... 

The equilibrium problem for the plate can be formulated as variational, namely, it corresponds to the minimum of the functional H over the set of admissible displacements. To minimize the functional H over the set we can consider the variational inequality... 

In this section we deal with the simplified nonpenetration condition of the crack faces considered in the previous section. We formulate the model of a plate with a crack accounting for only horizontal displacements and construct approximate equations using penalty and iterative methods. The convergence of these solutions is proved and its application to the onedimensional problem is discussed. Analytical solutions for the model of a bar with a cut are obtained. The results of this section can be found in (Kovtunenko, 1996c, 1996d). 

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